Mechanical Engineering
Ph.D. Thesis
EXERGY EVOLUTION OF THE MINERAL CAPITAL
ON EARTH
By Alicia Valero Delgado
July 2008
Directed by:
Antonio Valero Capilla, Ph.D.
Department of Mechanical Engineering
Centro Politécnico Superior
University of Zaragoza
Exergy evolution of the mineral capital on earth
Alicia Valero Delgado
Thesis submitted in partial fulfilment of the requirements for
the degree of Doctor of Philosophy
University of Zaragoza, Spain
Abstract
The 20th century has been characterized by the economic growth of many industrialized countries. This growth was mainly sustained by the massive extraction
and use of the earth’s mineral resources. The tendency observed worldwide in the
present, is that consumption will continue increasing, especially due to the rapid
development of Asia, the desire for a higher living standard of the developing world
and the technological progress. But the physical limitations of our planet might
seriously restrain world economies. In fact, many mineral commodities such as oil
or copper are already showing signs of scarcity problems, and consequently their
prices are increasing sharply.
Our society is based on an inefficient use of energy and materials, since there is a
lack of awareness of the limit. If resources are limited, their management must be
carefully planned. But it is impossible to manage efficiently the resources on earth,
if we do not know what is available and at which rate it is being depleted.
Therefore, the aim of this PhD has been the assessment of the physical stock on
earth and the degradation velocity of our mineral resources due to human action.
This has been accomplished through the exergy analysis under the exergoecological
approach. This way, the resources are physically assessed as the energy required
to replace them from a complete degraded state to the conditions in which they
are currently presented in nature. The main advantage of its use with respect to
other physical indicators is that in a single property, all the physical features of a
resource are accounted for. Furthermore, exergy has the capability of aggregating
heterogeneous energy and material assets. Unlike standard economic valuations,
the exergy analysis gives objective information since it is not subject to monetary
policy, or currency speculation.
i
Accordingly, in this work three imperative activities were carried out:
• A systematic analysis of the main chemical components and the mineral resources on earth has been accomplished. Furthermore, the first composition in
terms of minerals of the upper continental crust has been developed, through
a procedure that assures chemical coherence between species and elements.
The integration of all these data has provided a global overview of the geochemistry of our planet with special attention to the substances that compose
the earth’s outer spheres and to that part of the substances useful to man: the
mineral resources.
• The thermodynamic tools required for the physical assessment of natural resources and particularly for minerals have been provided. This way, the standard thermodynamic properties of the earth and its constituents (enthalpy,
Gibbs free energy and exergy) have been calculated. Additionally, the exergy
of the mineral resources of the earth (of fuel and non-fuel origin) has been
obtained and compared to that of other energy resources.
• With the help of different scarcity indicators developed in this PhD, an analysis
of the state of our mineral resources has been accomplished. For that purpose
the mineral exergy degradation throughout the 20th century has been studied.
This has allowed to estimate when the peak of production of the main mineral
commodities is reached. Additionally, an outlook of the scarcity degree of our
mineral capital in the 21st century has been undertaken.
The results of this study reveal that the exergy analysis of minerals could constitute
a universal and transparent prediction tool for assessing the degradation degree of
non-renewable resources, with dramatic consequences for the future management
of the earth’s physical stock.
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To my beloved grandfather
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‘‘In the end we will conserve only what we
love; we will love only what we understand;
we will understand only what we have been
taught”
Baba Dioum. Senegalese Environmentalist
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Acknowledgements
The work with this dissertation has been exciting, instructive, and fun, although
moments of hardship and frustration have also existed. Without help, support, and
encouragement from a great number persons, I would never have been able to
finish this PhD. In this long ride of almost 5 years, I have had the opportunity to
meet exceptional people around the world.
In the scientific field, many researchers have unselfishly supported me. I should
start to acknowledge the Russian geochemist N.A. Grigor’ev, that I discovered by
chance investigating the literature about the geochemistry of the earth. Through
a quite complicated communication procedure (via ordinary post and in Russian
language), Grigor’ev generously shared with me his not yet published results about
the mineralogical composition of the earth’s crust. Thanks to the translations of
the Russian teacher in the University of Zaragoza Helena Moradell, Grigor’ev’s
exceptional and pioneer work has been the base of the model of continental crust
developed in this PhD.
A deep debt of thanks is also owed to Gavin Mudd from the Institute for Sustainable
Water Resources in Monash University (Australia), who kindly made available and
prior to publication, his excellent and also pioneer study about average mineral ore
grades in his country. Thanks to Mudd’s work, a comprehensive case study of the
mineral exergy degradation of a nation was possible.
This thesis has required a high level of geological and geochemical knowledge.
Therefore, my chemical engineering background had to be reinforced with earth
science’s fundamentals. Of essential help was the continued support of Javier
Gómez, from the department of petrology in the University of Zaragoza. From
the very beginning, he became my unofficial advisor in the geological field and his
point of view has been very valued for this work. I should also thank the “Instituto
Geológico y Minero de España - IGME”, and in particular Miguel Ángel Zapatero,
for making available IGME’s information and mineral statistics.
Decisive for the accomplishment of this PhD, was my 3-month stay at the British
Geological Survey (BGS), one of the most renowned geological institutions in
Europe. Not only the exceptional library and data bases of BGS were crucial for this
work, but also the good advice of many of its premium researchers. I would like to
express my deepest gratitude to the BGS’s director, John Ludden, who immediately
accepted me in the organization and gave me access with no exception to all BGS
available information. Thanks go also to Andrew Bloodworth, head of the Mineral’s
UK department and to all his team, for their warm welcome and for treating me as
one more of the group. I cannot forget Tim Colman, who was always willing to help
me and from which I learnt so many things. I have met at BGS many good friends
that surely will remain in the future.
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The thermochemistry part of this PhD was strongly reinforced with the reviews
of Philippe Vieillard, probably the best European expert in the field of geothermochemistry, from the University of Poitiers. In these few lines, I want to express
my gratitude for the many hours that Vieillard spent in teaching me patiently the
different estimation methods for the calculation of the thermodynamic properties of
minerals and in reviewing the results obtained.
I would like to thank prof. Jan Szargut and Wojciech Stanek from the Institute of
Thermal Technology in the Silesian University of Technology. It has been an honor
to interact and discuss with my Polish friends the different exergy approaches used.
Very useful were also the advices of the Spanish renowned economist José Manuel
Naredo. He has been and is being a fundamental piece in the integration of
the exergoecological approach used and further developed in this PhD, into the
economic thinking.
I should not forget Juan Ignacio Pardo, from the department of physical chemistry
and Ma Cruz López de Silanes, from the department of applied mathematics, both
in the University of Zaragoza, who were always willing to help me.
If Javier Gómez was my geology advisor, César Torres, expert of thermoeconomics
and collaborator of the CIRCE Foundation, was doubtless my mathematics and LATEX
advisor. When I got stuck in a mathematical problem, he was the one in finding the
best solution. In the same way, he has solved most of my numerous doubts with
LATEX. In fact, he is the author of the layout of this PhD. Thank you very much indeed
for your invaluable help and time.
I wish to acknowledge the CIRCE Foundation for its financial support and for the
excellent working environment. All its members, starting from the administration
staff, teachers, students and researchers make the work very pleasant. Special
thanks are owed to my managers and fellows Javier Uche, Luis Miguel Romeo and
Inmaculada Arauzo, who have giving me every facility in the accomplishment of
this PhD. Thanks to their generosity and that of my CIRCE friends Amaya Martínez
and Francisco Barrio, I could dedicate most of my time in the last year in finishing
this work.
I would also like to thank all my friends from Zaragoza, and from other parts of
Spain for the great moments that I have shared with them.
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This PhD is dedicated to my beloved grandfather, who has always believed in me
and has supported and encouraged me. As you see I finally finished the work that
you were impatiently waiting for. In the same way, I want to deeply thank my
grandmother, for her endless care and affection. And of course I cannot forget my
uncles, aunts and cousins, which all constitute an important part of my life.
I am totally indebted to Stefan, who left family, friends and work in Germany
for living with me in Spain. Probably I will never be able to reward the huge
sacrifice you have made for me. I just hope that in some way, it has been worth.
Thanks for your love, patience and understanding. Thanks also for helping me in
the programming of the calculation tools used in this PhD, which has resulted in
the first scientific web portal devoted to exergoecology. The great success of the
"Exergoecology Portal", which every day gains supporters around the world, is due
to your effort and your well-doing. You are not only a good professional, but an
excellent person and I am very lucky to have you by my side.
My beloved mother, your wise advise, love and care are an essential support in my
personal and professional life. Your firm and sincere personality has affected me to
be steadfast and never bend to difficulty. You have taught me many indispensable
things of life that have helped me to face fearlessly important challenges and
decisions in my life.
I reserve my most grateful thanks to my father and supervisor Antonio Valero. To
be honest, at the beginning I was not sure whether this combination would work.
Today I am sure that it was worth and that you have been the best PhD director that
I could ever had. Obviously you have been very demanding with me, probably more
than with other of your students. But you have also been there many evenings,
week-ends and holidays, motivating me to work harder and to do my best. You are
an inspiration for me as a scientist, teacher, entrepreneur and most importantly as a
father. It has been a great pleasure to work with you. When the next one?
ix
Contents
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Starting point, objectives and scope . . . . . . . . . . . . . . . . .
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Economic growth and the consumption of natural resources
1.3 Scarcity indicators . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Exergy and the assessment of natural resources . . . . . . . .
1.5 The Exergoecology approach . . . . . . . . . . . . . . . . . . . .
1.6 Scope, objectives and structure of this PhD . . . . . . . . . . .
1.7 Scientific papers derived from this PhD . . . . . . . . . . . . .
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The earth and its resources
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2 The geochemistry of the earth. Known facts . . . . . . . . . . . . . .
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 The bulk earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 The composition of the earth . . . . . . . . . . . . . . . . .
2.3 The atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 The composition of the atmosphere . . . . . . . . . . . . .
2.4 The hydrosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Seawater . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1.1 The composition of the sea . . . . . . . . . . . .
2.4.2 Renewable water resources: surface and ground waters
2.4.2.1 Stream, river and lake waters . . . . . . . . . .
2.4.2.2 Ground waters . . . . . . . . . . . . . . . . . . . .
2.4.3 Ice caps, ice sheets and glaciers . . . . . . . . . . . . . . .
2.4.3.1 The composition of glacial runoff . . . . . . . .
2.5 The continental crust . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 The chemical composition of the upper continental crust
2.6 Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . . .
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3 The mineralogical composition of the upper continental crust . . . .
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3.1
3.2
3.3
3.4
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The classification of minerals . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 The silica minerals . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 The feldspar group . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 The pyroxene group . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 The amphibole group . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 The olivine group . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.6 The mica group . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.7 The chlorite group . . . . . . . . . . . . . . . . . . . . . . . . .
Grigor’ev’s mineralogical composition of the crust . . . . . . . . . . .
A new model of the mineralogical composition of the earth’s crust .
3.4.1 The mass balance . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 The mass balance applied to the continental crust . . . . . .
3.4.3 Aluminium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.4 Antimony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.5 Arsenic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.6 Barium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.7 Beryllium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.8 Bismuth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.9 Boron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.10 Bromine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.11 Cadmium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.12 Calcium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.13 Carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.14 Cerium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.15 Cesium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.16 Chlorine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.17 Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.18 Cobalt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.19 Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.20 Dysprosium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.21 Erbium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.22 Europium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.23 Fluorine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.24 Gadolinium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.25 Gallium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.26 Germanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.27 Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.28 Hafnium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.29 Holmium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.30 Indium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.31 Iodine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.32 Iridium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.33 Iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3.4.34
3.4.35
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3.4.41
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3.4.75
Lanthanum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lithium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lutetium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Magnesium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mercury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Molybdenum . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Neodymium . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Niobium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Osmium and Iridium . . . . . . . . . . . . . . . . . . . . . . . .
Palladium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Phosphorous . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Platinum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Potassium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Praseodymium . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rare Earth Elements: Praseodymium, Samarium, Europium, Gadolinium, Terbium, Dysprosium, Holmium, Erbium, Thulium and Lutetium . . . . . . . . . . . . . . . . . . .
Rhenium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rhodium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rubidium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ruthenium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Samarium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scandium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Selenium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Silver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sodium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Strontium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sulfur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tantalum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tellurium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Terbium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thallium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thorium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thulium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Titanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Uranium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vanadium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Wolfram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4 The resources of the earth . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Natural resources: definition, classification and early assessment
4.3 The energy balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Energy from the solid earth . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 The Geothermal energy . . . . . . . . . . . . . . . . . . . . .
4.4.2 Nuclear energy . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Tidal energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Energy from the sun . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.1 Solar power . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.2 Water power . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.3 Wind power . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.4 Ocean power . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.4.1 Ocean thermal gradient . . . . . . . . . . . . . . .
4.6.4.2 Ocean Waves . . . . . . . . . . . . . . . . . . . . . .
4.6.5 Biomass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.6 Fossil fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.6.1 Coal . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.6.2 Oil and natural gas . . . . . . . . . . . . . . . . . .
4.6.6.3 Unconventional fossil fuels . . . . . . . . . . . . .
4.7 Summary of the results of energy resources . . . . . . . . . . . . . .
4.8 Non-fuel mineral resources . . . . . . . . . . . . . . . . . . . . . . . .
4.8.1 The economic classification of minerals . . . . . . . . . . .
4.8.2 Mineral’s average ore grades . . . . . . . . . . . . . . . . . .
4.8.3 Mineral’s abundance . . . . . . . . . . . . . . . . . . . . . . .
4.9 Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . . . .
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105
105
105
106
107
108
109
111
112
112
113
114
115
116
117
118
119
119
121
124
127
127
129
130
136
138
3.5
3.6
3.7
3.4.76 Ytterbium . . . . . . . . . . . . . . . . . . . .
3.4.77 Yttrium . . . . . . . . . . . . . . . . . . . . .
3.4.78 Zinc . . . . . . . . . . . . . . . . . . . . . . .
3.4.79 Zirconium . . . . . . . . . . . . . . . . . . . .
Mathematical representation . . . . . . . . . . . . .
Results . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 Discussion of the most abundant minerals
3.6.2 Discussion of the most relevant minerals .
3.6.3 Discussion of the aggregated composition
3.6.4 Drawbacks of the model . . . . . . . . . . .
Summary of the chapter . . . . . . . . . . . . . . . .
xiii
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II
The thermodynamic properties of the earth and its exergy
evolution
5 Thermodynamic models for the exergy assessment of natural resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 The reference environment . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Selection of the best suitable reference environment . . . .
5.2.1.1 Partial reference environments . . . . . . . . . . . .
5.2.1.2 Comprehensive reference environments . . . . . .
5.2.1.3 Abundance criterion . . . . . . . . . . . . . . . . . .
5.2.2 Calculation methodology: standard chemical exergy of the
chemical elements . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2.1 Standard chemical exergy of chemical compounds
5.2.2.2 Gaseous reference substances . . . . . . . . . . . .
5.2.2.3 Solid reference substances . . . . . . . . . . . . . .
5.2.2.4 Reference substances dissolved in seawater . . . .
5.2.3 Update of Szargut’s R.E. . . . . . . . . . . . . . . . . . . . . . .
5.2.3.1 Update of the standard chemical exergy of chemical compounds . . . . . . . . . . . . . . . . . . . . . .
5.2.3.2 Update of the gaseous reference substances . . . .
5.2.3.3 Update of the solid reference substances . . . . . .
5.2.3.4 Update of the liquid reference substances . . . . .
5.2.3.5 The updated reference environment. Results . . .
5.2.4 Drawbacks of Szargut’s R.E. methodology . . . . . . . . . . .
5.3 The exergy of mineral resources . . . . . . . . . . . . . . . . . . . . . .
5.3.1 The energy involved in the process of formation of a mineral deposit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 The exergy of non-fuel mineral resources . . . . . . . . . . .
5.3.3 The chemical energy and exergy of fossil fuels . . . . . . . .
5.3.4 The exergy costs . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Prediction of Enthalpy and Gibbs free energy of formation of minerals
5.4.1 Calculation of ∆H 0f or ∆G 0f from s0 . . . . . . . . . . . . . . .
5.4.2 The ideal mixing model . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Assuming ∆G r and ∆H r constant . . . . . . . . . . . . . . . .
5.4.3.1 Thermochemical approximations for sulfosalts and
complex oxides . . . . . . . . . . . . . . . . . . . . .
5.4.3.2 The method of corresponding states . . . . . . . .
5.4.4 The method of Chermak and Rimstidt for silicate minerals .
5.4.5 The ∆O−2 method . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.5.1 The ∆O−2 method for hydrated clay minerals and
for phyllosilicates . . . . . . . . . . . . . . . . . . . .
5.4.5.2 The ∆O−2 method for different compounds with
the same cations . . . . . . . . . . . . . . . . . . . .
xiv
139
141
141
141
142
142
143
146
146
146
147
147
148
150
150
150
150
152
153
156
157
157
159
160
168
172
172
173
174
174
176
177
178
180
181
Assuming ∆S r zero . . . . . . . . . . . . . . . . . . . . .
Assuming ∆G r and ∆H r zero . . . . . . . . . . . . . . .
5.4.7.1 The element substitution method . . . . . .
5.4.7.2 The addition method for hydrated minerals
5.4.7.3 The decomposition method . . . . . . . . . .
5.4.8 Summary of the methodologies . . . . . . . . . . . . .
Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . .
5.4.6
5.4.7
5.5
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181
181
181
182
183
184
185
6 The thermodynamic properties of the earth and its mineral resources
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 The properties of the earth . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 The thermodynamic properties of the atmosphere . . . . . .
6.2.2 The thermodynamic properties of the hydrosphere . . . . .
6.2.3 The thermodynamic properties of the upper continental crust
6.2.4 The chemical exergy of the earth . . . . . . . . . . . . . . . .
6.3 An approach to the chemical composition of the crepuscular earth .
6.4 The exergy of the mineral resources . . . . . . . . . . . . . . . . . . .
6.4.1 The exergy contained in fossil fuels . . . . . . . . . . . . . . .
6.4.1.1 Coal . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1.2 Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1.3 Natural gas . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2 The exergy of non-fuel mineral resources . . . . . . . . . . .
6.4.3 The exergy of the natural resources on earth . . . . . . . . .
6.5 Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . . . . .
187
187
187
188
190
195
205
205
207
207
208
212
215
218
221
225
7 The time factor in the exergy assessment of mineral resources . . . .
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 The exergy distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 The tons of mineral equivalent . . . . . . . . . . . . . . . . . . . . . . .
7.4 The R/P ratio applied to exergy . . . . . . . . . . . . . . . . . . . . . .
7.5 The Hubbert peak applied to exergy . . . . . . . . . . . . . . . . . . .
7.6 The exergy loss of mineral deposits due to mineral extraction. The
case of copper in the US . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6.1 Copper mining features . . . . . . . . . . . . . . . . . . . . . .
7.6.2 Chemical exergy . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6.3 Concentration exergy . . . . . . . . . . . . . . . . . . . . . . . .
7.6.4 Total exergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6.5 Exergy costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6.6 The R/P ratio and the depletion degree of the deposits . . .
7.6.7 The Hubbert peak model . . . . . . . . . . . . . . . . . . . . .
7.6.8 Summary of the results . . . . . . . . . . . . . . . . . . . . . .
7.7 The exergy loss of a country due to mineral extraction. The case of
Australia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.7.1 Non-fuel minerals . . . . . . . . . . . . . . . . . . . . . . . . . .
227
227
227
230
232
232
xv
235
235
237
238
240
241
242
242
244
245
246
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247
249
252
254
255
259
261
262
263
264
267
267
275
277
8 The exergy evolution of planet earth . . . . . . . . . . . . . . . . . . . . .
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 The exergy loss of world’s mineral reserves in the 20th century . . .
8.2.1 Non-fuel minerals . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.2 Fuel minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3 The exergy loss of world’s fossil fuel reserves due to the greenhouse
effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.1 The carbon cycle and the greenhouse effect . . . . . . . . . .
8.3.2 Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.3 The fossil fuel exergy decrease . . . . . . . . . . . . . . . . . .
8.4 A prediction of the exergy loss of world’s mineral reserves in the
21st century . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4.1 Hubbert scenario . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4.2 The IPCC’s B1 scenario . . . . . . . . . . . . . . . . . . . . . . .
8.4.3 The IPCC’s A1T scenario . . . . . . . . . . . . . . . . . . . . . .
8.4.4 The IPCC’s B2 scenario . . . . . . . . . . . . . . . . . . . . . . .
8.4.5 The IPCC’s A1B scenario . . . . . . . . . . . . . . . . . . . . . .
8.4.6 The IPCC’s A2 scenario . . . . . . . . . . . . . . . . . . . . . . .
8.4.7 The IPCC’s A1FI scenario . . . . . . . . . . . . . . . . . . . . .
8.4.8 Summary of the scenarios . . . . . . . . . . . . . . . . . . . . .
8.5 Final reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.5.1 The Limits to Growth to be reconsidered? . . . . . . . . . . .
8.5.2 The need for global agreements on the extraction and use
of natural resources . . . . . . . . . . . . . . . . . . . . . . . . .
8.5.3 The need for an accountability theory of mineral resources.
The Physical Geonomics . . . . . . . . . . . . . . . . . . . . . .
8.6 Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . . . . .
281
281
281
282
291
9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
331
7.8
7.9
7.7.1.1 Gold . . . . . . . . . . . . . . . .
7.7.1.2 Copper . . . . . . . . . . . . . .
7.7.1.3 Nickel . . . . . . . . . . . . . . .
7.7.1.4 Silver . . . . . . . . . . . . . . .
7.7.1.5 Lead . . . . . . . . . . . . . . . .
7.7.1.6 Zinc . . . . . . . . . . . . . . . .
7.7.1.7 Iron . . . . . . . . . . . . . . . .
7.7.2 Fuel minerals . . . . . . . . . . . . . . . . .
7.7.2.1 Coal . . . . . . . . . . . . . . . .
7.7.2.2 Oil . . . . . . . . . . . . . . . . .
7.7.2.3 Natural gas . . . . . . . . . . . .
7.7.3 Summary and discussion of the results .
Conversion of exergy costs into monetary costs
Summary of the chapter . . . . . . . . . . . . . . .
xvi
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295
297
298
302
307
307
309
310
311
314
315
315
317
320
320
322
325
327
9.1
9.2
9.3
9.4
Introduction . . . . . . . . . . . . . .
Synthesis of the PhD . . . . . . . . .
Scientific contributions of the PhD
Perspectives . . . . . . . . . . . . . .
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331
331
340
346
A Additional calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1 Input data. Mineralogical composition of the earth’s crust . . . . . .
A.2 Calculation of average mineral ore grades . . . . . . . . . . . . . . . .
A.3 Calculation of the R.E. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.4 Calculation of the chemical exergy of gaseous fuels . . . . . . . . . .
A.5 Estimation of the thermodynamic properties of minerals . . . . . . .
A.5.1 Chermak’s methodology . . . . . . . . . . . . . . . . . . . . . .
A.5.2 Vieillard’s methodology for hydrated clay minerals . . . . .
A.5.3 Estimated values of the enthalpy and Gibbs free energy of
minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.6 Exergy calculation of the mineral resources . . . . . . . . . . . . . . .
A.7 Australian fossil fuel production . . . . . . . . . . . . . . . . . . . . . .
A.7.1 Coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.7.2 Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.7.3 Natural gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.8 World’s fuel production . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.8.1 Uranium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.8.2 Coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.8.3 Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.8.4 Natural gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.9 The Hubbert peak applied to world production of the main non-fuel
minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.10 Fuel consumption in the 21st century . . . . . . . . . . . . . . . . . .
351
351
376
384
386
386
386
387
Nomenclature, Figures, Tables and References
413
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
415
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
421
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
425
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
431
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387
397
402
402
403
404
404
404
405
406
407
408
410
Chapter
1
Starting point, objectives and
scope
1.1
Introduction
The aim of this first introductory chapter is to provide an overview of the fundamentals on which this PhD is based and to outline the main objectives and scope of the
study.
Since this work is focused on the assessment of earth’s resources, the most relevant
studies concerned with the depletion of natural resources are reviewed. The former studies reveal the urgent need for information about our natural capital and for
appropriate indicators for its assessment. Accordingly, the most common scarcity indicators are outlined and compared to the indicator used in this PhD: the exergy indicator, based on the second law of thermodynamics. Subsequently, an overview of the
different existing approaches connecting the entropy law with the consumption of
resources is provided. The latter are compared to the exergoecology approach, which
is the methodology applied in this PhD for the assessment of mineral resources.
Finally, the specific questions that this work tries to answer are outlined, together
with its scope.
1.2
Economic growth and the consumption of natural
resources
The earth’s continental crust is the source of the main goods essential for industrial
civilization. Fuels, metals and non-metallic minerals are the fundamental basis for
the technological development of any country. As Dunham [78] states, although the
whole continental crust is composed by rocks as solid solutions of minerals, these
1
2
STARTING
POINT, OBJECTIVES AND SCOPE
are not in practice recoverable. Only when a combination of natural processes has
worked together to produce an enrichment, is an ore to be found. And these complex
processes operate very slowly when compared with the whole life-span of our species
so far. Hence, it is clear the non-renewable nature of mineral resources, at least from
a human perspective.
The 20 th century was marked by great technological innovations leading to the consumption and further dispersion of huge amounts of mineral resources previously
concentrated in natural deposits. This fact pushed up the economies of industrialized countries, but also raised the concern about resources scarcity. Probably, the
possibility of running out of energy resources has provoked the most worries, especially due to the sharp rise of fuel prices. However non-fuel resources are also being
exhausted very rapidly, as shown by Morse [230]: only in the US, over the span of
the last century, the demand for metals grew from a little over 160 million tons to
about 3,3 billion tons.
The general attitude that has governed in the past was that the earth is nothing
more than resources to be used. Adam Smith’s invisible hand [321] has been a
guiding principle for those who believe that free trade or market will ultimately lead
to a natural order of things. Nevertheless, in the early seventies the first Arab oil
embargo, the peaking of oil production, together with the studies of the Club of
Rome (Forrester [96] and Meadows et al. [218]), started the alarm bells ringing
regarding resources scarcity as the limit to economic growth [221].
In fact, the theory that economic growth is irrevocably constrained by the finiteness of natural resources came at least1 a century before with the British economist
Thomas Malthus [206]. The theory of Malthus was that the efforts of an expanding
population to produce food on a limited land base would suffer diminishing returns,
and if reproduction was not checked through moral restraint it would be checked
by famine, war and pestilence. Malthus contemporary David Ricardo relativized the
Malthusian’s absolute scarcity of land. He showed that an expanding competitive
economy could always turn to lower-quality land, thereby increasing the required
labor to produce food and driving up its cost [302].
But classical economists were mainly focused on land and did not really faced the
problem of depletion of minerals and other non-renewable resources. It was not
until the beginning of the 20 th century, that the US conservation movement feared
that progress would end because the rapacious present generation would consume
the next of its needed natural resources. In the 1930s, Harold Hotelling [145] put
numbers to the not very rigorous statements of the conservationists. According to
Hotelling, resources would be depleted at a declining rate, and their price would rise
at a rate equal to their owners’ opportunity rate of interest.
In the seventies, the Club of Rome came into being and the first attempt at a global
model by J. Forrester was pubilshed in World Dynamics [96]. The limits to Growth
1
The French physiocrats came to the conclusion in the XVIII century that land is the source of all
wealth.
Economic growth and the consumption of natural resources
3
by Meadows et al. [218] followed in 1972, receiving great publicity. The works of
Meadows et al. in 1972 and later updates in 1993 [217] and 2004 [219], argue that
the current exponential growth cannot longer be supported as natural goods become
depleted. Through the World3 computer model, different scenarios of resources
consumption, pollution, population, policy, etc. were developed. The study claimed
that if no immediate actions are undertaken, an economical collapse is foreseeable
in the near future.
The truth is that even if the consumption of natural capital has increased dramatically, evidence until to date has not really supported the idea that natural resources
depletion has stopped economic growth. Some authors such as Barnett and Morse
[20] or Scott and Pearse [302] appealed to the role of technological progress in
improving the efficiency of extractive processes and redefining available resources.
They stated that there is no evidence for the hypothesis that natural resources will
lead to reduction of economic growth. Solow [326] argued that substitution of
capital goods of natural resources in production processes reduces resource requirements and, in general, technical change may overcome limits imposed on economic
activities in the environment.
On the contrary, Costanza and Daly [65], Ayres and Nair [17] or Cleveland and Ruth
[59], believe that technology will not overcome resource scarcity and environmental
degradation, since human capital ultimately is derived from and sustained by energy,
materials and ecological services. Until now, natural capital has been treated as a
free good, but nowadays it is becoming the limiting factor in development. Champan
and Roberts [53] argue also that resource substitution might be valid in the short
term, but will fail in the long term when there is equal resource scarcity on all
substitutable materials.
Some attempts have been made to measure the economic costs of depletion and
degradation and use them to correct standard measures of economic welfare such as
GDP (see for instance Ahmad, El Serafy and Lutz [2]; Daly and Cobb [70]; Costanza
[64]; Van Dieren [75]). Although the debate on how national accounting should be
extended towards environmental accounting is still open, all approaches reflect that
when depletions of natural capital, pollution costs, and income distribution effects
are accounted for, the improving of the economy is seriously questioned.
As we face the new century, the question of whether resource scarcity will constrain
economy is still in the air. But the rapid economic development of Asia and the desire for a higher living standard in the developing world demands an even greater
consumption of natural resources together with rapid technological progress to prevent increasing scarcity of the different commodities. Our society is based on an
inefficient use of energy and materials, since there is a lack of awareness of the
limit. If resources are limited, their management must be carefully planned in order
to be consistent with the sustainability doctrine. But for that purpose, we need to
know how many resources are available on earth and at which rate they are being
consumed. A responsible management can only be based thus on a comprehensive
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information source. As Faber [91] claimed, the true intertemporal scarcity of environmental goods must be analyzed and appropriate indicators for the scarcity of
these goods must be found.
In this PhD, we have dived in data bases of many different institutions, organizations,
universities and journals, searching for global numbers of the mineral capital on
earth. For someone that never faced that task, it is surprising the lack of existing
information about our resources not only in the past, but also in the present. This is
a clear indicator of the little importance that humankind has placed in investigating
the resources that nature gives us for free.
Generally, the institutions owning information about resources do not interpret the
compiled values. And ironically, many studies claiming the end of natural resources
are rarely based on the physical statistics provided by the formers.
More resources data bases, better global statistics, the opening of global information
channels and impartial and serious interpretations of the information are key factors
for transformation to sustainability. And the data interpretation must be undertaken
with the help of appropriate indicators.
This PhD has tried to fill with physical content some of the sociological messages
about resource scarcity published elsewhere. This has been accomplished by making
a rigorous analysis of the global minerals on earth through an indicator based on
the second law of thermodynamics. The next section provides an overview of the
different available scarcity indicators with its capabilities and drawbacks, so as to
compare them to the indicator chosen in this PhD.
1.3
Scarcity indicators
Consideration of scarcity and its measurement requires clarification of what we mean
by scarcity. As Zwartendyk et al. [414] argue, physical scarcity refers to the relative rarity of an element or mineral substance in nature; it has nothing to do with
human effort. Economic scarcity has very much to do with the interests and needs
of humans. It reflects that work is required to obtain mineral products and that we
are willing to pay a price for them. Generally, the greater the physical scarcity of a
mineral, the costlier it will be to obtain, so its economic scarcity may be greater as
well.
The scientific community has already started to study this issue and some physical
and economic indicators have been proposed.
In the renowned work Scarcity and Growth2 (1963) of Barnet and Morse [20], extraction costs were used as scarcity indicators. Extraction cost is computed as the
amount of labor and capital required to produce a unit of output. The same indicator
2
Scarcity and Growth was the first systematic empirical examination of historical trends.
Scarcity indicators
5
was used until the update of that work: Scarcity and Growth Reconsidered [325]. This
measure is founded on the classical economics view that with diminishing marginal
returns and finite natural resources, the cost of natural resource extraction should
increase as demand increases and depletion occurs. Krautkraemer [188] argued in
Scarcity and Growth Reconsidered that extraction cost is an inherently static measure;
it does not capture future effects that are important for indicating natural resource
scarcity. In addition, extraction cost captures information about only the supply side
of the market. If demand is growing more rapidly than extraction cost is declining,
then extraction cost will give a false indication of decreasing scarcity (the opposite
is also possible).
Probably the most used indicator nowadays is price. Price incorporates information
about the demand for the resource and possible expectations about future demand
and availability. According to Fisher [95], the resource price would “summarize the
sacrifices, direct and indirect, made to obtain a unit of the resource”.
Naredo [237] claims though that standard economy is only concerned with what
being directly useful to man, is also acquirable, valuable and produce-able. For this
reason, most of the natural resources, remain outside the object of analysis of the
economic system. And the price-fixing mechanisms, rarely take into account the
concrete physical characteristics which make them valuable.
Ruth [294] states that for prices to subsume all required information to make an intertemporally optimal choice about material and energy and the level of production,
markets must be efficient, and preferences of current and future generations have to
be anticipated. Additionally, current and future technologies must be fully described.
In contrast, prices rather reflect the incomplete description of current technologies,
preferences of present generations, and current institutional settings.
Though non renewable resources are becoming more and more scarce, prices have
not followed the same trend. According to Hotelling [145], prices should raise with
scarcity, since low cost resources normally would be used first and quantities of
extraction normally would decrease over time. On the contrary, historical statistics
show that costs of extraction and prices have mostly decreased over time [313].
This apparent contradiction is due to technological innovation but also to the lack of
information about scarcity. Reynolds [277] states that true scarcity is only revealed
through prices towards the end of exhaustion.
Physical indicators are usually based either on mass or energy. Generally, all energy
resources are assessed in terms of its energy content, what allows a direct comparison between them. On the other hand, non-fuel minerals are usually physically and
individually assessed in terms of tonnage and grade. It is obvious that mineral resources evaluated in that way cannot be easily compared, and a global number for
the mineral’s capital on earth cannot be given, as mass and grade are not additive.
Furthermore, assimilating such a great amount of information for each resource is
not always easy and not very useful for decision makers.
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Odum [245], [246] proposed an original physical unit of measure for assessing resources and products based on the solar emergy joule (sej). Emergy analysis is a
technique of quantitative analysis which determines the values of resources, services
and commodities in common units of the solar energy it took to make them. One
of its fundamental organizing principles is the maximum empower principle. It is
stated as “systems that will prevail in competition with others, develop the most
useful work with inflowing emergy sources by reinforcing productive processes and
overcoming limitations through system organization”. To derive solar emergy of a
resource or commodity, it is necessary to trace back through all the resources and
energy that are used to produce it and express them in the amount of solar energy
that went into their production [42]. The solar emergy per unit product or output
flow is called “solar transformity”, with units of seJ/J. Solar transformities have to be
obtained for each commodity. Most transformities cannot be considered as universal, as the processes involved in the formation of the commodities differ, depending
on the period of time and place considered.
The emergy analysis owns two fundamental capabilities that we think are required
to be used as a scarcity indicator: 1) it is based on the physical characteristics of the
resource and 2) all resources are measured with a single unit.
Generally, the emergy analysis can be successfully applied for renewable resources.
However it is very questioned the applicability of this approach for mineral resources, where the sun has not played a central role in their creation. No matter
how much solar energy is received from the sun, the quantity of gold or iron for
instance on earth, will not change. Consequently, the rigorousness of the transformities for mineral resource assessment is doubtful. Hence, the emergy analysis is not
suitable for the purpose of this PhD, which is the assessment of mineral resources.
The physical features that make mineral resources valuable are: a particular composition which differentiates them from the surrounding environment, and a distribution which places them in a specific concentration. And these intrinsic properties can
be in fact evaluated from a second law of thermodynamics point of view in terms of
a single property: exergy.
As it happens to emergy and unlike standard economic valuations, the exergy analysis gives objective information since it is not subject to monetary policy, or currency
speculation. Furthermore, all natural resources can be assessed in terms of exergy
and can be summed up. Exergy is a property of the resource and as such, the calculation methods are physically and mathematically supported, as opposed to emergy.
As explained in the next section, exergy is based on the notion of a reference environment, in which the quality and quantity of substances is fixed. Hence the analysis
places value to resources depending on the level of departure from the defined reference environment. And, as opposed to the emergy analysis, whether the substances
in it were created through the energy of the sun or through other processes is irrelevant and does not affect the final results.
Exergy and the assessment of natural resources
7
The exergy method is chosen in this PhD for assessing the evolution of mineral
scarcity. In the next section, an overview of the different existing approaches connecting the entropy law with the consumption of resources is provided.
1.4
Exergy and the assessment of natural resources
A fundamental law of nature (the first law of thermodynamics), tells us that energy
and matter can be neither created nor destroyed. The second law places additional
limits on energy transformations and reflects qualitative characteristics. It states that
energy can only be transformed by the consumption of quality. Locally, the quality
can be improved, but this can only occur at the expense of a greater deterioration
of the quality elsewhere. The level of quality deterioration or disorder is measured
through the property entropy. Hence, the second law of thermodynamics can be formulated as follows. In all real processes of energy transformation the total entropy
of all involved bodies can only be increased or, in an ideal case, unchanged. Beyond
these conditions, the process is impossible even if the first law is fulfilled [39].
The combination of both laws indicates that it is not a question of the existent
amount of mass or energy, but on the quality of that mass or energy, or in other
words on its exergy content. Technically, exergy is defined as the maximum amount
of work that may theoretically be performed by bringing a resource into equilibrium
with its surroundings by a sequence of reversible processes. The exergy of a system
gives an idea of its evolution potential for not being in thermodynamic equilibrium
with the environment. Unlike mass and energy, exergy is not a conserved property. It
is an extensive property, with the same unit as energy. In all physical transformations
of matter or energy, it is always exergy that is lost.
Exergy analysis is a powerful tool for improving the efficiency of processes and systems. This leads to less resources to be used and the emission of less wastes to
the environment. However it is a much more useful concept, and can be applied
for resource accounting. All materials have a definable and calculable exergy content, with respect to a defined external environment. The consumption of natural
resources implies destruction of organized systems and pollution dispersion, which
is in fact generation of entropy or exergy destruction. Furthermore, exergy has the
capability of aggregating heterogeneous energy and material assets. This is why the
exergy analysis can describe perfectly the degradation of natural capital. For that
reason, an increasing number of scientists, such as Szargut and coworkers [344],
[338], [339], Brodianski [39], Wall [393], [394], [395], Rosen [289], [290], Dincer [76], Sciubba [299] or Ayres et al. [14] believe that exergy provides useful
information within resource accounting and can adequately address certain environmental concerns.
Additionally, different renowned studies have shown up the connection between
economic scarcity and the entropy law. Some notable examples are briefly outlined
next.
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Georgescu-Roegen was one of the first authors in realizing the links between the
economic process and the second law of thermodynamics. In his seminal work The
Entropy Law and the Economic Process [111], he states that “the entropy law itself
emerges as the most economic in nature of all natural laws [...] and this law is the
basis of the economy of life at all levels”. Georgescu-Roegen stresses the importance
of the variable time in economic activity, which is clearly shown in the irreversibility
of the exploitation of resources. This author even postulated the Fourth Law of Thermodynamics, the entropy law of matter. According to this law, matter and not energy
is the limiting factor in economic growth. Georgescu-Roegen’s Fourth Law has been
criticized by a number of analysts in economics and physical sciences. It has been
pointed out that on a fundamental physical level, there is no such law. In principle,
it is always possible to use high quality energy to trace, collect and reassemble the
dissipated elements [59]. The theoretical flaws of the Fourth Law, have lead some
to dismiss Georgescu-Roegen’s ideas or deny their significance.
Faber et al. [92] developed a model integrating thermodynamic considerations into
a model of optimal resource use and environmental management. They analyzed the
relationship among resource use in the economic system, capital formation, resource
concentration and entropy production.
Ayres and Nair [17] state that the second law of thermodynamics has certain consequences for the production process which are not adequately reflected in the standard economic model. Among these consequences are that the exergy of the total
output of a sector must be less than the exergy of the inputs and overall entropy
is increased through the production of waste materials and heat. Ayres and Miller
[16] developed a model that treats natural resources, physical capital and knowledge (measured in terms of negative entropy or negentropy) as mutually substitutable inputs into the production process. In 1988, Ayres [13] used the model for
the calculation of optimal investment policies and simulation of optimal time paths
and substitution pattern for the world primary energy sources from the year 1869
to 2050. Recently, Ayres [15], calculated the exergy performed in the US economy
during the twentieth century. One of the conclusions of his study was that growth in
exergy consumption have had an enormous impact on past economic growth. The
increasing efficiency of the production in primary work tended to result in lower
costs, which triggered increasing demand that often resulted in greater exergy consumption. This fact is known as “Jevons paradox”.
Ruth [294] stated that use in economic production processes must consider thermodynamic limits on material and energy use in order to be optimal in the long-run.
And economic decisions must consider the finiteness of the resources available, the
interconnectedness of the economic system with other ecosystem components, the
time preference of consumers and producers and the technologies with which materials and energy are transformed in the production process. He developed a model
of nonrenewable resource use. As an example, Ruth determined the optimal extraction path and production of iron ore at each period of time, taking into account
thermodynamic limits on material and energy efficiency, the treatment of endoge-
The Exergoecology approach
9
nous technical change through the theory of learning curves and the evaluation of
alternative time paths from an economic and thermodynamic perspective.
In this PhD thesis, exergy has been used as a global scarcity indicator from the point
of view of the exergoecology paradigm. In the next section, exergoecology will be
explained in detail, and compared to other approaches, where exergy is also used as
an accounting tool.
1.5
The Exergoecology approach
Generally, the studies based on exergy and natural resources are focused on calculating the amount of exergy required for the production of a certain good. Probably,
the better known one is the thermo-ecological cost analysis proposed by Szargut and
coworkers [341], [344], [328]. The thermo-ecological cost analysis accounts for the
cumulative consumption of non-renewable exergy connected with the fabrication of
a particular product including the additional exergy consumption needed for the
compensation of environmental losses caused by the disposal of harmful substances
to the environment.
A similar approach is also used by Ayres and coworkers. For example, in [14], Ayres
et al. applied the exergy concept for accounting for the materials and energy use
and waste residuals of five basic metal industries in the US. This allowed to compare
systems on a common basis, to identify major loss streams that may correspond to
inefficiencies and to provide a first evaluation of their environmental burden.
Other exergy-based approaches are for instance those from Sciubba [300], Connely
and Koshland [61] or Cornelissen and Hirs [63]. Sciubba [300] extended Szargut’s
theory, including non-energetic quantities like capital, labor and environmetal impact on the calculation. Connely and Koshland [61], discussed the ties between
exergy and industrial ecology and proposed exergy-based definitions and methods
for addressing resource depletion. Cornelissen and Hirs [63] applied the exergy analysis to the Life Cycle Assessment (LCA) methodology and proposed the exergetic life
cycle assessment, which should account for the depletion of natural resources.
All these approaches provide very useful information for the optimization of processes, as they obtain the exergy costs of production, allowing a reduction in energy,
materials and harmful emissions.
The Exergoecology method proposed by Valero [365], which derives from the general
theory of exergy cost developed by the same author [370], uses also the property
exergy as an accounting tool, but differs radically from the approaches explained
above in the point of how resources are assessed. Exergoecology is defined as the
exergy assessment of natural resources, from a defined R.E. It allows to value these
resources, according to the physical cost that would require to obtain them from
the materials contained in a hypothetical earth that has reached the maximum level
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of deterioration. In other words, it quantifies the physical cost of replacing natural resources from a degraded state in the so called reference environment to the
conditions in which they are currently presented in nature. Its aim is to determine
the physical stock available in the current continental crust, how that stock is being
degraded and dispersed by mankind and at which rate. As Naredo [238] states, if
life came up and evolved from a primitive soup, human species pushes now strongly
towards a sort of crepuscular planet, whose composition would be hypothetically
equivalent to the R.E. This methodology allows to quantify the loss of the natural resource’s potential as the human effect pushes it towards that sort of entropic planet.
One of the questions that opens the exergoecology paradigm is the determination
of the degraded planet (or entropic planet) towards which civilization is moving.
The entropic planet could be assimilated to a dead planet where all materials have
reacted, dispersed and mixed and are in a hypothetical chemical equilibrium. A degraded earth would still have an atmosphere, hydrosphere and continental crust.
Nevertheless, there would not be any mineral deposits, all fossil fuels would have
been burned and consequently, the CO2 concentration in the atmosphere would be
much higher than it now is. Similarly, all water available in the hydrosphere would
be in the form of salt-water, due to the mixing processes. So far, the assessment of
mineral resources has been carried out from R.E. models designed for the optimization of industrial processes. It is open to question whether these kinds of models fit
the characteristics of the degraded planet that we are searching for. This topic will
be addressed in chapter 5 of this report.
Note the difference between extraction costs and replacement costs. The former
assesses the resource from the mine to market. However, the latter assesses the resource from the entropic planet to the mine. As Carpintero [50] and Naredo [238]
argue, economy puts value to natural goods considering its extraction costs and not
its replacement costs. Therefore, extraction and not recovery or recycling is promoted, thus enhancing the efficiency of the extraction processes rather than saving
those resources for future generations. Moreover, extraction implies more emissions
and more degradation. The exergoecological approach quantifies the physical costs,
both in minimum exergy terms and in actual exergy terms, required to replace the
resources with the best available technology. Thereby the anthropogenic view of
the value of resources is shifted to the nature’s point of view. This way, the earth
is not consider as an infinite reservoir of minerals. On the contrary, it is seen as a
warehouse with a finite number of exergy resources, whose extraction implies the
use of other exergy resources. Furthermore, as the warehouse becomes depleted,
the quantity of exergy resources required to extract more goods increases following
an exponential behavior. In exergoecology, conservation rather than efficiency is the
point.
Exergoecology has been developed so far for its application to inorganic substances,
focusing mainly on the mineral capital. Nevertheless, Jorgensen [176], [175] applies similar concepts for ecosystems, and introduces the term Eco-exergy. According
to this author, eco-exergy is defined as “the exergy of an ecosystem but with the same
The Exergoecology approach
11
THERMO-ECOLOGICAL COST
Solar energy
Exergy
Resources
NATURE
Exergy
Services of
products
Emissions
Technological
abatement process
Life cycle of
the product
Zero Exergy
Wastes, effluents
and emissions
Residues
Reference
Environment
Exergy distance
Technological process of
replacement of materials from
the Reference Environment
Exergy
EXERGOECOLOGICAL COST
Figure 1.1. Conceptual diagram of the terms exergoecology and thermo-ecology
system at the same temperature and pressure but consisting of dead inorganic material as reference”. Eco-exergy becomes then a measure of how far the ecosystem is
from thermodynamic equilibrium, or how developed the ecosystem is.
Let us outline the difference between the exergoecological method and the other
exergy approaches (leaded by the thermo-ecological method) through an example.
In the production of copper from a deposit, Szargut’s thermo-ecological analysis
would account for the exergy input of all industrial processes involved in the production of pure copper from the mine, including the abatement processes of the
emissions and wastes (see Fig. 1.1). The exergoecology approach closes the cycle of
Fig. 1.1, because it is concerned about the exergy needed to return the copper from
the depleted state of the R.E. to the conditions of the mine where it was found. The
exergy distance between the R.E. and the mine increases with the mine’s quality.
This means that as the mineral deposits become exhausted, the exergy difference
between the R.E. and the mine becomes lower. In the limit, when all natural resources have been extracted and dispersed, this distance is equal to zero or, what is
the same, the planet has lost all its natural exergy.
The exergoecology paradigm and its ideas were developed by Valero in the book of
Naredo and Valero [239] “Desarrollo económico y deterioro ecológico” (Economical
development and ecological degradation). In that book, the basis for a general theory of the physical cost of economic processes is proposed, and some examples of
the exergy replacement costs of minerals are provided.
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Additionally, two PhD thesis accomplished in the CIRCE institute of the University of
Zaragoza and directed by Antonio Valero, have applied and have further developed
the exergoecology approach. The first one entitled “Análisis De Los Costes Exergéticos De La Riqueza Mineral Terrestre. Su Aplicación Para La Gestión De La Sostenibilidad” [276] (Exergy cost analysis of the mineral wealth on earth. Applicaton for the
management of sustainability), was carried out by Lidia Ranz in 1999. The second
one was written by Edgar Botero one year later: “Valoración Exergética De Recursos Naturales, Minerales, Agua y Combustibles Fósiles” [34] (Exergy assessment of
natural resources, minerals, water and fossil fuels).
Ranz developed an approximation of the R.E., based on the methodology proposed
by Szargut [336] and calculated the chemical exergy of some important mineral
commodities. Her reference environment was chosen according to the abundance
criterion, i.e. the components of the R.E. should be the most abundant ones found
currently in nature. For that purpose, she carried out a comprehensive and systematic analysis of the most abundant minerals on earth for each chemical element. An
important message of her study was that exergoecology is irrevocably connected to
geology. A problem with Ranz’s proposed R.E. is that if we assign zero exergy to the
most abundant substances, we are decreasing arbitrarily the natural capital, because
many abundant minerals like sulfides naturally evolute to the most stable species.
Botero extended the exergy analysis to other natural resources such as water and
fossil fuels. In his PhD, the concept of exergy replacement costs was further developed,
and the exergy abatement costs, were firstly applied. The exergy replacement cost
was first calculated as the exergy required for replacing a resource from the R.E.
to the current conditions found in nature, with the best available technology. The
exergy abatement cost was proposed as a physical way to measure the exergy cost for
avoiding the environmental externalities associated to the use of fossil fuels, with
the best available technology.
Both PhD thesis, the book of Naredo and Valero [239], and the first paper describing
the exergoecological method (Valero [365]), constitute the basis and starting point
of the present study. The fundamental concepts described in the previous works are
used in this thesis and are further developed.
1.6
Scope, objectives and structure of this PhD
The aim of this PhD is the analysis of the state of the mineral’s exergy on earth and
its degradation velocity, due to the human action. As opposed to Botero’s and Ranz’s
PhDs, where the exergoecological analysis was applied in a static way, in this thesis
the time factor constitutes a fundamental variable. For that purpose, an exhaustive
analysis of the geochemistry of our planet and its past, current and future declining
resources needs to be carried out.
Scope, objectives and structure of this PhD
13
Although an exergy analysis of the entropic earth remains outside the scope of this
PhD, a previous step for modeling it, is the assessment of the composition of the
atmosphere, hydrosphere and continental crust. While the atmosphere and hydrosphere are well studied and its main components are reasonably known, the composition of the continental crust in terms of minerals has been barely studied. In fact,
only the chemical composition of it in terms of elements is approximately known,
and nowadays it is still being improved and updated. Therefore, an important milestone of this PhD, is to develop a model of the mineralogical composition of the
upper continental crust. With the upper crust’s model, an approach to the chemical
composition of the crepuscular earth can be provided.
Once the composition of the main components of the earth is known, a closer look
can be taken at its resources useful to man. The aim is to make a thorough analysis of the abundance and physical characteristics of renewable and non renewable
resources on earth, stressing the mineral capital. The whole physical stock on earth
will be later assessed with a single unit of measure in terms of exergy.
The use of exergy as an accounting tool, requires the thermodynamic properties of
the substances under analysis. We have dealt with more than 330 substances, for
which a little more than 50% empirical thermodynamic values are available from
the literature. Therefore, another milestone of this thesis is the semi-theoretical
estimation of the lacking properties.
With this information, the enthalpy, Gibbs free energy and exergy of each of the
components included in the three outer layers of the earth will be obtained for the
first time. In the same way, the exergy of the main mineral resources of fuel and
non-fuel origin will be calculated and compared to the other physical resources on
earth.
The accomplishment of a dynamic analysis of the resources on earth, requires the
time factor to be introduced. The final aim is to analyze the degradation of mineral
resources due to the human action, from the beginning of the industrialization period to nowadays. For that purpose, a comprehensive review of historical statistics of
fuel and non-fuel mineral extraction from different institutions needs to be carried
out. Additionally, with the help of scenarios, the possible degradation of mineral
resources in the future can be provided. The representation of the exergy degradation throughout history, will allows us to introduce new concepts and to apply
degradation models for assessing global mineral scarcity. An example of that is the
application of the Hubbert peak model, for determining the peak of production of all
kinds of minerals.
The objectives of this PhD cannot be accomplished only with a thermodynamic perspective. We have stated throughout this work, that other disciplines such as geology, geochemistry and economy are also crucial. Hence, for the completion of the
studies, interaction with experts from different knowledge areas was required. In
the geological field, the interaction with experts from the British Geological Survey
and the department of Petrology in the University of Zaragoza were decisive. In
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the same way, the geochemistry part of this PhD was reinforced with the reviews of
Dr. Vieillard, from the “Laboratoire d’Hydrogéologie, Argiles, Sols et Altérations” in
the University of Poitiers. In the economic field, the point of view of the Spanish
economist J.M. Naredo was especially taken into account.
This PhD is structured into two differentiated parts. Part 1, which includes chapters
2, 3 and 4, describes the geochemistry of the earth and its resources. Part 2 contains
chapters 5, 6, 7, and 8 and is focused on calculating the thermodynamic properties
of the earth and its exergy evolution.
Summarizing, this PhD tries to answer the following questions:
• Chapter 2: What is the chemical composition of the layers of the earth?
• Chapter 3: What is the average mineralogical composition of the continental
crust?
• Chapter 4: What are the available, potential and currently in use energy resources of the earth? What are the non-fuel mineral resources on earth and
which is their average ore grade?
• Chapter 5: Which is the R.E. and the thermodynamic models required for the
calculation of the thermodynamic properties of the earth?
• Chapter 6: What is the enthalpy, Gibbs free energy and exergy of the planet
and its resources? What is the exergy replacement cost of the mineral resources on earth?
• Chapter 7: How can we measure the level and the velocity of degradation of
mineral resources? How are these concepts applied to a specific nation?
• Chapter 8: How fast is humankind degrading the mineral exergy resources of
the earth? Have we reached the peak of production of minerals?
In short, the aim of this PhD is to improve the knowledge of the earth and its resources, from the exergoecological point of view. Because, as stated before, it is
impossible to manage efficiently the resources on earth, if we do not know what is
available and at which rate it is being depleted.
1.7
Scientific papers derived from this PhD
Some of the results obtained in this PhD have been presented in different conferences
and published in international journals. Here is a list of the papers developed from
the work carried out in this PhD ([343], [368],[377], [378], [375], [376], [374],
[373]).
Scientific papers derived from this PhD
15
1. J. Szargut, A. Valero, W. Stanek, and A. Valero D. Towards an international
legal reference environment. In Proceedings of ECOS 2005, pages 409–420,
Trondheim, Norway, June 2005.
2. A. Valero, E. Botero, and A. Valero D. Exergy accounting of natural resources.
Exergy, Energy System Analysis, and Optimization., from Encyclopedia of Life
Support Systems (EOLSS), Developed under the Auspices of the UNESCO Eolss
Publishers, Oxford, UK; Online encyclopedia: http://www.eolss.net, Retrieved
May 19, 2005.
3. A. Valero D., A. Valero, and A. Martinez. Exergy evaluation of the mineral
capital on Earth. Influence of the reference environment. In Proceedings of
IMECE 2005, Orlando, USA, 5-11 November 2005. ASME.
4. A. Valero D., A. Valero, A. Martínez, and G. Mudd. A physical way to assess the
decrease of mineral capital through exergy. The Australian case. In Proceedings
of ISEE 2006, New Delhi, India, 15-18 December 2006. Ninth Biennial Conference on the International Society for Ecological Economics (ISEE). “Ecological
Sustainability and Human Well-being”.
5. A. Valero D., A. Valero, and I. Arauzo. Exergy as an indicator for resources
scarcity. The exergy loss of Australian mineral capital, a case study. In Proceedings of IMECE2006, Chicago, USA, 5-10 November 2006. ASME.
6. A. Valero D., A. Valero, and I. Arauzo. Evolution of the decrease in mineral
exergy throughout the 20th century. The case of copper in the US. Energy,
33(2):107–115, 2008.
7. A. Valero D. Assessing world mineral deposits through the second law of thermodynamics. In Inproceedings of the Mineral Deposit Studies Group (MDSG)
conference, Nottingham (UK), 2-4 January 2008.
8. A. Valero, A. Valero D., and C. Torres. Exergy and the Hubbert peak. An extended analysis for the assessment of the scarcity of minerals on earth. In Proceedings of IMECE 2008, Boston, USA, 31 October - 6 November 2008. ASME.
Part I
The earth and its resources
17
Chapter
2
The geochemistry of the earth.
Known facts
2.1
Introduction
In this chapter a comprehensive analysis of the geochemistry of the earth is undertaken as the starting point for assessing its thermodynamic properties. The geochemical features of each layer of the earth are described: the atmosphere; hydrosphere
with the oceans, surface and ground waters as well as ice sheets; and the crust, focusing mainly on the upper part of it.
2.2
The bulk earth
The earth is an approximately spherical body, 12.756 km of diameter and 5, 98×1024
kg [23]. Its physical and chemical peculiarities have allowed the existence of life on
earth. The solid earth is divided into the crust (continental and oceanic), mantle and
core. The external layers above the crust are the hydrosphere and the atmosphere.
From all layers, the mantle and core are the largest, accounting for 67 and 33% of
the total mass of the earth [169]. The crust, hydrosphere and atmosphere together
make up less than 1% by mass. Only that small fraction of the mass of the earth is
available for direct study and analysis, and so it is necessary to use indirect methods
to estimate the earth’s inner composition. The continental crust, in concert with
the atmosphere and hydrosphere provides the nurturing and nourishing habitat in
which our species lives.
2.2.1
The composition of the earth
The earth can be considered as a closed system with a finite number of substances
in it, except for the very occasional and insignificant matter contribution of mete-
19
20
THE
GEOCHEMISTRY OF THE EARTH .
KNOWN
FACTS
orites [209]. The spheres are large reservoirs and between the reservoirs there are
flows of materials that balance out and keep the reservoir compositions nearly constant. Hence the composition of the atmosphere, hydrosphere and continental crust
is practically constant.
Table 2.1 shows the composition of the main layers on earth based on Javoy’s [169]
study. Only four elements constitute nearly 95% of the earth’s mass. In order of
abundance, these are O, Fe, M g and Si. The relative importance of M g relies on
the geochemistry of the mantle, rather than on the other layers of the solid earth,
where Si and Fe predominate in the upper crust and core, respectively. Other estimations were done by Mason [209], Ringwood [280], Ganapathy and Anders [105]
and Smith [322]. As Javoy [169] states, the only significant discrepancy between
chemical models of the earth lies in the lower mantle. All primary upper mantle
compositions agree to within a few percent relative for major and minor elements.
For the core, the composition is not so strictly defined but the dominant agreement
is on Fe − N i − C o − C r − M n − Si − O − S combinations.
If we only take into account the outer layers of the earth, i.e. the continental crust,
hydrosphere and atmosphere, these constitute 92,87%, 3,15% and 0,0712% by volume, respectively.
In the next sections, the geochemistry of the atmosphere, hydrosphere and upper
continental crust are explained in detail.
2.3
The atmosphere
The atmosphere is the colorless, odorless and tasteless gaseous layer surrounding
the earth and retained by it through the earth’s gravity. Its relative mass compared
to the other spheres of the earth is minuscule (see table 2.1). Nevertheless, it is a
crucial geochemical reservoir, providing conditions essential for sustaining life, such
as supplying O2 , CO2 , moisture and many nutrients. The atmosphere plays also a
very direct role in controlling the earth’s climate via the absorption and scattering
of sunlight and infrared radiation and reducing temperature extremes between day
and night.
The atmosphere is made up of several layers with different qualities [359], [182]
[331] (see figure 2.1):
• The troposphere is the lowest atmospheric layer. It begins at the surface and
extends between 7 to 17 km. It contains over 75% of all the atmospheric gases
and vast quantities of water and dust. Almost all phenomena of weather and
climate that physically affect man take place within the troposphere, caused by
the churning of its mass. The troposphere is the region in which the infrared
radiation is absorbed mainly by water vapor to raise the surface temperature.
The atmosphere
21
Table 2.1. Composition of the main envelopes derived from direct sampling or from
a chemical translation of a direct measurement (density), in the case of the core,
and the corresponding whole earth composition [169].
Mantle
% vol
% mass
O
Si
Mg
Al
Ca
Fe
Ni
Ti
Cr
Mn
Na
S
K
U
Th
Cl
Br
B
C
N
Rare
gases
81,89
67
44,12
20,89
25,09
1,24
1,49
6,53
0,17
0,058
0,169
0,081
0,14
0,01
0,03
5E-12
1,2E-11
Oceanic
crust
0,085
0,072
44,33
23,1
4,66
8,47
8,07
8,17
0,3
0,9
0,2
0,11
2,08
Continental
crust
0,44
0,36
47,25
27,58
2,65
8,36
4,57
5,13
Core
Oceans
Atmosphere
17,56
32,54
3
7
0,033
0,023
88,889
1,48E-08
0,842 ppm
23,16
0,0053
0,0412
80
4,65
0,42
0,09
2,37
0,77
0,57
4
0,12
2E-11
4,4E-11
1,58
1,00E-06
3,50E-06
1,0764
0,0902
0,0398
1,9383
0,04
0,0005
0,0028
75,56
1,28
Whole
earth
100
100
30,76
16,39
16,82
0,87
1,02
30,43
1,63
0,04
0,36
0,24
0,10
1,31
2,59E-02
6,96E-12
2,07E-11
4,46E-04
1,15E-07
2,68E-02
6,36E-08
1,08E-09
• The stratosphere extends from the troposphere to about 50 km. In this thin
layer, there is 19% of the atmospheric gases and a small quantity of water vapor. Temperature increases with height because of the absorption of ultraviolet
light by ozone. The ozone layer is contained in the stratosphere.
• The mesosphere extends from about 50 km to the range of 80 to 85 km. The
gases in the mesosphere are too thin to absorb much of the sun’s radiation, but
the air is thick enough to slow down meteorites. In this case, the temperature
decreases with height.
• The thermosphere ranges from 80-85 km to more than 640 km.The gases of
this sphere are even thinner than in the mesosphere, but they absorb ultraviolet light from the sun and as a consequence, temperature increases with
height.
• The ionosphere is part of the thermosphere and is made of electrically charged
gas particles ionized by solar radiation. It plays an important role since it
22
THE
GEOCHEMISTRY OF THE EARTH .
KNOWN
FACTS
Figure 2.1. The atmospheric layers. Source: http://www.atmosphere.mpg.de (Max
Plank Institute)
influences radio propagation to distant places on earth. Furthermore, it is
responsible for auras.
• And finally the exosphere, it is the outermost layer of the atmosphere and
extends from 500 to 1000 km up to 10.000 km. It is composed of free-moving
particles that may migrate into and out of the magnetosphere. In this layer,
gases get thinner and thinner and drift off into space.
The stability of the physical and geochemical conditions of the atmosphere is being
altered by the action of man through air pollution. The greatest source of emissions
are the burning of fossil fuels, emitting huge quantities of carbon dioxide, methane
and fluorocarbons, believed to contribute to global warming. Another man-made
consequence of the use of chlorofluorocarbons is the stratospheric ozone depletion,
which lowers the effectiveness of the atmosphere to protect us against UV radiation.
2.3.1
The composition of the atmosphere
In terms of its constituent gases, the atmosphere presents a notably uniform chemical
composition to heights of about 100 km [100], except for water which varies with
location and season as well as with elevation. Above this altitude, the atmosphere
becomes layered and non uniform in chemical composition.
The hydrosphere
23
The atmosphere is composed roughly by (volume content) 78% of usually inert nitrogen1 , around 21% of oxygen, 0,93% argon, 380 ppm of carbon dioxide, a variable amount of water vapor (average around 1%) and trace amounts of other gases.
That mixture of gases is commonly known as air. The latest atmospheric geochemical advances are compiled in Keeling [181]. Next, the main components of the
troposphere and their origin are explained basing on the information provided by
Turekian [359].
Nitrogen in the presence of oxygen at the surface of the oceans combines to form
nitrate in solution as the stable form. Both nitrogen and oxygen are maintained
at their levels by biological processes. Oxygen is more biologically controlled than
nitrogen but both are dependent on the chemical actions of life.
The argon in the atmosphere is believed to have been produced by the radioactive
decay of potassium-40 in the earth and released to the atmosphere by degassing of
the earth. It is not certain whether most of the argon was supplied from the argon
produced in the earth by potassium-40 decay at some major degassing epoch in the
earth’s early history or by the continuously generated argon in the earth’s crust and
mantle.
Methane and carbon dioxide are closely tied to biological activity. Methane oxidized
carbon dioxide and its presence is directly sustained by production by bacteria and
animals.
Man-made impurities such as sulphur dioxide and carbon monoxide, which are responsible for the physical discomforts of smog, are also sometimes highly concentrated in urban areas.
A summary of the composition of the atmosphere at the start of the twenty-first
century done by Prinn [272], from Brasseur et al. [36] and Prinn et al. [271] is
given in table 2.2.
2.4
The hydrosphere
The hydrosphere is the liquid water component of the earth. It includes oceans, seas,
lakes, rivers, rain, underground water, ice and atmospheric water vapor as in clouds.
It covers about 70% of the surface of the earth and is the home for many plants and
animals.
The hydrosphere is in continuous motion through the hydrologic cycle, which is a
conceptual model that describes the storage and movement of water between the
biosphere, atmosphere, lithosphere and the hydrosphere (see section 4.6.2 for more
details).
1
Normally inert except upon electrolysis by lightning and in certain biochemical processes of nitrogen fixation.
24
THE
GEOCHEMISTRY OF THE EARTH .
KNOWN
FACTS
Table 2.2. Gaseous chemical composition of the atmosphere [272].
Substance
Mole fraction in dry air
Major sources
Nitrogen
Oxygen
Argon
Carbon dioxide
Chemical
formula
N2
O2
Ar
CO2
78,084
20,948
0,934
360
%
%
%
ppm
Neon
Helium
Methane
Hydrogen
Ne
He
C H4
H2
18,18
5,24
1,7
0,55
ppm
ppm
ppm
ppm
Nitrous oxide
Carbon monoxide
N2 O
CO
0,31
50-200
ppm
ppb
Ozone (troposphere)
Ozone (stratosphere)
NMHC
Chlorofluorocarbon 12
Chlorofluorocarbon 11
Methylchloroform
Carbon tetrachloride
Nitrogen oxides
O3
O3
Cx H y
C F2 Cl2
C F C l3
C H3 C C l3
C C l4
N Ox
10-500
0,5-10
5,0-20
540
265
65
98
0,01-1
ppb
ppm
ppb
ppt
ppt
ppt
ppt
ppm
Ammonia
Hydroxyl radical
Hydroperoxyl radical
Hydrogen peroxide
Formaldehyde
Sulfur dioxide
N H3
OH
HO2
H2 O2
C H2 O
SO2
0,01-1
0,05
2
0,1-10
0,1-1
0,01-1
ppb
ppt
ppt
ppb
ppb
ppb
Dimethyl sulfide
Carbon disulfide
Carbonyl sulfide
C H3 SC H3
C S2
OC S
10-100
1-300
500
ppt
ppt
ppt
Hydrogen sulfide
H2 S
5-500
ppt
Biological
Biological
Inert
Combustion, ocean, biosphere
Inert
Inert
Biogenic, anthropogenic
Biogenic,
anthropogenic,
photochemical
Biogenic, anthropogenic
Photochemical,
anthropogenic
Photochemical
Photochemical
Biogenic, anthropogenic
Anthropogenic
Anthropogenic
Anthropogenic
Anthropogenic
Soils, lightning, anthropogenic
Biogenic
Photochemical
Photochemical
Photochemical
Photochemical
Photochemical,
volcanic,
anthropogenic
Biogenic
Biogenic, anthropogenic
Biogenic, volcanic, anthropogenic
Biogenic, volcanic
The hydrosphere
25
Table 2.3. Inventory of water at the earth’s surface [263].
Reservoir
Oceans
Ice Caps and Glaciers
Groundwater
Lakes
Soil Moisture
Atmosphere
Streams and Rivers
Biosphere
Sum
Volume, M km3
1370
29
9,5
0,125
0,065
0,013
0,0017
0,0006
1408,71
%
97,25
2,05
0,68
0,01
0,005
0,001
0,0001
0,00004
100,00
The planetary water supply is dominated by the oceans (see table 2.3). Approximately 97% of all water on the earth is the oceans. The other 3% is held as freshwater in glaciers and icecaps, groundwater, lakes, soil, the atmosphere and biosphere
[263]. The greater portion of the fresh water (75%) is in the shape of ice and permanent snow cover in the Antarctic, Arctic and mountainous regions. Next 25% are
fresh and ground waters. Only 0,33% of the total amount of fresh waters on the
earth are concentrated in lakes, reservoirs and river systems (surface waters), which
are most accessible for economic needs and very important for water ecosystems.
Considered as a whole, the earth has a comparatively stable water budget. The major problem is that most of it is overwhelmingly salty. Additionally, fresh water is not
evenly distributed over the lands. Furthermore, industrialization and unsustainable
land uses are increasing dramatically water pollution and thereby threatening world
water supply.
Next, the main water reservoirs of the earth are analyzed, stressing out their abundances, economic uses and chemical compositions.
2.4.1
Seawater
The oceans account for a little over 70% of the earth’s surface and comprise more
than 97% of the hydrosphere. The volume of ocean water is about 1, 37 · 109 km3
[263]. The Pacific ocean is by far the biggest in the world, followed by the Atlantic
and the Indian oceans (see table 2.4).
Oceans represent a relatively well-mixed system of considerable mass and potential
economic use. The prime functions of the oceans are those related to atmospheric
behavior. The oceans constitute the only major source of atmospheric moisture for
the lands, and they serve as gigantic “energy cells” for the receipt, storage, and release of the radiant sun energy that fuels the earth’s climatic and weather systems.
Besides of being a huge food reservoir, they have other uses such as pure water
26
THE
GEOCHEMISTRY OF THE EARTH .
KNOWN
FACTS
Table 2.4. Volume of Oceans and Seas. Adapted from [85]
Name
Atlantic Ocean
without marginal seas
with marginal seas
Pacific Ocean
without marginal seas
with marginal seas
Indian Ocean
without marginal seas
with marginal seas
Arctic Ocean
Mediterranean Sea and Black Sea
Gulf of Mexico and Caribbean Sea
Australasian Central Sea
Hudson Bay
Baltic Sea
North Sea
English Channel
Irish Sea
Sea of Okhotsk
Bering Sea
The world ocean
Volume, M km3
324,6
354,7
707,6
723,7
291
291,9
17
4,2
9,6
9,9
0,16
0,02
0,05
0,004
0,006
1,3
3,33
1.370
sources after the process of desalination and as chlorine and bromine sources2 . Nevertheless, its salinity avoids seawater to have more economic uses than the other
types of water reservoirs mentioned before. In fact it is frequently considered to be
a drain rather than a resource.
2.4.1.1
The composition of the sea
Despite their overall size, the oceans are sufficiently uniform to make description
of their chemical nature relatively straightforward. Studies have shown that the
relative compositions of major components: N a+ , M g 2+ , C a2+ , K + , C l − , SO4−2 ,
−
S r 2+ , H BO3− , CO32− , B(OH)3 , B(OH)−
of seawater were constant [69], [37],
4, F
[264] and [224]. The first six ions make up 99,4% of the dissolved salts (see table
2.5). Most of the chemicals in the ocean are brought from the water of rivers,
which in turn receive them from rocks of the crust that have suffered the process
of weathering. An average composition of river waters given by Livingstone [197] is
listed in table 2.8. It is remarkable the difference between river and ocean chemical
compositions. The explanation of that relies on the residence time of the ions. Most
abundant ions found in seawater have residence times of above one million years
[137]. The salinity of ocean water is about 35 parts per thousand by mass, but
2
See sections 3.4.16 and 3.4.10 for more details.
The hydrosphere
27
Table 2.5. The composition of average seawater. Adapted from [224]
Substance
C l−
N a+
M g 2+
SO42−
C a2+
K+
H CO3−
Br −
S r 2+
CO32−
B(OH)−
4
F−
B(OH)3
Sum
Concentration, mg/g
19,351
10,784
1,284
2,713
0,412
0,399
0,107
0,067
0,008
0,048
0,003
0,013
0,009
35,198
variations from about 33 to 38 parts per thousand are observed in the open oceans.
The variation in salinity results from a number of physical processes that control the
salt content of seawater such as temperature, rainfall, ice melting or land runoff.
But not all seawater substances have a crustal origin. In fact, the sea is a huge reservoir for many atmospheric substances such as carbon dioxide, a major contributor
to climate change. Through the air-sea interaction processes, all the components of
air can be expected to find their way into the ocean. Additionally, there are other
sources and mechanisms producing gases within the ocean that supplement those
supplied from the atmosphere. The dissolved gases in seawater are classified into
four general groups [148]. The first group contains the inert gases: nitrogen, argon, helium, neon, xenon, and krypton. These gases enter the oceans through the
air-sea interface or through the introduction of aerated water by land runoff. The
second group is composed by solely oxygen, coming from the same sources than the
other group plus from photosynthesis by the plants that exist in the ocean. The third
group also contains only one member, carbon dioxide. This gas is introduced into
the sea through the large chemical equilibrium system. Specific sources of carbon
dioxide include the atmosphere, land runoff and the ocean floor. The fourth group
is simply the collection of all the remaining gaseous ingredients found in seawater,
and its sources are air pollution, usually from industry, and chemical reactions other
than photosynthesis. Hydrogen sulfide resulting from the reduction of sulfate in the
absence of oxygen is one member of this fourth group.
Wilhelm Dittmar’s complete analysis of the seventy-seven seawater samples collected
in 1884 stood for almost a century. Nowadays, one of the most accepted composition
of minor species in seawater is the compilation of Quinby-Hunt and Turekian [273],
listed in table 2.6.
28
THE
GEOCHEMISTRY OF THE EARTH .
KNOWN
Table 2.6: Predicted Mean Oceanic Concentrations. Adapted from [273].
Element
Hydrogen
Helium
Lithium
Beryllium
Boron
Carbon
Nitrogen
Oxygen
Fluorine
Neon
Sodium
Magnesium
Aluminum
Silicon
Phosphorous
Sulfur
Chlorine
Argon
Potassium
Calcium
Scandium
Titanium
Vanadium
Chromium
Manganese
Iron
Cobalt
Nickel
Copper
Zinc
Gallium
Germanium
Arsenic
Selenium
Bromine
Krypton
Rubidium
Strontium
Yttrium
Zirconium
Niobium
Molybdenum
Species
H2
Concentration
Inorganic Boron
ΣCO2
N2
N O3
Dissolved O2
Silicate
Reactive Phosphate
Sulfate
Chloride
<
<
<
C r (tot)
Dissolved M n
<
As (V)
Dimethylarsenate
Se (tot)
Se (IV)
Se (VI)
Bromide
1,9
178
0,2
4,4
2200
590
30
150
1,3
8
10,781
1,28
1
110
2
2,712
19,353
15,6
399
415
412
1
1
1
330
330
250
10
40
2
480
120
390
10
<> 20
5
2
nmol/kg
µg/kg
ng/kg
mg/kg
µg/kg
µg/kg
µg/kg
µg/kg
mg/kg
nmol/kg
g/kg
g/kg
µg/kg
µmole/kg
µmole/kg
g/kg
g/kg
µmole/kg
mg/kg
mg/kg
mg/kg
ng/kg
ng/kg
µg/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
µg/kg
170
ng/kg
<
67
3,7
124
7,8
7,7
13
'
1
<
1
11
Continued on next page . . .
mg/kg
nmol/kg
mug/kg
mg/kg
mg/kg
ng/kg
µg/kg
ng/kg
µg/kg
FACTS
The hydrosphere
29
Table 2.6: Predicted Mean Oceanic Concentrations. Adapted from [273]. –
continued from previous page.
Element
Ruthenium
Rhodium
Palladium
Silver
Cadmium
Indium
Tin
Antimony
Tellurium
Iodine
Xenon
Cesium
Barium
Lanthanum
Cerium
Praeseodymium
Neodymium
Promethium
Samarium
Europeum
Gadolinium
Terbium
Dysprosium
Holmium
Erbium
Thulium
Ytterbium
Lutetium
Hafnium
Tantalum
Tungsten
Rhenium
Osmium
Iridium
Platinum
Gold
Mercury
Thallium
Lead
Bismuth
Polonium
Radon
Radium
Actinium
Thorium
Proactinium
Uranium
Species
Concentration
0,5
End of the table
ng/kg
3
70
0,5
0,5
0,2
ng/kg
ng/kg
ng/kg
ng/kg
µg/kg
59
60
0,5
0,3
11,7
4
4
0,6
4
µg/kg
µg/kg
nmol/kg
ng/kg
µg/kg
ng/kg
ng/kg
ng/kg
ng/kg
0,6
0,1
0,8
0,1
1
0,2
0,9
0,2
0,9
0,2
8
2,5
1
4
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
11
6
12
1
10
ng/kg
ng/kg
ng/kg
ng/kg
ng/kg
0,7
ng/kg
3,2
µg/kg
30
2.4.2
THE
GEOCHEMISTRY OF THE EARTH .
KNOWN
FACTS
Renewable water resources: surface and ground waters
The renewable water resources are the total amount of a country’s water resources,
both surface water and ground water, which are generated through the hydrological
cycle. It is mainly the river runoff estimated in the volume referred to a unit of
time (as for instance km3 /year) and formed in the region at issue or incoming from
outside, including the ground water inflow to the river network. This kind of water
resources includes also the yearly renewable upper aquifer ground water not drained
by the river systems.
Despite of their relative low abundance, renewable water resources on earth (see
table 2.3) in forms of lakes, streams3 , rivers and ground water play an important
role for life and especially for human-beings, since they are the main sources of
freshwater. They are also an important source of water for agricultural and industrial consumption. Rivers and flows are comparatively small but essential source of
energy. Many rivers are avenues of transportation. They have also a great scenic and
recreational value.
The mean renewable global water resources are estimated at 42.785 km3 /year, and
they are very variable with space and time. Table 2.7 presents the distribution of water resources and availability by the earth’s continents. This information is based on
a water balance approach by Shiklomanov [311], who provided country data for 51
countries on available water resources. Other comprehensive world renewable publications are the early work of L’vovich [204], Gleick [115] and the World Resources
Institute [410]. By an absolute value the largest water resources are characteristic
of Asia and South America. The smallest are typical for Europe and Australia with
Oceania. Due to rapid earth’s population, growth since 1970 to 1994, the potential
water availability of earth’s population decreased form 12,9 to 7,6 km3 per year and
person.
2.4.2.1
Stream, river and lake waters
The nature of aqueous solutions that are produced or modified by the processes
of weathering is determined by several factors, including chemical controls such as
reaction rate, solubility and interface reactions, as well as environmental controls
such as climate, geology and the hydrologic cycle. The solutions from weathering
may mix with other waters that effectively have not been involved in a weathering
process. In turn, the mixed waters may be modified by further reactions such as by
some cation exchange with clay or other mineral phases, or by the activities of man.
3
Stream is defined as a body of water that carries rock particles and dissolved substances, and
flows down a slope along a clearly defined path.
The hydrosphere
31
Table 2.7. Renewable water resources and potential water availability by continents
[311].
Continent
Europe
North
America
Africa
Asia
South
America
Australia
and Oceania
World
Area,
M km2
Population,
Millions
1995
Water resources,
km3 /year
Water availability,
1000m3 /year
Average
Max.
Min.
per km2
10,46
24,3
685
453
2900
7890
3410
8917
2254
6895
277
324
per
capita
4,23
17,4
30,1
43,5
17,9
708
3445
315
4050
13510
12030
5082
15008
14350
3073
11800
10320
134
311
672
5,72
3,92
38,2
8,95
28,7
2404
2880
1891
269
83,7
135
5633
42785
44751
39775
317
7,6
There is therefore a great variation in the concentrations of dissolved materials in
lake, stream and river water. Nonetheless an extensive amount of available data
allowed Livingstone [197] to estimate the mean composition of world river water
(see table 2.8).
Table 2.8. Mean chemical contents of world river water [197]
Substance
H CO3−
SO42−
C l−
N O3−
C a2+
M g 2+
N a+
K+
Fe2+
SiO2
Sum
Concentration µg/g
58,4
11,2
7,8
1
15
4,1
6,3
2,3
0,67
13,1
120
Different compilations of the average concentration of the main trace elements found
in rivers were later done by Li [196] and Gaillardet et al. [102]. The composition of
Li is lited in table 2.9.
Lake waters also vary greatly in composition, not only from lake to lake but often
within a lake where marked temperature and compositional stratifications can occur.
Reducing conditions often exist in the lower, more saline level of stratified lakes and
32
THE
GEOCHEMISTRY OF THE EARTH .
KNOWN
FACTS
Table 2.9. The average concentrations of elements in filtered river water. Concentration in ppb. Adapted from Li [196].
Element
Li
Be
B
F
Na
Mg
Al
Si
P
S
Cl
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
Rb
Sr
Y
Zr
Nb
Concentration
3
0,01
10
100
6300
4100
50
6500
20
3700
7800
2300
15000
0,004
3
0,9
1
7
40
0,1
0,3
7
20
0,09
0,005
2
0,06
20
1
70
Element
Mo
Ag
Cd
In
Sn
Sb
I
Cs
Ba
La
Ce
Pr
Nd
Sm
Eu
Gd
Tb
Ho
Er
Tm
Yb
Lu
Hf
Ta
W
Re
Au
Hg
Tl
Pb
Bi
Th
U
Concentration
0,6
0,3
0,01
0,04
0,07
7
0,02
20
0,05
0,08
0,007
0,04
0,008
0,001
0,008
0,001
0,001
0,004
0,001
0,004
0,001
0,03
0,002
0,07
1
0,1
0,04
The hydrosphere
33
these give rise to relatively high concentrations of nitrite ammonia and Fe2+ in the
water. The reducing conditions may also lead to the production of hydrogen sulphide
gas and the precipitation of some metal sulphides (including iron sulphides). Silica
and phosphorous may be released from the sediments. The thermocline zone, which
separates the upper and lower levels of a lake by a large change in temperature,
prevents the diffusion of atmospheric oxygen to go into the reduction layer [137].
2.4.2.2
Ground waters
As seen from table 2.3, less than 1% of the water on earth is ground water. Although
the total volume of ground water is small, it is about 35 times greater than the volume of water lying in fresh-water lakes of flowing in streams on the earth’s surface.
Nearly all the earth’s groundwater has its origin in rainfall. It is always slowly moving on its way back to the ocean, either directly through the ground or by flowing
out onto the surface and joining stream.
The hydrogeochemistry of ground waters reflects the source of the water, the lithology of the aquifer and the local chemical conditions such as temperature, pressure
and redox potential. White et al. [405] classified the source of ground waters as:
• magmatic,
• meteoric (e.g. precipitated and surface water),
• connate (i.e. water trapped in the pore spaced of a sediment at the time of
deposition),
• oceanic.
Extensive compilations of ground water compositions were recorded by White et al.
[405]. Table 2.10 shows examples of constituents of ground waters in Maryland and
New York from different rock types.
2.4.3
Ice caps, ice sheets and glaciers
Glaciers, ice sheets and ice caps are huge masses of ice, formed on land by the
compaction and re-crystallization of snow, that move very slowly down slopes or
move outward due to their own weight. If the rate of melting is greater than the
rate of accumulation, the glacier recedes; if it is less, the glacier advances. Many
recent studies on glacier runoff around the world have shown that the first tendency
is rather happening presumably due to climate change.
Around 10% of the earth’s surface is covered by glaciers (∼ 15, 9 × 106 km2 glacierized vs 148, 8 × 106 of total land surface [185]). Approximately 91% of the earth’s
land ice covers Antarctica, 8% Greenland and glaciers in other regions contribute
34
THE
GEOCHEMISTRY OF THE EARTH .
KNOWN
FACTS
Table 2.10. Constituents of ground waters from different rock types. Concentrations
in µg/g [405].
Substance
Cations or oxide
SiO2
Al
Fe
Ca
Mg
Na
K
Anions
H CO3
CO3
SO4
Cl
F
N O3
PO4
Granite
Serpentinite
Shale
39
9
1,6
27
6,2
9,5
1,4
31
0,2
0,06
9,5
51
4
2,2
5,5
0
3,5
227
29
12
2,7
93
0
32
5,2
0
7,5
0
276
0
2,6
12
0
6,8
0
288
0
439
24
0
0,9
0
to around 1% (see table 2.11). Current annual global glacial runoff range from
0,3×103 km3 to 1×103 km3 [173]. Glaciers are estimated to contribute to 0,6 to
1% to the global annual runoff.
There are two types of glaciers, those that are unconstrained by topography and
blanket the topography, including ice sheets and ice caps, and those that are constrained by topography, mainly valley glaciers. Ice sheets cover areas which are
typically > 5 × 104 km2 (mostly found in Antarctica and Greenland), whereas ice
caps cover smaller areas < 5×104 km2 . Ice masses constrained by topography cover
areas between 1 and 100 km2 . Most research on the geochemical weathering of
glaciers has been conducted mainly on valley glaciers. Fortunately it seems that to
a first approximation, the biochemical processes inferred from the small systems are
similar to those occurring in large systems [357].
Glaciers are very important to the stability of the environment. Changes in heat and
atmosphere can cause glaciers to melt, change shape and move more rapidly and
as a consequence, more land is reformed in its movement. Glaciers exert a direct
influence on the hydrologic cycle by slowing the passage of water through the cycle.
Like ground water, glaciers are considered to be key natural reservoirs of freshwater.
They are therefore extremely important sources of water for human consumption,
irrigation, electric power and other industrial uses, especially during the summer,
when the highest rate of melting is reached and precipitation is more scarce.
The hydrosphere
35
Table 2.11. Area of land surface covered by glaciers in different regions of the world,
together with estimates of volume and the equivalent sea level rise that the volume
implies [185].
2.4.3.1
Region
Area, km2
Volume, km3
Antarctica
Greenland
North America
Asia
Europe
South America
Australasia
Africa
Total
13600000
1730000
276000
185000
54000
25900
860
10
15900000
25600000
2600000
Sea level equivalent, m
64
6
200000
0,5
28400000
70,5
The composition of glacial runoff
The main source of water in most glacier systems is snow and/or ice melt. Some
water is also derived from rain, and a little is derived from geothermal melting and
internal deformation [257]. Table 2.12 shows the chemical composition of glacial
runoff compiled by Brown [43] for different regions of the world. It also includes an
estimation on the average composition of glaciers on earth, which is the weighted
sum of the average compositions in each region. Glacial runoff is a dilute solution
containing ions C a2+ , H CO3− , SO42− , with variable N a+ and C l − . Glacial runoff is
usually more dilute than global mean river4 .
4
See table 2.8 for comparisons between river and glacier compositions.
Region
Greenland
Antarctica
Iceland
Alaska
Canadian high Arctic
Canadian rockies
Cascades
European alps
Himalayas
Norway
Svalbard
Average
C a2+
2,60-3,40
1,44-26,01
2,20-7,00
11,00
5,20-52,01
19,20-22,0
0,70-1,60
0,40-12,8
1,50-11,8
0,18-12,5
2,40-20,0
12,69
M g 2+
0,82-1,19
1,45-4,07
0,36-1,45
0,44
0,25-7,75
3,51-3,75
0,10-0,24
0,07-1,69
0,08-2,78
0,02-0,80
1,20-6,54
2,59
N a+
1,79-2,53
8,28-32,2
0,69-11,0
0,57
0,02-4,37
0,09-0,83
0,06-0,39
0,11-2,11
0,57-1,49
0,19-4,83
2,53-6,21
18,44
K+
0,20-0,35
0,03-4,30
0,11-0,47
2,39
0,0039-1,53
0,23-0,36
0,38-1,45
0,23-1,29
0,86-1,99
0,04-1,13
0,20-1,60
1,98
H CO3−
13,42-20,74
5,55-97,62
11,59-34,78
26,24
12,81-42,1
54,3-56,13
5,06-6,10
0,67-24,41
12,20-44,54
0,09-41,49
6,71-57,35
48,15
SO42−
4,32-9,60
1,63-57,61
1,25-6,24
12,48
2,83-187,2
18,24-24,96
0,38-1,39
0,48-11,52
7,68-19,68
0,34-6,72
4,61-36,49
27,38
0,02-1,56
0,02-0,37
0,02-3,23
0,09-5,27
7,71
THE
0,03-0,43
C l−
0,27-0,51
0,01-17,01
0,51
0,03
Table 2.12. The concentration of major ions in glacial runoff from different regions of the world. Concentrations are reported in
mg/l. Adapted from [43]
36
GEOCHEMISTRY OF THE EARTH .
KNOWN
FACTS
The continental crust
2.5
37
The continental crust
The solid earth is composed by several layers. These can be classified into: core,
mantle and crust. Figure 2.2 shows an earth cutaway with its different layers. The
inner part of the earth is the core and is about 2900 km below the earth’s surface.
The core is further divided into the inner and outer core. The inner core, or center of
the earth is solid and about 1250 km thick. The outer core (approx. 2200 km thick)
is composed of high-density molten metals, highly concentrated in iron [403].
The core is surrounded by a solid mantle of iron-magnesium silicates and oxides. It
contains the inner mantle (between 300 and 2890 km below the earth’s surface) and
the outer mantle (between 10 and 300 km below the earth’s surface).
The outer shell covering the mantle is called the crust. According to Rudnick [291],
it constitutes only 0,6% of the silicate earth and is covered by geological rock formations and the oceans. It is made up of the oceanic and continental crust. The oceanic
crust is 7 km on average thick and is composed of relatively rock types such as
basalt. The continental crust is about 40 km thick and contains virtually every rock
type known on earth. The structure of the continental crust is defined to consist of
upper-, middle- and lower crustal layers. The deep continental crust is composed
of granulite-facies rocks and begins at 23 km depth on average. The middle crust
extends from 8 to 17 km depth. Estimates indicate that it is composed of rocks in
the amphibolite facies.
The upper continental crust is the reservoir of the main minerals and other natural
resources useful for mankind. Therefore, it will be our object of study. Furthermore,
being the most accessible part of our planet, the upper crust has long been the target
of geochemical investigations. According to Yoder [411], the mass of the upper
continental crust is about half the mass of the total crust, this corresponds to a
volume of 6, 55 × 1020 cm3 and thus a sphere with a radius of about 54±4 km as an
upper limit.
2.5.1
The chemical composition of the upper continental crust
There are two basic methods employed to determine the composition of the upper
crust [291]:
• establishing weighted averages of the compositions of rocks exposed at the
surface and,
• determining averages of the composition of insoluble elements in fine-grained
clastic sedimentary rocks or glacial deposits and using these to infer uppercrust composition.
The determination of the major-element composition of the upper continental crust
relies on the first method. It has been used by a variety of authors starting with
38
THE
GEOCHEMISTRY OF THE EARTH .
KNOWN
FACTS
Figure 2.2. Earth’s cutaway. Source: USGS [397]
Clarke et al. in 1889 [58] and continuing with Ronov and Yaroshevsky [287], Shaw
et al. [306], [308], Eade and Fahring [80], Condie [60] and Gao et al. [106]. The
results of these independent studies show a very similar composition for most majorelement averages, but not insignificant differences for rare earth elements (REEs).
Estimates of the trace-element composition of the upper crust rely on the natural
sampling processes of sedimentation and glaciation. This method was suggested by
Goldschmidt [116], [117], using the idea that glacial clays are compositionally representative of the crust from which they were derived. Elements that are insoluble
during weathering are transported from the site of weathering/glacial erosion to deposition and their concentrations in sedimentary rocks may provide robust estimates
of the average composition of their source regions. Relevant studies of the composition of the crust through these methods are: Taylor and McLennan [353], [354],
Plank and Langmuir [267] and the recent work of McLennan [215].
Table 2.13 shows average upper crustal compositions from the compilation works
done by Wedepohl [404], McLennan [215] and the latest recommended composition
of Rudnick et al. [292]. Rudnick et al. presented their best estimate for the chemical
composition of the upper continental crust based mainly on averages of the different
surface-exposure studies such as Shaw et al. [306], Fahring and Eade [93], Plank
and Langmuir [267], Taylor and McLennan [353], McLennan [215], Sims et al.
[314], Gao et al. [106], Teng et al. [355] or Newson et al. [243]. In the upper
crust, only eight elements account for 99% of the weight; the most prominent among
these is O, accounting for almost 50% of the weight.
The continental crust
Table 2.13: Average composition of the upper continental crust according to different studies. Elements in g/g.
Element
O
Si
Al
Fe
Ca
Na
Mg
K
Ti
C
P
Mn
S
Ba
F
Cl
Sr
Zr
Cr
V
Rb
Zn
Ce
N
Ni
La
Nd
Cu
Co
Y
Nb
Li
Sc
Ga
Pb
B
Th
Pr
Sm
Hf
Gd
Dy
Cs
Be
Wedepohl [404] McLennan [215] Rudnick et. al. [292]
4,72E-01
4,72E-01
2,88E-01
3,08E-01
3,09E-01
7,96E-02
8,04E-02
8,15E-02
4,32E-02
3,50E-02
3,92E-02
3,85E-02
3,00E-02
2,57E-02
2,36E-02
2,89E-02
2,73E-02
2,20E-02
1,33E-02
1,50E-02
2,14E-02
2,80E-02
2,32E-02
4,01E-03
4,10E-03
3,84E-03
1,99E-03
7,57E-04
7,00E-04
6,55E-04
7,16E-04
6,00E-04
7,74E-04
6,97E-04
6,20E-05
5,84E-04
5,50E-04
6,28E-04
5,25E-04
5,57E-04
4,72E-04
3,70E-04
3,33E-04
3,50E-04
3,20E-04
2,03E-04
1,90E-04
1,93E-04
1,26E-04
8,30E-05
9,20E-05
9,80E-05
1,07E-04
9,70E-05
7,80E-05
1,12E-04
8,40E-05
6,50E-05
7,10E-05
6,70E-05
6,00E-05
6,40E-05
6,30E-05
6,00E-05
8,30E-05
5,60E-05
4,40E-05
4,70E-05
3,00E-05
3,00E-05
3,10E-05
2,70E-05
2,60E-05
2,70E-05
2,50E-05
2,50E-05
2,80E-05
2,40E-05
1,70E-05
1,73E-05
2,40E-05
2,20E-05
2,10E-05
1,90E-05
1,20E-05
1,20E-05
1,80E-05
2,00E-05
2,40E-05
1,60E-05
1,36E-05
1,40E-05
1,50E-05
1,70E-05
1,75E-05
1,48E-05
1,70E-05
1,70E-05
1,10E-05
1,50E-05
1,70E-05
8,50E-06
1,07E-05
1,05E-05
6,70E-06
7,10E-06
7,10E-06
5,30E-06
4,50E-06
4,70E-06
4,90E-06
5,80E-06
5,30E-06
4,00E-06
3,80E-06
4,00E-06
3,80E-06
3,50E-06
3,90E-06
3,40E-06
4,60E-06
4,90E-06
2,40E-06
3,00E-06
2,10E-06
Continued on next page . . .
39
40
THE
GEOCHEMISTRY OF THE EARTH .
KNOWN
FACTS
Table 2.13: Average composition of the upper continental crust according to different studies. Elements in g/g. – continued from previous page.
Element
Sn
Er
Yb
As
U
Ge
Eu
Mo
Ta
Br
W
Ho
I
Tb
Tl
Lu
Sb
Tm
Se
Cd
Bi
Ag
In
Hg
Te
Au
Pd
Pt
Re
Ru
Rh
Ir
Os
Wedepohl [404]
2,30E-06
2,10E-06
2,00E-06
1,70E-06
1,70E-06
1,40E-06
1,30E-06
1,10E-06
1,10E-06
1,00E-06
1,00E-06
8,00E-07
8,00E-07
6,50E-07
5,20E-07
3,50E-07
3,00E-07
3,00E-07
1,20E-07
1,00E-07
8,50E-08
7,00E-08
5,00E-08
4,00E-08
5,00E-09
2,50E-09
4,00E-10
4,00E-10
4,00E-10
1,00E-10
6,00E-11
5,00E-11
5,00E-11
McLennan [215]
5,50E-06
2,30E-06
2,20E-06
1,50E-06
2,80E-06
1,60E-06
8,80E-07
1,50E-06
1,00E-06
2,00E-06
8,00E-07
6,40E-07
7,50E-07
3,20E-07
2,00E-07
3,30E-07
5,00E-05
9,80E-08
1,27E-07
5,00E-08
5,00E-08
1,80E-09
5,00E-10
4,00E-10
2,00E-11
5,00E-11
End of the table
Rudnick et. al. [292]
2,10E-06
2,30E-06
1,96E-06
4,80E-06
2,70E-06
1,40E-06
1,00E-06
1,10E-06
9,00E-07
1,60E-06
1,90E-06
8,30E-07
1,40E-06
7,00E-07
9,00E-07
3,10E-07
4,00E-07
3,00E-07
9,00E-08
9,00E-08
1,60E-07
5,30E-08
5,60E-08
5,00E-08
1,50E-09
5,20E-10
5,00E-10
1,98E-10
3,40E-10
2,20E-11
3,10E-11
Although a lot of effort has been placed in determining the chemical composition
of the upper continental crust, the mineralogical composition of it has been barely
studied. This is due mainly to the complexity and heterogeneity of the earth’s crust.
The thermodynamic properties of the earth are related to the species contained in it
and not to their elements, as we will see in later chapters. Therefore, a model of the
Summary of the chapter
41
mineralogical composition of the crust needs to be developed. This will be the aim
of chapter 3.
2.6
Summary of the chapter
In order to determine the thermodynamic properties of the earth, the geochemistry
of it must be analyzed in detail. For that purpose, the composition of each layer:
atmosphere, hydrosphere and continental crust has to be studied in terms of substances.
A comprehensive analysis of the physical and geochemical properties of the earth
has been undertaken in this chapter.
First, a coarse composition of the bulk earth with the relative mass proportions of
each sphere has been presented. This overview has given way to the more detailed
explanation of the geochemistry of the atmosphere, hydrosphere and upper continental crust.
The atmosphere is the gaseous layer surrounding the earth. It is further divided into
different parts. The troposphere, being the lowest of all, is the layer with which
human beings have more interaction. The chemical composition of the atmosphere
is rather uniform to heights up to 100 km. Apart from the natural occurring gases,
there are traces of anthropogenic substances in the atmosphere that may alter the
conditions on earth.
The hydrosphere is the liquid water component of the earth and includes seas (constituting over 97% of it); renewable water resources (rivers, lakes and underground
water); ice; and atmospheric water. The continuous motion of the hydrosphere is
governed by the hydrological cycle. The composition of seawater is, as it happened
to the atmosphere, quite uniform. Many components of the sea have a crustal origin. Nevertheless, it contains dissolved atmospheric gases such as CO2 , what makes
oceans to be huge and crucial reservoirs of GhG gases. Although the relative small
weight proportion, renewable water resources are essential for life on earth, as they
are the main sources of freshwater. No uniform composition can be applied to them,
but some examples and averages have been provided. Glaciers, ice sheets and ice
caps are huge amounts of frozen freshwater, and as a consequence they are important water suppliers for human beings. The composition of glacial runoff from the
different regions of the world has been presented.
The solid earth is composed by the core, mantle and crust. The crust is further
divided into the lower, middle and upper crust. The upper crust is the reservoir
of the main minerals and other natural resources for mankind and being the most
accessible, it is the best well studied part. Its chemical composition in terms of
elements is well known. However, the mineralogical composition has been barely
studied.
42
THE
GEOCHEMISTRY OF THE EARTH .
KNOWN
FACTS
In the next chapter, the only unknown composition of the earth’s outer spheres,
the upper continental crust, will be analyzed in detail and a new methodology for
obtaining its mineralogical composition will be developed.
Chapter
3
The mineralogical composition of
the upper continental crust
3.1
Introduction
In this chapter, a model of the mineralogical composition of the earth’s crust is developed. The starting point of the model is the composition given by the Russian
geochemist Grigor’ev. The new mineralogical composition is constrained by the conservation of mass statement, which must be satisfied not only in the crust, but in the
entire earth. Additionally, the model is given geological consistence, by introducing
a series of assumptions based on geological observations. This information, will allow to obtain in further chapters, the thermodynamic properties of the earth’s upper
crust and to propose an approximation of the entropic planet.
3.2
The classification of minerals
Minerals can be defined as natural occurring inorganic solids that possess an orderly
internal structure and a definite chemical composition, whereas rocks are indefinite
mixtures of naturally occurring substances, mainly minerals. According to the International Mineralogical Association1 there are more than 4000 known minerals. Of
these, around 150 can be called “common”, 50 are occasional and the rest are “rare”
or “extremely rare”.
Minerals can be classified according to different criteria including hardness, crystal
structure, specific gravity, color, luster or cleavage. Table 3.1 shows one of the most
commonly used mineral classifications based on the chemical composition. The most
1
The International Mineralogical Association (IMA) is responsible for the approval of and naming
of new mineral species found in nature.
43
44
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Table 3.1. Mineral classification based on Dana’s New Mineralogy [103]
I
II
III
IV
V
VI
VII
VIII
IX
Native Elements
Sulfides
Oxides
Hydroxides
Halides
Carbonates
Nitrates
Borates
Sulfates
Chromates
Phosphates
Arsenates
Vanadates
Tungstates
Molybdates
Silicates:
- Nesosilicates
- Sorosilicates
- Cyclosilicates
- Ionosilicates
- Phyllosilicates
- Tectosilicates
Organic Minerals
common minerals are the silicates, accounting for more than 90% of the earth’s crust,
whereas the most common non-silicates are carbonates, oxides and sulfides.
Minerals can be further classified into groups. Some of the main groups found in
nature are now briefly discussed, indicating the principal minerals included in each
group. The information has been primarily extracted from Mason [209].
3.2.1
The silica minerals
Silica (SiO2 ) occurs in nature as five different minerals: quartz (including chalcedony), tridymite, cristobalite, opal and lechatelierite or silica glass. Of these,
quartz is very common, tridymite and cristobalite are widely distributed in volcanic
rocks and can hardly be called rare; opal is not uncommon and lechatelierite is very
rare.
3.2.2
The feldspar group
The feldspar are the most common of all minerals. They are closely related in form
and physical properties, but they fall into two groups: the potassium and barium
feldspars, which are monoclinic or very nearly monoclinic in symmetry, and the
The classification of minerals
45
sodium and calcium feldspars (plagioclases), which are triclinic. The general formula of feldspars can be stated as X Al(Al, Si)Si2 O8 , being X elements N a, K, C a,
and Ba. The barium-containing feldspars are very rare and of no importance as rockforming minerals. The main K-feldspars are orthoclase, sanidine and microcline. In
the plagioclase subgroup, albite, oligoclase, andesine, labradorite, bytownite and
anorthite are the most important minerals.
3.2.3
The pyroxene group
The pyroxenes are a group of minerals closely related in crystallographic and other
principal properties, as well as in chemical composition, although they crystallize in
two different systems, orthorhombic and monoclinic. Pyroxenes have the general
formula X Y (Si, Al)2 O6 (where X represents C a, N a, Fe+2 and M g and more rarely
Z n, M n and Li and Y represents ions of smaller size, such as C r, Al, Fe+3 , M g,
M n, Sc, T i, V and even Fe+2 ). On the basis of chemical composition and crystal
structure, the following species are recognized: enstatite and hyperstene (both orthorhombic), augite, clinoenstatite, clinohypersthene, aegirine, diopside, pegeonite,
jadeite, spodumene, pigeonite or hedenbergite (all monoclinic).
3.2.4
The amphibole group
The amphibole group comprises a number of species, which, although falling both
in the orthorhombic and monoclinic systems, are closely related in crystallographic
and other physical properties, as well as in chemical composition. They form isomorphous series, and extensive replacement of one ion by others of similar size can take
place, giving rise to very complex chemical compositions. The difference in chemical composition between compounds of the amphibole type and corresponding
compounds of the pyroxene type is not great. A general formula for all members
of the amphibole group can be written (W, X , Y )7−8 (Z4 O11 )2 (O, OH, F )2 , in which
symbols W, X, Y, Z indicate elements having similar ionic radii and capable of replacing each other. W stands for C a, N a and K; X stands for M g and Fe+3 (sometimes
M n); Y for T i, Al and Fe+3 ; and Z for Si and Al. The main amphibole minerals
are tremolite, actinolite, cummingtonite, hornblende, glaucophane, arfvedsonite or
riebeckite.
3.2.5
The olivine group
The minerals of the olivine group are silicates of bivalent metals and crystallize in
the orthorhombic system. The composition of olivine generally corresponds closely
to (M g, Fe)2 SiO4 , there being little replacement by other elements. Minerals included in the olivine group are: forsterite, fayalite, olivine, tephroite, monticellite,
glaucochroite and larsenite.
46
3.2.6
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
The mica group
The minerals of the mica group have in common the perfect basal cleavage easily
recognizable. The composition of individual specimens may be very complex, but a
general formula of the type W (X , Y )2−3 Z4 O10 (OH, F )2 can be written for the group
as a whole. In this formula W is generally K or N a, X and Y represent Al, Li, M g,
Fe2+ , and Fe3+ ; Z represents Si and Al, the Si:Al ratio being generally about 3:1.
Some of the main mica minerals are biotite, muscovite, paragonite, phologipte and
lepidolite.
3.2.7
The chlorite group
The chlorites are a group of phyllosilicate minerals. Chlorites can be described
by the following four endmembers based on their chemistry via substitution of
M g, Fe, N i, and M n in the silicate lattice: clinochlore (M g5 Al)(AlSi3 )O10 (OH)8 ,
chamosite (Fe5 Al)(AlSi3 )O10 (OH)8 , nimite (N i5 Al)(AlSi3 )O10 (OH)8 and pennantite
(M n, Al)6 (Si, Al)4 O10 (OH)8 . The formula that emphasizes the group is (M g, Fe)3
(Si, Al)4 O10 (OH)2 · (M g, Fe)3 (OH)6 . And the main chlorite minerals are besides
of the ones mentioned above, clinochlore, ripidolite, pennantite, orthochamosite,
thuringite or penninite.
3.3
Grigor’ev’s mineralogical composition of the crust
As explained in the previous chapter, a lot of effort has been placed in determining
the chemical composition of the upper continental crust. The composition has been
refined and improved with the studies of many different authors throughout the last
century. Nevertheless, the mineralogical composition of it has been barely studied,
because of the complexity and heterogeneity of the earth’s crust.
A very general average mineralogical composition of the crust was obtained by
Wedepohl2 [402], [403], and Nesbitt and Young [242] (table 3.2). According to
these studies, only ten types of minerals are the main constituents of the upper
crust.
A more comprehensive study of the mineralogical composition of the upper crust
was recently carried out by Grigor’ev [127]. He calculated the average contents
of rock forming and accessory minerals in the upper part of the continental crust
through the model of Ronov et al. [288]. The average composition of 208 minerals
in the rocks of the upper crust was already calculated by the same author for the
first time in year 2000 [124]. The calculations were based on the quantitatively
analysis published in the literature of more than 3000 rock samples published mainly
2
The mineralogical composition of the crust given by Wedepohl was calculated using the mineral
composition of magmatic rocks.
Grigor’ev’s mineralogical composition of the crust
47
Table 3.2. Crustal abundance of minerals. Data in percent volume.
Mineral
Quartz
Plagioclase
Orthoclase
Biotite
Muscovite
Chlorite
Amphiboles
Pyroxenes
Olivines
Oxides
Others
Wedepohl [402]
21,0
41,0
21,0
4,0
6,0
4,0
0,6
2,0
0,5
Nesbitt and Young [242]
23,2
39,9
12,9
8,7
5,0
2,2
2,1
1,4
0,2
1,6
3,0
in the USSR and USA. In Grigor’ev’s 2007 [127] publication, additional data was
considered. The average content in rocks of 265 minerals, their varieties and their
non-mineral materials were calculated. The content of 80 fundamental minerals
of the list was corrected, in order to ensure the mass balance with the chemical
composition of the elements in the rocks. The output is the result of a partiallyquantitative mineralogical analysis. His main bibliographical sources were [38],
[119], [126], [228] and [301].
Table 3.3: Average mineralogical composition of the upper continental crust
according to Grigor’ev [127]. Results are given in mass percentage.
Mineral
Native Elements
Copper
Silver
Gold
Lead
Polixene
I-Platinum
Zinc
Bismuth
Tin
Graphite
Moissonite
Sulphur
Sulphides
Tetradymite
Chalcocite
Bornite
Acanthite
Argentite
Pentlandite
Sphalerite
Abundance, mass %
4,10E-07
1,20E-07
1,80E-08
1,80E-07
3,00E-10
3,00E-10
4,70E-08
4,90E-08
4,40E-08
1,20E-01
7,00E-07
9,00E-05
1,60E-08
1,80E-07
2,20E-06
3,90E-08
7,10E-08
8,40E-05
4,60E-05
Continued on next page . . .
48
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Table 3.3: Average mineralogical composition of the upper continental crust
according to Grigor’ev [127]. Results are given in mass percentage. – continued from previous page.
Mineral
Metacinnabar
Chalcopyrite
Tetrahedrite
Freibergite
Fahlerz Group
Cubanite
Pyrrhotite
Troilite
Nickeline
Galena
Cinnabar
Covellite
Cooperite
Antimonite/ Stibnite
Bismuthinite
Stephanite
Samsonite
Boulangerite
Pyrargirite
Violarite
Pyrite
Marcasite
Vaesite
Cobaltite
Gersdorffite
Lollingite
Arsenopyrite
Molybdenite
Realgar
Orpiment
Halides
Halite
Chlorargyrite
Sylvite
Fluorite
Bischofite
Carnallite
Oxides
Periclase
Spinel
Pleonaste
Magnetite
Ulvöspinel
Jacobsite
Chromite
Iotsite
Corundum
Hematite
Abundance, mass %
7,60E-10
1,10E-04
5,70E-08
3,90E-08
6,00E-06
2,90E-02
2,00E-07
5,10E-06
1,90E-05
5,90E-08
3,60E-06
3,00E-10
4,40E-09
9,20E-08
3,50E-08
2,80E-09
4,00E-10
7,40E-08
7,60E-06
6,30E-02
1,20E-03
7,60E-06
8,40E-07
3,00E-06
5,00E-10
8,80E-06
1,20E-05
2,80E-08
8,50E-07
1,90E-01
4,50E-09
6,60E-04
2,20E-03
2,60E-05
1,30E-04
2,40E-08
2,40E-03
1,10E-05
6,50E-01
6,60E-02
3,00E-04
1,90E-04
1,40E-06
3,80E-03
7,90E-02
Continued on next page . . .
Grigor’ev’s mineralogical composition of the crust
Table 3.3: Average mineralogical composition of the upper continental crust
according to Grigor’ev [127]. Results are given in mass percentage. – continued from previous page.
Mineral
Abundance, mass %
Ilmenite
1,90E-01
Perovskite
2,80E-05
Loparite
1,00E-06
Pyrochlore
1,00E-06
Microlite
7,60E-09
Quarz
2,40E+01
Tridymite
6,60E-05
Cristobalite
1,30E-03
Opal
1,30E+00
Pyrolusite
5,40E-04
Rutile
1,10E-02
Cassiterite
2,50E-06
Hollandite
6,40E-04
Ilmenorutile
2,50E-05
Cryptomelane
2,50E-04
Psilomelane
3,10E-04
Todorokite
8,60E-05
Vernadite
2,60E-05
Anatase
1,80E-03
Brookite
1,70E-05
Columbite
6,60E-06
Ferrotantalite
2,60E-07
Delorenzite/ Tanteuxenite
6,60E-09
Polycrase
4,00E-11
Euxenite
6,60E-06
Blomstrandite/ Betafite
9,00E-07
Fergusonite
2,40E-06
Baddeleyite
3,10E-07
Thorianite
3,40E-08
Uraninite
6,60E-06
Hydroxides
Hydragillite/ Gibbsite
4,30E-02
Diaspore
5,50E-02
Brucite
2,50E-04
Goethite
8,50E-02
Manganite
1,50E-04
Boehmite
1,80E-02
Carbonates
Magnesite
1,50E-02
Smithsonite
3,70E-08
Siderite
1,20E-01
Mg-Siderite
5,90E-03
Rhodochrosite
1,20E-03
Calcite
3,98E+00
Dolomite
7,00E-01
Ankerite
3,10E-02
Aragonite
3,80E-02
Strontianite
2,00E-07
Continued on next page . . .
49
50
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Table 3.3: Average mineralogical composition of the upper continental crust
according to Grigor’ev [127]. Results are given in mass percentage. – continued from previous page.
Mineral
Abundance, mass %
Cerussite
6,30E-07
Azurite
2,50E-06
Malachite
2,00E-06
Dawsonite
1,80E-04
Bastnasite
3,20E-04
Bismutite
1,10E-07
Sulphates
Anhydrite
4,50E-02
Celestine
1,70E-04
Anglesite
3,30E-07
Barite
7,30E-04
Alunite
7,60E-09
Jarosite
4,00E-04
Kieserite
6,70E-04
Gypsum
2,40E-02
Wolframates
Wolframite
7,80E-07
Powellite
4,00E-08
Scheelite
6,50E-06
Wulfenite
4,00E-09
Phosphates
Xenotime
3,70E-05
Monazite
1,30E-03
Rhabdophane
3,30E-07
Amblygonite
4,90E-08
Apatite
1,30E-01
Francolite
8,30E-03
Britholite
2,10E-06
Vivianite
1,30E-07
Weinschenkite/ Churchite
3,70E-08
Metatorbenite
7,40E-09
Nesosilicates (single tetrahedrons)
Phenakite
4,00E-06
Forsterite
1,10E-02
Olivine
3,70E-02
Fayalite
3,90E-03
Tephroite
1,40E-03
Almandine
8,50E-01
Spessartine
2,60E-03
Grossular
2,50E-03
Andradite
1,20E-03
Zircon
1,00E-02
Naegite
3,30E-08
Tsirtolite
1,90E-06
Thorite
5,70E-05
Uranium-Thorite
8,60E-08
Sillimanite
3,10E-01
Continued on next page . . .
Grigor’ev’s mineralogical composition of the crust
Table 3.3: Average mineralogical composition of the upper continental crust
according to Grigor’ev [127]. Results are given in mass percentage. – continued from previous page.
Mineral
Abundance, mass %
Andalusite
6,30E-02
Distene/ Kyanite
2,20E-02
Topaz
4,60E-04
Staurolite
5,10E-02
Sapphirine
2,20E-03
Kornerupine
6,00E-04
Chondrodite
2,20E-05
Humite
1,00E-03
Clinohumite
1,50E-03
Braunite
2,70E-03
Gadolinite
4,00E-06
Titanite
1,80E-01
Leucoxene
1,50E-02
Murmanite
1,70E-05
Dumortierit
7,60E-09
Thortveitite
7,60E-09
Yttrialite
1,60E-05
Wohlerite
1,30E-11
Lovenite/ Lavenite
2,50E-07
Rinkolite/ Mosandrite
5,30E-09
Lamprophyllite
5,00E-06
Bertrandite
4,00E-06
Lawsonite
2,40E-01
Clinozoisite
4,10E-02
Epidote
1,17E+00
Zoisite
3,10E-02
Orthite/ Allanite
4,80E-03
Chevkinite
4,20E-07
Pumpellyite
1,50E-02
Vesubianite/ Idocrase
2,70E-02
Prehnite
1,70E-01
Cyclosilicates
Eudialyte
1,10E-05
Neptunite
2,50E-06
Axinite -Fe
1,10E-05
Beryl
1,60E-04
Nordite
5,50E-08
Cordierite
8,80E-03
Tourmaline
4,30E-03
Chrysocolla
2,70E-09
Inosilicates (single and double chains)
Pigeonite
6,90E-02
Diopside
4,80E-01
Hedenbergite
8,20E-03
Ferrosilite
5,00E-02
Spodumene
9,60E-07
Jadeite
2,90E-03
Aegirine
9,00E-02
Continued on next page . . .
51
52
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Table 3.3: Average mineralogical composition of the upper continental crust
according to Grigor’ev [127]. Results are given in mass percentage. – continued from previous page.
Mineral
Abundance, mass %
Omphacite
2,50E-04
Augite
1,21E+00
Enstatite
4,40E-02
Bronzite
6,50E-02
Hypersthene
4,30E-01
Cummingtonite
4,60E-01
Tremolite
5,50E-02
Actinolite
3,90E-01
Riebeckite
1,70E-01
Arfvedsonite
3,10E-03
Glaucophane
1,50E-03
Crossite
5,10E-02
Hastingsite
3,10E-01
Hornblende
3,16E+00
Anthophyllite
3,30E-03
Gedrite
5,10E-03
Aenigmatite
1,10E-04
Wollastonite
5,70E-04
Rhodonite
3,30E-04
Miserite
1,80E-07
Ramsayite/ Lorenzenite
5,00E-06
Phyllosilicates (sheets)
Talc
4,60E-02
Pyrophyllite
1,00E-03
Paragonite
5,60E-01
Muscovite
1,99E+00
Glaukonite
1,30E-01
Phengite
3,90E-02
Phlogopite
1,30E-02
Biotite
7,49E+00
Lepidomelane/ Annite
7,60E-02
Hydromuscovite/ Illite
2,51E+00
Hydrobiotite
4,80E-01
Stilpnomelane
2,80E-02
Montmorillonite
4,30E-01
Beidellite
1,60E-01
Nontronite
5,70E-01
Vermiculite
5,40E-02
Pennine
2,70E-01
Clinochlore
6,90E-01
Ripidolite/ Cinochlore
1,89E+00
Sepiolite
5,50E-01
Thuringite/ Chamosite
1,20E-01
Clementite
4,00E-03
Chloritoid
3,30E-04
Kaolinite
2,60E-01
Serpentine/ Clinochrysotile
7,20E-02
Garnierite/ Falcondoite
1,30E-05
Continued on next page . . .
Grigor’ev’s mineralogical composition of the crust
53
Table 3.3: Average mineralogical composition of the upper continental crust
according to Grigor’ev [127]. Results are given in mass percentage. – continued from previous page.
Mineral
Hisingerite
Palygorskite
Tectosilicates (framework)
Nepheline
Analcime
Anorthite
Bytownite
Labradorite
Andesine
Oligoclase
Albite
Orthoclase
Sanidine
Cancrinite
Sodalite
Hydrosodalite
Nosean
Helvine/ Helvite
Scapolite
Natrolite
Thomsonite
Palagonite
Basic Crystal
Acid Crystal
C org
Sum
Abundance, mass %
1,80E-04
1,80E-04
6,20E-03
6,60E-03
3,30E-02
3,00E-01
3,02E+00
6,56E+00
1,43E+01
4,00E+00
9,81E+00
6,10E-02
2,20E-05
6,40E-05
2,50E-05
2,50E-04
4,00E-06
1,80E-02
8,80E-02
6,00E-02
1,70E-02
3,10E-01
3,10E-02
1,10E-01
99,51
End of the table
According to Grigor’ev’s composition, the molecular weight of the earth’s upper crust
is 142,1 g/mole3 . This value is important, because it will be required for the calculation of the chemical exergy of the elements, discussed in chapter 5.
Grigor’ev’s mineralogical composition, although comprehensive, does not satisfy the
mass balance of the earth. In the next section, a methodology for obtaining the average composition of the earth’s crust is developed, assuring that all species comprising
the analysis are mathematically, chemically and geologically consistent.
3
The calculation of the average molecular weight of the crust is carried out through the weighted
sum of the molecular weights of each mineral considered. The chemical composition and molecular
weights of the substances listed in table 3.3 are given in table 3.5.
54
THE
3.4
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
A new model of the mineralogical composition of the
earth’s crust
3.4.1
The mass balance
As explained in section 2.2, the earth can be assumed to be a closed system, with
a fixed number of substances contained in it. Hence, it will always be true that the
total mass of the earth is constant.
As an example, let us consider a very simplified earth containing ξi species (CO2 ,
H2 O, O2 , N2 , C aSO4 · 2H2 O and C aCO3 ), composed by ε j chemical elements
(C, H, O, N , S, C a), where ξi and ε j are expressed in moles of the substance per
gram of earth (mole/g). Then, the system of equations defined in Eq. 3.1 has to be
satisfied [369]:
Σr j,i · ξi = ε j
(3.1)
being R the stoichiometric coefficient matrix of the species of dimensions [ j × i], as
in the next table.
i→
R[ j × i] =
1
CO2
1
0
4
0
0
0
2
H2 O
0
2
1
0
0
0
3
O2
0
0
2
0
0
0
4
N2
0
0
0
2
0
0
5
C aSO4 · 2H2 O
0
4
6
0
1
1
6
C aCO3
1
0
1
1
0
0
C
H
O
N
S
Ca
j
↓
1
2
3
4
5
6
The resolution of the system of equations for vector ξ gives the general expression
of ξi = ε j · r −1
j,i . In our particular case, this is:
(i=1)
(i=2)
(i=3)
(i=4)
(i=5)
(i=6)
CO2
H2 O
O2
N2
C aSO4 · 2H2 O
C aCO3
ξ1 = C + S − C a
ξ2 = H/2 − 2S
ξ3 = −C + O/2 − H/4 − 3S/2 − C a/2
ξ4 = N /2
ξ5 = S
ξ6 = C a − S
As it happens to the entire earth, the substances contained in each sphere of our
planet can be considered to be constant. Therefore, the same methodology is applied
for the components of the atmosphere, hydrosphere and continental crust.
A new model of the mineralogical composition of the earth’s crust
3.4.2
55
The mass balance applied to the continental crust
If the continental crust is assumed to be a closed system, the elements contained in
the minerals of the crust, must be equal to the chemical composition of the crust. If
we assume to be correct the chemical composition defined by Rudnick et al. [292]
given in table 2.13, the application of Eq. 3.1 to Grigor’ev’s analysis, should give as
result Rudnick’s values.
However, the output of the mass balance between species and elements for Grigorev’s analysis does not correspond to the chemical composition of the upper earth’s
crust determined by Rudnick et al. [292], i.e. ε̂ j 6= ε j (see table 3.4)4 . Additionally,
not all the elements compiled in the chemical composition are taken into account in
the minerals of Grigor’ev’s analysis (Grigor’ev accounts for 56 elements, as opposed
to the 78 included in Rudnick et al. study). The reason for which many elements
are missing in Grigor’ev’s analysis is because many of them are minor elements not
appearing with enough concentration in the crust in order to form by themselves
mineral phases. They usually replace major elements in crystal structures. The ability of certain different elements to exist in place of each other in certain points of a
space lattice is called Diadochy.
Table 3.4: Comparison of Rudnick and Gao’s [292] chemical composition of
the upper earth’s crust and the one generated by Grigor’ev [127] according
to Eq. 3.1.
Element
O
Si
Al
Fe
Na
Ca
K
Mg
Ti
C
Mn
P
Ba
S
F
Cl
Sr
Zr
4
Rudnick and Gao [292] From Grigorev [127]
ε̂ j · M W j , g/g
ε j · M W j , g/g
4,72E-01
4,76E-01
3,09E-01
2,86E-01
8,15E-02
7,02E-02
3,92E-02
3,58E-02
2,73E-02
1,99E-02
2,57E-02
3,86E-02
2,32E-02
2,43E-02
1,50E-02
2,25E-02
3,84E-03
1,50E-03
1,99E-03
8,22E-03
7,74E-04
6,02E-05
6,55E-04
2,53E-04
6,28E-04
5,84E-06
6,20E-04
6,13E-04
5,57E-04
1,09E-03
3,70E-04
1,19E-03
3,20E-04
8,13E-07
1,93E-04
4,98E-05
Continued on next page . . .
Difference
(ε̂ j -ε j )/ε̂ j , %
-0,76
7,18
13,86
8,59
27,08
-50,54
-4,68
-50,18
60,95
-313,26
92,22
61,43
99,07
1,19
-95,46
-222,54
99,75
74,18
In table 3.4, the values are expressed in g of substance per g of crust, since this is the usual
way found in the literature of expressing the chemical composition of the crust. This means that ε j is
multiplied by the molecular weight of the substance M W j .
56
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Table 3.4: Comparison of Rudnick and Gao’s [292] chemical composition of
the upper earth’s crust and the one generated by Grigor’ev [127] according
to Eq. 3.1. – continued from previous page.
Element
V
Cr
Rb
N
Zn
Ce
Ni
La
Cu
Nd
Li
Y
Ga
Co
B
Pb
Sc
Nb
Th
Pr
Hf
Cs
As
Sm
Gd
Dy
U
Er
Be
Sn
Yb
W
Br
Ge
I
Mo
Eu
Ta
Tl
Ho
Tb
Sb
Lu
Tm
Bi
Se
Cd
Rudnick and Gao [292] From Grigorev [127]
ε̂ j · M W j , g/g
ε j · M W j , g/g
9,70E-05
9,20E-05
8,83E-07
8,40E-05
8,30E-05
6,70E-05
3,11E-07
6,30E-05
8,18E-06
4,70E-05
4,07E-07
3,10E-05
3,91E-06
2,80E-05
4,64E-07
2,70E-05
1,57E-06
2,40E-05
5,66E-10
2,10E-05
9,98E-07
1,75E-05
1,73E-05
2,98E-09
1,70E-05
1,45E-06
1,70E-05
4,84E-07
1,40E-05
1,83E-11
1,20E-05
1,19E-07
1,05E-05
1,09E-06
7,10E-06
5,30E-06
4,90E-06
4,80E-06
9,24E-08
4,70E-06
1,22E-09
4,00E-06
3,90E-06
2,70E-06
5,97E-08
2,30E-06
2,10E-06
9,64E-08
2,10E-06
2,01E-08
1,96E-06
2,39E-07
1,90E-06
4,63E-08
1,60E-06
1,40E-06
1,40E-06
1,10E-06
7,22E-08
1,00E-06
9,00E-07
1,60E-08
9,00E-07
8,30E-07
7,00E-07
4,00E-07
5,04E-10
3,10E-07
3,00E-07
1,60E-07
2,23E-09
9,00E-08
9,00E-08
Continued on next page . . .
Difference
(ε̂ j -ε j )/ε̂ j , %
99,04
100,00
99,54
87,01
99,13
87,39
98,34
94,20
100,00
95,25
99,98
91,48
97,15
99,01
89,66
98,07
99,97
97,79
95,41
99,04
87,82
97,56
93,44
98,22
99,87
98,60
A new model of the mineralogical composition of the earth’s crust
57
Table 3.4: Comparison of Rudnick and Gao’s [292] chemical composition of
the upper earth’s crust and the one generated by Grigor’ev [127] according
to Eq. 3.1. – continued from previous page.
Element
In
Ag
Hg
Te
Au
Pd
Pt
Ru
Re
Rh
Os
Ir
SUM
Rudnick and Gao [292] From Grigorev [127]
ε̂ j · M W j , g/g
ε j · M W j , g/g
5,60E-08
5,30E-08
3,04E-09
5,00E-08
5,16E-10
5,00E-09
5,79E-11
1,50E-09
1,80E-10
5,20E-10
5,14E-13
5,00E-10
4,89E-12
3,40E-10
1,98E-10
6,00E-11
3,10E-11
2,20E-11
1,00
0,98
End of the table
Difference
(ε̂ j -ε j )/ε̂ j , %
94,26
98,97
98,84
88,00
99,90
99,02
Assuming that the average chemical composition of Rudnick and Gao [292] is correct, if the difference between the mass content of a specific element given by Rudnick (ε̂ j ) and that included in the mineralogical composition of the crust given by
Grigor’ev (ε j ) is positive, i.e. ε̂ j − ε j > 0, then it can be due to two factors:
1. The quantity of one or more minerals containing the specific element under
consideration is greater than the assumption done by Grigor’ev.
2. There are other minerals not included in Grigorev’s analysis or ores containing
not insignificant quantities of the element under consideration.
On the other hand, if the difference is negative (ε̂ j −ε j < 0), it is clear that Grigor’ev
overestimated the quantity of the mineral or minerals containing the element under
consideration.
Basing on Grigorev’s
analysis, a new mineralogical composition of the upper conPm
tinental crust i=1 ξ̂i will be calculated. The model will be optimized so that it
complies with the following requirements:
1. The mass balance between species and elements must be satisfied.
P
j
r j,i ·
ξ̂i = ε̂ j , being ε̂ j the chemical composition of the upper crust determined by
Rudnick et al. [292].
2. The mass content of every mineral in the crust must be always greater than
zero, i.e. ξ̂i > 0.
58
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
3. Generally, the relative proportions of the minerals in Grigorev’s model will be
kept if constraints 1 and 2 are satisfied.
4. If an important5 mineral of a certain element is not considered in Grigor’ev
analysis, it will be included in our model, making reasonable assumptions on
its abundance based on the literature.
Next, the minerals of each element found in the upper continental crust will be
briefly described, stressing out their main uses, terrestrial abundance and distribution. The specific optimization method for each element will be also outlined6 . The
information about uses and main minerals and ores of the different elements has
been extracted mainly from geochemical books: Wedepohl [402], [403] and Greenwood and Earnshaw [122]; mineral books and databases: Hey [140], Duda [77],
the Geochemical Earth Reference Model [329], [114], Jolyon [172] and Barthelmy
[21]; and from commodity databases: US Geological Survey (USGS) [363] and
British Geological Survey (BGS) [28].
The descriptive procedure for obtaining the mineralogical composition shown next,
is represented in a mathematical way in section 3.5.
3.4.3
Aluminium
Aluminium is a light, malleable, ductile, easily machined and strong metal used
for many different applications. It has excellent corrosion resistance and durability.
Some of the many uses for aluminium are in transportation (automobiles, aircraft,
trucks railcars, marine vessels, etc.), packaging (cans, foil, etc.), transmission lines,
machinery, mirrors, cooking utensils, water treatment, etc.
Aluminium is the most abundant metal in the earth’s crust. It is a major constituent
of many common igneous minerals, including feldspars and micas. Aluminim is a
very reactive metal and it requires a lot of energy to extract it from its ore bauxite,
which is composed mainly of the minerals gibbsite Al(OH)3 , diaspore AlO(OH) and
boehmite AlO(OH). Therefore, recovery of this metal from scrap has become so
important and about 50% of its production comes from recycled Al.
In our model of continental crust, we have considered 84 Al-containing minerals,
one more than in Grigorev’s analysis. Their abundance in the earth’s crust will be
determined applying the constraints explained above.
5
A mineral is considered to be important here, especially when it constitutes an ore of a certain
element.
6
Note that when we refer to percentages in the optimization process, they are always based on a
volume basis.
A new model of the mineralogical composition of the earth’s crust
3.4.4
59
Antimony
Antimony is a semimetallic chemical element increasingly being used in the semiconductor industry. As an alloy, it increases lead’s durability and mechanical strength.
Antimony compounds are used to make flame-proofing materials, paints, glass and
pottery.
Stibnite S b2 S3 is the most important ore of antimony and it occurs in large quantities in China, South Africa, Mexico, Bolivia and Chile. Other sulfide ores include
ullmanite N iS bS, livingstonite H gS b4 S8, boulangerite P b5 S b4 S11 or jamesonite
FeP b4 S b6 S14 and small amounts of oxide minerals formed by weathering are also
known. Considerable amounts of S b are also obtained as a byproduct in lead and
copper refining, especially from galena.
Grigorev’s S b minerals are stibnite, boulangerite, tetrahedrite and the silver minerals samsonite, freibergite, stephanite and pyrargirite. Since stibnite is by far the
most important mineral of S b, the quantity of that mineral on earth should presumably account for a very important part of S b in the crust. The quantity of antimony
in stibnite considered by Grigor’ev is about four orders of magnitude smaller than
Rudnick’s S b estimations in the upper crust. Therefore, we will ignore Grigorev’s
estimations about stibnite and assume that most S b comes at equal rates from stibnite and in solution with galena P bS. Grigorev’s estimation for boulangerite and
tetrahedrite will be assumed to be correct. The quantity of the S b-Ag-containing
minerals are fixed by their silver content.
3.4.5
Arsenic
Arsenic is a semi-metallic poisonous element. Its compounds are used as insecticides
of fruit trees, as wood preservatives, in making special types of glass and lately, in
the semiconductor gallium arsenade, which has the ability to convert electric current
to laser light. Many other arsenic compounds used in the past have fallen out of use
due to their toxicity and reactivity.
Arsenic minerals are widely distributed throughout the world and small amounts of
the free element have also been found. Most arsenic is found in conjunction with
sulphur such as realgar As4 S4 and orpiment As2 S3 , and the oxidized form arsenolite
As2 O3 . But non is mined as such because it is produced as a byproduct of refining
ores of other metals such as iron, copper, cobalt or nickel. The main economic
source of As is arsenopyrite FeAsS. But it can be also recovered from loellingite
FeAs2 , safflorite C oAs, nickeline N iAs, cobaltite C oAsS, gersdoffite N iAsS, enargite
Cu3 AsS4 , etc.
The arsenic-containing minerals considered by Grigor’ev are: the sulphides arsenopyrite, orpimnet, realgar, freibergite and the sulfosalt group “fahlerz group”,
which will be assumed to be represented by the mineral tennantite Cu11 Fe2+ As4 S13 .
60
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Less abundant N i, Fe and C o arsenides recorded in his model are nickeline, gersdorffite, loellingite and cobaltite. In addition to the minerals considered by Grigor’ev,
the cobalt arsenide smaltite7 is also included. Due to the importance of its oxidized
form, arsenolite will be also taken into account, assuming that it is responsible for the
same quantity of As on earth as realgar. The relative proportions given by Grigor’ev
will be kept in our model. The abundance of cobaltite, smaltite and freibergite are
fixed by their C o and Ag contents.
3.4.6
Barium
Barium is an alkaline-earth metal that is chemically similar to calcium. Barium and
its compounds have many industrial uses. For instance barite BaSO4 is extremely important for the petroleum industry, which accounts for more than 85% of the barite
consumption in the world. It is used as a weighting agent in petroleum well-drilling
mud. Barium-nickel alloys are used for spark-plug electrodes and in vacuum tubes
as drying and oxygen-removing agents. Barium nitrate and chlorate give fireworks
a green color. Other compounds of barium are used to make bricks, tiles, glass or
rubber.
Barium is rather abundant in the earth’s crust. The chief mined ore is barite. A
subsidiary mineral is barium carbonate witherite, BaCO3 .
Barium-containing minerals analyzed by Grigor’ev are barite, psilomenane, hollandite and lamprophyllite. We take into account in our model all four minerals given
by Grigorev’s analysis and include additionally witherite, for being an important Ba
ore. It will be assumed that witherite accounts for about 10% of the Ba content of
all barite in the crust. The relative concentrations of the minerals in Grigor’ev model
will be kept. Nevertheless, the quantity of lamprophyllite is fixed as a result of the
strontium mass balance8 .
3.4.7
Beryllium
Beryllium is a light alkaline-earth metal and has one of the highest melting points of
any light metal. It is used as an alloying agent in the production of beryllium-copper.
Thanks to their electrical and thermal conductivity, high strength and hardness, good
stability over a wide temperature range, Be − Cu alloys are used in many applications. Some of them are in the defense and aerospace industries, in the field of X-ray
detection diagnostic and in the manufacture of computer equipment.
Beryllium is relatively unabundant in the earth’s crust. It occurs as bertrandite
Be4 Si2 O7 (OH)2 , beryl Be3 Al2 Si6 O18 , chrysoberyl BeAl2 O4 and phenakite Be2 SiO4 .
Precious forms of beryl are aquamarine and emerald.
7
8
See section 3.4.18 for details about the assumptions done for cobaltite and smaltite.
See section 3.4.63 for details about the optimization procedure for lamprohyllite
A new model of the mineralogical composition of the earth’s crust
61
Grigor’ev accounted in his model for beryl, phenakite, bertrandite and helvite
M n4 Be3 (SiO4)3 . In addition to those minerals, chrysoberyl is included in our model,
assuming that it has the same Be content as beryl. The relative proportions of the
minerals given by Grigor’ev will be kept and the concentrations of each mineral will
be obtained assuring that constraint 1 is satisfied.
3.4.8
Bismuth
Bismuth is a metal used for metallurgical additives for castings and galvanizing, in
the manufacture of low melting solders and fusible alloys as well as low toxicity bird
shot and fishing sinkers. Additionally, it finds some application in the pharmaceutical
industry.
The most important ores of bismuth are bismuthinite Bi2 S3 , bismutite (BiO)2 CO3
and bismite B2 O3 . It occurs naturally also as the metal itself and is found as crystals
in the sulphide ores of nickel, cobalt, silver and tin. The main commercial source of
the element is as a byproduct from lead-zinc and copper plants.
Grigor’ev takes into account four minerals containing bismuth: bismutite, bismuthinite, native bismuth and tetradymite. Because of its importance, we include in our
model bismite as well, assuming that it accounts for the same quantity of Bi as
bismuthinite. Nevertheless, the relative proportions of bismutite, bismuthinite and
native bismuth as well as the quantity of tetradymite9 given by Grigor’ev will be kept
in our model.
3.4.9
Boron
Boron is a non metallic element and the only non-metal of the group 13 of the periodic table. The most economically important compound of boron is borax, used for
insulating fiberglass and sodium perborate bleach. Boric acid is also an important
compound used in textile products. Other uses of boron are in synthetic herbicides
and fertilizers, porcelain enamels, detergents, soaps, cleaners and cosmetics, catalysts or corrosion control.
More than 200 minerals contain boron, but only a few of commercial importance.
Boron is usually found combined in tincal N a2 B4 O7 ·10H2 O (natural borax), sassolite
H3 BO3 (natural boric acid), colemanite C a2 B6 O11 · 5H2 O, kernite N a2 B4 O7 · 4H2 O,
ulexite N aC aB5 O9 · 8H2 O and boracite M g3 B7 O13 C l. Only four minerals make up
almost 90% of the borates used by industry worldwide: borax, kernite, colemanite
and ulexite.
Non of these minerals are included in Grigorev’s model. However, boron element
is present in his analysis as the borate silicates tourmaline, kornerupine, axinite
9
See section 3.4.66 for the derivation of the assumption for tetradymite.
62
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
and dumortierite. Nevertheless, we cannot forget the four most important boroncontaining minerals for industrial applications. Therefore, we keep in our model the
concentrations of the borates given by Grigor’ev and assume that the rest quantity
of boron in the crust is in form of borax, kernite, colemanite and ulexite having all
of them the same boron content.
3.4.10
Bromine
Bromine is a brownish-red liquid at ambient temperature and is used in industry to
make organobromo compounds. These compounds find application as insecticides,
fire extinguishers, water purification, flame retardants, pharmaceuticals, fumigants,
dyes or photography.
Like chlorine, the largest amount of bromine is the oceans. Salt lakes and brine wells
are also rich sources of bromine, and these are usually richer in bromine than the
oceans. It occurs in nature as bromide salts in very diffuse amounts in crustal rock,
which are accumulated in sea water after leaching processes.
Grigor’ev does not include any bromine-containing minerals. We will account for
them in our model as “dispersed Br”.
3.4.11
Cadmium
Cadmium is used as a protective coating for iron and steel, as a pigment, and as a
stabilizer for plastics. But its main application (about three-fourths of its production)
is used in Ni-Cd batteries.
No cadmium ore is mined for the metal, because more than enough is produced as a
byproduct of the smelting of zinc from its ore, sphalerite (Z nS), in which greenockite
C dS is a significant impurity making up as much as 3%.
No cadmium ores are recorded by Grigor’ev. We will assume in our model that
greenockite is the only ore containing C d.
3.4.12
Calcium
Calcium is a silvery white metal belonging to the alkaline earth group. The metal is
used as a reducing agent in the extraction of other metals, as a deoxidizer, desulfurizer and decarbonizer in the manufacture of many steels, as separating material for
gaseous mixtures, as an alloying agent used in the production of aluminium, beryllium, copper, lead and magnesium alloys as well as in the making of cements and
mortars to be used in construction. Calcium compounds are used in a wide variety
of applications such as insecticides, manufacture of plastics, as an additive in food
and vitamin pills, as a disinfectant, as a fertilizer, in paints lights and X-rays, etc.
A new model of the mineralogical composition of the earth’s crust
63
Calcium is the fifth most abundant element in the earth’s crust and the third most
abundant metal after Al and Fe. Vast sedimentary deposits of C aCO3 , which represent the fossilized remains of earlier marine life, occur over large parts of the earth’s
surface. Other important minerals are gypsum C aSO4 · 2H2 O, anhydrite C aSO4 ,
fluorite C aF2 and apatite C a5 (PO4 )3 F .
Sixty-six minerals contain C a in our model. The mass balance between elements
and species for carbon in Grigorev’s model gives a quantity of C a greater than the
accepted value for C a in the earth’s crust in Rudnick et al. [292]. Probably, Grigor’ev
overestimated the quantity of some calcium-containing minerals in the upper crust.
3.4.13
Carbon
Carbon is a non metallic element that forms more chemical compounds than any
other element except hydrogen. The major economic use of carbon not in living
material or organisms is in the form of hydrocarbons. The free element has a lot
of uses, including jewelry (as diamonds), as a black fume pigment in automobile’s
rims, printer’s ink, for pencil tips, dry cell and arch electrodes and as a lubricant.
Carbon compounds have also plenty of uses. Carbon dioxide is used in drinks, in fire
extinguishers and in solid state, as a cooler. Carbon monoxide is used as a reduction
agent in many metallurgic processes. Other carbon compounds are used as solvents,
cooling systems, for welding and cutting materials.
Carbon occurs both as the free element (graphite, diamond) and in combined form
mainly as the carbonates of C a, M g, and other electropositive elements. It also
occurs as CO2 , a minor but very important constituent of the atmosphere, because
of its important contribution to the greenhouse effect. Additionally, carbon is widely
distributed in the organic form of coal and petroleum.
The carbon-containing substances included in Grigorev’s model are graphite, organic
carbon, moissonite and the carbonates calcite, dolomite, siderite, aragonite, magnesite, dawsonite, cancrinite, strontianite, bismutite, bastnasite, smithsonite cerussite,
azurite, malachite, ankerite and rhodocrossite. Additionally, we have included in
our model the barium carbonate witherite, for being an important Ba ore. It must
be pointed out, that the mass balance between elements and species for carbon in
Grigorev’s model gives a quantity of C greater than the accepted value for C in the
earth’s crust in Rudnick et al. [292]. Probably, Grigor’ev overestimated the quantity
of some carbon-containing minerals in the upper crust.
3.4.14
Cerium
Cerium is a silvery metallic element, belonging to the lanthanide group. The metal
is used as a core for the carbon electrodes of arc lamps, in incandescent mantles for
gas lighting, in aluminium and iron alloys, in stainless steel as a hardening agent
and to make permanent magnets.
64
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Although cerium is part of the REE, it is not rare at all. In fact it is the most common rare earth and is more abundant than lead. It is commonly found in orthite,
monazite, bastnaesite, rhabdophane or in zircon.
Further Ce-containing minerals considered in Grigor’ev model are miserite, loparite,
rhabdophane, chevkinite, tanteuxenite, euxenite rinkolite, polycrase, gadolinite,
nordite britholite and fergusonite. In addition to those minerals, the cerium included
in the crystal structure of other minerals such as zircon, gadolinite or bastnasite is
accounted in our model as “diadochic C e”. The quantity of it will be calculated
as the difference between the cerium content in the crust and the cerium content
of the minerals included in the model. Except for miserite, which will be assumed
to have the same concentration on earth than the one given by Grigor’ev, all other
C e-containing minerals are fixed by their REE, U, Z r, Ba and Ta contents.
3.4.15
Cesium
Cesium is the most electropositive and least abundant of the five naturally occurring alkali metals. The most important use for cesium has been in research and
development, primarily in chemical and electrical applications.
Cesium occurs as the hydrated aluminosilicate pollucite, Cs0.6 N a0.2 Rb0.04 Al0.9 Si2.1 O6 ·
(H2 O), but the world’s only commercial source is at Bernic Lake, Manitoba. Cesium
is mainly obtained as a byproduct of the Li industry.
Cesium is not included in any of the minerals given by Grigor’ev. We will account for
it in our model in the form of pollucite, assuming that it is the only main Cs ore.
3.4.16
Chlorine
Chlorine is the most common element of the halogens. In pure form, it is a greenyellow diatomic gas. Chlorine is very reactive and combines with nearly all other
elements. It is used in water purification, disinfectants, in bleach and in mustard
gas. Chlorine is also used extensively in the manufacture of many products directly
or indirectly, i.e. in paper product production, antiseptics, food, insecticides, paints,
petroleum products, plastics, medicines, etc.
In nature it the upper continental crust it is found in the form of halite N aC l, but
also in carnallite KC l and sylvite K M g C l3 · 6(H2 O). Nevertheless, it is so abundant
in the ocean, that it is extracted mainly from the sea and underground brine deposits
for commercial uses.
In addition to the minerals mentioned above, Grigor’ev considers also the following
C l-containing minerals: apatite, scapolite, sodalite, bischofite, eudialyte and chlorargirite. The mass balance between elements and species for chlorine in Grigorev’s
model gives a quantity of C l grater than the accepted value for C l in the earth’s crust
in Rudnick et al. [292]. Probably, Grigor’ev overestimated the quantity of halite. All
A new model of the mineralogical composition of the earth’s crust
65
of them are included in our model keeping their relative proportions. The quantity
of eudyalite and chlorargirite are however fixed by the Z r and Ag mass balance.
3.4.17
Chromium
Chromium is a hard transition metal. In iron, steel and nonferrous alloys it imparts
hardness and resistance to corrosion and oxidation. The use of chromium to produce
stainless steel and nonferrous alloys are two of its more important applications. It
finds also applications as dyes and paints to produce synthetic rubies, as a catalyst
in dyeing and in the tanning of leather or to make molds for the firing bricks.
The only ore of chromium of any commercial importance is chromite FeC r2 O4 . Other
less plentiful sources are crocoite P bC rO4 and chrome ochre C r2 O3 , while the gemstones emerald and ruby owe their colors to traces of chromium. Like in Grigorev’s
analysis, we include chromite as the main chromium-containing mineral, since the
other C r ores can be assumed to be insignificant when compared to chromite. Dietzeite C a2 (IO3 )2 (C rO4 ) is the other C r-containing mineral considered but its concentration is fixed by its iodine content.
It must be pointed out that there are big discrepancies between chromite concentration in Grigorev’s model and in our model. Nevertheless, we leave chromite as the
sole chromium mineral for the reasons explained before.
3.4.18
Cobalt
Cobalt is a hard ferromagnetic, silver-white transition metal. The largest use of
cobalt is in superalloys, which are used to make parts of gas turbine aircraft engines. Cobalt is also used in corrosion resistant alloys, high-speed steels, cemented
carbides, in magnets and magnetic recording media, as catalysts for the petroleum
and chemical industries and as drying agent for paints and inks.
More than 200 ores are known to contain cobalt but only a few are of commercial value. The more important are arsenides and sulfides such as smaltite, C oAs2 ,
cobaltite C oAsS and linnaeite C o3 S4 .These are invariably associated with nickel and
also with copper and lead, so that C o is usually obtained as a byproduct or coproduct
of these metals.
The only cobalt-containing mineral considered in Grigorev’s analysis is cobaltite. In
our model, we take also into account the other two minerals mentioned before, assuming that all three contribute with the same amount of C o to the cobalt content
of the upper earth’s crust. Although important, only those three minerals are not
responsible for the whole C o on earth10 . Therefore, we will assume that the concentration of cobaltite given by Grigor’ev is correct and will account for the rest C o in
the earth crust as “dispersed C o”.
10
If cobaltite, smaltite and linnaeite would be assumed to be the only cobalt-carriers in the earth’s
crust, the mass balance for arsenic would not be satisfied.
66
3.4.19
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Copper
Copper is one of the coinage metals with gold and silver because of its former usage. It is an excellent conductor of heat and electricity and therefore is a key metal
in the electric and electronic industry. Electrical uses of copper, including power
transmission and generation, building wiring, telecommunication and electrical and
electronic products account for about three quarters of total copper use. Further
applications of copper are in construction, such as roofing and plumbing, industrial
machinery such as heat exchangers. It is also commonly used in the manufacture of
brass and other alloys with zinc, tin, nickel, lead aluminium, etc.
Copper is found mainly as the sulfide, oxide or carbonate, its major ores being copper pyrite (chalcopyrite) CuFeS2 , which is estimated to account for about 50% of
all Cu deposits; copper glance (chalcocite), Cu2 S; cuprite, Cu2 O, and malachite
Cu2 CO3 (OH)2 . Bornite Cu5 FeS4 , azurite Cu3 (CO3 )2 (OH)2 , and covellite CuS are
other minor ores of Cu. Native copper is found as well occasionally.
In addition to the minerals explained above, other Cu-containing minerals in Grigorev’s model are chrysocolla, metatorbenite, tennantite, freibergite and tetrahedrite.
No additional minerals will be taken into account in our model, since the most important are already gathered in Grigorev’s analysis. The quantities for metatorbenite
and tennantite have been fixed by their uranium and arsenium content, while for
freibergite and tetrahedrite by their silver content. For the rest substances, the relative proportions given by Grigor’ev will be maintained, assuring the compliance of
constraint 1.
3.4.20
Dysprosium
See section 3.4.52.
3.4.21
Erbium
See section 3.4.52.
3.4.22
Europium
See section 3.4.52.
3.4.23
Fluorine
Fluorine is the lightest and most reactive element of the halogens. Atomic and molecular fluorine are used for plasma etching in semiconductor manufacturing, flat panel
A new model of the mineralogical composition of the earth’s crust
67
display production and microelectromechanical systems fabrication. Sodium hexafluoroaluminate (cryolite), is used in the electrolysis of aluminium. It is indirectly
used for the production of plastics such as teflon and halons such as freon. Fluorides
are added to toothpaste to prevent dental cavities. Other components of fluorine
are used in pharmaceuticals as antibiotics, antidepressants and for the prevention of
infections.
The three most important minerals of fluorine are fluorite C aF2 , cryolite N a3 Al F6
and flourapatite C a5 (PO4 )3 F . Of these, however, only fluorite is extensively the
only commercial deposit. Cryolite is a rare mineral, the only commercial deposit
being in Greenland, and most of it is used in the aluminium industry. But by far the
largest amount of fluorine in the earth’s crust is in the form of of fluorapatite. Minor
occurrences of fluorine are also in the rare elements topaz or bastanesite.
The fluorine-containing minerals taken into account by Grigor’ev are: apatite, fluorite, topaz, bastnaesite, lamprophyllite, amblygonite, britholite, lavenite, rinkolite, wohlerite, microlite, apatite, bastnasite, francolite, pyrochlore, miserite, biotite,
muscovite, hydrobiotite, phlogopite, clinohumite, fluorite, humite and chondrodite.
In addition to those, we include in our model cryolite because of its industrial relevance, assuming that it contributes to the same F content to the earth than topaz.
3.4.24
Gadolinium
See section 3.4.52
3.4.25
Gallium
Gallium is a rare element and found little use until its properties as a semiconductor
were discovered. Analog integrated circuits are the largest application for gallium
with optoelectronic devices (mostly laser diodes and light-emitting diodes) as the
second largest end use.
The highest concentrations (0,1-1%) are found in the rare mineral germanite
(Cu26 Fe4 Ge4 S32 ); concentrations in sphalerite (Z nS), bauxite or coal are a hundredfold less. It was formerly recovered from flue dusts emitted during sulfide roasting or
coal burning (up to 1,5% Ga), but is now obtained as a byproduct of the Al industry.
Grigor’ev does not explicitly include any mineral containing Ga. It will be included
in our model as “dispersed Ga”.
3.4.26
Germanium
Germanium is a semiconductor and was used for transistors, diodes and rectifiers
until it was replaced by pure silicon in the early 1970’s. Meanwhile germanium
68
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
is used in fiber optics communication networks, infrared night vision systems and
polymerization catalysts.
Germanium minerals are extremely rare, but the element is widely distributed in
trace amounts among the silicates of rocks, igneous as well as sedimentary and
metamorphic ones. Recovery is achieved normally from the flue dusts of smelters
processing Z n ores. Germanite is the only commercial mineral of Germanium
(Cu26 Fe4 Ge4 S32 ), but it is not considered in Grigorev’s analysis.
In order to account for Ge in our model, it will be included as “dispersed Ge”, which
will represent all germanium included in the different ores where it is found.
3.4.27
Gold
Gold is mostly used in the manufacture of jewelry. However, because of its superior
electrical conductivity and resistance to corrosion, it has also emerged in the late
20th century as an essential industrial metal in computers, communication equipment, spacecraft, etc.
Gold is widely but sparsely distributed both native and in tellurides. Grigo’ev considers native gold as the only carrier of Au in the upper crust.
Since tellurides are also important ores for gold, we will include in our model the
tellurides calaverite AuTe2 and sylvanite Au0.75 Ag0.25 Te2 , assuming that 15% in volume of Au in the upper continental crust comes from them at equal rates and the
rest from native gold.
3.4.28
Hafnium
Hafnium is a transition metal similar to zirconium. It resists corrosion and has a high
melting point. Its major end uses are in nuclear control rods because of its excellent
properties in absorbing neutrons, nickel-based superalloys, nozzles for plasma arc
metal cutting and high-temperature ceramics.
Hafnium ores are rare, but two are known: hafnon and alvite. However, H f is
mostly found in quantities of about 2% of the Z r content in zirconium ores such as
zircon Z rSiO4 and baddeleyite Z rO2 .
H f will be considered in our model only as a diadochic element in zirconium ores,
since Grigor’ev did not provide any information about the hafnium ores explained
before.
3.4.29
Holmium
See section 3.4.52.
A new model of the mineralogical composition of the earth’s crust
3.4.30
69
Indium
Indium is a rare metal used in low-melting fusible alloys, solders and electronics.
Large-scale application for indium was also as a protective coating for bearings and
other metal surfaces in high-performance aircraft engines. Nowadays, its main application is in the manufacture of indium-tin-oxide thin films for Liquid Crystal Displays
(LCD).
Indium tends to associate with the similarly sized Z n in its sulfide minerals, hence
it is mainly produced from residues generated during zinc and lead sulfide ore processing, mainly from sphalerite Z nS. The indium metal indite Fe2+ I n2 S4 has been
found in Siberia but it is very rare.
We will include I n in our model as being in the crystal lattice of sphalerite (“diadochic I n in sphalerite”).
3.4.31
Iodine
Iodine is the most electropositive halogen and is used in medical treatment as tincture and iodoform. It is employed in the preparation of certain drugs, and in the
manufacture of printing inks and dyes. Silver iodine is used in photography and
iodine is added to table salt and is used as a supplement to animal feed. It is also an
ingredient of water purification tablets.
Iodine is considerably less abundant than the lighter halogens. It can be found
naturally in air, water and soil. But the most important sources are the oceans. It
occurs but rarely as iodide minerals. Commercial deposits are usually iodates, e.g.
lautarite C a(IO3 )2 and dietzeite C a2 (IO3 )2 (C rO4 ).
None of these minerals or other iodine-containing minerals were considered by
Grigor’ev. We will assume that the minerals above account for all I in the upper
continental crust in the same proportion.
3.4.32
Iridium
See section 3.4.46.
3.4.33
Iron
Iron is the most used of all the metals, including 95% of all the metal tonnage
produced worldwide. Thanks to the combination of low cost and high strength it is
indispensable. Its applications go from food containers to cars, from screwdrivers to
washing machines, from cargo ships to paper staples. Steel is the best known alloy
of iron and some of the forms that iron takes include pig iron, cast iron, carbon steel,
wrought iron, alloy steels and iron oxides.
70
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Iron is the most abundant element in the universe and on earth. widely distributed
as oxides and carbonates, of which the chief ones are haematite Fe2 O3, magnetite
Fe3 O4 and siderite FeCO3 .
Eighty-two Fe-containing minerals are included in our model.
3.4.34
Lanthanum
Lanthanum is a rare earth element (REE) and gives its name to the lanthanide group.
It can be found in domestic equipment such as in color televisions, fluorescent and
energy-saving lamps and optical glasses. If added in small amounts, it improves the
malleability and resistance of steel. Lanthanum is also used as the core material in
carbon arc electrodes and in zeolite catalysts for the petroleum industry.
Lanthanum is one of the most abundant REE. Its major ores are minerals monazite
and bastnasite, in percentages of up to 25 to 38 percent of the total lanthanide
content.
In addition to monazite and bastnasite, Grigor’ev considers in his analysis the Lacontaining minerals britholite, chevkinite, loparite, rhabdophane and nordite. All
these minerals with their respective proportions are included in our model assuring
the satisfaction of constraint number 1. The abundance of nordite is however fixed
by its Ba content.
3.4.35
Lead
Lead is a very corrosion-resistant, malleable and toxic bluish-white metal that has
been known for at least 5000 years. Ancient romans used lead as drains from the
baths. Nowadays lead is a major constituent of the lead-acid battery, it is used as a
coloring element in ceramic glazes, as projectiles, as electrodes for electrolysis and
in the glass of computer and television screens, shielding the viewer from radiation.
Lead alloys include pewter and solder. The toxicity of lead leaded in the twentieth
century to strong environmental regulations that significantly reduced or eliminated
its use in nonbattery products including gasoline, paints, solders and water systems.
Lead is the most abundant of the heavy elements. It can be found native, but its most
important ore is the heavy black mineral galena P bS. Other important minerals are
anglesite P bSO4 and cerussite P bCO3 . It is usually found in zinc, silver and copper
ores and it is extracted together with these minerals. However, the largest current
source of lead is recycling, primarily of automobile batteries.
In addition to galena, anglesite and cerussite, Grigor’ev takes into account minerals
boulangerite P b5 S b4 S11 , native lead P b and wulfenite P bM oO4 . All these are included in our model keeping the relative proportions of galena, cerussite, anglesite
A new model of the mineralogical composition of the earth’s crust
71
and native lead given by Grigor’ev. The concentrations of wulfenite and boulangerite
are fixed by their M o and S b contents respectively11 .
3.4.36
Lithium
Lithium is an alkali metal of very high chemical reactivity. As a consequence, it takes
part in a huge number of reactions. The carbonate can be used in the pottery industry and in medicine as antidepressant. Low-density alloys are used for armor plate
and for aerospace components. The bromine and chloride both form concentrated
brine, which have the property of absorbing humidity in a wide temperature range;
these brines are also used for air conditioning systems. Lithium finds additional use
in nuclear breeder reactors as a coolant and as a source for tritium. Other important
uses for lithium are as lubricants, in porcelain glaze, as an additive to extend the life
and performance of alkaline storage batteries and in welding.
Lithium is a moderately abundant element. Its most important mineral commercially is spodumene LiAsSi2 O6 , followed by lepidolite K Li2 AlSi4 O1 0F (OH). It is
commonly found in nature as silicates and phosphates. However it is usually recovered from brines.
Grigor’ev has included in his model spodumene, the silicate neptunite and the phosphate amblygonite. Additionally, we will include lepidolite in our model because of
its industrial importance, assuming that the Li quantity coming from it in the crust is
10% of that of spodumene. Our model keeps the relative proportions of the different
lithium minerals considered by Grigor’ev, but assuring the satisfaction of the mass
balance.
3.4.37
Lutetium
See section 3.4.52.
3.4.38
Magnesium
Magnesium is a light, chemically reactive metal, belonging to the alkaline earth
group. It is known as the lighter structural metal in the industry, due to its low
weight and its capability of forming mechanically resistant alloys. Magnesium alloys
are used in beverage cans, as structural components of automobiles and machinery.
Magnesium compounds, primarily magnesium oxide, are used mainly as refractory
material in furnace linings for producing iron and steel, nonferrous metals, glass
and cement. Magnesium oxide and other compounds are also used in agricultural,
chemical and construction industries.
11
See sections 3.4.41 and 3.4.4 for details about the assumptions done for wulfenite and boulangerite, respectively.
72
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Magnesium is among the eight most abundant elements. It usually occurs in crustal
rocks mainly as the insoluble carbonates and sulfates and less accessibly as silicates.
Important magnesium-containing minerals are dolomite C aM g(CO3 )2 , magnesite
M g CO3 , carnallite K2 M g C l4 · 6H2 O, olivine (M g, Fe)2 SiO4 , talc M g3 Si4 O10 (OH)2
or spinel M gAl2 O4 .
Fifty-five magnesium-containing minerals have been considered in our model.
3.4.39
Manganese
Manganese is a grey-white chemically active metal. It resembles iron and is essential
in the iron and steel production by virtue of its sulfur-fixing, deoxidizing and alloying properties. It is also widely used in aluminium alloys. Further applications for
manganese and its compounds are as additive in gasoline to boost octane rating, as
a reagent in organic chemistry, as a colorizing and decolorizing agent for glass, as a
paint, as a disinfectant and in batteries.
Manganese is found over 300 different and widely distributed minerals of which
about twelve are commercially important. It occurs in primary deposits as the silicate metal. Of more commercial importance are the secondary deposits of oxides
and carbonates such as pyrolusite M nO2 and to a lesser extent as rhodochrosite
M nCO3 . Vast quantities of manganese exist in manganese nodules (manganese, iron
and other metal-containing agglomerates) of the ocean floor. But no economically
viable methods of harvesting manganese nodules have been found yet.
The M n-containing minerals included in Grigorev’s model are: rhodochrosite, pyrolusite, chloritoid, ankerite, todorokite, vernadite, spessartine, wolframite, jacobsite,
cryptomelane, manganite, tephroite, braunite, rhodonite, samsonite, psilomelane,
hollandite, neptunite, helvite, eudyalite, lavenite and nordite. The quantity of the
nine latter minerals is fixed by their W , Ag, Ba, Li, Be, Z r and S r contents. The
rest minerals are assumed to have in our model the relative proportions given by
Grigor’ev.
3.4.40
Mercury
Mercury is the only common metal which is liquid at ordinary temperatures. Because
of its high density it is used in barometers and manometers. It is extensively used in
thermometers thanks to its high rate of thermal expansion that is fairly constant over
a wide temperature range. Amalgams of silver, gold and tin (alloys of mercury) are
used in dentistry. Most mercury is used for the manufacture of industrial chemicals
and form electrical and electronic applications.
Cinnabar, H gS is the only important ore and source of mercury, being the deposits
at Almaden in Spain the most famous and extensive ones.
Grigor’ev records two minerals of mercury: cinnabar and metacinnabar. Both minerals will be kept in our model, maintaining their respective proportions.
A new model of the mineralogical composition of the earth’s crust
3.4.41
73
Molybdenum
Molybdenum is a refractory metal able to withstand extreme temperatures without
significantly expanding or softening. Those properties make M o useful in applications that involve intense heat, including aircraft parts, electrical contacts and filaments. Molybdenum is used in alloys, mainly in steel, cast iron and superalloys. It is
also used in electrodes, lubricants, pigments and catalysts.
The most important ore of molybdenum is the sulphide molybdenite M oS2 , which
can be found in tungsten and copper ores, being molybdenite a byproduct of W and
Cu production. Less important ores are wulfenite P bM oO4 and powellite C aM oO4 .
All three minerals are considered in Grigorev’s model and will be considered in our
model, keeping Grigorev’s relative proportions.
3.4.42
Neodymium
Neodymium is a member of the lanthanide series and hence has few properties
which distinguish it from the other members of the series. Like lanthanum and other
REE, it can be found in houses equipment such as televisions, lamps and glasses.
Neodymium forms an important alloy (neodybium), found to produce very high
magnetic field strengths with small masses.
Neodymium is the second most abundant of the REE after cerium. It is found in
minerals that include other lanthanide elements such as monazite and bastnasite.
N d is included in the empirical formula of the minerals fergusonite, britholite and
monazite given by Grigor’ev. In addition to those minerals, we include the rest of
N d in the upper continental crust as “diadochic N d” in our model, which should
account mainly for N d found as an ion solution in bastnaesite.
3.4.43
Nickel
Nickel is a transition metal that belongs to the iron group. It is mainly used in
the preparation of alloys, giving to them good strength, ductility and resistance to
corrosion properties. About 65% of the nickel consumed in the western world is used
to make stainless steel. The remaining is divided between alloy steels, rechargeable
batteries, catalysts, coinage, foundry products and plating.
The bulk of the nickel mined comes from two types of ore deposits. The first are
laterites where the principal ore minerals are nickeliferous limonite12 and garnierite
N i3 M gSi6 O15 (OH)2 · 6(H2 O). The second are magmatic sulfide deposits where the
2+
principal ore mineral is pentlandite Fe4.5
N i4.5 S8 . Arsenide ores such as nickeline
12
Nickeliferous limonite is the term used to describe poorly crystalline nickel-bearing ferric oxides
of which the main constituent is goethite Fe3+ O · OH.
74
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
N iAs or gersdorffite N iAsS can be also found. N i appears as well in the crystalline
structure of many other minerals including pyrrhotite, chalcopyrite, pyrite, ilmenite
or magnetite.
The laterites group is represented in Grigorev’s model by garnierite, while the second by pentlandite. Other arsenides and sulphides of N i considered are violarite
Fe2+ N i23+ S4 , vaesite N iS2 , cooperite P t 0.6 P d0.3 N i0.1 S, nickeline and gersdorffite.
Additionally to those, we will include in our model “diadochic N i”, which should
account for the whole N i appearing in small quantities in the crystal lattice of the
minerals mentioned before. It will be assumed that diadochic N i contributes to the
same N i amount than pentlandite. The relative proportions given by Grigor’ev will
be maintained, although cooperite13 , nickeline and gersdorffite14 are fixed by their
P d, and As contents.
3.4.44
Niobium
Niobium, sometimes called columbium, is a rare soft transition metal, used mainly
for the production of high-temperature resistant alloys and special stainless steels.
Small amounts of niobium impart greater strength to other metals. The applications
of those alloys are in nuclear reactors, jets, missiles, cutting tools, pipelines, super
magnets, surgical implants and welding rods. Niobium is additionally used as a
superconductor when lowered to cryogenic temperatures.
Niobium has been mainly mined as columbite FeN b2 O6 . Two other important N bcontaining minerals are euxenite (Y, C a, C e, U, T h)(N b, Ta, T i)2 O6 and pyrochlore
N a1.5 C a0.5 N b2 O6 (OH)0.75 F0.25 the latter is now its most important ore. Due to its
similarities to tantalum, minerals that contain niobium also contain tantalum, so
that columbite gets the name of tantalite when tantalum preponderates.
Besides of columbite, pyrochlore and tantalite, other N b-containing minerals included in Grigorev’s model are ilmenorutile, murmanite, loparite, tanteuxenite,
lavenite rinkolite, wohlerite, polycrase, blomstrandite and fergusonite. No additional minerals will be included in our model. It will be assured the satisfaction of
the mass balance, keeping the relative proportions of the different minerals given by
Grigor’ev.
3.4.45
Nitrogen
Nitrogen is a common inert gas and an essential element in most of the substances
that make up living organisms, including proteins. Its main application is as a component in the manufacture of ammonia, subsequently used as fertilizer and to produce nitric acid. It can be used also as a refrigerant for freezing and transporting
food products.
13
14
See section 3.4.47 for details about the optimization method used for cooperite.
see section 3.4.5 for details about the optimization method used for nickeline and gersdorffite.
A new model of the mineralogical composition of the earth’s crust
75
Despite its ready availability in the atmosphere, constituting 78% of the air by volume, nitrogen is relatively unabundant in the continental crust. The only major
minerals are K N O3 (nitre, salpetre) and N aN O3 (sodanitre, nitratine). Both occur
widespread.
Grigor’ev did not consider any of both minerals. We will assume that they are the
only carriers of Nitrogen in the upper continental crust at equal relative proportions.
3.4.46
Osmium and Iridium
Osmium is a silvery metal of the platinum group metals. It has the distinction of
being the most dense of all the naturally occurring elements. Its main application is
as an alloy with other platinum metals.
Iridium is a transition metal of the platinum family and it is notable for being the
most corrosion resistant element known. Demand for iridium comes mainly from the
electronic, automotive and chemical industry, where it is used to coat the electrodes
in the chlor-alkali process and in catalysts.
Osmium and iridum are very rare metals. Osmium is usually found in combination
with iridium and ruthenium. The most important ores are iridosmine and osmiridium. The same main ores are found for iridium.
Grigor’ev did not account for any of both substances. We will include both minerals
in the proportions so that they comply with the mass balance for elements osmium
and iridium.
3.4.47
Palladium
Palladium is a silver-white metal belonging to the platinum group metals. Because
of its corrosion resistance, a major use of palladium is in alloys used in low voltage
electrical contacts. It is also used as a catalyst, replacing platinum for reducing
car exhaust emissions and it is alloyed with certain metals in jewelry. Palladium is
nowadays being more and more used in electrical appliances in the form of multilayer ceramic capacitors.
Palladium is usually associated with the other platinum metals and occur either native or as sulfides or arsenides in N i, Cu and Fe sulfide ores. However, much of it
is extracted as a by-product from copper-nickel ores such as chalcopyrite, pyrrhotite
and pentlandite or chromite.
The only mineral considered by Grigor’ev in his model is cooperite P t 0.6 P d0.3 N i0.1 S.
The rest of palladium found in nature will be considered in our model to be included
dispersed in the copper-nickel ores mentioned before.
76
3.4.48
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Phosphorous
Phosphorous is a nonmetal of the nitrogen group. Concentrated acids are used in fertilizers for agriculture and farm production. Phosphates are used for special glasses,
sodium lamps, in steel production, in military applications and in other applications
such as pyrotechnics, pesticides, toothpaste or detergent.
Phosphorous is an abundant mineral on earth. All its known terrestrial minerals are
orthophosphates. Some 200 crystalline phosphate minerals have been described,
but by far the major amount of P occurs in the family of apatites, and these are the
only ones of industrial importance. Common members are fluorapatite C a5 (PO4 )3 F ,
chlorapatite C a5 (PO4 )3 C l and hydroxylapatite C a5 (PO4 )3 OH. In addition, there
are vast deposits of amorphous phosphate rock phosphorite, which approximates in
composition to fluoroapatite.
The phosphates taken into account in Grigorev’s model are: apatite, xenotime,
rhabdophane, amblygonite, metatorbernite, monazite, weinschenkite, francolite, vivianite. All three kinds of apatite are included in the general formula C a5 (PO4 )3
(OH)0.3333 F0.3333 C l0.3333 . No other minerals are taken into account in our model.
Except for weinschenkite and vivianite, which are assumed to have the same concentration than the given by Grigor’ev, the quantity of all those minerals are fixed
by the mass balance of C l,Y b, Li, U, Y , F and La. Additionally, the amorphous
phosphate rock phosphorite is included in our model due to its abundance. It will
be assumed to have the composition C a3 (PO4 )2 .
3.4.49
Platinum
Platinum gives the name to the platinum-group metals (PGM), which comprise platinum, palladium, rhodium, ruthenium, iridium and osmium. It has outstanding
catalytic properties and its resistance is well suited for making fine jewelry. Platinum and its alloys are used also in surgical tools, laboratory utensils, electrical
resistance wires, etc. The glass industry uses platinum for optical fibers and liquid
crystal display glass.
Platinum occurs generally associated with the other platinum metals and occur
also in native form or as sulfides or arsenides in N i, Cu and Fe sulfide ores.
Three-quarters of the world’s platinum comes from South Africa, where it occurs
as cooperite. It is also extracted as a by-product from copper-nickel ores such as
chalcopyrite, pyrrhotite and pentlandite or with chromite.
Platinum is included in three minerals of Grigorev’s model: cooperite, ferroplatinum
and native platinum. We will maintain the concentrations given by Grigor’ev for the
latter two and assume that the rest platinum in the upper crust is equally distributed
in cooperite and in the copper-nickel ores mentioned before.
A new model of the mineralogical composition of the earth’s crust
3.4.50
77
Potassium
Potassium is a soft, silvery-white metal, member of the alkali group. Most potassium goes into fertilizers. Potassium carbonate is used in the glass manufacture for
making televisions. Potassium hydroxide is used to make liquid soaps and detergents. Further application of other potassium compounds are in the pharmaceutical
industry, photography and to make iodize salts.
Potassium is a very abundant element on earth. Most of it occurs as minerals such as
feldspars and clays. Potassium is leached from these by weathering, which explains
why there is quite a lot of this element in the sea. Important ores for potassium are
sylvite KC l, carnallite K M g C l3 · 6(H2 O) and alunite KAl3 (SO4 )2 (OH)6 .
Potassium-containing minerals in Grigor’ev analysis are: orthoclase, hydromuscovite, glauconite, lepidomelane, nepheline, sanidine, stilpnomelane, jarosite, alunite, neptunite, sylvite, carnallite, miserite, biotite, muscovite, hydrobiotite, phlogopite, todoroskite and cryptomelane. In addition to those, niter, carnotite and lepidomelane are other potasium-containing minerals included in our model, because
of its nitrogen, uranium and lithium contents15 . The quantity of the latter 9 minerals mentioned above of Grigorev’s analysis is fixed by their Li, U, C l, F and M n
content. For the remaining minerals, their respective proportions given by Grigor’ev
are kept in our model. It must be pointed out, that the mass balance between elements and species for potassium in Grigorev’s model gives a quantity of K greater
than the accepted value for K in the earth’s crust in Rudnick et al. [292]. Probably,
Grigor’ev overestimated the quantity of some potassium-containing minerals in the
earth’s crust.
3.4.51
Praseodymium
See section 3.4.52
3.4.52
Rare Earth Elements: Praseodymium, Samarium, Europium,
Gadolinium, Terbium, Dysprosium, Holmium, Erbium, Thulium
and Lutetium
All fourteen members of the lanthanide series have very similar geochemical properties. Many applications of rare earth elements (REE) are characterized by high
specificity and high unit value. For example, europium is used for color cathoderay tubes and liquid crystal displays used in monitors and televisions. A major use
of praseodymium is in misch metal, used in making cigarette lighters. Samarium
is used as a catalyst in certain organic reactions. Erbium finds extensive use in
15
See sections 3.4.73, 3.4.36 and 3.4.39 for more details about the optimization process for uranium, lithium and manganese.
78
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
laser repeaters for fiber-optic telecommunication cables. Permanent magnet technology has been revolutionized by alloys containing gadolinium, dysprosium and other
REE. Terbium, gadolinium or europium are used in new energy-efficient fluorescent
lamps. Lutetium can be used as a catalyst in petroleum cracking in refineries and in
alkylation, hydrogenation and polymerization applications. Holmium and thulium
are being used in lasers for medical applications.
There are over 100 minerals known to contain lanthanides but the only two of commercial importance are monazite, a mixed La, T h, Ln phosphate and bastnaesite, a
La, Ln fluorocarbonate. Tamarium, terbium and erbium are also found in xenotime
and euxenite, while gadolinite is also an important source for Holmium, Terbium
and Thulium.
Grigor’ev accounted for the mineral fergusonite in his model, which contains the
REE Sm and traces of P r. We will keep in our model the same concentration of fergusonite on earth given by Grigor’ev. Not being specifically in the empirical formula
of the minerals explained above, the REE Gd, T b, D y, H o, E r, T l and Lu will be
considered in our model as diadochical elements.
3.4.53
Rhenium
Rhenium was the last naturally-occurring element to be discovered. Its main
applications in industry are found in the manufacture of tungsten-rhenium and
molybdenum-rhenium alloys. Other important uses of rhenium are in platinumrhenium catalysts, used primarily in producing lead-free, high octane gasoline and
in high-temperature superalloys used for jet engine components.
The concentration of rhenium in the earth’s crust is extremely low and it is also very
diffuse. Being chemically akin to molybdenum it is in molybdenites that its highest
concentrations (0,2%) are found.
No Re mineral is included in Grigorev’s model. We will account for it as “diodochic
Re”.
3.4.54
Rhodium
Rhodium is part of the platinum group metals. Most part of its production goes into
catalytic converters for cars and in some industrial processes. It is used in alloys with
platinum and iridium, giving improved high-temperature strength and oxidation resistance to furnace windings, high-temperature thermocouple and resistance wires,
spark plugs, bearings, electrical contacts, etc.
Rhodium occurs as rare deposits of the native element and in rare minerals associated with other metals of the platinum group. But usually, the commercially available metal comes as a by product of the refining of copper and nickel ores which
contain up to 0,1% rhodium.
A new model of the mineralogical composition of the earth’s crust
79
There is no rhodium mineral in Grigorev’s analysis. We will account for it as being
included in the ores mentioned before.
3.4.55
Rubidium
Rubidium is a silvery white, very active metal as are the other alkali metals. Rubidium and its salts have few commercial uses. The metal is used in the manufacture
of photocells and in the removal of residual gases from vacuum tubes. Rubidium
salts are used in glasses and ceramics and in fireworks to give them a purple color.
Although very abundant, no purely Rb-containing mineral is known and much of
the commercially available material is obtained as a byproduct of lepidolite processing for Li. It occurs also naturally in the minerals pollucite, lepodite, carnallite,
zinnwaldite and leucite.
All Rb on earth will be accounted in our model as “diadochic Rb”.
3.4.56
Ruthenium
Ruthenium is one of the six platinum metals. It finds use in the electronic and chemical industry, with smaller amounts being used in alloying for increasing hardness
and corrosion resistance. It is used in electrical contact alloys and filaments, in jewelry, in pen nibs and in instrument pivots. Like the other metals of its group, it is a
versatile catalyst used in different industrial processes.
Ruthenium is one of the rarest metals on earth. It is found native and sometimes
associated with platinum, osmium and iridium. Like the other platinum metals, it is
commercially extracted from nickel and copper deposits.
In addition to osmiridium, we will assume that most part of ruthenium is found in
nickel and copper ores.
3.4.57
Samarium
See section 3.4.52
3.4.58
Scandium
The transition metal scandium is mainly used in aluminium alloys for sporting equipment, metallurgical research, high-intensity metal halide lamps, analytical standards, electronics, oil well tracers and lacers.
Scandium occurs in many ores in trace amounts, but has not been found in sufficient
quantities to be considered as a reserve. Therefore, scandium has been produced
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THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
exclusively as a byproduct during processing of various ores or recovered from previously processed tailings or residues. Considerable amounts of scandium oxide
Sc2 O3 can be obtained as a byproduct of the extraction of uranium. Its only rich
mineral is the rare thortveitite Sc2 Si2 O7 .
We will keep the value given by Grigor’ev for thortveitite, and assume that the rest of
it is widely dispersed in other minerals. The latter is called in our model “Diodochic
Sc”.
3.4.59
Selenium
Selenium is a non metallic chemical element, resembling sulfur and tellurium in its
chemical activity and physical properties. It has good photovoltaic and photoconductive properties, and it is used extensively in electronics, such as photocells, light
meters and solar cells. The second largest use of selenium is the glass industry, used
to remove color from glass. It finds also extensive application as animal feeds and
food supplements. Additionally, it can be used in photocopying, in the toning of
photographs, in metal alloys and to improve the abrasion resistance in vulcanized
rubbers.
Selenium is among the rarer elements on the earth’s crust. It is occasionally found
native, but it is usually associated with sulfur, copper, zinc and lead, such as in the
form of clausthalite CuSe or klockmanite P bSe. Selenium is recovered commercially
as a byproduct of the electrolytic refining of copper where it accumulates in anode
residues.
There is no selenium mineral considered in Grigorev’s analysis. We will account for
the element as being part of copper ores, since they are its main sources.
3.4.60
Silicon
Silicon is a brittle steel-gray metalloid. It has many industrial uses. It is the main
component of glass, cement, ceramics, most semiconductor devices and silicones.
Silicon is also an important constituent of some steels and a major ingredient in
bricks. It is also used as an alloy to provide resistance to aluminium, magnesium,
copper and other metals. Metallurgic silicon is used as a raw material in the manufacture of organosilic and silicon resins, seals and oils. Silicon chips are used in
integrated circuits and photovoltaic cells are made of thin cut slices of simple silicon
crystals.
Silicon is the most abundant element in the earth’s crust after oxygen. It never
occurs free, it occurs invariably combined with oxygen and with trivial exceptions
is always 4-coordinate in nature. Sand is used as a source of the silicon produced
commercially. A few silicate minerals are mined, e.g. talc and mica. Other mined
silicates are feldspars, nepheline, olivine, vermiculite, perlite, kaolinite, etc.
Our model accounts for 136 Si-containing minerals.
A new model of the mineralogical composition of the earth’s crust
3.4.61
81
Silver
In addition to coinage, silver is used mainly in tableware, mirrors, electronic products, photography, jewelry and as a catalyst in oxidation reactions.
Silver is widely distributed in sulfide ores of which argentite (Ag2 S) is the most
important. Silver can be also found native in nature and associated to chlorine as
Ag C l. Only about 10% of all silver mined is won from deposits primarily exploited
for the metal; 90% or more represents a by-product of copper, lead, zinc and gold
mining.
Grigor’ev accounted in his model for the most important compounds of silver found
in nature, namely native silver, argentite, acantithe, stephanite, pyrargirite, chlorargirite, freibergite and samsonite. In addition to those, we take into account the
gold-silver telluride sylvanite.
3.4.62
Sodium
Sodium is a white-silvery metal, belonging to the alkali group, and hence of high
reactivity. Sodium in its metallic form is very important in making esters and in the
manufacture of organic compounds. Sodium is also a component of sodium chloride
N aC l, a very important compound found everywhere in the living environment.
Other applications of sodium are: in alloys to improve their structure, in soap, to purify molten metals, in sodium vapor lamps, as a heat transfer fluid and as a desiccant
for drying solvents.
Sodium is a very abundant element in the earth’s crust. After chloride, sodium is
also the second most abundant element dissolved in seawater. Sodium occurs as
rock-salt (N aC l) and as the carbonate, nitrate, sulfate, borate, etc.
Fifty N a-containing minerals have been considered in our model.
3.4.63
Strontium
Strontium is a bright silvery alkaline-earth metal. Principal uses of strontium compounds are in pyrotechnics, vacuum tubes to remove the last traces of air and as the
carbonate in special glass for television screens and visual display units. Further uses
of strontium and its compounds are in toothpastes, in aerosol paint or for medical
treatment of osteoporosis.
Strontium commonly occurs in nature, averaging about 0,034% of all igneous rocks.
It is found chiefly in the form of the sulfate mineral celestine S r CO4 and the carbonate strontianite S r CO3 .
Grigorev’s strontium-containing minerals are celestine, strontianite and the rare minerals lamprophyllite and nordite. Our model will keep the relative proportions of
82
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
celestine and strontianite given by Grigor’ev, but assuring that they satisfy the mass
balance for strontium in the upper crust. The abundance of nordite and lamprophyllite given by Grigor’ev is assumed to be correct. Although the S r content in Grigorev’s analysis does not fulfill constraint number 4 on page 57, no more strontiumcontaining minerals will be included in our model because celestine and strontianite
are their most important ores should account for almost all Sn in the earth’s upper
crust.
3.4.64
Sulfur
Sulfur is a yellow solid nonmetal. Its main compound is sulfuric acid H2 SO4 , one
of the most important substance in industrial and fertilizer complexes. In fact, the
yearly consumption of sulfuric acid is an index of industrial development of a country. Sulfur is also used in batteries, detergents, fungicides, manufacture of fertilizers,
gun power, matches and fireworks. It finds also application in the manufacture of
corrosion-resistant concrete.
Sulfur is widely distributed in nature. The three most important commercial sources
are: 1) elemental sulfur in the caprock salt domes in the USA and Mexico and the
sedimentary evaporite deposits in eastern Poland and western Asia; 2) as H2 S in sour
natural gas and as organosulfur compounds in crude oil. They represent currently
the main commercial source of the element. 3) from pyrites FeS2 and other metalsulfide minerals. Common naturally occurring sulfur compounds include the sulfide
minerals cinnabar H gS, galena P bS, sphalerite Z nS, stibnite S b2 S3 and the sulfates
gypsum C aSO4 · 2H2 O, alunite KAl3 (SO4 )2 (OH)6 and barite BaSO4 .
Our model accounts for 47 S-containing minerals.
3.4.65
Tantalum
Tantalum is a hard transition metal highly corrosion-resistant and a good conductor
of heat and electricity. The major use for tantalum is in the manufacture of electronic components, mainly capacitors. Additionally, it is used in high-temperature
applications such as aircraft engines and for handling corrosive chemicals.
Tantalum occurs invariably together with niobium. The chief mineral for Ta is
known as tantalite FeTa2 O6 . Deposits are widespread but rarely very concentrated.
Microlite and euxenite are other minor ores for Ta.
Grigor’ev accounts for Ta in minerals ferrotantalite, microlite, tanteuxenite and euxenite, as well as in polycrase and blomstrandite. The relative proportions of the
four minerals given by Grigor’ev are kept in our model, while the quantities of the
last two are fixed by the uranium mass balance16 .
16
dite.
See section 3.4.73 for details about the optimization procedure used for polycrase and blomstran-
A new model of the mineralogical composition of the earth’s crust
3.4.66
83
Tellurium
Tellurium is a semiconductor. Its chemistry is similar to that of sulfur and has properties both of metals and non metals. It is used as an additive to steel and it is often
alloyed to aluminium, copper, lead or tin. It can be used for cast iron, ceramics,
blasting caps, solar panels or rubber.
Tellurium is a relatively rare element. Commercial tellurium comes mainly as a
byproduct of copper processing. Samples of tellurium can be found uncombined
in nature, but they are extremely rare. There are some tellurium minerals such as
calaverite, sylvanite or tellurite, but none is mined as a source of the element.
The only mineral containing tellurium considered by Grigore’ev is tetradymite. We
will keep the concentration given by Grigor’ev for tetradymite and include tellurite
(assuming that it has the same Te concentration as sylvanite and calaverite) and “dispersed Te”, which should account for the rest of tellurium in the crust found mostly
in copper ores. Remember that sylvanite and calaverite were already accounted for
gold-containing minerals.
3.4.67
Terbium
See section 3.4.52
3.4.68
Thallium
Thallium is a soft and malleable heavy metal that is used in a wide variety of applications. Some of them are as a semiconductor material for selenium rectifiers, in
gamma radiation detection equipment, in infrared radiation detection and transmission equipment, in crystalline filters for light diffraction, in medical diagnostic tests
to detect heart diseases, etc.
Although thallium is reasonable abundant in the crust, it exists mostly in association
with potassium minerals such as sylvite and pollucite and is not generally considered
to be commercially recoverable from those forms. Very rare minerals of thallium
occur in nature as sulfide or selenide complexes with antimony, arsenic, copper,
lead and silver such as hutchingsonite P bT lAs5 S9 , but they have no commercial
importance as sources either. Thallium is commercially recovered as a byproduct
from the flue dust and residues generated during the roasting and smelting of Z n
and P b sulfide ores.
No thallium mineral has been recorded by Grigor’ev. We will include T l in our model
as “dispersed T l”, which should account for all T l in the crust in the forms of the
sources mentioned above.
84
3.4.69
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Thorium
Thorium is a silver-grey heavy metallic element of the actinide series. Thorium
demand worldwide is relatively small. Some of its applications are as an alloying
element in magnesium, as a coating for wolfram wire used in electronic equipment,
to control grain size of plutonium used for electric lamps, as a catalyst, in the manufacture of refractory materials for the metallurgical industries, or as a fertile material
for producing nuclear fuel.
Thorium is very abundant in the earth’s crust (three times more abundant than uranium). Thorium occurs naturally in the minerals thorite, uranothorite, thorianite
and is a major component of monazite, where it is usually commercially extracted
as a byproduct. It is present also in significant amounts as diodochic element in the
minerals zircon, titanite, gadolinite and blomstrandite.
Grigor’ev records all the main thorium-containing minerals in his model explained
above, as well as britholite, polycrase, yttrialite and chevkinite. They are all included
in our model, maintaining the relative proportions provided by Grigor’ev.
3.4.70
Thulium
See section 3.4.52.
3.4.71
Tin
Tin is a silvery-white metal that finds extensive use as a protective layer for mild
steel. Alloys of tin are used in many ways, such as solder for joining pipes or electronic circuits, bell and babbit metal, dental amalgams, etc. The principal alloys of
tin are bronzite (tin and copper), soft solder (tin and lead), pewter (75% tin and
25% lead) and britannia metal (tin with small amounts of antimony and copper).
There are few tin-containing minerals, but only one is of commercial significance
and that is cassiterite SnO2 .
Grigor’ev accounts for Sn in cassiterite as well as native tin. We keep the relative
proportions of both minerals given by Grigor’ev in our model but assuring that they
fulfill the mass balance of Sn on earth. No more tin-containing minerals will be
included because cassiterite is its most important ore and should account for almost
all Sn in the earth’s upper crust.
3.4.72
Titanium
Titanium is a light, strong transition metal, well known for corrosion resistance and
for its high strength-to-weight ratio. Most of it is consumed in the form of titanium
A new model of the mineralogical composition of the earth’s crust
85
dioxide T iO2 , a white pigment in paints, paper and plastics. Titanium alloys are
used in aircraft, pipes for power plants, armor plating, naval ships and missiles. In
medicine, titanium is used to make hip and knee replacements, pace-makers, boneplates and screws.
Titanium is an abundant element on earth and is found in minerals rutile T iO2 ,
brookite T iO2 , anatase T iO2 , illmenite Fe2+ T iO3 , leucoxene C aT iSiO5 and titanite C aT iSiO5 . The chief mined ore is ilmenite, but leucoxene and rutile are also
important economic ores for titanium.
Titanium-containing minerals considered by Grigor’ev are: ilmenite, leucoxene, rutile, brookite, titanite, augite, ulvöspinel, anatase, aenigmatite, perovskite, ramsayite, lamprophyllite, neptunite, blomstrandite, polycrase, lavenite, rinkolite, delorenzite, loparite, chevkinite, murmanite, ilmenorutile and euxenite. No additional
minerals are included in our model.
3.4.73
Uranium
Uranium is a silvery metallic radioactive element of the actinide group. It gained
importance with the development of practical uses of nuclear energy. Depleted uranium is used as shielding to protect tanks and also in bullets and missiles. However,
the main use of uranium is to fuel commercial nuclear power plants.
Uranium is widely distributed, being the most important ores uraninite UO2 and
carnotite K2 (UO2 )2 (V O4 )2 · 3H2 O. However, even these are usually dispersed so
that typical ores contain only about 0,1%, and many of the more readily exploited
deposits are nearing exhaustion. Significant concentrations of uranium occur in
some minerals such as monazite sands or lignite.
Grigor’ev considers five uranium-containing minerals: uraninite, betafite, metatorbenite and polycrase. In addition to those minerals, we include also carnotite in
our model, assuming that it has the same U content as uraninite. The relative proportions of all minerals accounted by Grigor’ev are kept and their quantities are
obtained by satisfying constraint 1.
3.4.74
Vanadium
Vanadium is a transition metal and finds extensive use in the manufacture of special steels with exceptional strength and toughness. Steel alloys are used in axles,
crankshafts, gears and other critical components. Mixed with aluminium in titanium
alloys, it is used in jet engines and high speed air-frames.
Vanadium is widely, though sparsely distributed; thus although more than 60 different minerals of vanadium have been characterized, there are few concentrated
deposits and most of it is obtained as a byproduct of iron, uranium, phosphor, copper, lead, zinc or titanium ores. Most important vanadium minerals are patronite
86
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
V S4 , vanadinite P b5 (V O4 )3 C l and carnotite K2 (UO2 )2 (V O4 )2 · (H2 O). Vanadium is
also found in some crude oils, coal, oil shale and tar sands.
No vanadium-containing minerals are registered by Grigor’ev. We take into account
in our model carnotite, for being an uranium important ore. The rest vanadium is
assumed to come from dispersed sources.
3.4.75
Wolfram
Wolfram, also known as Tungsten, is a transition metal, having the highest melting
point of any metal. Hence, it is used in filaments in incandescent light bulbs, in
electric contacts and arc-welding electrodes. It imparts great strength to alloys such
as steel. Tungsten is also used in X-ray tubes and in microchip technology. Its most
important application though is in the manufacture of cement carbide, since its main
component is wolfram carbide (W C).
There are several minerals of wolfram, the most important ones are scheelite and
wolframite.
Both minerals have been considered by Grigor’ev and will be taken into account in
our model, keeping the relative proportions of Grigorev’s analysis. The quantity of
both minerals in our model almost exceeds two orders of magnitude the values given
by Grigorev. However, all references consulted coincide in giving most relevance
only to those two substances. Therefore, no additional minerals are going to be
considered.
3.4.76
Ytterbium
Ytterbium is a rare earth element used in certain steels for improving the grain refinement, strength and other mechanical properties of stainless steel. Some ytterbium
alloys have been used in dentistry. Like other REE, it can be used to dope phosphors,
or for ceramic capacitors and other electronic devices.
Ytterbium is found with other rare earth elements in several rare minerals as gadolinite, monazite and xenotime. It is most often recovered commercially from monazite
sand.
The latter minerals have been considered by Grigor’ev. We will assume that Grigorev’s quantity for xenotime is correct and will account for Y b in monazite as the
difference between the contents in the earth’s crust and in xenotime.
3.4.77
Yttrium
Yttrium is a silver-metallic rare earth metal. The largest use of the element is as its
oxide yttria Y2 O3 , which is used in making red phosphors for color television picture
A new model of the mineralogical composition of the earth’s crust
87
tubes. It is also used in small amounts to increase the strength of aluminium and
magnesium alloys. Additional uses of yttrium are in camera lenses and to make
superconductors.
Yttrium, like lanthanum is invariably associated with lanthanide elements in minerals such as xenotime, monazite, fergusonite or gadolinite.
Yttrium-containing minerals in Grigorev’s model are: fergusonite, thortveitite, polycrase, gadolinite, rinkolite, euxenite, tanteuxenite, ytriallite, orthite and weinschenkite. The concentration of all those minerals on earth, except for weinschenkite
are fixed by their content in other elements in our model. For weinschenkite, we will
assume that it has the concentration given by Grigor’ev. Additionally, “diodochic Y ”
is included in our model in order to account for the Y found in the crystalline structure of other lanthanide minerals.
3.4.78
Zinc
Zinc is a bluish-white transition metal. It is the fourth metal mostly consumed in the
world. The main use of zinc is for the galvanizing of iron sheets or wires. Zinc is
used in making alloys such as brass or bronze. Zinc oxide is used as a white pigment
in plastics, cosmetics, paper, printing inks, etc. and as an activator in the rubber
industry.
The major ores of zinc are sphalerite Z nS and smithsonite Z nCO3 . Less impor2+
3+
tant ores are franklinite Z n0.6 M n2+
0.3 Fe0.1 M n0.5 O4 , hemimorphite Z n4 Si2 O7 (OH)2
2+
and wurtzite Z n0.9 Fe0.1
S.
Grigorev’s Z n-containing minerals are sphalerite, smithsonite, nordite and native
zinc. In our model we will assume that all those four minerals account for the majority of the zinc found in the upper crust and hence we will omit the less important
ores mentioned above. The abundance of nordite is fixed by its S r content.
3.4.79
Zirconium
Zirconium is a silver-gray metal with chemical and physical properties similar to
those of titanium. It is extremely resistant to heat and corrosion. Zircon is its most
used compound and is used in refractories, ceramic opacification and foundry sands.
It is also considered as a semi-precious gemstone used in jewelry. Further uses for
zirconium are in alloys such as zircaloy, which is used in nuclear applications since
it does not absorb neutrons. It is also used in catalytic converters.
Zirconium is not particularly a rare element and occurs in nature mainly as the
silicate mineral zircon Z rSiO4 . Baddeleyite Z rO2 is also an important ore for Z r.
Grigorev’s model includes eight different zirconium-containing minerals: zircon,
naegite (a variety of zircon that contains U, T h, Y and other REE in its lattice),
88
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
sirtolite (a variety of zircon that contains T h and H f in its lattice), eudialyte, baddeleyite, lavenite, mosandrite and wohlerite. An interesting aspect about his analysis is
that eudialyte is a more abundant mineral than baddeleyite, which is more common.
All eight minerals are also included in our analysis. Grigorev’s relative proportions
are kept, but assuring the satisfaction of the constraints described before.
3.5
Mathematical representation
The problem described in a qualitatively way in the last section, can be represented
mathematically according to Eq. 3.2. The objective is to minimize (M in) with a
least squares
Pprocedure the difference between the
P mineralogical composition of
our model ( ξ̂i ) and that of Grigor’ev’s analysis ( ξi ). This optimization must be
constrained by physical and geological restrictions.
The physical restrictions are constraints 1 and 2 defined in section 3.4, namely the
satisfaction of the mass balance and the positiveness requirement for all minerals.
The geological restrictions are based on reasonable assumptions and, as opposed to
the physical ones, may change with new mineral discoveries and with the point of
view of the analyst. Hence, the model that we have developed must not be considered as final and closed. On the contrary, it is the first step for obtaining a comprehensive, physically and geologically coherent mineralogical composition of the
upper earth’s crust. Remember that the chemical composition of the crust has been
improved throughout decades and is still under research.
Vector ε̂ j , containing the elements that compose the minerals in our model are
showed in table A.1 (page 351). Vector ξi , containing the minerals described by
Grigor’ev’s analysis is represented in table A.2 (page 352). Finally, the matrix of
coefficients R[ j × i] is showed in tables A.3 and A.417 (page 360).
The objective function is showed in equation 3.2:
M inkξ̂i − ξi k2
(3.2)
The physical restrictions to be applied are:
• Σr j,i · ξ̂i = ε̂ j
• ξ̂i > 0
The geological restrictions based on reasonable assumptions and described in sections 3.4.3 through 3.4.79 for each substance are the following:
17
For the sake of a more flexible representation of matrix R[ j × i], its transposed is given R0 [i × j].
Mathematical representation
89
• Gold: ξ̂1 = ε̂1 · 0, 85/r1,1
• Calaverite: ξ̂2 = ε̂1 · 0, 075/r1,2
• Sylavanite: ξ̂3 = ε̂1 · 0, 075/r1,3
• Thortveitite: ξ̂6 = ξ6
• Lautarite: ξ̂22 = ε̂28 /(r28,22 + r28,23 )
• Dietzeite: ξ̂23 = ε̂28 /(r28,22 + r28,23 )
• Nitratine: ξ̂25 = ε̂31 /(r31,25 + r31,26 )
• Niter: ξ̂26 = ε̂31 /(r31,25 + r31,26 )
• Xenotime: ξ̂31 = ξ31
• Tetradymite: ξ̂35 = ξ35
• Tellurite: ξ̂36 = (r2,2 · ξ̂2 )/(r2,36 )
• Polixene: ξ̂40 = ξ40
• I-Platinum: ξ̂41 = ξ41
• Cooperite: ξ̂42 = (ε̂46 − r46,40 · ξ̂40 − r46,41 · ξ̂41 )/(2 · r46,42 )
• P t in N i-Cu ores ξ̂43 = (ε̂46 − r46,40 · ξ̂40 − r46,41 · ξ̂41 )/(2 · r46,43 )
• Fergusonite: ξ̂47 = ξ47
• Stibnite: ξ̂50 = (ε̂41 − r41,34 · ξ̂34 − r41,51 · ξ̂51 − r41,309 · ξ̂309 − r41,310 · ξ̂310 −
r41,312 · ξ̂312 )/(2 · r41,50 )
• Boulangerite: ξ̂51 = ξ51
• S b in galena: ξ̂52 = (ε̂41 − r41,34 · ξ̂34 − r41,51 · ξ̂51 − r41,309 · ξ̂309 − r41,310 ·
ξ̂310 − r41,312 · ξ̂312 )/(2 · r41,52 )
• Lamprophyllite: ξ̂55 = ξ55
• Tourmaline: ξ̂58 = ξ58
• Kornerupine: ξ̂59 = ξ59
• Axinite - Fe: ξ̂60 = ξ60
• Dumortierite: ξ̂61 = ξ61
• Sassolite: ξ̂62 = (ε̂62 −r62,58 · ξ̂58 −r62,59 · ξ̂59 −r62,60 · ξ̂60 −r62,61 · ξ̂61 )/(4·r62,62 )
90
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
• Colemanite: ξ̂63 = (ε̂62 − r62,58 · ξ̂58 − r62,59 · ξ̂59 − r62,60 · ξ̂60 − r62,61 · ξ̂61 )/(4 ·
r62,63 )
• Kernite: ξ̂64 = (ε̂62 − r62,58 · ξ̂58 − r62,59 · ξ̂59 − r62,60 · ξ̂60 − r62,61 · ξ̂61 )/(4· r62,64 )
• Ulexite: ξ̂65 = (ε̂62 − r62,58 · ξ̂58 − r62,59 · ξ̂59 − r62,60 · ξ̂60 − r62,61 · ξ̂61 )/(4· r62,65 )
• Witherite: ξ̂68 = 0, 1 · ξ̂67
• Bismutite: ξ̂72 = (r42,70 · ξ̂70 )/(r42,72 )
• Carnotite: ξ̂85 = (r66,81 · ξ̂81 )/(r66,85 )
• Chyroberyl: ξ̂90 = (r71,86 · ξ̂86 )/(r71,90 )
• Cobaltite: ξ̂125 = ξ125
• Smaltite: ξ̂126 = ξ̂125
• Linnaeite: ξ̂127 = (r76,125 · ξ̂125 )/(r76,127 )
• Arsenolite: ξ̂136 = (r77,131 · ξ̂131 )/(r77,136 )
• Diadochic N i: ξ̂141 = (r48,137 · ξ̂137 )/(r48,141 )
• Miserite: ξ̂151 = ξ151
• Weinschenkite: ξ̂153 = ξ153
• Vivianite: ξ̂155 = ξ155
• Cryotile: ξ̂165 = (r60,163 · ξ̂163 )/(r60,165 )
• Lepidolite: ξ̂179 = (r64,73 · ξ73 · 0, 1)/r64,179
• Tetrahedrite: ξ̂313 = ξ313
• Nordite: ξ̂314 = ξ314
The problem described above was not able to be solved with a mathematical software18 . The reasons for which the mathematical applications could not solve it
might have been:
• Matrix R [ j × i] is a sparce matrix, composed mainly by zeros.
• There are differences between the orders of magnitude of the minerals of a
factor of up to 1012 .
18
The problem was tried to be solved with the software Matlab 7.0. The function used was lsqlin
with the constraints described previously.
Results
91
• The orders of magnitude are very small (down to 10−15 ) and may be below
the significant figures of the programmes.
The resolution of the system through a mathematical application is open for further
studies. Probably, more powerful software will be required.
3.6
Results
Fortunately, the optimization problem was solved in a manual way through a trial
and error procedure. For that purpose, the relative proportions of the minerals in
Grigorev’s model were always tried to be kept. The fitting of the elements, i.e.
assuring that ε̂ j −ε j = 0, was carried out gradually in increasing order of appearance
in the minerals recorded by Grigor’ev. This way, element Au was the first to be
fitted, since native gold is the only Au-containing mineral in Grigor’ev’s model. The
last element to be adjusted was Si, since it is the element mostly contained in the
minerals of the crust. It must be pointed out that elements O and H have been left
free, i.e. without constraints.
Table 3.5 shows the mineralogical composition of the earth’s crust obtained in order
of abundance. The abundance of the minerals in mass terms, is calculated with Eq.
3.3.
ξ̂i · M Wi
Abund ance(%) = Pm
· 100
i=1 (ξ̂i · M Wi )
(3.3)
In table A.2 in page 352, the difference between our mineralogical composition and
that of Grigor’ev is shown. It contains 324 species, 57 more than in Grigor’ev’s
model19 . Of the 324 substances, 292 are minerals and the rest are mainly diadochic
elements included in the crystal structure of other minerals. That is the case for
elements C e, N d, N i, Y , Rb, C o, D y, E r, Eu, Ga, Gd, Ge, H o, Lu, Re, Sc, T b, T l,
T m, V , H f , I n, P d, P r, P t, Rh, Ru, S b, Se, Sm, Te, Y b. The resulting molecular
weight of the upper continental crust according to this model is 157,7 g/mole20 .
Next, the results obtained are discussed, stressing out the differences for the most
abundant and relevant minerals with Grigor’ev’s model. Additionally, the minerals
are aggregated into the main groups explained in section 3.2 and are compared to
the values given by Wedepohl [402], [403] and Nesbitt and Young [242]. Finally
the drawbacks of the model are also explained.
19
20
The non-mineral materials of Grigor’ev’s model have not been taken into account.
Remember that the molecular weight of the crust in Grigor’ev’s model was M Wcr = 142, 1 g/mole.
92
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Table 3.5: Mineralogical composition of the earth’s crust according to the
calculations of this study
Mineral
Formula
SiO2
N aAlSi3 O8
N a0.8 C a0.2 Al1.2 Si2.8 O8
KAlSi3 O8
N a0.6 C a0.4 Al1.4 Si2.6 O8
N aAl3 Si3 O10 (OH)2
2+
K M g2.5 Fe0.5
AlSi3 O10 (OH)1.75 F0.25
2+
K0.6 (H3 O)0.4 Al2 M g0.4 Fe0.1
Si3.5 O10 (OH)2
MW
g/mole
60,08
263,02
265,42
278,33
268,62
800,00
433,53
392,65
Abundance
mass, %
2,29E+01
1,35E+01
1,19E+01
1,18E+01
5,46E+00
3,96E+00
3,82E+00
3,03E+00
Quarz
Albite
Oligoclase
Orthoclase
Andesine
Paragonite
Biotite
Hydromuscovite/
Illite
Augite
Hornblende
(Fe)
Labradorite
Nontronite
Opal
Ripidolite
Almandine
Muscovite
Sillimanite
Epidote
Kaolinite
Calcite
Magnetite
Riebeckite
Beidellite
Ilmenite
Titanite
Clinochlore
Sepiolite
Aegirine
Diopside
Natrolite
Cummingtonite
Ankerite
Phosphate rock
Hypersthene
Hastingsite
Bytownite
Actinolite
Hydrobiotite
Montmorillonite
Andalusite
Lawsenite
Diaspore
Pennine
Glauconite
Prehnite
Dolomite
2+
C a0.9 N a0.1 M g0.9 Fe0.2
Al0.4 T i0.1 Si1.9 O6
2+
3+
C a2 Fe4 Al0.75 Fe0.25 (Si7 AlO22 )(OH)2
236,35
947,32
3,00E+00
2,63E+00
N a0.5 C a0.5 Al1.5 Si2.5 O8
N a0.3 Fe23+ Si3.7 Al0.3 O10 (OH)2 · 4(H2 O)
SiO2 · 1.5(H2 O)
2+
Si3 Al2 O10 (OH)8
M g3.75 Fe1.25
Fe32+ Al2 (SiO4 )3
KAl3 Si3 O10 (OH)1.8 F0.2
Al2 SiO5
C a2 Fe3+ Al2 (SiO4 )3 (OH)
Al2 Si2 O5 (OH)4
C aCO3
Fe23+ Fe2+ O4
N a2 Fe32+ Fe23+ (Si8 O22 )(OH)2
N a0.33 Al2.33 Si3.67 O10 (OH)2
Fe2+ T iO3
C aT iSiO5
2+
M g3.75 Fe1.25
Si3 Al2 O10 (OH)8
M g4 Si6 O15 (OH)2 · 6(H2 O)
N aFe3+ Si2 O6
C aM gSi2 O6
N a2 Al2 Si3 O10 · 2(H2 O)
M g7 (Si8 O22 )(OH)2
2+
C aFe0.6
M g0.3 M n2+
(CO3 )2
0.1
C a3 (PO4 )2
M g Fe2+ Si2 O6
N aC a2 Fe42+ Fe3+ (Si6 Al2 O22 )(OH)2
N a0.2 C a0.8 Al1.8 Si2.2 O8
C a2 M g3 Si8 O22 (OH)2 Fe22+
3+
M g2.3 Fe0.6
K0.3 C a0.1 Si2.8 Al1.3 O10 (OH)1.8 F0.2 · 3(H2 O)
N a0.165 C a0.0835 Al2.33 Si3.67 O10 (OH)2
Al2 SiO5
C aAl2 Si2 O7
AlO(OH)
2+
M g3.75 Fe1.25
Si3 Al2 O10 (OH)8
3+
2+
K0.6 N a0.05 Fe1.3
M g0.4 Fe0.2
Al0.3 Si3.8 O10 (OH)2
C a2 Al2 Si3 O10 (OH)2
C aM g(CO3 )2
Continued on next page . . .
270,21
496,67
87,11
595,22
497,75
398,71
162,05
483,23
258,16
100,09
231,54
935,90
367,54
151,73
196,04
595,22
613,82
231,00
216,55
380,22
780,82
206,39
310,00
232,32
990,86
275,01
875,45
463,51
367,09
162,05
314,24
59,99
595,22
426,93
395,38
184,40
2,50E+00
1,93E+00
1,24E+00
1,20E+00
1,04E+00
1,01E+00
9,97E-01
9,06E-01
8,36E-01
8,00E-01
7,95E-01
5,74E-01
5,10E-01
4,71E-01
4,46E-01
4,37E-01
3,48E-01
3,04E-01
3,04E-01
2,97E-01
2,91E-01
2,82E-01
2,79E-01
2,72E-01
2,58E-01
2,50E-01
2,47E-01
2,44E-01
2,39E-01
2,03E-01
2,00E-01
1,77E-01
1,71E-01
1,56E-01
1,41E-01
1,41E-01
Results
93
Table 3.5: Mineralogical composition of the earth’s crust according to the
calculations of this study. – continued from previous page.
Mineral
Formula
Al(OH)3
MW
g/mole
78,00
Abundance
mass, %
1,38E-01
Hydragillite/
Gibbsite
Ulvöspinel
Goethite
Neptunite
Hematite
Lepidomelane/
Annite
Sanidine
Barite
Distene/ Kyanite
Celestine
Staurolite
Thuringite/
Chamosite
Ferrosilite
Halite
Boehmite
Thomsonite
Serpentine/
Clinochrysotile
Pigeonite
Bronzite
Apatite
Zircon
Stilpnomelane
Spodumene
Psilomelane
Leucoxene
Tremolite
Clinozoisite
Crossite
Pyrite
Niter
Talc
Vermiculite
Enstatite
Anorthite
Rutile
Zoisite
Nitratine
Braunite
Siderite
Graphite
Spessartine
Anhydrite
Olivine
T i Fe22+ O4
Fe3+ O(OH)
2+
K N a2 Li Fe1.5
M n2+
T i2 Si8 O24
0.5
Fe2 O3
2+
3+
K Fe2.5
M g0.5 Fe0.75
Al0.25 Si3 O10 (OH)2
223,57
88,85
907,69
159,69
512,40
1,16E-01
1,04E-01
9,97E-02
9,66E-02
9,11E-02
K0.75 N a0.25 AlSi3 O8
BaSO4
Al2 SiO5
274,30
233,39
162,05
7,31E-02
7,09E-02
7,08E-02
S rSO4
Fe2+ Al9 Si4 O23 (OH)
3+
3+
Fe32+ M g2 Al0.5
Fe0.5
Si3 AlO10 (OH)2
183,68
851,86
562,80
6,70E-02
6,54E-02
6,43E-02
Fe2+ M gSi2 O6
N aC l
AlO(OH)
N aC a2 Al5 Si5 O20 · 6(H2 O)
M g3 Si2 O5 (OH)4
263,86
58,44
59,99
806,56
277,11
6,11E-02
5,89E-02
5,79E-02
4,99E-02
4,56E-02
219,70
232,32
509,12
183,31
1391,50
186,09
745,37
196,04
812,37
454,36
815,09
119,98
101,10
379,27
415,30
200,78
277,41
79,88
454,36
84,99
604,64
115,86
12,01
495,03
136,14
153,31
4,37E-02
4,11E-02
4,03E-02
3,88E-02
3,85E-02
3,83E-02
3,80E-02
3,72E-02
3,48E-02
3,41E-02
3,31E-02
3,30E-02
3,00E-02
2,91E-02
2,81E-02
2,78E-02
2,75E-02
2,73E-02
2,58E-02
2,52E-02
2,45E-02
2,41E-02
2,41E-02
2,36E-02
2,36E-02
2,34E-02
2+
C a0.1 Si2 O6
M g1.35 Fe0.55
M g Fe2+ Si2 O6
C a5 (PO4 )3 (OH)0.33 F0.33 C l0.33
Z rSiO4
K0.8 Fe82+ Al0.8 Si11.1 O21 (OH)8.6 · 6(H2 O)
LiAlSi2 O6
Ba2 M n3+
O10 · H2 O
5
C aT iSiO5
C a2 M g5 Si8 O22 (OH)2
C a2 Al3 (SiO4 )3 (OH)
N a2 M g2 Fe2+ Al2 (Si8 O22 )(OH)2
FeS?2
K N O3
M g3 Si4 O10 (OH)2
M g3 Si4 O10 (OH)2 · 2(H2 O)
M g2 Si2 O6
C aAl2 Si2 O8
T iO2
C a2 Al3 Si3 O12 (OH)
N aN O3
M n2+ M n3+
6 SiO12
Fe2+ CO3
C
M n2+ 3Al2(SiO4)3
C aSO4
2+
M g1.6 Fe0.4
(SiO4 )
Continued on next page . . .
94
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Table 3.5: Mineralogical composition of the earth’s crust according to the
calculations of this study. – continued from previous page.
Mineral
Formula
3+
2+
Ba0.8 P b0.2 N a0.125 M n4+
6 Fe1.3 M n0.5 Al 0.2 Si0.1 O16
N aAlSi2O6 · (H2 O)
C
Fe2+ C r2 O4
C a10 M g2 Al4 (SiO4 )5 (Si2 O7 )2 (OH)4
MW
g/mole
848,06
220,15
12,01
223,84
1422,09
Abundance
mass, %
2,23E-02
2,23E-02
2,21E-02
1,98E-02
1,71E-02
Hollandite
Analcime
C org
Chromite
Vesuvianite/
Idocrase
Pyrrhotite
Tephroite
Gypsum
Corundum
Rhodochrosite
Arfvedsonite
Monazite (Ce)
Sphalerite
Jadeite
Dispersed V
Pumpellyite
Diodochic Rb
Aragonite
Nepheline
Forsterite
Hedenbergite
Chalcopyrite
Phlogopite
Witherite
Pentlandite
Cordierite
Pyrolusite
Fayalite
Anatase
Francolite
Tourmaline
Orthite-Ce/ Allanite
Lepidolite
Gedrite
Beryl
Pyrophyllite
Rhodonite
Magnesite
Chloritoid
Ilmenorutile
Ulexite
Diadochic Ce
Jacobsite
Clementite
Kernite
Bastnaesite
Fe2+ S
M n2+
(SiO4 )
2
C aSO4 · 2H2 O
Al2 O3
M nCO3
N a3 Fe42+ Fe3+ (Si8 O22 )(OH)2
C e0.5 La0.25 N d0.2 T h0.05 (PO4 )
Z nS
3+
N aAl0.9 Fe0.1
(Si2 O6 )
V
C a2 M gAl2 (SiO4 )(Si2 O7 )(OH)2 · (H2 O)
Rb
C aCO3
N a0.75 K0.25 Al(SiO4 )
M g2 SiO4
C aFe2+ Si2 O6
CuFeS2
K M g3 AlSi3 O10 F (OH)
BaCO3
2+
N i4.5 S8
Fe4.5
M g2 Al4 Si5 O18
M nO2
Fe22+ SiO4
T iO2
C a5 (PO4 )2.63 (CO3 )0.5 F1.11
N aFe32+ Al6 (BO3 )3 Si6 O18 (OH)4
C a1.2 C e0.4 Y0.133 Al2 Fe3+ (Si3 O12 )(OH)
87,91
201,96
158,14
101,96
114,95
958,89
240,21
97,44
205,03
51,00
502,25
85,00
100,09
146,08
140,69
248,09
183,53
419,25
197,34
771,94
584,95
86,94
203,78
79,88
501,26
1053,38
519,03
1,57E-02
1,27E-02
1,26E-02
1,22E-02
1,09E-02
1,05E-02
1,03E-02
9,96E-03
9,80E-03
9,71E-03
9,49E-03
8,30E-03
7,64E-03
7,43E-03
6,96E-03
6,82E-03
6,64E-03
6,62E-03
5,99E-03
5,75E-03
5,57E-03
4,90E-03
4,77E-03
4,46E-03
4,35E-03
4,30E-03
4,05E-03
K Li2 AlSi4 O10 F (OH)
M g5 Al2 (Si6 Al2 O22 )(OH)2
Be3 Al2 Si6 O18
Al2 Si4 O10 (OH)2
M n2+ SiO3
M g CO3
2+
Fe1.2
M g0.6 M n2+
Al Si O (OH)4
0.2 4 2 10
2+
T i0.7 N b0.15 Fe0.225
O2
N aC aB5 O9 · 8H2 O
Ce
2+
3+
3+
M n2+
0.6 Fe0.3 M g 0.1 Fe1.5 M n0.5 O4
2+
3+
Fe3 M g1.5 Al Fe Si3 AlO12 (OH)6
N a2 B4 O7 · 4H2 O
La(CO3 )F
Continued on next page . . .
388,30
783,97
537,50
360,31
131,02
84,31
484,71
92,01
405,23
140,00
227,38
692,09
290,28
219,12
3,99E-03
3,23E-03
3,22E-03
3,22E-03
3,04E-03
3,02E-03
3,00E-03
2,96E-03
2,92E-03
2,83E-03
2,72E-03
2,64E-03
2,61E-03
2,54E-03
Results
95
Table 3.5: Mineralogical composition of the earth’s crust according to the
calculations of this study. – continued from previous page.
Mineral
Formula
C a2 B6 O11 · 5H2 O
H3 BO3
MW
g/mole
411,09
61,83
Abundance
mass, %
2,46E-03
2,22E-03
Colemanite
Sassolite (natural boric acid)
Cryptomelane
Murmanite
Anthophyllite
Grossular
Diadochic Ni
Amblygonite
Diadochic Y
Scapolite
Pollucite
Dispersed Ga
Dispersed Co
Spinel
Diadochic Nd
Sapphirine
Dispersed Sc
Manganite
Cristobalite
Fluorite
Andradite
Glaucophane
Todorokite
Ferrocolumbite
Clinohumite
Pr in Monazite
and Bastnasite
Thorite
Galena
Marcasite
Kornerupine
Hf in Zr ores
Vaesite
Violarite
Humite
Jarosite
Wollastonite
Arsenopyrite
Sm in Monazite
and Bastnasite
Kieserite
Garnierite
Euxenite
Dispersed Dy
Cubanite
Dispersed Gd
Nickeline
K M n4+
M n2+
O
7.5
0.5 16
N a4 T i3.6 N b0.4 (Si2 O7 )2 O4 · 4(H2 O)
M g7 Si8 O22 (OH)2
C a3 Al2 (SiO4 )3
Ni
Li0.75 N a0.25 Al(PO4 )F0.75 (OH)0.25
Y
N a2 C a2 Al3 Si9 O24 C l
Cs0.6 N a0.2 Rb0.1 Al0.9 Si2.1 O6 · (H2 O)
Ga
Co
M gAl2 O4
Nd
M g4 Al6.5 Si1.5 O20
Sc
M nO(OH)
SiO2
C aF2
C a3 Fe22+ (SiO4 )3
N a2 (M g3 Al2 )Si8 O22 (OH)2
O12 · 3(H2 O)
M n3+
N a2 M n4+
2
4
Fe2+ N b2 O6
2+
M g6.75 Fe2.25
(SiO4 )4 F1.5 (OH)0.5
Pr
707,12
773,84
780,82
450,45
59,00
151,41
89,00
287,93
290,16
70,00
59,00
142,27
144,00
689,23
45,00
87,94
60,08
78,07
508,18
783,54
621,65
337,66
695,05
141,00
2,19E-03
2,15E-03
2,09E-03
2,08E-03
1,98E-03
1,95E-03
1,86E-03
1,83E-03
1,78E-03
1,76E-03
1,73E-03
1,52E-03
1,46E-03
1,40E-03
1,40E-03
1,36E-03
1,24E-03
1,12E-03
9,99E-04
9,49E-04
8,33E-04
8,10E-04
7,64E-04
7,10E-04
T hSiO4
P bS
FeS2
2+
M g3.5 Fe0.2
Al5.7 (SiO4 )3.7 (BO4 )0.3 O1.2 (OH)
Hf
N iS2
Fe2+ N i2 S4
2+
M g5.25 Fe1.75
(SiO4 )3 F1.5 (OH)0.5
3+
K Fe3 (SO4 )2 (OH)6
C aSiO3
FeAsS
Sm
324,12
239,27
119,98
649,39
178,00
122,82
301,49
538,58
500,81
116,16
162,83
150,00
6,91E-04
6,67E-04
6,29E-04
6,00E-04
5,29E-04
5,20E-04
5,20E-04
5,09E-04
4,79E-04
4,74E-04
4,71E-04
4,69E-04
M gSO4 · (H2 O)
N i2 M gSi2 O5 (OH)4
Y0.7 C a0.2 C e0.1 (Ta0.2 )2 (N b0.7 )2 (T i0.025 )O6
Dy
CuFe2 S3
Gd
N iAs
Continued on next page . . .
138,38
345,92
385,10
163,00
271,44
157,00
133,61
4,24E-04
4,10E-04
3,93E-04
3,91E-04
3,62E-04
3,19E-04
2,73E-04
96
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Table 3.5: Mineralogical composition of the earth’s crust according to the
calculations of this study. – continued from previous page.
Mineral
Formula
Aenigmatite
Scheelite
Cassiterite
Carnotite
Vernadite
Topaz
Dispersed Er
Chrysoberyl
Hisingerite
Covellite
Sylvite
Yttrialite
Molybdenite
Yb in monazite
Gersdorffite
Dispersed Br
Omphacite
Brucite
Uraninite
Azurite
Dietzeite
Sb in galena
Dispersed Ge
Bornite
Nosean
Pyrochlore
Malachite
Palygorskite
Lautarite
Dispersed Eu
Dispersed Tl
Hydrosodalite
Dispersed Ho
Gadolinite
Phenakite
Bertrandite
Helvine/
Helvite
Strontianite
Dispersed Tb
Perovskite
Tridymite
Cryolite
Sulphur
Orpiment
Brookite
Eudialyte
Carnallite
N a2 Fe52+ T iSi6 O20
C aW O4
SnO2
K2 (UO2 )2 (V O4 )2 · 3H2 O
3+
M n4+
0.6 Fe0.2 C a0.2 N a0.1 O1.5 (OH)0.5 · 1.4(H 2 O)
Al2 (SiO4 )F1.1 (OH)0.9
Er
BeAl2 O4
Fe23+ Si2 O5 (OH)4 · 2(H2 O)
CuS
KC l
Y1.5 T h0.5 Si2 O7
M oS2
Yb
N iAsS
Br
2+
C a0.6 N a0.4 M g0.6 Al0.3 Fe0.1
Si2 O6
M g(OH)2
UO2
Cu3 (CO3 )2 (OH)2
C a2 (IO3 )2 (C rO4 )
Sb
Ge
Cu5 FeS4
N a8 Al6 Si6 O24 (SO4 )
N a1.5 C a0.5 N b2 O6 (OH)0.75 F0.25
Cu2 (CO3 )(OH)2
M gAlSi4 O10 (OH) · 4(H2 O)
C a(IO3 )2
Eu
Tl
N a8 (AlSiO4 )6 (OH)2
Ho
Y2 Fe2+ Be2 (Si2 O10 )
Be2 SiO4
Be4 Si2 O7 (OH)2
M n4 Be3 (SiO4 )3 S
S r CO3
Tb
C aT iO3
SiO2
N a3 Al F6
S8
As2 S3
T iO2
2+
N a4 C a2 C e0.5 Fe0.7
M n2+
Y Z rSi8 O22 (OH)1.5 C l0.5
0.3 0.1
K M g C l3 · 6(H2 O)
Continued on next page . . .
MW
g/mole
861,60
287,93
150,71
902,18
112,17
182,25
167,00
126,97
351,92
95,61
74,55
417,54
160,07
173,00
165,68
80,00
213,67
58,32
270,03
344,67
545,96
879,29
73,00
501,84
1012,38
362,38
221,12
412,69
389,88
152,00
204,00
932,00
165,00
569,31
110,11
238,23
555,10
Abundance
mass, %
2,73E-04
2,67E-04
2,61E-04
2,52E-04
2,45E-04
2,34E-04
2,30E-04
2,28E-04
2,20E-04
2,17E-04
2,05E-04
1,94E-04
1,83E-04
1,72E-04
1,61E-04
1,60E-04
1,60E-04
1,58E-04
1,51E-04
1,51E-04
1,51E-04
1,42E-04
1,41E-04
1,33E-04
1,31E-04
1,26E-04
1,21E-04
1,14E-04
1,08E-04
1,00E-04
8,98E-05
8,44E-05
8,30E-05
8,05E-05
8,05E-05
8,05E-05
8,05E-05
147,63
159,00
135,96
60,08
209,94
256,53
246,04
79,88
938,82
277,85
7,88E-05
7,00E-05
6,94E-05
6,30E-05
4,95E-05
4,72E-05
4,55E-05
4,21E-05
4,04E-05
4,03E-05
Results
97
Table 3.5: Mineralogical composition of the earth’s crust according to the
calculations of this study. – continued from previous page.
Mineral
Formula
Y bPO4
N aAl(CO3 )(OH)2
2+
Fe0.5
M n2+
(W O4 )
0.5
Lu
Tm
S b2 S3
Cu
P bCO3
3+
U0.3 C a0.2 N b0.9 T i0.8 Al0.1 Fe0.1
Ta0.5 O6 (OH)
MW
g/mole
268,01
144,00
303,24
175,00
169,00
339,70
63,55
267,21
413,09
Abundance
mass, %
3,70E-05
3,62E-05
3,21E-05
3,10E-05
3,00E-05
2,75E-05
2,48E-05
2,21E-05
2,05E-05
Xenotime
Dawsonite
Wolframite
Dispersed Lu
Dispersed Tm
Stibnite
Copper
Cerussite
Blomstrandite/
Betafite
Sodalite
Britholite
Ferrotantalite
Ramsayite/
Lorenzenite
Anglesite
Greenockite
Chondrodite
Axinite -Fe
Chalcocite
Zinc
Se in copper
ores
Loparite (Ce)
Bischofite
Smithsonite
Sirtolite
Pleonaste/
Magnesioferrite
Lead
Bismutite
Cinnabar
In in ZnS
Arsenolite
Bismuthinite
Bismite
Tin
Cancrinite
Chevkinite
Bismuth
RhabdophaneCe
Fergusonite
Native silver
Iotsite
Realgar
Pyrargirite
Argentite
N a8 Al6 Si6 O24 C l2
C a2.9 C e0.9 T h0.6 La0.4 N d0.2 Si2.7 P0.5 O12 (OH)1.8 F0.2
Fe2+ Ta2 O6
N a2 T i2 Si2 O9
969,21
783,69
513,74
341,91
1,98E-05
1,71E-05
1,58E-05
1,24E-05
P bSO4
C dS
2+
M g3.75 Fe1.25
(SiO4 )2 F1.5 (OH)0.5
2+
C a2 Fe Al2 BO3 Si4 O12 (OH)
Cu2 S
Zn
Se
303,26
144,48
382,12
570,12
159,16
65,39
79,00
1,16E-05
1,16E-05
1,12E-05
1,10E-05
1,09E-05
1,01E-05
9,00E-06
N a0.6 C e0.22 La0.11 C a0.1 T i0.8 N b0.2 O3
M g C l2 · 6(H2 O)
Z nCO3
Z rSiO4
M g Fe23+ O4
168,78
203,30
125,40
183,31
158,04
8,13E-06
8,06E-06
7,98E-06
7,37E-06
6,96E-06
Pb
Bi2 (CO3 )O2
H gS
In
As2 O3
Bi2 S3
Bi 2O3
Sn
N a6 C a2 Al6 Si6 O24 (CO3 )2
2+
3+
C e1.7 La1.4 C a0.8 T h0.1 Fe1.8
M g0.5 T i2.5 Fe0.5
Si4 O22
Bi
C e0.75 La0.25 (PO4 ) · (H2 O)
207,20
509,97
232,66
115,00
197,84
514,16
465,96
118,69
1052,50
1212,52
208,98
252,80
6,32E-06
6,09E-06
5,73E-06
5,61E-06
5,55E-06
5,10E-06
4,62E-06
4,59E-06
4,42E-06
3,35E-06
2,71E-06
2,62E-06
N d0.4 C e0.4 Sm0.1 Y0.1 N bO4
Ag
FeO
As4 S4
Ag3 S bS3
Ag2 S
Continued on next page . . .
294,57
107,87
71,80
106,99
541,55
247,80
2,38E-06
2,09E-06
1,71E-06
1,50E-06
1,29E-06
1,24E-06
98
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
Table 3.5: Mineralogical composition of the earth’s crust according to the
calculations of this study. – continued from previous page.
Mineral
Formula
Baddeleyite
Uranium- Thorite
Lavenite
Z rO2
T hSiO4
Cobaltite
Acanthite
Freibergite
Smaltite
Powellite
Stephanite
Linnaeite
Microlite
Lamprophyllite
Te in Cu ores
Thorianite
Delorenzite/
Tanteuxenite
Miserite
Fahlerz Group:
Tennantite
Metatorbenite
Moissanite
Vivianite
Naegite
Gold
Chrysocolla
Troilite
Chlorargirite
Metacinnabar
Wulfenite
Tetrahedrite
Nordite
Samsonite
Pd in Ni-Cu
ores
Cooperite
Weinschenkite
Ru in Ni-Cu
ores
Sylvanite
Lollingite
Calaverite
Pt in Ni-Cu ores
Rinkolite/
Mosandrite
Dispersed Re
Tellurite
MW
g/mole
123,22
327,12
Abundance
mass, %
1,20E-06
1,04E-06
2+
N a0.5 C a0.5 M n2+
Fe0.5
Z r0.8 T i0.1
0.5
N b0.1 (Si2 O7 )O0.6 (OH)0.3 F0.1
C oAsS
Ag2 S
2+
Ag7.2 Cu3.6 Fe1.2
S b3 AsS13
C oAs2
C aM oO4
Ag5 S bS4
C o3 S4
N a0.4 C a1.6 Ta2 O6.6 (OH)0.3 F0.1
N a2 S r BaT i3 Si4 O16 (OH)F
Te
T hO2
Y0.7 C a0.2 C e0.12 (Ta0.7 )2 (N b0.2 )2 (T i0.1 )O5.5 (OH)0.5
388,58
1,01E-06
165,92
247,80
1929,46
125,40
200,02
789,36
305,06
547,81
818,87
128,00
264,04
480,83
8,40E-07
6,79E-07
6,79E-07
6,35E-07
6,10E-07
6,09E-07
5,15E-07
4,77E-07
4,59E-07
4,47E-07
4,12E-07
4,00E-07
KC a2 C e3 Si8 O22 (OH)1.5 F0.5
Cu11 Fe2+ As4 S13
1151,28
1471,40
2,30E-07
1,82E-07
Cu(UO2 )2(PO4 )2 · 8(H2 O)
SiC
Fe33+ (PO4 )2 · 8(H2 O)
Z rSiO4
Au
Cu2 Si2 O6 · (H2 O)4
FeS
Ag C l
H gS
P bM oO4
Cu9 Fe3 S b4 S13
N a2.8 M n2+
S r0.5 C a0.5 La0.33 C e0.6 Z n0.6 M g0.4 Si6 O17
0.2
Ag4 M nS b2 S6
Pd
937,67
40,10
501,61
183,31
196,97
351,32
87,91
143,32
232,66
367,14
1643,31
758,57
922,31
106,00
1,69E-07
1,41E-07
1,30E-07
1,28E-07
1,28E-07
1,25E-07
1,05E-07
7,83E-08
7,38E-08
6,10E-08
5,70E-08
5,46E-08
4,87E-08
4,51E-08
P t 0.6 P d0.3 N i0.1 S
Y PO4 · 2(H2 O)
Ru
186,91
219,91
101,00
3,95E-08
3,70E-08
3,37E-08
Au0,75 Ag0,25 Te2
FeAs2
AuTe2
Pt
N a2 C a3 C e1.5 Y0.5 T i0.4 N b0.5 Z r0.1 (Si2 O7 )2 O1.5 F3.5
429,89
205,69
452,17
195,00
922,39
3,27E-08
2,68E-08
2,58E-08
2,47E-08
2,07E-08
Re
TeO2
186,00
159,60
1,98E-08
1,82E-08
Continued on next page . . .
Results
99
Table 3.5: Mineralogical composition of the earth’s crust according to the
calculations of this study. – continued from previous page.
Mineral
Formula
Bi2 Te2 S
M gO
KAl3 (SO4 )2(OH)6
Sc1.5 Y0.5 Si2 O7
Al6.9 (BO3 )(SiO4 )3 O2.5 (OH)0.5
Rh
MW
g/mole
705,23
40,30
414,21
280,05
569,73
103,00
Abundance
mass, %
1,60E-08
1,52E-08
9,11E-09
7,60E-09
7,60E-09
6,01E-09
Tetradymite
Periclase
Alunite
Thortveitite
Dumortierite
Rh in Ni-Cu
ores
Osmium
Iridium
Polycrase (Y)
Boulangerite
I-Platinum
Polixene/ Tetraferroplatinum
Wohlerite
Sum
Os0.75 I r0.25
I r0.5 Os0.3 Ru0.2
Y0.5 C a0.1 C e0.1 U0.1 T h0.1 T i1.2 N b0.6 Ta0.2 O6
P b5 S b4 S11
Pt
P t Fe
190,71
173,39
354,85
1887,90
195,08
167,00
3,00E-09
2,61E-09
8,71E-10
4,00E-10
3,00E-10
2,00E-10
N aC a2 Z r0.6 N b0.4 Si2 O8.4 (OH)0.3 F0.3
396,41
155,2
5,05E-11
105,0
End of the table
3.6.1
Discussion of the most abundant minerals
The 10 most abundant minerals according to our calculations are: quartz, albite,
oligoclase, orthoclase, andensine, paragonite, biotite, hydromuscovite, augite, and
hornblende. Grigor’ev’s 10 most abundant minerals are quartz, oligoclase, orthoclase, biotite, andesine, albite, calcite, hornblende, labradorite and hydromuscovite.
From the top ten most abundant minerals in Grigor’ev’s model, calcite and labradorite do not appear in the 1 to 10 ranking of abundance in our model. They appear in
positions 20 and 11, respectively. On the contrary, minerals paragonite and augite
appearing in our model as most abundant, are in Grigor’ev’s composition in positions: 15 and 14. The difference for labradorite in both models is very small, around
17%. However, the significant difference between the concentration of calcite in
both models (75%) is because its quantity is fixed by element C. The quantity of
carbon generated by Grigor’ev’s model in the upper earth’s crust is much greater
than the one given by Wedepohl21 [404] (see table 3.4). According to Grigor’ev’s
composition, calcite would account for around 50% of all carbon in the earth’s crust,
what seems to be very unlikely, due to the vast amount of other important substances
containing that element22 . It could also be possible, that Wedepohl’s concentration
Rudnick and Gao [292] or McLennan [215] did not provide any number for element C and hence,
the value of Wedepohl [404] was considered.
22
For instance all carbonates.
21
100
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
for element C was underestimated. In that case, calcite would occupy a more relevant position in the ranking of abundance of minerals in the crust, according to our
model.
Paragonite and augite are about 2,5 and 1,5 times more abundant in our model
than in Grigor’ev’s, respectively. This is due to the fact that their contents are fixed
by elements N a and M g. The discrepancy between both models for M g and N acontaining minerals is explained in the next section.
3.6.2
Discussion of the most relevant minerals
Next, the abundances of some of the most important minerals for industrial uses
are discussed and compared to Grigor’ev’s analysis. Those are the minerals of gold,
silver, copper, iron, aluminium, titanium, magnesium, calcium, sodium, sulfur, mercury, zinc, lead and uranium.
The abundance of gold obtained in our model is around one order of magnitude
greater than that of Grigor’ev’s. As explained in section 3.4.27, it is widely found as
native gold and in the form of tellurides. The number given by Grigor’ev for gold,
would imply that only 12% of Au comes from native gold, instead of the 85% that
we assumed. It is believed that the main source of element Au is native gold and not
tellurides, and therefore we keep the assumptions made.
Grigorev’s silver mineral’s concentration are also about one order of magnitude
greater than in our model. It is considered, that most important Ag-containing minerals are included in both models. Hence, the mass balance indicates that the
concentration for them should be around one order of magnitude greater.
We have assumed that the minerals for copper considered in Grigor’ev’s model are
the most important and no additional substances were taken into account. The mass
balance for Cu brought the result that the Cu-containing minerals in our model are
around two orders of magnitude greater than in Grigor’ev’s analysis.
A great amount of Fe-containing minerals was considered in both models. The differences between them are usually less than 25% for the oxides and the most important silicates, being the numbers given by Grigor’ev greater. For sulfates, Grigorev’s
iron-containing minerals are around 50% greater.
The most important Al-containing minerals show a difference between both models
of around 220%, such as for sillimanite or boehmite.
The concentration of T i-containing minerals in our model is about 1,5 times greater
than in Grigor’ev’s composition. Since most important titanium minerals have been
considered, the mass balance for T i indicates that the values estimated by Grigor’ev
are slightly low.
The difference between the main M g and C a-containing minerals in both models
is around 37% and 17% respectively, being the concentrations of our study smaller
Results
101
Table 3.6. Crustal abundance of minerals according to this and Grigor’ev’s model in
mass % [127]
Mineral
Quartz
Plagioclase
Others
Orthoclase
Oxides
Micas
Pyroxene
Amphibole
Chlorite
This study
56,7
18,9
6,5
6,3
4,3
3,7
2,5
0,6
0,5
Grigor’ev [127]
58,8
15,6
11,6
5,2
3,2
2,9
1,4
0,6
0,7
than in Grigor’ev’s model, since the latter overestimated the abundance of the magnesium and calcium minerals, as revealed by the value of ε j , greater than ε̂ j .
Sodium-containing minerals in our model are around 2,5 times greater than in
Grigor’ev’s analysis for minerals like albite, nontronite, riebeckite or aegirine, where
the limiting element is N a, but are around 17% smaller for those minerals that also
contain C a. That is the case for oligoclase, andesine or labradorite.
The abundance of sulfur minerals in our model differ from Grigor’ev’s study in less
than 50% for native sulfur, gypsum or pyrite, but in two orders of magnitude in
others, such as cinnabar. The differences depend on the limiting element that contain
the substance. For the case of cinnabar, the limiting element is H g and not S. The
discrepancy for the latter mineral and that for metacinnabar is because only two
H g-containing minerals were considered (the most important ones).
Zinc-containing minerals in our model are more than two orders of magnitude
greater than in Grigor’ev’s studies. This is due to the fact that only a few zinc minerals were considered: sphalerite, smithsonite, nordite and native zinc. Probably,
other minerals of zinc should be taken into account, such as franklinite, hemimorphite or wurtzite.
We have considered only 6 uranium and 6 lead-containing minerals and that might
be the reason why their concentrations in our model are around one and two orders
of magnitude greater than in Grigor’ev’s study, respectively. As in the case of zinc,
other minerals of uranium and lead are likely to be taken into account.
3.6.3
Discussion of the aggregated composition
A comparison between the aggregated composition of the minerals in the crust (as
carried out by Wedepohl [402], [403] and Nesbitt and Young [242], table 3.2)
obtained in this and in Grigor’ev’s study, is shown in table 3.6.
102
THE
MINERALOGICAL COMPOSITION OF THE UPPER CONTINENTAL CRUST
The most significant differences between these two new models and the older ones
from Wedepohl and Nesbitt and Young are the abundances of quartz and plagioclase.
According to the recent models, quartz accounts for nearly 60% of the minerals
on the upper earth’s crust. Plagioclase occupies the second position in abundance
(representing more than 15%) and not the first, like in the older models. All four
studies agree in that orthoclase is the third group of importance, although the new
calculated values are significantly lower than the older ones, especially between
Wedepohl’s and Grigor’ev’s. The relative proportion of micas (including biotite and
muscovite) are much lower than in the older analysis. The same thing happens to
chlorites, amphiboles and olivine, the latter with imperceptible abundance. However
oxides are more abundant in the recent models, while the abundance of pyroxenes
is close to the analysis of Nesbitt and Young.
3.6.4
Drawbacks of the model
The first thing to me noted in the composition of table 3.5 is that the total mass
of the minerals contained in the upper crust is greater than 100%. As mentioned
above, the oxygen and hydrogen quantities in the crust have been left free. In the
chemical compositions of the crust given by Rudnick et al. [292], Wedepohl [404]
or McLennan [215], no H or O values are provided. However the value for O can
be determined from the first two authors, as some of the elements are given as the
corresponding oxides. That is the case for SiO2 , T iO2 , Al2 O3 , FeO, M nO, M gO,
C aO, N a2 O, K2 O and P2 O5 . The oxygen concentration resulting from those oxides
gives in Rudnick’s and Wedepohl’s models of the crust 2, 95 × 10−2 mole/g. In the
model developed in this PhD, the concentration of oxygen is 4,8% greater: 3, 10 ×
10−2 mole/g, while in Grigor’ev’s 0,7% greater: 2, 97 × 10−2 mole/g. Hence, if
the chemical composition of the crust is right, then there is an excess of oxygen in
the minerals of our model and that of Grigor’ev. This oxygen could be in the form
of molecules O2 or H2 O, which would be in the concentration of 1, 5 × 10−2 and
1, 1 × 10−3 mole/g, respectively. An excess of oxygen could be attributed to the fact
that the minerals considered may not be electronegatively neutral. Nevertheless, we
have assured the neutrality of the charges of every mineral considered. If the oxygen
quantity is fixed in our model, then the Si content is significantly smaller than the
one given by Rudnick: 1, 01×10−2 instead of 1, 10×10−2 g/mole. With the chemical
composition of the minerals given in table 3.5, there is no possible solution to Eq. 3.2
if the concentration of oxygen is also fixed. Hence, it seems that the problem comes
from the chemical formulae used. It must be pointed out, that many of the minerals
given by Grigor’ev do not have a fixed chemical composition. They represent a
variety of minerals with changing concentrations of certain elements. That is the
case for biotite, apatite, phosphate rock, etc. We have tried to take into account an
average chemical formula, given by the empirical formula recorded under [172],
but assuring the neutrality of the charges and the general molecular structure of the
Summary of the chapter
103
mineral. Nevertheless, many different formulas are possible. Therefore, this aspect
should be checked in further developments of the model.
Another aspect that should be taken into account, is that the chemical composition
of the earth in terms of elements has been assumed to be correct and not the one
generated by Grigor’ev. The decision to do so was because the first one has been
subject of many research studies throughout history, while the last one has just begun
to be analyzed. Nevertheless, in some cases the procedure developed in this PhD
could serve as a tool for assuring the chemical composition of the crust. The low
concentration of calcite obtained in our model for example, has set the alarms for
the concentration value of C in the crust, which might have been underestimated by
Wedepohl.
3.7
Summary of the chapter
In this chapter, a revision of the studies concerning the mineralogical composition of
the earth’s crust has been carried out. It has been verified, that the literature about
this topic is very limited and inaccurate, due to the heterogeneity and complexity
of the crust. Nevertheless, one single author, the Russian geochemist Grigor’ev has
been very recently the first one in giving a comprehensive mineralogical composition
of the upper crust.
With the help of Eq. 3.1, we were able to check the satisfaction of the mass balance
between the minerals proposed by Grigor’ev and the better known chemical composition in terms of elements of the crust. The no satisfaction of the mass balance, lead
us to propose a new composition, based on the Grigor’ev’s semi-empirical analysis.
The methodology used minimizes the difference between Grigor’ev’s and our proposed compositions under the constraint of assuring chemical coherence with the
average chemical composition of the earth’s crust in terms of elements. We have
made assumptions based on the literature for those important minerals not taken
into account in Grigor’ev’s analysis, and included them in our model. As a result,
we have obtained a mean mineralogical composition of the upper crust, consisting
of the 292 most abundant minerals.
This composition does not have to be taken as final and closed, since many assumptions had to be made. Nevertheless, it is the first step for obtaining a coherent
mineralogical composition of the crust.
In chapters 2 and 3, we have tried to describe the composition of the earth as a
whole. From the global components of the earth, only a few are used by man. The
next chapter is focused on describing that part of the earth useful to man: the natural
resources.
Chapter
4
The resources of the earth
4.1
Introduction
In this chapter, a deeper look at the earth’s components useful to man is undertaken.
For that purpose, a revision of energy and non-energy resources is carried out. The
energy resources have been divided into energy coming from the solid earth, i.e.
nuclear and geothermal energy; tidal energy; and energy coming from the sun, including solar, water, wind, ocean power and hydrocarbons.
In addition to the energy resources, mineral resources are also studied, stressing out
their abundance and average crustal concentration.
4.2
Natural resources: definition, classification and early
assessment
A natural resource can be defined as any form of matter or energy obtained from the
environment that meets human needs. Therefore water, air, oil, biomass or minerals
are classified as natural resources. On the other hand, Costanza [65], defines the
natural capital as a stock that yields a flow of variable goods in the future.
Natural resources are frequently classified as renewable or non-renewable. Renewable resources are defined as resources that are regenerated on a human time scale.
Examples of renewable resources are water, biomass or the energy from the sun.
Non-renewable resources can be considered as a stock that has a regeneration rate
of zero over a relatively long period. That is the case for minerals [203].
Minerals can be further classified as fuel and non-fuel mineral resources. Fuel resources are those from which energy can be potentially extracted. That is the case
for coal, fuel or uranium. The rest are non-fuel minerals, including construction
materials, metals, etc.
105
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Table 4.1. World energy use in 1984 [130]
Fuel source
Coal
Oil
Gas
Uranium
Tar sands+Oil shale
Current
(EJ/y)
97,6
127,3
63,1
12,6
-
use
Proven
reserves (EJ)
21500
4300
3700
813
550+
Resources
(EJ)
238000
10000
10000
1324
1600+
Approx. total
Fluxes (EJ/year)
300,6
30850+
Practical
Hydro
21,7
100
260900+
Ultimate potential
200
Biomass
47
80
720
Wind
Photovoltaic
v. small
v. small
30
infinite
100
infinite
Geothermal
Approx. total
Overall total
0,1
63,8
368,4
large
210
large
1020+
Resource uncertainty
±20%
-30% + 60%
-40% + 70%
±50
highly uncertain
little
uncertainty
highly uncertain
speculative
rapidly reducing price
An early assessment of the renewable and nonrenewable energy resources on earth
was done by Hall et al. [130] and can be seen in table 4.1.
The degree of knowledge about resources and technological development has improved notably since the eighties, what has lead to better estimations of the available
resources on earth.
In the next sections, the numbers given in table 4.1 are updated and new figures are
provided for other types of resources. The results are summarized in section 4.7,
table 4.8.
4.3
The energy balance
The sun is the main source of energy sustaining life on earth. According to Skinner [317], [318] the sun sends around 17, 3 × 1016 W of power in form of shortwavelength solar radiation towards the earth. From this, approximately 30% is directly reflected by clouds and by the earth’s surface, but most rays pass through the
atmosphere, heating the layers of the earth and causing winds, rains, snowfalls and
ocean currents. These transformations lead to progressive depreciation of energy
quality, and therefore, to exergy losses. The devaluated energy in form of heat is
however sent back to space and the earth’s surface remains in thermal balance. One
part of solar radiation is used for photosynthesis and is temporarily stored in the bio-
Energy from the solid earth
Short wavelength
solar radiation
17,3x1016 W
107
Short wavelength
radiation
Long wavelength
radiation
Tidal energy
27,3x1012
Direct reflection
Tides, tidal energy, currents, etc.
5,2x1016 W
2,7x1012 W
Direct conversion to heat
8,1x1016 W
Winds, ocean currents, waves, etc.
Conduction 21x1012 W
0,035x1016 W
Evaporation and precipitation
4x1016 W
Photosynthesis
0,004x1016 W
Plant
storage
bank
Water
storage
bank
Submarine volcanism
11x1012 W
Volcanoes, hot springs on land
0,3x1012 W
Decay
Organic matter
Earth’s thermal energy
32,3x1012 W
Common
sedimentary rocks
1026 J
Recoverable
fossil fuels
2,5x1023 J
Thermal energy
1,3x1027J to 10
km depth
GEOTHERMAL ENERGY
Spontaneous
nuclear decay
Uranium and
Thorium withing 1
km of surface
5x1029 J
Figure 4.1. Energy flow sheet for the surface of the earth [317]
sphere as organic matter and eventually as coal, oil and natural gas. Another small
fraction of the solar-derived energy is stored in water reservoirs such as lakes and
rivers. But the sun is not the solely source of energy on earth, geothermal energy is
the second most powerful source of energy, at 23 TW or 0,013 % of the total. This
energy reaches the surface in the form of volcanoes, hot springs or conduction and
plays an important role in the rock cycle. The third and smallest source of energy
on earth is the tidal energy produced by the interaction of gravitational potential
energy of the moon and the earth’s rotation. The transfer of tidal energy accounts
for about 3 TW or 0,002 % of the total energy budget. Figure 4.1 shows the energy
cycle on earth according to Skinner [317], which was adapted in part from Hubbert
[147].
4.4
Energy from the solid earth
Two different sources of energy come from the solid earth. The first one is geothermal energy, which is considered as a renewable resource, but it has found less applicability on a global scale. The second one is the non-renewable nuclear energy,
coming from the mining of radioactive minerals found on earth, mainly from uranium isotopes. The latter, although socially and politically controversial constitutes
108
THE
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nowadays a key source of energy for many countries. Next, both sources of energy
will be explained in detail.
4.4.1
The Geothermal energy
The temperature of the earth’s interior increases with depth. The geothermal gradient varies in different parts of the world from 15 to 75o C/km. The geothermal
gradient creates obviously a heat flow leading to a heat loss escaping the crust. The
amount of heat that escapes through the earth’s surface is due to the superposition
of four components [168]:
Q = QC + Q L + QB + QT
(4.1)
where Q B is the heat input at the base of the lithosphere1 due to mantle convection,
Q T is a long-term transient due to cooling after a major tectonic or magmatic perturbation, Q L is the radiogenic heat production in the mantle part of the lithosphere,
and Q C is the radiogenic heat production of the crust.
The radiogenic heat production is due to the decay of the radioactive elements
238
U, 235 U, 232 U and 40 K either in the crust or in the upper mantle. For geological provinces older than ∼100 million years, Q L , Q B and Q T are lumped together
into a single parameter called mantle heat flow Q M . There are different ways to
estimate the bulk crustal heat flow of the earth. Some estimates [251], [7], [104]
are obtained by redistributing the heat producing elements in the bulk silicate earth
between the continental crust and various reservoirs in the mantle. They require
assumptions regarding the structure of the convecting mantle, the composition and
the homogeneity of the reservoirs. Other estimates are based on measurements either from representative rock types and their proportions in crustal columns derived
from geophysical profiles [129], [60], [404], [32] or on large-scale production data
sets [81], [307] [106].
Jaupart [168] suggested to estimate the bulk crustal heat production directly from
the heat flow data and local studies of crustal structure and estimating the mantle
heat flow Q M with different ways. He obtained the values of heat production for
three age groups: Archean, Proterozoic, and Phanerozoic (see table 4.2). The average of heat production was estimated to be between 0,79 and 0,95 µW m−3 and the
crustal heat flow component ranges from 32 to 38 mW m−2 , considering an average
crustal thickness of 40 km. According to these numbers, the continental crust contributes to 5,8 to 6,9 TW to the total energy budget of the earth2 . Active provinces
and continental margins now represent 30% of the total volume of the crust; 50%
error on their heat production would lead to a 15% error in the global budget. These
1
The lithosphere is the rigid strong outer layer of the earth, consisting of the crust and upper
mantle, approximately 100 km thick.
2
For a total volume of the continental crust of 7,3×1018 m3 .
Energy from the solid earth
109
Table 4.2. Estimates of bulk continental crust heat production from heat flow data
[168].
Age group
Archean
Proterozoic
Phanerozoic
Total continents
Range of heat production µW m−3
0,56-0,73
0,73-0,90
0,95-1,10
0,79-0,95
Range of crustal heat
flow, mW m−2
23-30
30-37
37-43
32-38
Fraction of total continental surface, %
9
56
35
numbers differ from the values given by Skinner [317], in which the the flow is estimated to be 63 mW m−2 or 32,3 TW across the entire earth’s surface (not only the
crust). It seems though that the numbers given by Jaupart are more updated and in
consonance with the order of magnitude of the geothermal studies mentioned before. Extrapolating Jaupart’s values to the entire surface of the earth, would lead to
an average geothermal energy contribution3 of 17,9 TW.
Geothermal energy constitutes a renewable source of energy. However, its reserves
represent only a tiny fraction of all geothermal heat. Besides, like tidal energy,
geothermal energy can be important locally but will be minor on a global scale. According to the Renewables Global Status Report [208], the 2005 worldwide geothermal capacity was 28 GWth for direct thermal use and 9,3 GW for electricity production. The Geothermal Energy Association [109] reports that geothermal resources
using today’s technology have the potential to support between 35.448 and 72.392
MW of electrical generation capacity. Using enhanced technology currently under
development (permeability enhancement, drilling improvements), the geothermal
resources could support between 65.576 and 138.131 MW of electrical generation
capacity. Assuming a 90% availability factor, which is well within the range experienced by geothermal power plants, this electric capacity could produce as much as
1, 09 × 109 MWh of electricity annually (124 GW) (Table 4.8). Nevertheless, these
values need to be taken with precaution, until the USGS submits its geothermal
energy report updating these numbers.
4.4.2
Nuclear energy
Nuclear energy derives from the huge binding force of the nucleus of elements. Theoretically, there are two kinds of processes that can release nuclear energy: fusion
and fission.
Fusion consists in binding light elements, such as hydrogen and lithium, and thereby
forming heavier elements. This is the process that goes on in the sun. Fusion has not
yet been achieved in the laboratory under conditions such that the energy produced
3
For a total surface of the earth of 5,12×1014 m2
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THE
RESOURCES OF THE EARTH
exceeds the energy used. Nevertheless, many scientists believe that it might be the
solution of future energy supply. Hermann [138] estimated the exergy reservoir
for the fusion cycle between deuterium (coming from the ocean) and tritium (bred
from an isotope of lithium) as around 74 Ttoe. Furthermore, if deuterium, the
isotope of 1 in every 5000 hydrogen atoms, is fused with another deuterium nucleus
at higher temperatures, the resulting resource contained in the ocean is on the order
of magnitude of 10 million YJ.
Fission nuclear energy is produced during controlled transformation of suitable radioactive isotopes, when neutrons are fired into the nucleus, making the atoms
unstable and subject to spontaneous disintegration. Uranium is the crucial fission
energy raw material due to the fact that as mined it contains 0,71% of 235 U (the
only naturally occurring fissionable atom). Thorium, beryllium, lithium and zirconium are other low-demand raw materials with potential or specific uses in nuclear
power production [71]. When 235 U undergoes fission, it releases heat and forms
new elements and ejects some neutrons from its nucleus. These neutrons are then
used to induce more 235 U to fission. According to Skinner [317], once separated
235
U from 238 U (an energy intensive process), the disintegration of a single atom releases 3, 2×10−11 J; because one gram of 235 U contains 2, 56×1021 atoms, fission of
a gram of uranium produces 8, 19 × 1010 J (equivalent to the energy released when
2,7 metric tons of coal are burned). Eq. 4.2 shows a representative fission process
of 235 U.
1
235
0 n +92
95
−11
U →137
J
37 Cs +37 Rb + 3n + 3, 2 × 10
(4.2)
Estimated uranium resources in the continental crust amounted in year 1986 to
3.457 kton [317] (see table 4.3), representing an exergy reservoir of 2, 8×1014 GJ or
6.741 Gtoe. More recent estimations of uranium sources indicate that these amount
to about 13 Mt according to Grubler [128] and 14,8 Mt according to the OECD
[247], which represent an exergy reservoir of around 23.800 and 27.100 Gtoe, respectively. With current state of technology, which makes use of only 0,7% of the
natural fuel in a “once-through” fuel cycle, the reserves would last only a few hundred years (174 Gtoe). With fast spectrum reactors operated in a “closed” fuel cycle
by reprocessing the spent fuel and extracting the un-utilized uranium and plutonium produced, the reserves of natural uranium may exceed 5.200 Gtoe (Table 4.8).
However, if advanced breeder reactors could be designed in the future to efficiently
utilize recycled or depleted uranium and all actinides, then the reserves of natural
uranium may be extended to several thousand years at current consumption levels
[249].
Additionally, Hermann [138], estimated the exergy reserves of thorium as around
7.500 Gtoe and of seawater uranium as around 8.350 Ttoe.
At the end of year of 2006, 6% of the world’s primary energy consumption was
derived from nuclear power plants (see figure 4.4), and amounted to 635,5 Mtoe. In
Tidal energy
111
Table 4.3. Estimated uranium resources in ores rich enough to be mined for use
in 235 U power plants [317], together with estimated rates of production for 2005
according to the BGS [139]. Data reported as ktons of metal content. No distinctions
are drawn between reserves and resources, and no data for resources are reported
by the former URSS countries.
Country
Australia
USA
Rep. Of South Africa
Canada
Niger
Namibia
France
Other
Total
Reasonably assured
resources, kton
1357
758
332
199
136
113
47
516
3457
Production
2005, kton
9,516
1,034
0,674
11,627
3,093
3,08
12,876
42
rate
in
France, more than half of all the electrical power comes from nuclear plants and in
other European countries and Japan, the fraction is high too. Nuclear power capacity
forecasts out to 2030 vary between 279 - 740 GWe when proposed new plants and
the decommissioning of old plants are both considered [163]. Nuclear energy has
the advantage against fossil fuels that it does not emit greenhouse gases and its
reserves are greater (see table 4.3). Some renowned scientists such as Lovelock
[200] claim that: “there is no alternative but nuclear fission energy until fusion
energy and sensible forms of renewable energy arrive as a truly long-term provider”.
However, other problems are associated with nuclear energy. The isotopes used in
power plants are the same used in atomic weapons, so a political problem exists. The
possibility of a power plant failing in some unexpected way creates a safety problem
as it happened in the Chernobyl disaster in 1986. Finally, the problem of safe burial
of dangerous radioactive waste matter must be faced, since some of the waste matter
will retain dangerous levels of radioactivity for thousand years.
4.5
Tidal energy
Tidal energy is the smallest source of energy on earth. Tides result from the gravitational attraction exerted upon the earth by the moon and to a lesser extent by the
sun [346]. As the earth spins on its axis, the bulges move and produce two high
and two low tides everywhere each day. Tidal heights are not uniform everywhere.
They rarely exceed a meter in the deep ocean, but over continental shelves, they may
reach 20 meters. Movement of such vast masses of water requires a great deal of
exergy, which is estimated to be 2,7 TW. Through a year, this amounts to 0, 85× 1020
J, according to Skinner [317].
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THE
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Tidal electricity generation involves the construction of a barrage across a delta, estuaries, beaches, or other places that are affected by the tides. Like in a hydraulic
power plant, normal turbines will produce electricity as the water flows out. However, tidal stations differ from hydraulic ones in the two-dimensional flow. They
are able to produce electricity when both water enters the basin and when it leaves
[54]. Tidal energy provides a non-polluting and inexhaustible supply of energy and
assures the regularity of power production from year to year with less than 5% annual variation. The specific tidal exergy is about 10 kJ for each m2 of reservoir and
each meter of height difference, according to Hermann [138]. The high capital cost
for construction and the limited number of potential sites (about 20) are its main
drawbacks. Tidal heights of 5 meters or more and easily dammed bays or estuaries
are needed in order for tidal plants to operate effectively. To date, relatively few
tidal power plants have been constructed. Of these, the oldest and by far the largest
is the La Rance 240 megawatt barrage located near St. Malo, in Brittany, Northern France. The worldwide tidal power production is about 300 MW [208]. Tidal
projects worldwide have been estimated to have a potential energy output of around
166 GW, according to the World Energy Council.
4.6
Energy from the sun
According to Skinner [317], solar radiation is the largest energy input of the earth,
accounting for about 99,985 % of the total. From the 173.000 TW of incoming solar
radiation, about 30% is directly reflected unchanged, back into space, by the clouds,
sea, continents, and ice and snow. Around 350 TW are used for causing winds,
ocean currents, waves, etc. Evaporation and precipitation use approximately 4.000
TW of sun’s energy, which will lead to the storage of water and ice. Only 40 TW
are effectively used in the process of photosynthesis, leading to the production of
biomass and eventually of fossil fuels.
4.6.1
Solar power
The exergy flow of solar radiation heating the land and oceans amounts to 43.200
TW (Szargut [337]), that is about three thousand times more than the present power
needs of the whole world: 14 TW in 2006 and 17 TW in 2010. Energy supplied by
the sun in one minute is enough to meet the global power need for one year (Khan
[184]). Unfortunately, technology is not developed enough to make use of this huge
amount of energy provided directly by the sun.
Solar power density at the earth’s surface is 125-375 W/m2 and an average photovoltaic panel, with 15% efficiency, may deliver 15-60 W/m2 . But solar cell conversion efficiency has increased from 6% in 1954 to 40% in 2006 and thus the size
of solar power stations has exponentially increased form 500 kW in 1977 to more
than 3 GW in 2005 [208]. Electricity generated directly by utilizing solar photons to
Energy from the sun
113
create free electrons in a PV cell is estimated to have a technical potential of at least
450.000 TWh/year or around 51 TW [170], [297] (Table 4.8).
In addition to the direct use of solar radiation through photovoltaic panels, solar
heating collectors use the sun’s energy to heat water. Solar thermal power capacity
was 88 GWth in 2005 [208] and is expected to increase dramatically due to new
building regulations, especially in Europe4 .
Additionally, promising experiences with concentrating solar thermal power plants
(CSP) show that this technology could be an alternative way of producing clean
electricity from the sun. In CSPs, the solar flux is concentrated by parabolic troughshaped mirror reflectors (30 - 100 suns concentration), central tower receivers requiring numerous heliostats (500 - 1000 suns), or parabolic dish-shaped reflectors
(1000 - 10.000 suns) to heat a working fluid, which in turn transfers the heat to a
thermal power conversion system. According to Philibert [261], 1 km2 of land sited
at lower latitudes in areas receiving high levels of direct insolation, such as desserts
is enough to generate around 125 GWh/year from a 50 MW plant at 10% conversion
of solar energy to electricity. Thus about 1% of the world’s desert areas (240.000
km2 ), if linked to demand centers by high voltage DC cables, could in theory be
sufficient to meet total global electricity demand as forecast out to 2030. Installed
capacity is 354 MWe from nine plants in California. New projects totalling over 1400
MW are being constructed in different parts of the world [208]. Technical potential
estimates for global CSP vary widely from 630 GWe installed by 2040 [10] to 4700
GWe by 2030 [149] (Table 4.8).
4.6.2
Water power
About 23% of the incoming solar radiation (around 40 PW) is the driving force of the
hydrologic cycle, which is a conceptual model that describes the storage and movement of water between the biosphere, atmosphere, lithosphere and the hydrosphere
(see figure 4.2). About 320.000 km3 of water are evaporated each year form the
oceans, while evaporation from the land (including lakes and streams) contributes
to 60.000 km3 of water. Of this total, about 284.000 km3 fall back to the ocean
and the remaining 96.000 km3 fall on the earth’s land surface. Since 60.000 km3
of water evaporate from the land, 36.000 km3 of water remain to erode the land
during the journey back to the oceans [346].
According to Szargut [337], the exergy flow used for the evaporation of water is
around 38.100 TW. This exergy is transformed into the potential exergy of clouds
(300 TW) and only a small part (5 TW) is transformed into the potential exergy of
rivers. Additionally, he calculated the chemical exergy of fresh water reaching the
land with the rain and snow as about 6 TW. Hence, the total water power is 11 TW,
if the potential and chemical exergy components are summed (Table 4.8). Valero et
4
See the Directive 2002/91/EC on the energy performance of buildings.
114
THE
RESOURCES OF THE EARTH
al. [371] calculated the exergy replacement costs of renewable water resources and
world’s ice sheets5 considering their chemical and potential components as between
3.592 and 53.304 Mtoe/year for freshwater and 3, 84 × 108 and 7.210 × 109 Mtoe
for ice sheets.
Humans use only part of the renewable exergy of water. That is the potential exergy
of rivers in form of hydropower. The chemical and thermal exergy of the freshwater
in rivers or ice sheets cannot be transformed into useful energy yet, at least with the
current state of technology.
Hydropower is the most highly developed renewable energy resource. The power
present in water that runs off continents was calculated in 1962 as 2,9 TW [317].
The International Water Power & Dam Construction (IWP&DC) classified and calculated more recently the world hydroelectric potentials according to the following
criteria [166]:
• Gross Hydroelectric Potential: the hydroelectric potential of a country if all
its water flows were turbined until sea level or to the country borders (if the
flow continues into other countries) under 100% system efficiency. It has been
estimated as 4.200 GW.
• Technically Useful Hydroelectric Potential: the hydroelectric energy obtained
from all the exploitable or exploited places under existing technological limits,
without taking into account environmental, economic or other restrictions. It
has been estimated as 1.800 GW (Table 4.8).
• Economically Exploitable Hydroelectric Potential: part of technically feasible
potential that can be or that has been developed under the local economic
conditions and in a competitive way with other energy supply sources. Some
of the places that can be exploited economically can have restrictions from
the environmental point of view. Nonetheless, this limitation is not taken into
account when determining this potential. It has been estimated as around
1.200 GW.
At the end of 2006, worldwide hydropower consumption was 688,1 Mtoe, accounting for about 6% of the total energy consumption [35].
4.6.3
Wind power
According to Skinner [317], around 350 TW of solar energy is used for driving winds
and ocean waves. Wind is horizontal air movement arising from differences in air
pressure created by the uneven heating of the atmosphere. It always flows from a
5
Exergy replacement costs are defined as the energy required by the best available technologies to
return a resource to the same conditions as it was delivered by the ecosystem(s).
Energy from the sun
115
Figure 4.2. The hydrologic cycle. Source: http://www.ec.gc.ca/water (Environment
Canada)
place of high pressure to one of low pressure. Wind’s speed and direction are also
affected by the Coriolis effect6 and friction occurring between wind and solid objects
of any kind such as the ground, trees, etc. Most places around the world have wind
speeds that average between 10 and 30 km/h [318]. The average global wind speed
at 50 m is 6,6 m/s (23,7 km/h) [240] and with an exergy content of about 336
W /m2 perpendicular to the wind direction, according to Hermann [138].
Estimates of the total global wind power are very large (on the order of 1015 W) but
much of the power is in high altitude winds and is not recoverable by devices on the
land surface [317]. Global wind power generated at locations with mean annual
wind speeds ≥ 6,9 m/s at 80 m is found to be ∼ 72 TW [9]. A technical potential
of 72 TW installed global capacity at 20% average capacity factor would generate
126.000 TWh/yr or around 14,5 TW (Table 4.8). In 2005, the existing exergy power
capacity worldwide was 59 GW [208].
4.6.4
Ocean power
The sun is responsible for three effects occurring in the oceans: an ocean thermal
gradient, from which thermal energy could be eventually extracted; the thermohaline circulation, which is in part caused by the thermal gradient and causing vast
6
The Coriolis effect is the deviation from a straight line in the path of a moving body due to the
earth’s rotation.
116
THE
RESOURCES OF THE EARTH
volumes of water to move around the globe; and ocean waves, indirectly generated
by the sun through blowing of winds.
4.6.4.1
Ocean thermal gradient
The sun heats the surface of the ocean, generating a thermal gradient that varies
from around 22◦ C to 2◦ C in the deep ocean. This temperature difference gives
a specific exergy of about 800 J/kg seawater [138]. Considering the mass of the
oceans equal to 1, 37 × 1023 kg, this gives an absolute exergy of 1, 13 × 108 Gtoe
(Table 4.8). Theoretically, this thermal gradient could be used for drawing energy
from the oceans. However, the small temperature difference involved makes ocean
thermal power to be unpracticable with current technology and no commercial plant
exists. However, if this source of energy would be used with an efficiency of less than
1%, the ocean’s thermal energy potential would exceed the potential of fossil fuels
[317].
Another consequence of the thermal gradient of oceans is the so called thermohaline
circulation (THC) or “the great ocean conveyor belt” [40]. This global ocean circulation is driven by density differences, which depend on temperature and salinity. The
salinity and temperature differences arise from heating/cooling at the sea surface
and from the surface freshwater fluxes (evaporation and sea ice formation enhance
salinity; precipitation, runoff and ice-melt decrease salinity). It transports enormous
volumes of cold, salty water from the North Atlantic to the Northern Pacific, and
brings warmer, fresher water in return.
In the North Atlantic warm and salty water that has been transported north from
tropical regions is cooled, forming frozen water without salts, and thereby, increasing the salinity of the remaining, unfrozen water. The dense, saline waters drop to
the floor of the ocean. This water begins a great circuit through the world’s oceans
(see the path of this circuit in fig. 4.3). In the Pacific, the current mixes with warmer
water, where it undergoes upwelling and warming once again. When this warmer,
saltier water reaches again the high northern latitudes, it chills, and eventually becomes North Atlantic deep water, completing the circuit.
The volume transport of the overturning circulation at 24 N has been estimated
from hydrographic section data as around 17 × 1016 m3 /s [286], its heat transport
as 1.200 TW. The heat transport was estimated as well by Munk et al. [235] as
2.000 TW. The corresponding exergy flow assuming a difference of 20 K is about
100 TW transferred to the thermal gradient [138]. Unfortunately, there is currently
no energy-conversion technology of this nature.
The climatic effect of the THC is still to some extent under discussion, and is due to
the heat transport of this circulation [274]. This amount of heat transported into the
northern North Atlantic (north of 24 N) should warm this region by around 5o C (the
difference sea surface temperature in the North Atlantic as compared to the North
Pacific at similar latitudes). Global surface air temperatures show that over the three
Energy from the sun
117
Figure 4.3. A simplified summary of the path of the Thermohaline Ocean Circulation
[274]
main deep water formation regions of the world ocean, air temperatures are warmer
by up to around 10o C compared to the latitudinal mean.
The concerns about the possible collapse of the THC through the anthropogenic
greenhouse effect have increased recently. When the strength of the haline forcing increases due to excess precipitation, runoff, or ice melt, the conveyor belt will
weaken or even shut down. The variability in the strength of the conveyor belt will
lead to climate change in Europe (decreasing the temperatures down to 9o C) and it
could also influence other areas of the global ocean.
4.6.4.2
Ocean Waves
Waves are another expression of solar energy. They are formed from winds blowing
over the ocean, and their energy content is many thousands of times greater than
that in tides. The momentum to currents and surface gravity waves transferred by
the wind is estimated as 60 TW [396], but the wave breaking and internal friction
reduces the wave exergy flow to 3 TW breaking on the world’s coast [138]. For
example, a single wave that is 1,8 meters high and moving in water 9 meters deep
generates around 10 kW for each meter of wave front [317]. Different wave energy
conversion schemes have been developed, but none are currently in large-scale use.
The only two commercial wave power projects total 750 kW [163].
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THE
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Table 4.4. Specific exergy on a dry basis of representative biomass samples [138]
Biomass type
Eucalyptus
Poplar
Corn stover
Bagasse
Water hyacinth
Brown kelp
Exergy
MJ/kg
19,9
19,2
18,2
17,8
15,2
10,9
(dry),
The best wave energy climates have deep water power densities of 60-70 kW/m but
fall to about 20 kW/m at the foreshore. Around 2% of the world’s 800.000 km of
coastline exceeds 30kW/m giving a technical potential of around 500 GW assuming
off-shore wave energy devices have 40% efficiency [163].
4.6.5
Biomass
Plants depend on sunlight of photosynthesis and hence biomass is another expression of solar power. The radiation flow absorbed by the vegetation has an energy of
about 40 TW according to Skinner [317] and an exergy about 37 TW, according to
Szargut [337].
Biomass is a term used for plant and animal derived material and includes wood,
energy crops, crop residues and animal dung. It consists mostly of cellulose, lignin,
protein and ash. Specific exergy of biomass ranges form 15 to 20 MJ/kg on a dry
basis depending on carbon and ash content. Woody biomass tends to have a higher
carbon content, as opposed to marine biomass [138] (see table 4.4).
The photosynthetic efficiency of converting solar energy into energy-rich organic
compounds averages around 1%. And only 2,5 TW of energy and 2,9 TW of exergy is
transformed into the chemical exergy of plants [337]. Estimates of the dry weight of
all living plant matter on earth’s land surface vary but average about 2×1012 metric
tons [317]. Considering a specific exergy of biomass of 17 MJ/kg, the exergy content
of dry biomass on earth is around 810 Gtoe7 The theoretical biomass potential was
estimated by Johansson [170] as around 92 TW, what implies an available exergy
capacity of 70 Gtoe each year (Table 4.8).
Humans own about 16 TW of the land productivity. From these, about 5 TW contributes to the consumption of 1,5 TW in the form of wood fuel and around 0,2 TW
goes into the production of 20 GW of ethanol [138]. The world biomass production
energy potential vary greatly depending on the assumptions taken into account. Fulton and Howes [98] compiled the different estimates of world biomass production.
7
This number represents the total exergy we could extract from biomass, if it were not renewable.
Energy from the sun
119
The IPCC [161] estimates a raw biomass energy potential of 10,4 Gtoe/year (14
TW) and a liquid biofuels energy potential of 3,6 Gtoe/year (4,8 TW), while Moreira [229] 31,2 Gtoe/year (41,5 TW) and 10,8 Gtoe/year (14,4 TW), respectively
(Table 4.8).
4.6.6
Fossil fuels
Fossil fuels represent the remains of plants or animals that gathered their energy
from the sun millions of years ago and constitute reservoirs of chemical exergy.
Around 40 GW of biological matter are buried under sediments and will eventually
form fossil fuels [26]. Like the other minerals, they are nonrenewable resources,
since they cannot be replenished at least in our lifetime. The main commercial types
of fossil fuels are coal, oil and natural gas. Other unconventional fossil fuels include
tight gas sands, coal bed methane, clathrate hydrates, shale and heavy oil and tar
sands, but no commercial way of extraction has been discovered yet.
The specific exergies of fossil fuels vary with the carbon content and the percentage
of inert components. Different authors such as Shieh and Fan [310] or Stepanov
[330] have derived expressions for the exergy estimation of fuels. In many cases,
especially for substances containing mainly C, H, O and N , the High Heating Value
(HHV) is essentially identical to the specific exergy.
Fossil fuels are by far the most important sources of energy nowadays, accounting for
87,8% of world energy consumption. Production of fossil fuels reached at the end of
2006 over 9.500 Mtoe [35]. The remaining 12% is distributed at almost equal rates
into nuclear and hydroelectrical power. See figure 4.4 for the world distribution of
energy consumption.
4.6.6.1
Coal
Coal is a sedimentary and metamorphic rock. It is formed from plants that grew in
ancient swamps. The remains of the plants accumulated in a nonoxidizing environment and were eventually buried by other sediments, usually sand or mud, which are
now the sandstone and shale typically associated with coal beds. The coal deposits
start off as organic materials made chiefly of carbon, oxygen and hydrogen. With
rising the temperature and pressure, due to the burial of the deposits, the hydrogen
and oxygen are gradually lost [195].
In addition to carbon, oxygen and hydrogen, coal contains many other elements in
small amounts. Sulfur is one of its most common impurities, making coal a dangerous pollutant of air and water. Table 4.5 shows the ASTM D388 coal-rank classification according to the high heating value (HHV). Coal’s specific exergy varies from
about 20 to 30 MJ/kg [138], although some low-carbon coals such as lignites may
have specific exergies as low as 15 MJ/kg.
120
THE
Coal; 3090,1;
28%
Oil; 3889,8; 36%
RESOURCES OF THE EARTH
Nuclear Energy;
688,1; 6%
Natural Gas;
2574,9; 24%
Hydroelectric;
688,1; 6%
Figure 4.4. Primary world energy consumption by fuel type at the end of 2006.
Values in Mtoe [35].
Coal accounts for about 28% of the energy consumption in the world. World proved8
reserves of coal at the end of 2006 were estimated by British Petroleum [35] to
be 909.064 millions of tons (see figure 4.5) and by the WEC [401], 847.488 Mt.
Considering an average heating value of 25 MJ/kg, the world’s coal proven reserves
are about 523 Gtoe, taking the average reserves given by BP and the WEC. The exact
exergy of the coal reserves will be calculated later in chapter 6.
The WEC [401] estimates additional resources amount in place as around 1770
Mtons or 1100 Gtoe. From these, additional recoverable reserves are estimated at
180 Mtons or 110 Gtoe.
Unlike oil or natural gas, coal is more evenly distributed worldwide and consumption
and production rates are rather equilibrated (see figure 4.6). At the end of 2006,
world coal consumption was 3.090,1 Mtoe [35]. The demand for coal is expected
to more than double by 2030 and the IEA has estimated that more than 4.500 GW
of new power plants (half in developing countries) will be required in this period
[150].
8
Proved reserves of coal - Generally taken to be those quantities that geological and engineering
information indicates with reasonable certainty can be recovered in the future from known deposits
under existing economic and operating conditions.
Energy from the sun
121
Table 4.5. Rank of coal according to the norm ASTM D388.
Class rank
Anthracite
Anthracite
Meta-anthracite
Semianthracite
Bituminous
Low-volatile
Medium volatile
High-volatile A
High-volatile B
High-volatile C
Subbituminous
Subbituminous A
Subbituminous B
Subbituminous C
Lignite
Lignite A
Lignite B
Fix carbon limits
≥
<
Volatile limits
≥
<
98
92
86
98
92
2
8
2
8
14
78
69
-
86
78
69
14
22
31
22
31
-
HHV Limits, MJ/kg
≥
<
32,56
30,24
26,75
32,56
30,24
24,42
22,1
19,31
26,75
24,42
22,1
14,65
19,31
14,65
Another young form of coal, peat, (partially decayed plant matter together with minerals) has been used as a fuel for thousands of years and is still in use, particularly
in Northern Europe. The reserves of peat have not been estimated but are very large.
4.6.6.2
Oil and natural gas
Oil and natural gas have proved to be economical, efficient and relative clean fuels.
As a result, by 1950, they had overtaken coal as the primary source of energy.
Almost without exception, petroleum and natural gas are associated with sedimentary rocks of marine origin. Both are mixtures of hydrocarbon compounds (composed largely of hydrogen and carbon) with minor amounts of sulphur, nitrogen and
oxygen. Hydrocarbon production takes place in two stages [195]. First, biological, chemical and physical processes begin to break down the organic matter into
what is called kerogen, a precursor of oil and gas. The second stage is marked by
the thermal alteration of kerogen to hydrocarbons as the deposit is buried deeper
by younger, overlying sediments. The production of hydrocarbons begins at a temperature of about 50 to 60o C and a depth of 2 to 2,5 km. Hydrocarbon formation
continues to depths of 6 to 7 km and temperatures of 200 to 250o C. Formation of oil
dominates in the lower range of temperature and burial and gas in the higher range.
The British standard BS2869:1998 classifies fuel oil into six classes according to its
boiling temperature, composition and purpose. No. 1 and No. 2 are referred to as
distillate fuel oils, while No. 4, No. 5 and No. 6 are labelled residual fuel oils. In
122
THE
RESOURCES OF THE EARTH
Figure 4.5. Coal proved reserves at the end 2006. Values in thousand millions tonnes
(share of anthracite and bituminous coal in brackets) [35].
Table 4.6. Rank of oil according to the British standard BS2869:1998
Class rank
Density (kg/l)
Residual carbon (%)
Sulphur (%)
Oxygen and Nitrogen (%)
Hydrogen (%)
Carbon (%)
Water and sediments (%)
Ashes (%)
HHV (kJ/kg)
No. 1
0,824
Traces
0,1
0,2
13,2
86,5
Traces
Traces
46.365
No. 2
0,864
Traces
0,4-0,7
0,2
12,7
86,4
Traces
Traces
45.509
No. 4
0,927
2,5
0,4-1,5
0,48
11,9
86,1
0,5 max.
0,02
43.920
No .5
0,952
5
2,0 max.
0,7
11,7
85,55
1,0 max.
0,05
43.353
No. 6
1
12
2,8 max.
0,92
10,5
85,7
2,0 max.
0,08
42.467
a more commercial sense: No. 1 fuel oil is kerosene; No. 2 is diesel oil and No. 4,
5 and 6 are heavy fuel oils. Table 4.6 shows the chemical composition, density and
high heating value of classes 1, 2, 4, 5 and 6. Low molecular weight petroleum has
an exergy content between 40 to 46 MJ/kg. Higher molecular weight petroleum and
the hydrocarbon portion of the inorganic mixtures have a chemical exergy close to
40 MJ/kg [138].
Natural gas consists primarily of methane but including significant quantities of
ethane, butane, propane, carbon dioxide, nitrogen, helium and hydrogen sulfide.
Energy from the sun
123
2000
Mtoe
1500
1000
500
0
Total North
America
Total S. &
Cent.
America
Total Europe Total Middle Total Africa
& Eurasia
East
Coal: Production
Total Asia
Pacific
Coal: Consumption
Figure 4.6. Coal production and consumption at the end of 2006. Elaborated from
data included in [35].
Table 4.7. Physical properties of different compositions of natural gas [34]
CO2
5,5
3,51
26,2
0,17
0,2
-
N2
32
0,7
87,7
0,6
0,6
0,5
H2 S
7
0,5
-
Composition
C H4 C2 H6
77,7
5,5
52,5
3,7
59,2
13,9
10,5
1,6
99,2
79,4
21,8
C3 H8
2,4
2,2
20
77,7
C4 H10
1,18
2,02
-
C5 H12
0,63
3,44
-
Density
kg/N m3
0,9
1,06
1,08
1,14
0,72
1,41
1,77
HHV
kJ/N m3
kJ/kg
39.575
43.915
32.600
30.750
31.668
29.261
5.073
2.552
37.524
52.126
72.176
51.079
89.110
50.049
The main properties of natural gas are listed in table 4.7. The specific exergy of
natural gas is around 50 MJ/kg [138].
Oil accounts for 36% of world energy consumption, while natural gas for about 24%.
World proved reserves of oil and gas are much smaller than those of coal. At the end
of 2006, they were estimated as 1.208,2 thousand million barrels or 164,8 Gtons
and of gas 181,46 trillion of cubic meters or 163,4 Gtoe, considering the conversion
factor given in the BP report [35] (see figures 4.7 and 4.9).
124
THE
RESOURCES OF THE EARTH
In terms of exploration, the oil industry is relatively mature and the quantity of additional reserves that remain to be discovered is unclear. The general and rather
pessimistic believe concerning oil discoveries is that few new oil fields are being
discovered, and that most of the increases in reserves results from revisions of underestimated existing reserves (Ivanhoe and Leckie [165], Laherre [190], Campbell
[45] or Hatfield [133]). The optimistic views appeal to improvements in technology, such as 3D seismic surveys and extended reach (e.g. horizontal) drilling, that
have improved recovery rates from existing reservoirs and made profitable the development of fields previously regarded as uneconomic (Smith and Robinson [324]).
Masters et al. [211] reflect the current state of knowledge as to the uncertainties in
future potentials for conventional oil resources. These estimates assess in addition
to the conventional oil reserves a corresponding range of additionally recoverable
resources between 38 and 141 Gtoe.
Estimates of gas reserves and resources are being revised continuously. The International Gas Union (IGU) estimates that additional reserves, including gas yet to be
discovered could be as high as 200 Gtoe [156]. Gregory and Rogner [123] suggest
an optimistic estimate for ultimately recoverable reserves of additional 500 Gtoe .
World major oil suppliers are by far middle-east countries. Except of them, south
and central America and Africa, the rest of the world is a net importer of oil, even if
some countries like north America produce considerable amounts of the resource as
well (see figure 4.8). Oil world consumption at the end of 2006 was 3889,8 Mtons
[35].
Major natural gas consumers in the world are Asian-Pacific countries, and most part
of it has to be imported. The largest producers in the world are the Russian federation, followed by north America, Iran, Norway and Algeria (see figure 4.10). Natural
gas world consumption at the end of 2006 was 2574,9 Mtoe [35].
4.6.6.3
Unconventional fossil fuels
Besides of the fossil fuels mentioned before, there is a great quantity and variety of
unconventional fossil fuel resources, not on a large-scale commercially recoverable.
Oil that requires extra processing such as from shales, heavy oils, and oil (tar) sands,
is classified as unconventional. Together contributed around 3% of world oil production in 2005 (66 Mtoe) and could reach 110 Mtoe by 2020 [230] and up to 140 Mtoe
by 2030 [151]. Resource estimates are uncertain but could have a potential of over
830 Gtoe [163].
Methane stored in a variety of geologically complex, unconventional reservoirs, such
as tight gas sands, fractured shales, coal beds and hydrates, is even more abundant
than conventional gas. Worldwide coal bed methane may be larger than 190,5 Gtoe
but a scarcity of basic information on the gas content of coal resources makes this
number highly speculative [163]. A similar quantity is estimated to be in the form of
Energy from the sun
125
Figure 4.7. Oil proved reserves at the end 2006. Values in thousand millions of
barrels [35].
1400
Mtoe
1200
1000
800
600
400
200
0
Total North
America
Total S. &
Cent.
America
Total Europe Total Middle Total Africa
& Eurasia
East
Oil: Production
Total Asia
Pacific
Oil: Consumption
Figure 4.8. Oil production and consumption at the end of 2006. Elaborated from
data included in [35].
126
THE
RESOURCES OF THE EARTH
Figure 4.9. Natural gas proved reserves at the end 2006. Values in trillion cubic
meters [35].
2000
Mtoe
1500
1000
500
0
Total North
America
Total S. &
Cent.
America
Total Europe Total Middle Total Africa
& Eurasia
East
Natural Gas: Production
Total Asia
Pacific
Natural Gas: Consumption
Figure 4.10. Natural gas production and consumption at the end of 2006. Elaborated from data included in [35].
Summary of the results of energy resources
127
tight sands. Methane clathrate is a solid form of water that contains a large amount
of methane within its crystal structure. It is usually found in vast quantities under
sediments on the ocean floor. According to the IPCC [160], technologies to recover
these resources economically could be developed in the future, if demand for natural
gas continues to grow in the longer run, in which case gas resource availability would
increase enormously. The reserves are estimated by the USGS [360] to be greater
than 1.400 Gtoe.
The great drawback of these kinds of unconventional fuels is the elevated quantity of
energy required for their extraction. The refinement of oil shale for instance, needs
two or three times more energy than the production of conventional fuel oil. Furthermore, the associated environmental footprint is huge, since usually vast forest
areas need to be destroyed and the important amount of water used and emissions
produced threatens the biodiversity of the surroundings.
4.7
Summary of the results of energy resources
Table 4.8 summarizes the results discussed in the previous sections. It shows the
available energy, potential energy use and current energy consumption of most important energy resources on earth. With potential energy, we mean probable energy
capacity using advanced technology, not necessarily developed nowadays. Consumption values are referred to the end of 2006, except for geothermal, PV, wind, biomass
and tidal energy, which are 2005 values.
It must be pointed out that the data must be still considered as an approximation
and in any case, it might increase, as technology allows to make a more efficient use
of the resources and to exploit non currently recoverable fuels.
The detailed analysis of the results will be carried out in chapter 6, when all resources, including non-fuel minerals are assessed with the same unit of measure.
In the next section the remaining type of natural resources will be studied. Namely,
the non-fuel mineral resources.
4.8
Non-fuel mineral resources
In addition to energy resources, non-fuel minerals are the other kind of resources
essential for civilization. The quantity of minerals on earth is finite and hence they
are classified as non-renewable. The physical and chemical properties of minerals
are directly influenced by the two major energy sources of the earth: the sun and
the geothermal power. They are responsible for the movement of materials from the
earth’s interior, to the crust, from these to the sea or to rivers through currents and
from the sea to form rocks in the so called geochemical cycle. The resulting dynamic
equilibrium is called the geochemical balance [68].
128
THE
RESOURCES OF THE EARTH
Table 4.8. Available energy, potential energy use and current consumption of natural
resources on earth.
Resource
Available energy
Geothermal
17,9 TW
Potential energy
use
59 - 124 GWe
Uranium - fission
Thorium - fission
Deutorium + Tritium (fusion)
Tidal power
Solar PV
Solar thermal power
Water power
Wind power
Ocean thermal gradient
Ocean conveyor belt
Ocean waves
Biomass
Coal
Natural gas
Oil
Unconventional fuels
27.100 Gtoe
7.500 Gtoe
74 Ttoe
2,7 TW
43,2 PW
43,2 PW
11 TW
1000 TW
1, 4 × 108 Gtoe
1.200 - 2.000 TW
3 TW
92 TW
1615 Gtoe
365-665 Gtoe
200-300 Gton
∼ 2600 Gtoe
5.200 Gtoe
166 GW
51,4 TW
630 - 4700 GWe
1.800 GW
14,5 TW
500 GW
19 - 56 TW
523 Gtoe
163,4 Gtoe
164,8 Gton
-
Current
energy
consumption
9,3 GWe / 28
GWth
635,5 Mtoe
300 MW
3 GWe
354 MWe
688,1 Mtoe
59 GW
750 kW
1,7 TW
3090 Mtoe
2574,9 Mtoe
3889,8 Mton
66 Mtoe
In chapter 3 we obtained an estimation of the average mineralogical composition of
the crust. The figures given in table 3.3 show the relative abundance of the minerals
on earth. Of course minerals are not found in the same concentration everywhere
in the crust. Fortunately for mankind, nature provides us with areas accounting for
high-concentrated deposits, that allow us to extract them in a relatively cost-effective
way. Minerals become concentrated in five ways [318]:
1. Concentration by hot, aqueous solutions flowing through fractures and pore
spaces in crustal rock to form hydrothermal mineral deposits.
2. Concentration by magmatic processes within a body of igneous rock to form
magmatic mineral deposits.
3. Concentration by precipitation from lake water or seawater to form sedimentary mineral deposits.
4. Concentration by flowing surface water in streams or along the shore to form
placers.
5. Concentration by weathering processes to form residual mineral deposits.
Besides of the physical way of classifying mineral concentrations, there is an economical way of classifying them. This is explained in the following section.
Non-fuel mineral resources
4.8.1
129
The economic classification of minerals
Concentrations of minerals can be classified as resources, reserves and reserve base,
depending on the different factors explained next.
The US Bureau of Mines defines a resource as a concentration of naturally occurring
solid, liquid, or gaseous material in or on the earth’s crust in such form and amount
that economic extraction of a commodity from the concentration is currently or potentially feasible.
Reserve base is defined as that part of an identified resource9 that meets specified
minimum physical and chemical criteria related to current mining and production
practices, including those for grade, quality, thickness, and depth. And reserves are
that part of the reserve base which could be economically extracted or produced at
the time of determination. Reserve base and reserves are subdivided in order of increasing confidence into demonstrated and inferred. The latter are estimates based
on an assumed continuity beyond indicated resources, for which there is geologic
evidence. There may be no samples or measurements. Demonstrated reserves are
the sum of measured and indicated. If the quantity is computed from dimensions
revealed in outcrops, trenches, workings or drill holes; grade and or quality are computed from the results of detailed sampling; the sites of inspection are spaced closely
and the geologic character is so well defined that size, shape, depth and mineral
content of the resource are well established, then we talk about measured resources.
Indicated resources are those in which the grade and or quality are computed from
information similar to that used for measured resources, but the sites for inspection,
sampling, measurement are farther apart or are otherwise less adequately spaced.
It is clear then, that all the classifications listed above are related to economy, especially reserves. Figure 4.11 shows the mineral resources and reserves classification
after McKelvey [214]. Increasing geological information expands the amount of reserves. So do commodity prices and development of efficient technologies, as lower
grades become economically profitable.
Hence, neither reserve base, nor reserves are good indicators for assessing the earth’s
mineral capital. In fact, total world reserves of most mineral commodities are larger
now than at any time in the past [141] due to wider geological information, more
efficient technologies and price changes. The best approximation of numbers compiling the mineral capital would be using resources data. However, for being indeed the
most comprehensive classification, the information is often scarce, inaccurate and
incomplete as it can be seen in table 4.10. Estimates of resources are necessarily dynamic. For example, the realization that it was economic to mine copper porphyry
deposits for their ore in the early part of the 20th century increased the world’s
known copper reserves, and therefore resources, by several hundred per cent [121].
Too little is known about the earth’s crust, since exploration costs are extremely high.
9
Identified resources: resources whose location, grade, quality and quantity are known or estimated from specific geologic evidence.
130
THE
RESOURCES OF THE EARTH
Figure 4.11. A classification of mineral resources and reserves [141].
Most of the deposits worked at present are close to the surface but the earth’s crust
is on average 40 km thick and the deepest open-pit mine is less than 1 km deep,
while the deepest underground mine goes down to 3,5 km to the surface and few
exceed 2 km [29]. Thus only approximately the outer one-tenth of the continental
crust is of present interest [78]. Besides, there are many minerals and metals such
as bismuth, cesium, germanium, gallium, etc. that are just byproducts of other more
demanded metals such as gold, copper, zinc, lead, etc. No exploration efforts will be
undertaken for those specific minerals until demand significantly increases.
4.8.2
Mineral’s average ore grades
For some time, many geologists have assumed that the amount of less common
metals existing at different grades in the crust could be represented by lognormal
or similar unimodal frequency distributions. This assumption was questioned by
Skinner [316] for the metals that make up less than 0,1% of the earth’s crust. He
suggested that for these scarce metals the distribution might be bimodal and that
the small mode at higher grades would represent metal concentrations of nonsilicate
minerals localized in mineral deposits [73] (see fig. 4.12).
There are mathematical procedures that correlate the tonnage of the ore with its
mean grade. Much of the original work on this problem was carried out by Lasky
[193]. He argued that a linear relation is obtained if the logarithm of the tonnage
of ore with grades above a specified value is plotted against grade. Cargill et al.
[48] suggested that a linear relation was obtained if the logarithm of the tonnage
Non-fuel mineral resources
131
Tonnage
a. Unimodal
Grade
Tonnage
b. Bimodal
Grade
Figure 4.12. Two possible relationships between ore grade and the metal, mineral,
or energy content of the resource base [316].
was plotted against the logarithm of the grade. Later on, the fractal relationship,
exhibited by a variety of natural processes, was proved to be better applicable to
mineral deposits. Turcotte [358], showed that the tonnage of ore with a mean
grade was proportional to the mean grade raised to a power for mercury, copper
and uranium deposits in the US. This fractal relationship follows the expression of
Eq. 4.3.
x̄ m
xc
=
Mc
M
F
3
(4.3)
Where x̄ m is the average concentration in the deposit; x c the concentration in the
earth’s crust; M the tonnage of the deposit; Mc the tonnage of the piece of land
under consideration and F the fractal relationship to be determined.
These theoretical methodologies have mainly the objective to determine the tonnage
of ore with grades above a specified value, providing thus a basis for estimating
ore reserves. But they require as input for estimating F , information about already
existing deposits with ore grades and tonnage, which is what we are searching for.
A comprehensive study of average ore grades was undertaken by Cox and Singer
[66]. In their study, a compendium of geologic models was presented, includ-
132
THE
RESOURCES OF THE EARTH
ing 85 descriptive models identifying attributes of the deposit type and 60 gradetonnage models giving estimated pre-mining tonnage’s grades from over 3900 wellcharacterized deposits all over the world.
We have calculated with Eq. 4.4 the weighted average grades (x̄ m ) of the different
mineral models of Cox and Singer [66], considering the average tonnage (M ) and
grade (x m ) of the different deposits containing the particular mineral (see section
A.2 in the appendix). The minerals under consideration in Cox and Singer’s study
were: rare earths, uranium oxide, zircon, niobium oxide, barite, alumina, phosphorous, potash, titanium, chromium, manganese, iron, cobalt, nickel, copper, molybdenum, wolfram, palladium, platinum, rhodium, iridium, ruthenium, osmium, silver,
gold, zinc, mercury, tin, lead and antimony. Table 4.9 shows the final average grade
obtained.
RM
xmd M
x̄ m = 0R M
dM
0
(4.4)
Some of the values may appear to be quite low. Nevertheless, it must be pointed
out that the figures are averages of mineral extraction of deposits. Most deposits
extract many minerals as byproducts, with a relatively low grade which would not
be cost-effective if they were to be extracted alone.
Table 4.9: Summary statistics of grade-tonnage models. After [66]
Deposit
RE2 O5 (%)
Monazite (%)
U3 O8 (%)
Zircon (% Z rO2 )
N b2 O5 (%)
Barite (%)
Al2 O3 (%)
P (%)
P2 O5 (%)
Ilmenite (% T iO2 )
Rutile (% T iO2 )
Leucocite (% T iO2 )
C r2 O3 (%)
M n (%)
Fe (%)
C o (%)
N i (%)
x̄ m
0,10
0,03
0,33
0,27
0,64
83,02
45,97
0,11
24,01
1,27
0,21
0,23
43,52
31,49
51,05
0,11
1,30
Deposit
Cu (%)
M o (%)
W O3 (%)
P d (ppb)
P t (ppb)
Rh (ppb)
I r (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Z n (%)
H g (%)
Sn (%)
P b (%)
S b (%)
x̄ m
0,58
0,03
0,72
158,51
802,39
12,92
20,62
220,02
82,22
4,27
0,22
4,06
0,38
0,48
2,05
3,78
Non-fuel mineral resources
133
No average numbers have been found in the literature for the rest of the minerals
not included in Cox and Singer [66]. Most of those minerals are not mined as the
principal product and are only commercially produced in the case they are found
as reasonable byproducts of other important minerals. In those cases, values found
in the literature (as in Carr [51]) of certain deposits have been taken as reference.
We are aware that those figures cannot be considered as global mineral ore grades.
Nevertheless, they are good enough for giving an order of magnitude.
The following assumptions have been made in order to estimate the average mineral
ore grades not included in Cox and Singer:
• Arsenic: Northparkes copper-gold ore grade for arsenic is 0,11% [323]; Mt
Piper Gold Project in Victoria (Australia) contains 3% [252]. We will assume
an average grade of 1%.
• Beryllium: ore grades range from 0,2 to 3,5 % of beryllium oxide [260]. We
will assume an average grade of 1%.
• Bismuth: Bonfim W-Au-Bi-Te Skarn deposit (Brazil) contains 475 to > 2000
ppm [327]. We assume the value of 2000 ppm.
• Boron: According to the USGS [363], average grades of boron oxide mined
all over the world range from 11 to 39%. We will assume an average grade of
20%.
• Bromine: an important source of bromine is the Dead Sea. Its bromine concentration is around 5000 ppm [406].
• Cadmium: cadmium is usually found in zinc ores. According to the Mineral
Information Institute10 , zinc ores around the world average about 1/400 th as
much cadmium as zinc. Hence, if Z n average grade is 4,06%, C d grade is
estimated to be around 100 ppm.
• Cesium: it is usually found in the mineral pollucite. The world largest pollucite
deposit is in a zoned pegmatite at Bernic Lake, Canada, grading 23,3% cesium
oxide11 .
• Feldspar: the major commercial feldspar deposits occur in pegmatites, granitic
rocks, granitic rock types known as alaskite and aplite and certain river, dune
and beach sands. The feldspar content of these deposits range from 15 to up
to 75% of the different feldspar minerals [180]. We will assume an average of
45%.
10
11
Mineral Information Institute: http://www.mii.org/Minerals/photocad.html
Source: Houston Lake Mining Inc. http://www.houstonlakemining.com
134
THE
RESOURCES OF THE EARTH
• Fluorite (fluorspar): The compilation of Fulton and Montgomery [99], gives
averages for the different types of deposits where fluorite is found: fissure
veins (from 25 to 80%), statiform deposits (from 15% upward), stockworks
(about 14%), gangue mineral (from 10 to 20%), lake sediments (50 to 60%
of the clayey parts and 15% of the sandy parts). Specific examples of fluorite
deposits are for example in the southwestern United States, deposits often
assay less than 10% fluorite [131] and in the Pöhrenk deposit of Turkey ore
grades range from a few to more than 40% C aF2 [110]. We will assume an
average fluorite grade of 25%.
• Gallium: the most important ore in which gallium is found as a trace element
is bauxite in an average of 50 ppm, according to the Mineral Information Institute. Assuming that the average grade of alumina alumina in laterite bauxite
is 45,97% [66], gallium grade is estimated here as about 23 ppm.
• Germanium: grades of a few tens to several hundred ppm Ge are known in
sulphide deposits [142], [220]. We will assume an average grade of 50 ppm.
• Graphite: economic deposits of graphite include five main geological types:
flake graphite disseminated in metamorphosed (with an average deposit of 10
to 12%), silica-rich sedimentary rocks (1-10%), flake graphite disseminated in
marble amorphous deposits formed by metamorphism of coal or carbon-rich
sediments (50-95%), veins filling fractures (85-98%) and contact metasomatic
or hydrothermal deposits in marble (irregular concentrated). We will assume
an average grade of 50%.
• Gypsum: it is usually found in very high grades, ranging from 45 to 95%
[174]. We will assume an average grade of 80%.
• Hafnium: it is always present in 1,5 to 3,0 % in zirconium compounds [315].
Assuming an average of zinc of 0,27% [66], the hafnium average grade ranges
from 40,5 to 81 ppm. We will assume an average of 60 ppm.
• Helium: it is recovered usually as a byproduct in natural gas production. Some
natural gas deposits have as much as 7% helium, found in Texas, Russia,
Poland, Algeria, China and Canada12 .
• Indium: the average value in ore deposits varies drastically up to percent levels. In the Kuroko deposits of Japan, the I n-content of Cu-concentrates had
been reported at about 10 ppm and in Z n concentrates is 100 ppm. Some
skarn deposits and Pb-Zn veins have ranges of I n concentration similar to
these. Atypical maximum concentrations of I n are up to 3000 ppm. We will
assume an average content of 140 g/t which is reported for one of the most
well known I n deposits in Japan, the Toyoha mine in Hokkaido [236].
12
Source: Mineral Information Institute (http://www.mii.org/Minerals/photohelium.html
Non-fuel mineral resources
135
• Iodine: iodine is primarily retrieved from underground brines. Dried seaweeds, particularly those of the Liminaria family, contain as much as 0,45%
iodine. Japan is the largest iodine producing country. The maximum iodine
content of the brines is about 160 ppm [171].
• Lithium: some lithium is recovered from the mineral spodumene with an Li
grade of 1 to 4%. But most lithium is recovered from brine. Lithium grades in
brine range from 0,015 to 0,06% [260]. We will assume an average grade of
0,04%.
• Magnesium compounds: one of the most important magnesium minerals is
magnesite, M g CO3 , which represents the world’s largest source of magnesia,
M gO. The next most used sources for magnesia are magnesia-rich brines and
seawater. Dolomite is another important source for industrial magnesium. The
crude ore of magnesite contains typically around 45% of magnesia.
• Potash: potash oxide grades in Canada, the most important producer in the
world, range from 14 to 32% [407]. In Saskatchewan, ore grades range between 23 and 27%13 . We assume an average grade of K2 O of 25%.
• Rhenium is a very rare element produced mainly as a byproduct in the processing of porphyry copper-molybdenum ores. The Re contents in the majority of
the concentrates range from 6 to 460 ppm [27]. We assume an average of 233
ppm.
• Selenium: it is widely distributed within the earth’s crust and does not occur
in concentrations high enough to justify solely for their content. It is recovered as byproduct of nonferrous metal mining, mostly from the anode slimes
associated with electrolytic refining copper. The economic concentration14 is
2,5% [34].
• Strontium: celestine and strontianite are the only S r-containing minerals having sufficient quantities to make its recoveral practical. From these, only celestine has been found to occur in deposits of sufficient size. Celestine is mined
in many countries all over the world. Reported average ore grades of S rSO4
range from 54% in Cyprus to more than 90% in Iran [244]. We will assume
an average grade of 70% of celestine or 34% of S r content.
• Tantalum: it is recovered from tantalite and columbite ores. The average ore
grades are similar to those of niobium, since it is recovered from the same ores.
Therefore, we assume that the average grade of tantalum oxide is 0,64%, the
same as the grade of niobium oxide recorded by Cox and Singer [66].
13
14
Source: the Canadian Encyclopedia (http://thecanadianencyclopedia.com)
Economic concentration: concentration at which a mineral is economically producible
136
THE
RESOURCES OF THE EARTH
• Tellurium: it is widely distributed within the earth’s crust and does not occur
in concentrations high enough to justify solely for their content. It is recovered as byproduct of nonferrous metal mining, mostly from the anode slimes
associated with electrolytic refining copper. The economic concentration is 1
ppm [34].
• Thorium: it has been mined at an average grade of nearly 3% of T hO2 in the
Bokan Mountain in Alaska [356].
• Vanadium: average ore grades for vanadium range from 0,3 to 5% [260]. We
will assume an average of 2%.
4.8.3
Mineral’s abundance
Table 4.10 shows world reserves, reserve base, and resources of the main naturaloccurring non-fuel minerals of economic importance according to the USGS [362].
It shows also the average ore grades obtained in the previous section. The most
abundant ores in the crust are those of iron, followed by phosphate rock, potash,
manganese and aluminium. On the contrary, the ores of the platinum group metals,
thallium, tellurium and rhenium are the scarcest in the world.
Table 4.10: Mineral world reserves, reserve base and world resources in 2006
Production
Reserves
Reserve base
Resource
Aluminium
Antimony
Arsenic
Barite
Beryllium
Bismuth
Boron
(as
B2 O3 )
Bromine
tons
3,37E+07
1,34E+05
5,98E+04
7,96E+06
1,79E+02
5,70E+03
4,26E+06
tons
4,55E+09
2,10E+06
1,20E+06
1,90E+08
N.A.
3,20E+05
1,70E+08
tons
5,82E+09
4,30E+06
1,20E+06
8,80E+08
N.A.
6,80E+05
4,10E+08
5,45E+05
Large
Large
Cadmium
Cesium
Chromium
Cobalt
Copper
Feldspar
Fluorspar
Gallium
Germanium
1,93E+04
N.A.
5,85E+06
6,75E+04
1,51E+07
1,54E+07
5,33E+06
7,30E+01
9,00E+01
4,90E+05
1,20E+06
7,00E+04
1,10E+05
N.A.
N.A.
7,00E+06
1,30E+07
4,90E+08
9,40E+08
Large
Large
2,40E+08
4,80E+08
N.A.
N.A.
N.A.
N.A.
Continued on next page . . .
World
resources
tons
1,36E+10
N.A.
> 11000000
2,00E+09
> 8E+04
N.A.
N.A.
Unlimited
(dead
sea
contains
1
billion tons of
bromine)
6,00E+06
N.A.
3,80E+09
1,50E+07
> 3,00E+09
Large
5,00E+08
1,00E+06
N.A.
Ore grades
%
45,97
3,78
1,00
83,02
1,00
0,50
20,00
0,50
100 ppm
23,30
43,52
0,11
0,58
45,00
25,00
23 ppm
50 ppm
Non-fuel mineral resources
137
Table 4.10: Mineral world reserves, reserve base and world resources in 2006
– continued from previous page.
Production
(year 2006)
tons
2,46E+03
1,03E+06
1,25E+08
N.A.
Reserves
Reserve base
tons
4,20E+04
8,60E+07
Large
6,10E+05
tons
9,00E+04
2,10E+08
Large
1,10E+06
World
resources
tons
N.A.
> 8,00E+08
Large
N.A.
2,81E+04
5,81E+02
2,50E+04
N.A.
8,66E+08
3,47E+06
3,33E+05
N.A.
1,10E+04
1,50E+07
N.A.
7,30E+10
7,90E+07
4,10E+06
6,47E+06
1,60E+04
2,70E+07
N.A.
1,60E+11
1,70E+08
1,10E+07
N.A.
N.A.
3,40E+07
N.A.
2,30E+11
> 1,50E+09
>1,3E+07
Magnesium
6,89E+05
N.A.
N.A.
Manganese
Mercury
Molybdenum
Nickel
Niobium
Osmium
Palladium
Phosphate
rock
Platinum
group metals
Platinum
Potash
Rare Earths
1,19E+07
1,48E+03
1,84E+05
1,58E+06
4,45E+04
N.A.
2,24E+02
1,42E+08
4,60E+08
4,60E+04
8,60E+06
6,70E+07
2,70E+06
N.A.
N.A.
1,80E+10
5,20E+09
2,40E+05
1,90E+07
1,50E+08
3,00E+06
N.A.
N.A.
5,00E+10
Large to unlimited
Large
6,00E+05
1,30E+07
N.A.
N.A.
N.A.
N.A.
N.A.
5,18E+02
7,10E+04
8,00E+04
> 1,00E+05
2,21E+02
2,91E+07
1,23E+05
N.A.
8,30E+09
8,80E+07
N.A.
1,80E+10
1,50E+08
Rhenium
Ruthenium
Selenium
Silicon
Silver
Strontium
Tantalum
Tellurium
Thallium
Thorium
Tin
4,72E+01
N.A.
1,54E+03
3,87E+06
2,02E+04
5,85E+05
1,39E+03
1,32E+02
1,00E+01
N.A.
3,02E+05
2,50E+03
1,00E+04
N.A.
N.A.
8,20E+04
1,70E+05
N.A.
N.A.
2,70E+05
5,70E+05
6,80E+06
1,20E+07
1,30E+05
1,80E+05
2,10E+04
4,70E+04
3,80E+02
6,50E+02
1,05E+06
1,23E+06
6,10E+06
1,10E+07
Continued on next page . . .
N.A.
2,50E+11
Undiscovered
resources
are
thought
to be very
large relative
to
expected
demand
1,10E+04
N.A.
N.A.
N.A.
Large
> 1,00E+09
N.A.
N.A.
6,47E+05
N.A.
N.A.
Resource
Gold
Graphite
Gypsum
Hafnium
H f O2 )
Helium
Indium
Iodine
Iridium
Iron ore
Lead
Lithium
(as
Ore grades
%
0,22 g/t
50,00
80,00
60 ppm
7,00
140 g/t
160 ppm
20,6 ppb
51,05
2,05
0,04 (Lithium
brines)
45 as MgO
31,49
0,38
0,03
1,30
0,64
82,2 ppb
158,5 ppb
0,11
See Pt, Pd, Rh,
Ru, Ir and Os
802,4 ppb
25,00
0,10
223 ppm
220,0 ppb
2,50
N.A.
4,3 g/t
34,00
0,65
1 ppm
N.A.
3,00
0,48
138
THE
RESOURCES OF THE EARTH
Table 4.10: Mineral world reserves, reserve base and world resources in 2006
– continued from previous page.
Resource
Titanium (as
T iO2 )
Vanadium
Wolfram
Yttrium
(as
Y2 O3 )
Zinc
Zirconium (as
Z rO2 )
Production
(year 2006)
tons
5,80E+06
Reserves
Reserve base
tons
7,30E+08
tons
1,50E+09
World
sources
tons
N.A.
re-
Ore grades
5,63E+04
9,08E+04
8,90E+03
1,30E+07
2,90E+06
5,40E+05
3,80E+07
6,30E+06
6,10E+05
> 6,30E+07
N.A.
N.A.
2,00
0,72
N.A.
1,00E+07
1,18E+06
1,80E+08
3,80E+07
4,80E+08
7,20E+07
1,90E+09
N.A.
4,06
0,27
%
0,69
End of the table
4.9
Summary of the chapter
This chapter closes the analysis of the earth’s components (Part I of this report), by
undertaking a review of the different natural resources, useful to man.
With the most updated information sources, the available energy, potential energy
use and current energy consumption of all known renewable and non-renewable
energy resources has been obtained. That is for geothermal, nuclear, tidal, solar,
wind and ocean power, as well as for biomass, coal, natural gas, oil and unconventional fuels.
In addition to energy resources, non-fuel minerals have been analyzed. As opposed
to fossil fuels, the abundance of minerals is not important if these are dispersed
throughout the crust. Hence, besides of the available resources registered, which
are very uncertain, average ore grades for the main mineral resources have been
provided. Both figures (abundance and concentration), will allow us to calculate the
exergy of non-fuel minerals.
With the next chapter, begins Part II of this report, whose aim is to assess the exergy
of the earth and its resources. Chapter 5, provides the thermodynamic tools required
for calculating the exergy of the earth, including the mineral resources (of fuel and
non-fuel nature) just reviewed. Consequently, all resources will be able to be evaluated with a single unit of measure, allowing us to compare them and to analyze
their scarcity.
Part II
The thermodynamic properties of
the earth and its exergy evolution
139
Chapter
5
Thermodynamic models for the
exergy assessment of natural
resources
5.1
Introduction
This aim of this chapter is to provide the thermodynamic tools for the exergy assessment of natural resources and particularly for minerals.
The exergy of any substance or process is always fixed by the so called reference
environment (R.E.). Therefore, for calculating the exergy of any natural resource,
an appropriate R.E. should be defined. In section 5.2, the different reference environments proposed in the literature are reviewed and the best suitable R.E. so far,
for assessing the natural capital is chosen.
Once the R.E. is fixed, the exergy of mineral resources can be calculated with the
help of the thermodynamic models provided in section 5.3. For that purpose, the
energy involved in the process of formation of a mineral deposit is described. Next,
the formulas for obtaining the exergy and exergy cost of mineral resources (including
fossil fuels) are provided. And finally, 12 models for estimating the Gibbs free energy
values of mineral resources, required for the calculations, is shown.
5.2
The reference environment
The R.E. can be assumed as being a thermodynamically dead planet where all materials have reacted, dispersed and mixed. This R.E. must be determined by the
natural environment and is fixed by its chemical composition. In past years, there
141
142
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
have been many contributions to the determination of the best suitable R.E. The divergences between standard chemical exergies of the elements obtained from different R.E. conceptions can be very significant. Each R.E. definition generate different
exergies, what implies that the determination of the natural capital’s exergy is necessarily linked to the definition and thermodynamic properties of the R.E. In order
to correctly evaluate the natural resources, it is necessary to know how does the modification of reference substances or physical variables of the R.E. change the exergy
calculation of a system. Most of the contributions concerned with that topic deal
with the exergy variation of processes according to physical parameters of the environment such as pressure or temperature (see for instance Brodianski et al. [304]
[39]). Other authors have studied the influence of environment CO2 or temperature
on the exergy of fossil fuels (Valero and Arauzo [366]) and hydrocarbons (Rivero
et al. [282]). Nevertheless, it is crucial to analyze the influence of the reference
environment’s chemical composition if the point is to evaluate the natural capital’s
exergy.
Next, the different models of reference environments are reviewed, and the best
suitable R.E. is selected and improved for the evaluation of natural resources.
5.2.1
Selection of the best suitable reference environment
The different R.E. conceptions can be divided into two main groups:
• Partial reference environments
• Comprehensive reference environments
5.2.1.1
Partial reference environments
Some authors such as Bosjankovich [33], Gaggioli and Petit [101] and Sussman
[332] established that the R.E. should be defined according to the specific characteristics of the analyzed process. This criterion is based on that being the exergy a
parameter that quantifies the theoretical evolution of a system with respect to the
R.E., some of the possible evolutions of the system, cannot be attained because of
process limitations. Hence, only possibilities of evolution that the system can practically attain are analyzed. The conception of these R.E. are very far removed from
the idea of degraded earth. For computing exergy changes of variable composition
or chemically reactive steady flow processes, a Comprehensive reference environment
is generally unnecessary.
However, this is not the case when the point is to evaluate the natural capital on
earth. In that case, there are no process limitations and the resources can follow an
evolution process towards the dead state. Thus a comprehensive R.E. is required.
The reference environment
5.2.1.2
143
Comprehensive reference environments
Within the known Comprehensive reference environments, all authors agree in dividing the Reference Substances (R.S.) that compose the R.E. into gaseous components of the atmospheric air, solid components of the external layer of the earth’s
crust, and molecular components of seawater. Nevertheless, there are also criterion
differences between the different authors. They can be classified into environments
based on:
• Szargut’s criterion
• Chemical equilibrium
• Abundance
Szargut’s R.E. could be considered as an environment based on partial abundance,
even though Szargut itself regards his R.E. as based only on abundance. We will
show next, that his R.E. is not only based on abundance, as opposed to the criterion
taken by Ranz [276].
According to Szargut’s criterion, among a group of reasonable abundant substances,
the most stable will be chosen if they also fulfill the “earth similarity criterion”. That
is, if the stability of the possible different reference substances for a specific element
(measured in terms of the formation Gibbs energy) is within a certain threshold, then
the most abundant R.S. will be chosen. If the differences exceed this threshold, the
most stable substance will be taken as R.S. as long as the “earth similarity criterion”
is not contradicted. The stability threshold has not a fix value and depends on each
element considered, since it is subject to geological uncertainties. Thus for example
in the case of S b, the substance S b2 S3 is more abundant than S b2 O5 , nevertheless,
according to Szargut’s criterion, S b2 O5 , which is much more stable, will be taken
as reference substance. This happens also with the substances listed in table 5.1.
Nevertheless nitrates such as C a(N O3 )2 , N aN O3 , K N O3 are discarded, because being most stable but not abundant in the natural environment, they would break the
similarity criterion if they are taken as R.S. Therefore, Szargut’s [333] dead environment is similar to the real physical environment and should represent the products
of an interaction between the components of the natural environment and the waste
products of the processes. The most probable products of this interaction should
be chosen as reference species. Section 5.2.2 explains purposively the well known
Szargut’s methodology for obtaining the chemical exergy of the elements from the
R.E.
144
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
Table 5.1: Exergy difference of selected elements considering either as reference species the most abundant or the most stable substances in the R.E.
[367]
Element
Most
abundant species
Most
stable
species
Sb
As
S
Bi
Cd
Ce
Zn
Co
Cu
Mo
Os
Ag
Pt
Pb
Re
Ru
U
S b2 S3
FeAsS
FeS2
Bi
C dS
C ePO4
Z nS
C o 3 S4
CuFeS2
M oS2
Os
Ag2 S
Pt
P bS
ReS2
Ru
UO2
S b2 O5
As2 O5
SO4−2
BiO+
C dC l2
C eO2
Z n+2
C o3 O4
Cu+2
M oO4−2
OsO4
AgC l2−
P tO2
P bC l2
Re2 O7
RuO2
UO3 .H2 O
Exergy difference
between
both
R.E. (kJ/mole)
1235,58
1201,32
963,63
228,88
745,75
258,33
717,22
967,70
1423,18
1675,9
306,81
330,65
84,59
710,34
1556,65
254,82
127,49
Another group of authors derive the chemical exergy of the elements from the hypothetical chemical equilibrium that could be attained on earth in a very distant future.
Ahrendts [3], [4] and Diederichsen [74] for example, stated that if the amount of
different elements in the reference system is known and the temperature of the
system is fixed, the quantity of each chemical compound and the value of each chemical potential is uniquely determined by the condition of chemical equilibrium. This
criterion is thermodynamically consistent and thus does not generate any negative
exergies as it happens with the other two comprehensive R.E. classifications.
Ahrendt’s R.E. relied on the model of Ronov and Yaroshevsky [287] to ascertain 15
elements, making up more than 99% of the earth’s crust: H, C, N , O, N a, M g,
Al, Si, P, S, C l, Ar, K, C a, T i, M n and Fe. These elements were allowed to react
until chemical equilibrium was attained. The composition of this environment in
chemical equilibrium, had as a variable parameter the thickness of the crust layer
(between δ = 1 m and δ = 1000 m). The resulting equilibrium reference system
based on an earth’s crust of δ = 1000 m, showed that the exergy of oxygen was even
smaller than that of fuels. He found that the exergy of oxygen increased, when the
considered thickness of the crust was smaller. In order to overcome this paradox,
Ahrendts considered a crust layer on only 1 m.
Szargut criticizes Ahrendt’s model, stressing that it is not possible to attain an equilibrium with the system being not in the state of internal equilibrium (and the natural
The reference environment
145
environment is far removed from such equilibrium). Valero, Ranz and Botero [371],
explained already why Ahrendt’s R.E. was not suitable to evaluate the natural capital
on earth. Most of the metals cannot be evaluated because they form part of the 1%
of the earth’s crust neglected by Ahrendts. His obtained R.E. is very different from
the real environment and it is very unlikely an eventual evolution towards it, since
some processes are kinetically, biologically and/or geologically blocked.
Diederichsen updated and extended Ahrendt’s model with new geochemical data
and obtained among others, a R.E. including 75 elements. Furthermore, he allowed
the composition of this environment to change with two variable parameters: thickness of the earth’s crust and ocean’s depth. The final chosen environment should
fulfill the “earth similarity criterion”. The similarity with the earth was measured
with the equilibrium pressure, the oxygen and nitrogen content in the gas-phase
and the equilibrium salt content in the oceans.
Even though Diederichsen [74] added more elements than Ahrendts [4] and included a new variable parameter, the composition of his new reference environment
was still too different from the real earth. According to the “earth similarity criterion”, the R.E. that best fits with the earth’s environment takes a crust thickness of
only 0,1 m and an ocean’s depth of 100 m. Greater values would move further away
the R.E. from the real earth, and would have among other features, reduced pressures and oxygen contents. As it happened with Ahrendt’s model before, Diederichsen obtained high exergy values for oxygen. This happens because nearly all the
oxygen of the air is consumed basically by the formation of nitrates and only in the
limit, for a crustal thickness of 0 m, the mean earth pressure matches with that of the
model. It seems therefore that achieving a R.E. in chemical equilibrium is in disagreement with the “earth similarity criterion” and is not appropriate for the evaluation of
natural capital on earth. This idea fully fits with Lovelock’s Gaia hypothesis [199]:
“the earth is a life being and fights against thermodynamic stable equilibrium.”
Van Gool’s methodology [379] assures as well a R.E. in which all the substances
have positive exergy values. However as he discards the geological information of
mineral abundance, his R.E. does not guarantee a good model for a dissipated earth,
which is critical in our research.
Kameyama et al. [177] proposed a reference environment with the criterion of chemical stability. The references are the most stable compounds among those with
thermo-chemical data and can be integrated in the solid, liquid and gaseous environments. As Szargut stated in [336], some of the most stable compounds selected
by Kameyama et al. like nitrates, compounds between rare elements (e.g. P t Br2 ) or
compounds with F r as the reference species for the elements F , C l, Br or I should
not be recommended, because the probability of their formation in the environment
is very small. Therefore, Kameyama et al. R.E. is not very suitable either to evaluate
the scarcity of the natural capital.
146
5.2.1.3
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
Abundance criterion
According to Ranz [276], lots of minerals are compounds with the most common
components of the upper continental crust, but are not very stable and do not represent the products of an interaction between the components of the natural environment and the waste products of industrial processes. Hence, Ranz [276] proposes
a new R.E. very close to the real environment based on abundance and following
Szargut’s methodology. The solid phase of this new R.E. reproduces accurately the
earth’s upper continental crust, since the solid reference species that make up this
environment are the same as the most abundant types found in the earth’s upper
continental crust. A problem with Ranz’s proposed R.E. is that if we assign zero
exergy to the most abundant substances, we are decreasing arbitrarily the natural
capital, because many abundant minerals like sulfides naturally evolute to the most
stable oxides. Therefore, as proposed by Valero, Ranz and Botero [371], we must return to Szargut’s criterion of using the most stable substance, within the limits fixed
by the “earth similarity criterion”.
Hence, our first goal is to obtain a reference state for evaluating the natural resources on earth, based on Szargut’s criterion and methodology and using the more
precise data used by Ranz and other authors such as Rivero [281], as well as new
geochemical updates.
In the next section, Szargut’s methodology for obtaining the standard chemical
exergy of the chemical elements is explained and the variables used are discussed.
5.2.2
5.2.2.1
Calculation methodology: standard chemical exergy of the
chemical elements
Standard chemical exergy of chemical compounds
The chemical exergy expresses the exergy of a substance at ambient temperature
and pressure. It is defined as the maximum work which can be obtained when
the considered substance is brought in a reversible way to the state of reference
substances present in the environment, using the environment as a source of heat
and of reference substances necessary for the realization of the described process.
Standard chemical exergy results from a conventional assumption of a standard ambient temperature and pressure and standard concentration of reference substances
in the natural environment.
The chemical exergy of any chemical compound (bch i ), can be calculated by means
of the exergy balance of a reversible formation reaction;.
bch i = ∆G f i +
X
j
r j,i bch j
(5.1)
The reference environment
where:
∆G f i
r j,i
bch j
147
Gibbs free energy of substance i
amount of mole of element j per mole of substance i
standard chemical exergy of element j contained in substance i.
If the chemical element does not belong to the reference substances, its standard
chemical exergy can also be calculated from Eq. 5.1. The standard chemical exergy
of the reference substances are calculated prior to the standard chemical exergy of
the element.
5.2.2.2
Gaseous reference substances
Free chemical elements present in the atmospheric air (O2 , N2 , Ar, H e, N e, K r, X e)
and the compounds H2 O, CO2 are assumed as reference substances. Their standard chemical exergy results from the conventional standard concentration in the
atmosphere.
P0
bch i = −R̄ T 0 ln i0 = −R̄ T 0 ln x i
(5.2)
P
where:
R̄
universal gas constant (8,314E-3 kJ/(mole K)),
0
T
standard ambient temperature (298,15 K),
Pi0 conventional mean ideal gas partial pressure in the atmosphere (kPa),
P 0 standard pressure (101,325 kPa),
xi
molar fraction in the environment.
The values of standard chemical exergy of gaseous reference substances O2 , H2 O,
CO2 , N2 are calculated before other values because they are necessary in the calculation of standard chemical exergy of non-gaseous reference substances.
5.2.2.3
Solid reference substances
For a prevailing part of chemical elements, solid R.S. commonly appearing in the
external layer of the continental part of earth’s crust, are assumed. However, the
earth’s crust is a very complicated mixture of solid solutions and an exact calculation
of the chemical exergy of its components is impossible. We can only approximately
evaluate that exergy, assuming that the reference species behave as components of
an ideal solution. Hence, Eq. 5.2 can be applied also in this case.
The evaluation of the standard molar concentration of solid R.S. in the external
layer of the earth’s crust is difficult and as stated in chapter 3, there wasn’t any
average mineralogical composition until the recent publications of Grigor’ev [124],
[127] arrived. In past geochemical publications (such as Allègre [6], [8], Shan Gao
[106], Rudnick [291], Condie [60], Javoy [169], McDonough [212], Taylor and
148
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
McLennan [353], [216], [215], or Wedepohl [404]) one can only find mean mass
concentrations of particular chemical elements and the most common oxides found
in the continental crust, namely SiO2 , T iO2 , Al2 O3 , FeO, M nO, M gO, C aO, N a2 O,
K2 O and P2 O5 . Hence, the best considered way so far to obtain the standard molar
concentration of R.S. in the solid environment, has been with the following equation
suggested by Szargut in [336].
xi =
where:
εj
lj
cj
M Wc r
1
lj
ε j c j M Wcr
(5.3)
mean molar concentration of the j-th element in the continental part of the
earth’s crust (mole/g),
number of the atoms of j-th element in the molecule of the reference
species,
fraction of the j-th element appearing in the form of reference species,
mean molecular weight of the upper continental crust (g/mole).
The reference reactions of the elements having solid reference substances contain
usually gaseous reference substances such as O for example. Sometimes there appear also solid or liquid reference species. In such case the standard chemical exergy
of the appearing solid or liquid reference substance should be calculated prior to the
calculation of the chemical exergy of the considered element.
5.2.2.4
Reference substances dissolved in seawater
Assumption of ionic or molecular R.S. dissolved in seawater ensures in many cases
more exact determination of standard chemical exergy of chemical elements when
compared with solid R.S. The calculation methods of thermodynamic functions of
monocharged and bicharged ions are relatively exact. This is the case also when
the reference substance is dissolved in molecular form with a very small degree of
ionization.
The method of calculation of standard chemical exergy of elements with R.S. dissolved in seawater was developed by Morris [340]:
bch j =
−∆ G f i + 0, 5 z + bch H2 −
X
rk,i bch k −
k
0
+
− R̄ T [2, 303 z (pH) + ln mi γi ]
(5.4)
The reference environment
where:
∆G f i
z+
rk,i
bch H2 , bch k
mi
γi
pH
149
Gibbs free energy of the R.S.,
number of elementary positive charges of the reference ion,
number of molecules of additional elements k present in the molecule of
reference substance i,
standard chemical exergy of hydrogen gas and of the k-th additional element.
conventional standard molarity of the reference substance i in seawater,
activity coefficient (molarity scale) of the reference substance in seawater,
exponent of the concentration of hydrogen ion in seawater (=8,1)
Eq. 5.4 should be multiplied by 2 for the diatomic elements Br2 , C l2 and I2 .
The activity coefficient of a single ion can be calculated by means of the DebyeHuckel equation:
p
A1 (z + )2 I
− log γi =
(5.5)
p
1 + ai A2 I
where:
A1
A2
ai
I
= 0,51 kg1/2 mole−1/2 for water at 25o C,
= 3,287 * 109 kg1/2 m−1 mole−1/2 for water at 25o C,
effective diameter of the ion,
ionic strength of the electrolyte.
The ionic strength of the electrolyte results from the following equation:
I =
1X
2
mi (z + )2
(5.6)
i
where:
mi molarity of the ion, mole/kg H2 O,
z + number of elementary electric charges of the ion.
The ion C l − prevails among the negative ions in seawater. Therefore, the data of
chlorides can be assumed for activity coefficients of the positive ions N a+ and K + .
The activity coefficients of the negative ions C l − and SO4−2 can be estimated in reference to the predominant positive ion N a+ . The positive ionic reference substances
were assumed for the elements from the first column of the periodic system and
for the monocharged and bicharged negative ions formed from acids. The elements
from the second column of the periodic system appear in seawater in the form of
positive bicharged ions, however, they are not recommended as R.S., because the
so calculated standard chemical exergy of the elements leads to negative values of
chemical exergy of some solid compounds common in the earth’s crust.
150
THERMODYNAMIC
5.2.3
Update of Szargut’s R.E.
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
Next, Szargut’s R.E. will be updated with the help of new geochemical data and the
information provided by other authors such as Ranz [276] or Rivero [281].
5.2.3.1
Update of the standard chemical exergy of chemical compounds
The only variable included in Eq. 5.1 that is subject to be updated is ∆G f . The Gibbs
free energy used by Szargut [336] was revised by Rivero [281] using [258], [391],
[194], [19] and [399]. No substantial differences were found, except for sillimanite
(Al2 SiO5 ), whose new value was ∆G f = 2440, 9 kJ/mole. The information source
of Ranz [276] for obtaining ∆G f , was Faure [94], which is a compilation of the
literature from several authors. This source corroborates Rivero’s revision and thus,
it will be considered for the calculation of this particular R.E.
5.2.3.2
Update of the gaseous reference substances
Rivero and Garfias [281] accepted the reference pressure of Eq. 5.2 according to the
conventional unit “physical atmosphere”, thus 101,325 kPa. We are assuming the
mean partial pressure calculated by Szargut and used by Ranz [276], which is the
really appearing mean value and is equal to 99,31 kPa.
5.2.3.3
Update of the solid reference substances
The mean molar concentration of the elements in the upper continental crust ε j of
Eq. 5.3 used in Szargut [336], was the recommended by Polanski and Smulikowski
[268]. Ranz [276] used updated values mainly from Taylor and McLennan [354],
[353]. For the elements: Br, C, C l, F , S, P t, Pu, Ra, Rh, Ru, Te, I, H g and N ,
Taylor and McLennan did not provide any information, therefore, Ranz used the
values given by Wedepohl [404] for S, Br, C, F , I, H g, N and for the remaining
elements, the values used by Szargut [336]. Some authors like Plank and Langmuir
[267] basing on their studies on marine sediments, suggested already in 1998 some
revisions of the estimated values by Taylor and McLennan [354], [353] for N b,
Cs,T i, Ta. As a consequence, McLennan [215] published in year 2001 new mean
molar concentrations of the upper continental crust for the elements: Sc, T i, V , C o,
N i, N b, Cs, P b, Ta. The most recent data about the chemical composition of the
upper continental crust has been published by Rudnick and Gao [292], taking into
account the studies published so far.
The recent values provided by Rudnick and Gao will be used for the update of
Szargut’s R.E. Nevertheless, values for Pu and Ra that are not provided in their
tables, will be assumed to be the ones given by Polanski [268].
The reference environment
151
As explained in chapter 3, Grigor’ev published in year 2000 [125] the average mineral content of the upper continental crust obtained through a great number of
quantitative mineralogical analysis of important rocks. In 2007, Grigor’ev updated
this information; the new analysis comprises 265 minerals, their varieties and their
non-mineral materials, corresponding to 99,13% of the total mineral content of the
upper continental crust. With this valuable information, we have been able to propose a new model of the continental crust, based on Grigor’ev’s composition, but
assuring the mass balance of the earth. This information allows to obtain directly
the standard molar concentration of the following 14 reference substances in the
solid environment without using Eq. 5.3: Al2 SiO5 , BaSO4 , Be2 SiO4 , C aCO3 , Au,
Fe2 O3 , M g3 Si4 O10 (OH)2 , M nO2 , SiO2 , S r CO3 , T hO2 , SnO2 , T iO2 , Z rSiO4 . For the
rest substances, Eq. 5.3 must be used, taking ε j from the latest geochemical publications explained before.
For the fraction of the j-th element appearing in the form of reference species (coefficient c j ), Szargut [335] associates values comprised between 0,5 for more abundant
substances and 0,001 for less frequent substances from geochemical data given by
Polanski and Smulikowski [268]. Ranz [276] obtained more accurate c j coefficients
for solid R.S. containing the most abundant elements in the upper continental crust.
For this purpose, she used the mineralogical composition of the earth’s upper layer
obtained with the CIPW norm before and updated geochemical information, mainly
from Taylor and McLennan [354]. For minority elements, due to the lack of information, Szargut’s [335] values were used. As long as a better mineralogical composition
of the earth’s crust is not developed and the c j coefficients are recalculated with this
information, we will assume the c j values obtained by Ranz [276].
The mean molecular mass of the upper layer of the continental part of the earth’s
crust, was first estimated by Szargut [334]. The obtained value was M Wcr = 135,5
kg/kmole, applying the following estimation method: according to the geochemical
data, the mean concentration values (in mole/kg) of particular chemical groups
or elements in the external layer of the continental earth’s crust and the chemical
compound formed from these groups were assumed. The first considered group was
CO2 , which appears in the earth’s crust mainly as the carbonates of C a, M g and Fe.
Per 1 mole of (C aO + M gO + FeO) 0,035 mole of CO2 is present. The group CO2
was partitioned between the mentioned groups and elements Z n, Cu, P b and C d,
appearing also in the form of carbonates. The group SO3 was partitioned between
C aO and M gO forming sulphates. It was assumed that a prevailing part of metals
(Sn, C o, M n, Fe, N i) appears in the form of different oxides (C o2 O3 , C o3 O4 , Fe2 O3 ,
Fe3 O4 ). It was also assumed that 8% of Fe appears in the form of the free oxide
Fe2 O3 . The remaining part appears in the form of FeT iO3 , FeC r2 O3 and silicates. For
example, the following silicates were assumed: N aAlSi3 O8 , KAlSi3 O8 , N aFeSi2 O6 ,
M gSiO3 , C aO.Al2 Si2 O7 . Because of the large content of SiO2 , a considerable part of
it was assumed in the free form. After estimating the composition of a mean sample
of the lithosphere, its molecular mass was calculated.
152
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
Ranz [276] updated the molecular mass of the upper continental crust using more
recent geochemical information and adopting not only a geochemical approach, but
also a geological one. The methodology used was as follows: the international accepted norm CIPW [262] was applied to the mass fractions of the principal oxide
groups obtained by Carmichael [49] for the cratonic and sedimentary layers, in order
to redistribute the chemical components from the oxides to the mineral molecules
that are representative in real minerals appearing in a rock. Next, the minerals of
the norm and their respective relative masses were modified to adjust them to the
real volumes of the principal groups of each rock. Finally, their molar fractions were
calculated and the mean molecular mass of the whole was obtained. The resulting M Wc r was equal to 145,5 g/mole. Even though this methodology used better
geochemical values than the ones in Szargut [334], and included the geological
approach, we cannot forget that the CIPW norm is an artificial way to obtain the
possible minerals that can appear in a rock. It is therefore only an approximation as
well.
In the light of Grigor’ev’s analysis, a more accurate molecular weight of the upper
continental crust, based on experimental results rather than assumptions, can be
easily obtained. The new calculated value is M Wcr = 142,1 g/mole, which is very
close to the estimation done by Ranz. Our model threw up a mean molecular weight
of the upper crust of M Wc r =155,2 g/mole.
5.2.3.4
Update of the liquid reference substances
Rivero and Garfias [281] have found the influence of salinity of seawater on the
calculated values of standard chemical exergy of elements calculated by means of
reference substances dissolved in seawater. However, an increased salinity (greater
than 35 per thousand) appears seldom (Red Sea), and the deviations are not large
(usually less than 1,6%). Every introduction of solid reference substances can decrease the accuracy of calculations. Therefore we are assuming the solid reference
substances only for the elements from the second column of the periodic system.
Following ionic and molecular reference substances dissolved in seawater have been
accepted in the recent publication of Szargut [338] and will be used for this proposal:
C l − , Ag C l2− , B(OH)3 (aq), BiO+ , Br − , C d C l2 (aq), Cs+ , Cu+2 , H PO4−2 , HAsO4−2 ,
H g C l4−2 , IO3− , K + , Li + , M oO4−2 , N a+ , N i +2 , P bC l2 (aq), Rb+ , SO4−2 , SeO4−2 , W O4−2 ,
Z n+2 .
Major ions in seawater are ions with fractions greater than 1 ppm. The seawater
reference environment taken into account in this proposal comprises the following
major ions: N a+ , K + , HAsO4−2 , BiO+ , C l − , SO4−2 , Br − , B(OH)3 . Values of the
activity coefficients and molarity of these species basing on information presented
in Millero [224], [225], Pilson [264] and Mottl [231] were reviewed and compared
with those which Ranz and Rivero took into account.
The reference environment
5.2.3.5
153
The updated reference environment. Results
Table 5.4 shows the results obtained in this study for the chemical exergy of the
elements with the geochemical information of the crust (M Wcr and z0i ) obtained
in this PhD (This study 1) and the one provided by Grigor’ev [127] (This study 2).
The solid R.S. assumed are those taken by Szargut [336], basing on the Szargut’s
criterion mentioned before. Additionally, the values are compared to those given by
Szargut [336], Valero, Ranz and Botero [371] and Rivero and Garfias [281]. The
different reference substances divided into liquid, gaseous and solid R.S. and the
values required for the calculations are shown in tables A.13, A.14 and A.15 in the
appendix, page 384.
The average difference between our study (1) and Szargut’s values is around 0,66%
on average, while between study (2) with Grigor’ev’s model and Szarguts’, about
0,93%. Hence, in both cases, the average differences are very small. Nevertheless,
small differences multiplied by huge numbers, such as the quantity of all minerals
on earth, make these discrepancies to be not so insignificant. Next, each of the
three subsystems (gaseous, liquid and solid R.S.) is analyzed, stressing the biggest
differences found in the different models.
The obtained values for gaseous R.S. are the same of those obtained by Szargut
[336] and Valero, Ranz and Botero [371], since the methodology and the values
used for this R.E. have been the same. The differences between this study (1) and
(2) and that of Rivero and Garfias [281] are due to the different partial pressures in
the atmosphere assumed.
The new chemical exergies obtained differ in 0,5% in average for study (1) and
1% for study (2) with respect to the values obtained by Szargut in [336] for solid
reference substances. Taking the empirical standard molar concentration of solid
R.S. from our model instead of obtaining it with Eq. 5.3, implies a difference in the
element chemical exergy of about 0,2% except for Au (9,5%) and F (6,7%). For
the latter elements, the greater difference is due to the greater sensitivity of Au to
x i (since its ∆G f is equal to zero) and the great proportion of atoms of C a in the
reference substance of F (C aF2 ), respectively. It must be stressed that choosing a
certain c j or another a 100 times greater, throws less differences in the chemical
exergy of the elements than choosing another R.S., as can be seen in the models of
Valero et al. [371] and Rivero et al. [281], when other R.S. are considered. The
same thing happens with the molecular weight of the earth’s crust. An M Wcr of
142,1 or 155,2 only modifies the chemical exergy of the elements in 0,03%, and
hence that parameter is not crucial at all.
For the liquid R.S., with the exception of SO4−2 the differences are negligible from
the point of view of the influence on the final exergy of the considered element. In
the case of SO4− , Szargut and Valero et al. assumed a value of mSO−2 = 1,17E-2, and
4
Rivero mSO−2 = 1,24E-2. The molarity calculated basing on the three independent
4
sources [225], [264] and [231] is estimated as mSO−2 = 2,93E-2 and is almost 2,5
4
154
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
times greater. This difference decreases the chemical exergy of sulfur only about 2
kJ/mole. The rest of the obtained results are very similar to previous investigations
and the differences are negligible.
Table 5.4: Standard chemical exergies of the elements
Element
Ag
Al
Ar
As
Au
B
Ba
Be
Bi
Br2
C
Ca
Cd
Ce
C l2
Co
Cr
Cs
Cu
Dy
Er
Eu
F2
Fe
Ga
Gd
Ge
H2
He
Hf
Hg
Ho
Standard chemical exergy of the elements, bch j (kJ/mole)
This study This study Szargut
Valero et al. Rivero et al.
1
2
[336]
[371]
[281]
69,7
69,7
70,2
70,3
R.S.=AgC l
99,3
794,3
795,8
888,2
R.S. =Al2 O3 795,7
796,7
11,7
11,7
11,7
11,7
11,6
494,1
494,1
494,6
R.S.=As2 O5
492,6
411,5
51,5
56,4
50,5
53,4
50,6
628,6
628,6
628,5
628,5
628,1
765,5
777,2
775,1
774,3
775,4
602,6
606,4
604,4
R.S.=BeO
604,3
615,6
274,8
274,8
274,5
274,6
274,8
101,1
101,1
101,2
101,3
101,0
410,3
410,3
410,3
410,3
410,3
723,8
719,9
729,1
R.S.=C a2+
729,1
712,4
293,2
293,2
293,8
293,8
R.S.=C dCO3
298,4
1054,2
1054,5
1054,6
1054,4
1054,7
124,2
124,2
123,6
123,7
123,7
308,9
308,6
312,0
R.S.=C o3 O4
313,4
270,4
584,4
584,5
584,3
R.S.=C r2 O3
584,4
559,1
404,5
404,5
404,4
404,6
404,6
134,0
134,0
134,2
134,2
R.S.=CuCO3
132,6
974,9
975,1
975,9
975,3
976,0
973,0
973,2
972,8
973,1
972,8
1003,9
1004,1
1003,8
1004,4
1003,8
556,1
595,5
504,9
R.S.=C aF2
505,8
482,7
376,8
377,1
374,8
374,8
374,3
514,6
514,7
514,9
514,7
515,0
969,9
970,1
969,0
969,6
969,0
556,5
556,7
557,6
556,3
557,7
236,1
236,1
236,1
236,1
236,1
30,4
30,4
30,4
30,4
31,3
1061,3
1061,5
1062,9
1061,3
1063,1
114,8
114,8
115,9
115,9
R.S.=H gC l2
107,9
979,3
979,5
978,6
979,5
978,7
Continued on next page . . .
The reference environment
Table 5.4: Standard chemical exergies of the elements – continued from previous page
Element
I2
In
Ir
K
Kr
La
Li
Lu
Mg
Mn
Mo
N2
Na
Nb
Nd
Ne
Ni
O2
Os
P
Pb
Pd
Pr
Pt
Pu
Ra
Rb
Re
Rh
Ru
S
Sb
Sc
Se
Si
Sm
Sn
Sr
Ta
Tb
Te
Th
Ti
Tl
Standard chemical exergy of the elements, bch j (kJ/mole)
This study This study Szargut
Valero et al. Rivero et al.
1
2
[336]
[371]
[281]
175,0
175,0
174,7
174,8
175,7
437,4
437,5
436,8
437,6
436,9
256,1
256,4
246,8
256,5
247,0
366,5
366,5
366,6
366,7
366,7
34,4
34,4
34,4
34,4
34,3
994,3
994,5
994,6
994,5
994,7
392,9
392,9
393,0
393,0
392,7
946,6
946,9
945,7
946,7
945,8
629,6
629,4
626,1
R.S.=M g +2
626,9
611,0
484,6
490,1
482,0
482,9
487,7
730,5
730,5
730,3
730,3
731,3
0,7
0,7
0,7
0,7
0,7
336,6
336,6
336,6
336,7
336,7
900,2
900,3
899,7
899,4
899,7
969,8
970,0
970,1
970,1
970,1
27,2
27,2
27,2
27,2
27,1
232,5
232,5
232,7
232,7
R.S.=N iO
242,6
4,0
4,0
4,0
4,0
3,9
370,8
371,0
368,1
369,8
368,4
861,6
861,6
861,4
861,4
861,3
232,2
232,2
232,8
232,8
R.S.=P bCO3
249,2
145,7
145,9
138,6
146,0
138,7
963,8
964,1
963,8
964,0
963,9
146,5
146,7
141,0
140,9
141,2
1099,7
1099,9
1100,0
1099,8
1100,1
825,8
826,1
823,9
823,7
824,2
388,8
388,8
388,6
388,9
388,7
561,3
561,4
559,5
560,3
559,6
183,0
183,1
179,7
176,6
179,7
315,2
315,5
318,6
318,4
318,6
607,3
607,3
609,6
609,6
609,3
437,1
437,2
438,0
438,0
438,2
923,8
923,9
925,2
924,1
925,3
346,7
346,7
346,5
346,5
347,5
854,2
854,1
854,9
854,2
855,0
993,9
994,1
993,6
994,2
993,7
547,6
536,8
551,9
549,2
551,8
758,8
773,6
749,8
748,6
749,8
974,8
975,0
974,0
973,8
974,1
999,0
999,2
998,4
999,4
998,5
326,4
326,6
329,2
329,1
329,3
1214,5
1220,7
1202,6
1202,1
1202,7
904,4
902,0
907,2
902,9
907,2
193,8
194,0
194,9
194,2
194,9
Continued on next page . . .
155
156
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
Table 5.4: Standard chemical exergies of the elements – continued from previous page
Element
Tm
U
V
W
Xe
Y
Yb
Zn
Zr
5.2.4
Standard chemical exergy of the elements, bch j (kJ/mole)
This study This study Szargut
Valero et al. Rivero et al.
1
2
[336]
[371]
[281]
952,5
952,7
951,7
952,5
951,8
1196,1
1196,3
1196,6
1196,2
1196,6
721,5
721,6
720,4
722,2
721,3
827,7
827,7
827,5
827,5
828,5
40,3
40,3
40,3
40,3
40,3
966,3
966,5
965,5
966,4
965,6
944,9
945,2
944,3
944,8
944,3
339,0
339,0
339,2
339,2
R.S.=Z nCO3
344,7
1077,4
1080,9
1083,4
R.S.=Z rO2
1083,0
1060,7
End of the table
Drawbacks of Szargut’s R.E. methodology
As stated in section 5.2, the R.E. can be considered as one, in which all the substances
contained in it have reacted, dispersed and mixed. Such an environment, would
have probably a hydrosphere with a composition of groundwaters, rivers, lakes, etc.
similar to that of the sea. The atmosphere would have a much greater CO2 and other
pollutant’s content than it does now, due to the complete burning of fossil fuels. And
the continental crust would have likely a very similar composition to the current one
(except for the absence of fossil fuels), but completely dispersed with no enriched
mineral deposits.
Szargut’s and subsequent reference environments are composed of only one reference substance per element, i.e. 85 R.S. Obviously a degraded earth would contain
many more substances. Additionally, the variables used in Szargut’s and subsequent
models are based on current and not eventual values1 . Furthermore, many minerals
that are more stable than the R.S. have negative exergies. This fact occurs not that
often than with Ranz’s abundance criterion, but it still happens, as we will see later
in chapter 6. A chemically inactive R.E. would be the one created by Ahrendts [4]
and further developed by Diederichsen [74]. In both models the positiveness of any
substance is assured. But as stated before, these reference environment’s compositions are far removed from the currently known and from an eventually degraded
earth.
1
For instance partial pressures of gaseous R.S., temperatures or molalities are taken as those appearing currently in the atmosphere and the sea.
The exergy of mineral resources
157
Hence, the reference environment based on Szargut’s criterion should not be considered as a dead R.E., but rather as a mathematical tool for obtaining standard
chemical exergies of the elements. Furthermore, it is always subject to updates, as
new geochemical information is more available.
5.3
5.3.1
The exergy of mineral resources
The energy involved in the process of formation of a mineral
deposit
As stated in Ranz’s PhD [276], a mineral deposit can be seen as a very unfrequent
aggregates of rocks, which in turn rocks are aggregate of minerals, and these are
aggregates of certain molecular substances, which are composed by aggregates of
atoms. This definition can be summarized as in Eq. 5.7:
P
PP
Deposi
t
=
r
ocks
=
miner
PPP
PPP
P als =
mol ecul es =
at oms
(5.7)
Each aggregate is characterized by two different properties: a cohesion energy or
binding energy, represented by its enthalpy of formation, and the entropy of the
mixture or of formation, which indicates the probability degree of forming the substance under consideration. The four steps implicated in the formation of the mineral
deposit are outlined as follows [276]:
Step I:
Step II:
Step III:
Step IV:
Formation of the molecule: Σ Atoms (g) → Molecule (g)+ ∆ H, ∆ S
Solidification: Molecule (g) → Molecule (s)+ ∆ H, ∆ S
Solid 1 + Solid 2 → Mineral+ ∆ H, ∆ S
Formation of the deposit: % Mineral + Rocks → Mine + ∆ H, ∆ S
The first two steps are basically chemical processes, in which the energies involved
are determined by the change of enthalpy and entropy that accompanies the formation of 1 mole of a substance from its constituent elements. The solidification
energy is much smaller than the thermodynamic process of formation of the mineral. Usually, the process of formation of a mineral proceeds directly to its solid
phase.
The third step is subdivided into two processes: mineralization and formation of
the rock. The mineralization stage is a chemical process, in which the molecules
combine to form the mineral. The formation of the rock is a physical process, where
the solids (or minerals) are mixed to form a conglomeration. The general expression
for the entropy generated in a mixture process of two ideal gases, solids or liquids is
expressed as in Eq. 5.8.
∆S = ∆S1 + ∆S2 = −n1 R̄
Z
x1 P
P
dP
P
Z
x2 P
− n2 R̄
P
dP
P
= −R̄ n1 l nx 1 + n2 l nx 2 (5.8)
158
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
Generally, the generation of entropy in mixtures, and especially in solid solutions,
is much smaller than that for thermal exchanges associated to the formation of the
compound, temperature increases or phase changes.
Finally, the fourth step deals with the formation of the mineral deposit. Mineral
deposits have the special feature that contain certain minerals at much greater concentrations than in the earth’s crust.
According to Faber [90], if the resource of a mineral deposit at a concentration
x i is extracted, the entropy will decrease, and the entropy change per mole of the
resource is given by Eq. 5.9.
(1 − x i )
∆S = R̄ l nx i +
l n(1 − x i ) < 0
xi
(5.9)
According to the second law of thermodynamics, this negative entropy flux is only
possible if there is another system to which it flows. Hence, an external energy
supply is needed. The standard energy involved in separating the resource from the
mineral deposit is then the concentration exergy bc , in kJ/mole:
(1 − x i )
bc i = −R̄T 0 l nx i +
l n(1 − x i )
xi
(5.10)
where R̄ is the universal gas constant (8,314 kJ/kmole K), T 0 is the standard ambient
temperature (298,15 K) and x is the molar concentration of the substance.
Additionally to the concentration exergy, which accounts for a minimum, the binding forces in the formation of the crystal should be accounted for [276]. The bonds
generated are of different nature. 1) Covalent or ionic bonds, forming a threedimensional crystalline structure. In the absence of crystalline defects, the energy
needed to separate them is equal to the interatomic bonding energy. 2) Cohesion of
interphase forces and capillarity suction, which is commonly found in the agglomeration of a solid by a liquid, acting as an adhesive cement. 3) Intermolecular and
electrostatic forces, binding very thin particles. 4) Mechanical interpenetration of
particles, typically formed by compression.
The energy needed to separate a solid particle from others of smaller size depend on
different physical aspects such as size, hardness or surface area. Some expressions
have been developed for relating the particle size with the grinding energy. Kicks’s
law or Bond’s law are two of those studies (see for instance, [259] for more details).
Both laws indicate that the grinding energy increases exponentially as the particle
size decreases.
As we will see in later sections, the chemical energies involved in the formation of
the deposit are considerably higher than the physical energies explained in this last
step.
The exergy of mineral resources
5.3.2
159
The exergy of non-fuel mineral resources
The thermodynamic value of a natural resource can be defined as the minimum
work necessary to produce it with a specific structure and concentration from common materials in the environment. This minimum amount of work is theoretical
by definition and is equal to the material’s exergy (Riekert [278]). The exergy of
a system gives an idea of its evolution potential for not being in thermodynamic
equilibrium with the environment, or what is the same, for not being in a dead state
related to the reference environment (R.E.).
The physical features that make minerals valuable are mainly their specific composition and the greater concentration in the ores in which they are found [371]. The
energy involved in the process of formation of a mineral comprises the formation of
the compound from its elements, and the cohesion of the molecules to form the mineral’s crystal structure (step 1 to 3 in section 5.3.1). The minimum theoretical work
that nature should invest to provide minerals at a specific composition and structure
from a degraded earth is equal to the standard chemical exergy [336] and it can be
calculated by means of the exergy balance of a reversible formation reaction as in
Eq. 5.1.
bch i = ∆G f i +
X
r j,i bch j
j
Once the mineral has been created, it mixes with other minerals to form rocks, which
in turn, are combined with other rocks forming the deposit (step 4 in section 5.3.1).
The minimum theoretical work needed to concentrate a substance from an ideal
mixture of two components is given by the concentration exergy (bc ), as in Eq. 5.10.
The binding energy between minerals and rocks is not considered in the ideal case.
Therefore, the exergy needed to separate the minerals from the deposit is the same
as the exergy to mix them. Nevertheless this binding exergy is taken into account
through the unit exergy costs explained in section 5.3.4.
The difference between the concentration exergies obtained with the mineral concentration in a mine (x m )2 and with the average concentration in the earth’s crust
(x c ) 3 is the minimum energy that nature had to spend to bring the minerals from the
concentration in the reference state to the concentration in the mine. The concentration exergy of a mineral in a completely degraded planet is zero, and it increases,
as its concentration increases. The work needed to separate a substance from a
mixture does not follow a linear behavior with its concentration. On the contrary,
the second law of thermodynamics, reflected in Eq. 5.10 and represented in Fig.
5.1 dictates that the effort required to separate the mineral from the mine follows
a negative logarithmic pattern with its ore grade. This means that as the ore grade
2
3
x m replaces x in Eq. 5.3.4 for obtaining the concentration exergy of the mineral in the mine
x c replaces x in Eq. 5.3.4 for obtaining the concentration exergy of the mineral in the R.E.
160
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
35
bc, MJ/kmole
30
25
20
15
10
5
0
0,00001
0,15
0,4
0,65
0,9
xi
Figure 5.1. Exergy required for separating a substance from a mixture, according to
Eq. 5.10.
tends to zero, the energy needed to extract the mineral tends to infinity. Right that
component of the mineral’s exergy is what makes exergy a more realistic measure of
magnitude than mass, for instance [392]. Furthermore, it invalidates the statement
of Brooks and Andrews [41] that exhaustion of minerals is ridiculous because the
entire planet is composed of minerals. The energy that nature saves us when concentrating minerals in high grade ores, is too elevated to reproduce it with current
technology.
The unit exergies are converted into absolute ones (here denoted by Bch and Bc ), by
multiplying bch and bc with the moles of the resource under consideration (n). The
sum of Bch and Bc , indicates the total exergy of the mineral deposit (B t ), including
the chemical and concentration components (see Eq. 5.11).
B t i = ni · bch i + ni · bc i = Bch i + Bc i
5.3.3
(5.11)
The chemical energy and exergy of fossil fuels
Fossil fuels are a type of minerals and therefore, their chemical and concentration
exergies can be calculated with Eqs. 5.1 and 5.10. Liquid and gaseous fuels have
the particularity, that their quality (grade) keeps nearly constant with extraction,
The exergy of mineral resources
161
whereas solid minerals don’t (mineral’s concentration decreases as the deposit is
being exploited). Hence, for those cases, the concentration exergy is not so relevant
than with other types of mineral resources and it will not be taken into account for
our calculations. Furthermore, the value of fuels is tightly related to its chemical
exergy content.
The heterogeneity and complexity of the chemistry of fuels make the chemical exergy
to be very difficult to predict with Eq. 5.1. But different thermodynamic models
have been proposed to calculate the exergy of fossil fuels. Stepanov [330], compiles
some of the different methodologies proposed. Rant [275], for instance, calculated
the ratios of exergies to heating values and then estimated average values of these
ratios for liquid and gaseous fuels4 . Szargut and Styrylska [342] corrected Rant’s
formulas by taking into consideration the chemical composition of fuels. Shieh and
Fan [310] obtained expressions for the exergy calculation of materials with complex
structures. We will focus on the models developed by Valero and Lozano [369]
for obtaining the chemical exergy of fossil fuels, but it must be pointed out, that
more complex calculation procedures, do not mean more reliable results. Both, the
experimental error associated to the determination of the heating values and the
error associated to the correlations are comprised reasonably in an interval close to
±2 %. Additionally, it has been largely demonstrated, that the chemical exergy of
fuels can, in many cases, be satisfactorily approximated to the HHV.
For the case of gaseous fuels, Valero and Lozano [369], showed that the chemical
exergy can be estimated as the exergy of a mixture of ideal gases (Eq. 5.12).
bch g as =
X
0
x i (bch
i + R̄T0 l nx i )
(5.12)
0
Where x i is the molar fraction of the chemical substance i and bch
is the standard
i
chemical exergy of substance i.
The exergy for gaseous fuels can thus be calculated with Eq. 5.12, or with the general
methodology applied to liquid and solid fuels, explained next.
The procedure is based on the general molecular formula of Eq. 5.13.
C HhOo Nn Ss + Ww + Zz
(5.13)
Where W represents the moles of liquid water (moisture) and Z of the ashes. Coefficients h, o, n, s, w and z are the moles of elements H, O, N , S, water and ashes
contained in the molecular structure of the fuel, per mole of C content, respectively:
h=
H 12,011
C 1,008
o=
O 12,011
C 15,999
n=
N 12,011
C 14,007
s=
S 12,011
C 32,064
w=
W 12,011
C 18,015
z=
Z 12,011
C 1,000
4
The ratios determined by Rant were 0,975 for liquid fuels and 0,95 for gaseous fuels. This
indicates that the chemical exergy is very close to the high heating value of the substance.
162
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
Note that W and Z apply only to solid fossil fuels and s = 0 in gaseous fuels. The
standard average energy and exergy of the fuel on a molar basis is then:
e0f uel = eC0 H
h Oo Nn Ss
0
+ ze0Z
+ weW
(5.14)
b0f uel = bC0 H
h Oo Nn Ss
0
+ z b0Z
+ w bW
(5.15)
And ei0 and bi0 are calculated as follows:
ei0 = ∆H 0f ,i −
X
bi0 = ∆H 0f ,i − T 0 si0 −
f j H j,00
(5.16)
X
(5.17)
f j µ j,00
Where ∆H 0f ,i and si0 are the standard enthalpy and entropy of the fuel, T 0 the standard ambient temperature, f j the elements of the atomic composition vector of the
fuel f = [1, h, o, n, s]0 , and H j,00 and µ j,00 the enthalpy and the chemical potential
of the elements in the dead state.
The atomic composition vector of a gaseous fuel f j,gas , can be obtained with Eq.
5.18:
Pn
f j,gas =
i=1 r j,i
· ξi
(5.18)
d1
Being r j,i the number of atoms j contained in component i of the mixture of gases
5
and ξi the molar composition of substance i in the
. The moles of C contained
Pfuel
n
in the fuel is expressed as d1 and is calculated as i=1 rC,i · ξi .
The formation enthalpy can be calculated with the high or low heating values (HHV,
LHV), using the following expressions:
h
∆H 0f , f uel = H H V + ∆H f ,CO2 + ∆H 0f ,(H O) + s∆H 0f ,SO
2
2
l
2
H H V = LH V +
h
2
h
+w
∆H 0f ,(H
2 O) g
− ∆H 0f ,(H
i
2 O)l
(5.19)
(5.20)
In case the experimental heating values are not available, they can be approximated
through the following expressions:
5
Gaseous fuels are assumed to contain the following 7 gases: C H4 , C2 H6 , C3 H8 , C4 H10 , C5 H12 , N2
and CO2 .
The exergy of mineral resources
163
Liquid fossil fuels. Lloyd’s correlation [198] in cal/mole C:
H H V = 102720 + 27360 · h − 32320 · o + 19890 · n + 85740 · s
(5.21)
Solid fossil fuels. Boie correlation [279] in cal/ mole C:
H H V = 100890 + 27990 · h − 42400 · o + 21010 · n + 80160 · s
(5.22)
For gaseous fuels, ∆H 0f can be calculated with the following equation:
P
∆H 0f , f uel
=
ξi · ∆H 0f ,i
(5.23)
d1
The standard entropy is calculated with the correlations proposed by Ikumi [158]
for liquid fossil fuels and those of Eisermann, Johnson and Conger [83] for solid
fuels.
Liquid fossil fuels, in cal/(mole C· K):
s0f uel = 1, 12 + 4, 40 · h + 10, 66 · o + 20, 56 · n + 20, 70 · s
(5.24)
Solid fossil fuels, in cal/(mole C· K):
s0f uel = 8, 88272 − 7, 5231e
h
−0,56482 1+n
+ 4, 80748

o
‹
1+n
+ 12, 9807

n ‹
1+n
+ 10, 6767

s
‹
1+n
(5.25)
Gaseous fossil fuels, in cal/(mole C· K):
P
s0f uel =
Š
€
P
ξi si0 − R̄l n( P 0i )
(5.26)
d1
The calculation of the enthalpy and chemical potential for each element (H j,00 and
µ j,00 ) are calculated with Eqs. 5.27 and 5.28 and depends on the species composing
the reference environment.
€
Š
H j,00 = ∆H f , j + ∆C p, j T0 − T 0
µ j,00 = ∆H f , j − T0 ∆s j + ∆C p, j
0
T0 − T − T0 l n
T0
T0
+ R̄T0 l n
(5.27)
x j,00 · P0
P0
(5.28)
164
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
Where x j,00 is a vector, including the molar concentration of the gases in the reference environment, ∆H f , j , ∆s j and ∆C p, j are the enthalpy and entropy of formation
and the specific heat change of the species in the reference environment required to
form the element as in equations 5.29 and 5.30. Subscript 0 denotes the environment, while superscript 0, the standard reference environment.
Lozano [201] proposed the three R.E. (I, II and III) shown in table 5.5, for calculating
the chemical energy and exergy of the substances:
Table 5.5. Composition of the three R.E. proposed
(j=1) C ↔(jj=1)
(j=2) H ↔(jj=2)
(j=3) O ↔(jj=3)
(j=4) N ↔(jj=4)
(j=5) S ↔(jj=5)
(j=6) C a ↔(jj=6)
I
CO2 (g)
H2 O (g)
O2 (g)
N2 (g)
SO2 (g)
II
CO2 (g)
H2 O (l)
O2 (g)
N2 (g)
SO2 (g)
III
CO2 (g)
H2 O (l)
O2 (g)
N2 (g)
C aSO4 · 2H2 O (s)
C aCO3 (s)
For R.E. I and II, ∆H f , j is calculated as in Eqs. 5.29. The expression for the calculation of ∆s j and ∆C p, j are analogous to that of ∆H f , j . Note that for element H, the
enthalpy and specific heat taken for H2 O must be in the gaseous and liquid state for
R.E. I and II, respectively.
( j = 1)
∆H f ,C = ∆H f ,CO2 − ∆H f ,O2
∆H f ,H2 O ∆H f ,O2
( j = 2) H : ∆H f ,H =
−
2
4
∆H f ,O2
( j = 3) O : ∆H f ,O =
2
∆H f ,N2
( j = 4) N : ∆H f ,N =
2
( j = 5) S : ∆H f ,S = −∆H f ,O2 + ∆H f ,SO2
C:
For R.E. III, the following expressions are valid:
(5.29)
The exergy of mineral resources
( j = 1)
C:
( j = 2)
H:
( j = 3)
O:
( j = 4)
N:
( j = 5)
S:
165
∆H f ,C = ∆H f ,CO2 − ∆H f ,O2
∆H f ,H2 O ∆H f ,O2
−
∆H f ,H =
2
4
∆H f ,O2
∆H f ,O =
2
∆H f ,N2
∆H f ,N =
2
(5.30)
∆H f ,S = ∆H f ,CO2 − 2∆H f ,H2 O −
( j = 6) C a : ∆H f ,C a = −∆H f ,CO2 −
∆H f ,O2
2
3∆H f ,O2
2
+ ∆H f ,C aSO4·2H2 O − ∆H f ,C aCO3
+ ∆H f ,C aCO3
The resolution of Eq. 5.28 is given in table 5.6.
1
1
1
0
0
0
R.E. I
R.E. II
R.E. III
R.E. I
R.E. II
R.E. III
T0 − T 0 − T0 l n
0
0
0
0
0
-1
T
0
T0
0
0
-194398
Ca
0
0
0
0,5
0
0
2,259
7,245
7,245
H
O
N
S
∆C p, j , cal/(mole K)
3,508
3,481
2,515
3,508
3,481
2,515
3,508
3,481
-12,717
e2
0
0
0
0
0
0
0
0
0
e5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1,702
Ca
-98546
-98546
-98546
-1
-1
-1
2,065
2,065
2,065
C
-32760
-32767
-32767
-0,25
-0,25
-0,25
10,302
-3,876
-3,876
H
O
N
S
∆s j , (cal/ mole K)
24,502
22,885
10,285
24,502
22,885
10,285
24,502
22,885
-31,77
e3
0,5
0
-1
0,5
0
-1
0,5
0
-1,5
µ j,00 , cal/mol e
-7777
-6902
-85372
-7777
-6902
-85372
-7777
-6902
-145967
—
”
+ R̄T0 l n (x CO2 ,00 · P0 )e1 · (x H2 O,00 · P0 )e2 · (x O2 ,00 · P0 )e3 · (x N2 ,00 · P0 )e4 · (x SO2 ,00 · P0 )e5
0
0
0
0
0
0
1,855
1,855
1,855
C
(5.31)
0
0
-173192
0
0
-0,5
0
0
-53,373
Ca
τ0 = T0 − 273, 15; F1 = −741, 9242; F2 = −29, 7210; F3 = −11, 55286; F4 = −0, 868535; F5 = 0, 1094098; F6 = 0, 439993; F7 = 0, 2520658
0
Where: e1, e2, e3, e4 and e5 are the exponentials used to calculate the contribution of the entropy change for gaseous reference substances. x j,00 is calculated
with the following equations for each gaseous component [11]: x CO2 ,00 = 0, 0003(1 − x H2 O,00 ); x O2 ,00 = 0, 2099(1 − x H2 O,00 ); x N2 ,00 = 0, 7898(1 − x H2 O,00 );
h
i
P8
1−1
x SO2 ,00 = 10−9 (1 − x H2 O,00 ); x H2 O,00 = Pv,H2 O (T0 ) = 217, 99ex p 0,01
F
(0,
65
−
0,
01τ
)
(374,
16
−
t
)
i
0
0
i=1
T
O
N
S
∆H f , j , cal/mole
-28898
0
0
-70960
-34158
0
0
-70960
-34158
0
0
-152032
e1
0
0
0
0
0
0
0
0
0
0
0
1
e4
0
0
0,5
0
0
0
0,5
0
0
0
0,5
0
H
THERMODYNAMIC
µ j,00 = ∆H f , j − T0 ∆s j + ∆C p, j
-94052
-94052
-94052
C
R.E. I
R.E. II
R.E. III
Element j
Table 5.6. Calculation of the chemical potential of the elements according to three different R.E.
166
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
The exergy of mineral resources
167
If the ambient temperature is different to that of the standard, then bi0 is replaced
by bi in Eq. 5.15 (see Eq. 5.32). And bi is calculated with Eq. 5.33. Similarly, ei0 is
replaced by ei in Eq. 5.14 and ei is calculated with Eq. 5.34.
b f uel = bC Hh Oo Nn Ss + w · bW + z · b Z
bi = ∆H f ,i − T0 si −
ei = ∆H f ,i −
X
X
f j µ j,00
f j µ j,00
(5.32)
(5.33)
(5.34)
The enthalpy and entropy of the clean fuel and the moisture for liquid and solid fuels
is obtained with Eqs. 5.35 and 5.36.
∆H f ,i =
si =
∆H 0f ,i
si0
+
Z
+
Z
T
C p (T )d T
(5.35)
T0
T
T0
C p (T )
T
dT
(5.36)
The specific heat for liquid fuels at a density of 15◦ C (ρ15 ) comprised in an interval
between 0,75 and 0,96 k g/d m3 , can be obtained through Eq. 5.37 in cal/(kgK)
[258].
1
C p,L (T ) = p
(181 − 0, 81T )
ρ15
(5.37)
The specific heats in cal/(kgK) for the clean solid fuel, the moisture W and the ashes
Z are calculated with the correlations of Kirov6 [258]:
C p,F (T ) = −52 + 0, 909T − 0, 420 · 1−3 T 2
(5.38)
C p,W (T ) = 703 + 0, 632T + 9, 610 · 106 /T 2
(5.39)
C p,Z (T ) = 142 + 0, 140T
(5.40)
The exergy of the ashes Z is obtained directly through Eq. 5.41:
6
Note that C p,L , C p,F and C p,W must be converted into cal/mole K for the calculation of the enthalpy
and entropy.
168
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
bZ =
T
Z
1−
CZ
T0
T0
(5.41)
dT
T
The enthalpy of gaseous fuels can be calculated with Eq. 5.42:
Pn
∆H f ,i =
∆H 0f ,i
+
i=1
”
—
x i h∗i (T ) − h∗i (T 0 )
(5.42)
d1
Where h∗i (T ) is obtained with the help of the method of Zelenik and Gordon [413]:
‚
h∗i (T )
= RT
a1 + a2
T
2
+ a3
T2
3
+ a4
T3
4
+ a5
T4
5
+
a6
Œ
(5.43)
T
The entropy of the gaseous fuel can be calculated with Eq. 5.44:
Pn
s=
i=1
—
”
P
x i si∗ (T ) − Rl n P 0i
(5.44)
d1
Where si∗ (T ) is obtained through [413] with Eq. 5.45
‚
si∗ (T )
= R a1 l nT + a2 T + a3
T2
2
+ a4
T3
3
+ a5
T4
4
Œ
+ a7
(5.45)
Coefficients a1 through a7 for the calculation of h∗ (T ) and si∗ (T ) are provided in
table A.16 in the appendix for the different gases composing the gaseous fuel.
From Eqs. 5.17 through 5.32, one can conclude that the exergy of fuels is a function
of the conditions of the ambient. This means, that if the temperature, pressure or the
concentration of for instance CO2 change, the exergy of fuels will do so accordingly.
5.3.4
The exergy costs
The sum of the chemical and concentration components defined previously in section
5.3.2 represents the total exergy that can be understood as the minimum energy
required for restoring the resource from the reference environment.
As stated before, fuel minerals are useful for their inherent chemical exergy. Consequently, the value associated to fossil fuels is tightly related to its exergy. However,
non-fuel minerals are not necessarily useful for their chemical exergy content. The
value of a non-fuel mineral resource is rather associated to the extraction costs. A
very abundant and concentrated mineral in the crust, such as iron, will have a high
exergy value and a low exergy cost of extraction. On the contrary, a very dispersed
The exergy of mineral resources
169
and scarce mineral such as gold, has a low exergy value, but a very high exergy cost
of extraction. Obviously, the cost is a very important ingredient of the final price in
the market and that is why scarce minerals tend to be the most expensive ones.
The exergy replacement cost (B ∗ ) of minerals measures something similar to their
natural cost. It was defined by Valero et al. [370] as the exergy required by the given
available technology to return a resource from the dispersed state of the reference
environment, into the physical and chemical conditions in which it was delivered by
the ecosystems. Actual energy requirements to obtain a resource are always greater
than those dictated by the second law.
For instance, the thermodynamic energy required to separate two substances such
as sugar and salt, is equal to the energy to mix them, which is in fact very low.
This is the reason why concentration exergies of minerals are usually one order of
magnitude greater than chemical ones. However, current processes are far from ideal
conditions because of inefficiencies of our technology resulting in irreversibilities.
In order to overcome that problem, we must include the actual physical unit costs,
here named as unit exergy replacement costs, in the thermodynamic evaluation of
resources. Valero et al. [370] defined them as the relationship between the energy
invested in the actual process for obtaining the resource and the minimum energy
required if the process were reversible. Unit exergy replacement costs are dimensionless and measure the number of exergy units needed to obtain one unit of exergy of
the product.
The actual exergy value of a resource (total exergy replacement cost) B ∗ is determined then by the sum of Bc and Bch multiplied respectively by the unit exergy
replacement costs of the processes to obtain it (kch and kc ) as in Eq. 5.46.
B ∗t = kch · Bch + kc · Bc
(5.46)
Where kc is the physical unit exergy replacement cost of concentration, calculated as
the ratio between the real energy invested in the process and the minimum concentration exergy (Bc ). It has to be determined for each type of mineral. It is assumed
that the same technology is applied in all concentration ranges, including the range
between the concentration of the reference environment and the average concentration in the mineral deposits.
And kch is the physical unit exergy replacement cost of the refining process, calculated as the ratio between the real energy invested in the process, and the minimum
chemical exergy (Bch). As opposed to kc , the chemical unit cost of refining a mineral
from the mine to the metallic state cannot be applied to the process of refining the
mineral from the R.E. to the mine, due to the differences of both processes. However, once the refining costs of mineral oxides and sulfides were analyzed, Valero and
Botero [371] realized that on average, the energy expenditure for obtaining a ton of
the pure element from the oxide was about 80 GJ greater than from the sulfide. This
170
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
is as if sulfides would have a natural bonus of 80 GJ/ton and a chemical unit exergy
replacement cost kch of 10 on average. On the other side, oxides and monatomic
minerals are assumed to have a kch at least equal to one.
The contribution of the chemical and concentration components to the actual exergy
value of a resource is usually well balanced, since unit chemical exergy costs are one
or two orders of magnitude smaller than unit concentration exergy costs.
Note that it has no sense to apply exergy replacement costs to fossil fuels, due to the
impossibility of current technology to replace the photosynthetic process that once
created the resource.
Table 5.7 shows the unit exergy replacement costs of some minerals, according to
Valero and Botero [371], which in turn were improved from the initial ones given
by Botero [34]. Martínez et al. [207] studied additionally the unit exergy costs for
some minerals of industrial importance and updated Botero’s values of aluminium,
gold, iron, zinc, lead, copper, nickel and silver.
Table 5.7: Exergy costs of selected substances [371] & [207]
Substance
Ag
Al
As
Au
Ba
Be
Bi
Cd
Co
Cr
Cs
Cu
F
Fe
Ga
Ge
Hf
Hg
In
K
Li
Mg
kc
7042
2250
80
422879
N.A.
112
90
804
1261
37
N.A.
343
2
97
N.A.
N.A.
N.A.
1707
N.A.
39
158
1
kch
10
8,0
10
1
1
1
10
10
10
1
1
80,2
1
5,3
1
1
1
10
10
1
1
1
Substance
Mn
Mo
Na
Nb
Ni
P
Pb
Pt
Re
Sb
Se
Si
Sn
Ta
Te
Ti
U
V
W
Zn
Zr
kc
284
947
38
N.A.
432
44
219
N.A.
1939
28
N.A.
2
1493
12509
N.A.
348
7723
572
3105
126
7744
kch
1
1
1
1
58,2
1
25,4
1
10
10
1
1
1
1
1
1
188,3
1
1
13,2
1
Exergy replacement costs represent a suitable indicator for assessing the value of
non-fuel mineral resources, as they integrate in one parameter, concentration, composition and also the state of technology. Nevertheless, as opposed to exergy, they
The exergy of mineral resources
171
cannot be considered as a property of the resource, since unit exergy costs introduce
to some extent an uncertain factor to the calculation. Something similar happens to
the emergy analysis, explained in section 1.3, through the introduction of the transformities. It should be noted that as stated by Naredo and Valero [239], unit exergy
replacement costs are a function of the state of technology and hence vary with time.
A way to assess the evolution of technological development, is through the theory of
learning curves. With learning-by-doing, increases in material and energy efficiency
increase with cumulative production. Alchian [5] was the first to estimate the effects
of cumulative production on changes in efficiency. He found a linear relationship
between the logarithm of direct labor inputs per unit output and the logarithm of
cumulative production, as in Eqs. 5.47.
l n j(t) = a j1 − a j2 l nΓ(t)
l ne(t) = ae1 − ae2 l nΓ(t)
(5.47)
With j(t) and e(t), the flows of materials and energy used to perform a certain
process; a j1 and ae1 the intercepts of the learning curve with the vertical axes and
a j2 and ae2 parameters relating material and energy inputs per unit output at time
period t to cumulative production in period t, Γ(t).
Ruth [294] argued that such a specification of the learning curves, allows materials
and energy input per unit output to approach zero as cumulative production approaches infinity, thus violating thermodynamic lower limits on j(t) and e(t). The
expressions of Eqs. 5.48 are according to Ruth more realistic in the sense that material and energy efficiencies decrease asymptotically towards zero in double-log space
as Γ(t) approaches infinity. Thus as cumulative production increases, material and
energy use per unit output can at best assume the value one, indicating perfect efficiency.
l n j(t) = a j1 e x p(−a j2 l nΓ(t))
l ne(t) = ae1 e x p(−ae2 l nΓ(t))
(5.48)
In this PhD, we have considered unit exergy replacement costs constant, i.e. we have
assumed that the state of technology has been the same throughout the 20 th century.
A more exact determination of the exergy costs of minerals throughout history would
imply changing unit exergy replacement costs. These could be calculated through
the help of the learning curves explained above. But this task remains outside the
scope of this PhD and is open for further refinements.
172
THERMODYNAMIC
5.4
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
Prediction of Enthalpy and Gibbs free energy of
formation of minerals
The determination of the thermodynamic properties of the substances requires the
knowledge of their corresponding enthalpies and Gibbs free energies of formation.
Many of these have been already estimated through empirical and semi-empirical
processes7 and are tabulated. Comprehensive compilations of the thermodynamic
properties of inorganic substances can be found in Faure [94], Wagman [391], Robie
et al. [284], [285] or Weast et al. [400].
Unfortunately, not all the enthalpies and Gibbs free energies of the minerals that
we have taken into account in our model are recorded in the literature. Nevertheless, many of them can be predicted satisfactorily through different semi-empirical
methods. In the next sections, the estimation methods of the thermodynamic properties used to obtain the standard enthalpy and Gibbs free energy of formation of
the minerals in the model of the upper crust developed in chapter 3 will be provided.
5.4.1
Calculation of ∆H 0f or ∆G 0f from s0
If either ∆H 0f or ∆G 0f and the entropy (s0 ) of the mineral under consideration are
available, the unknown property can be easily calculated applying Eq. 5.49.
∆G 0f = ∆H 0f − T0 · ∆S
(5.49)
Where the entropy change ∆S is calculated from the standard entropy of the mineral
and its constituent elements in the standard state (T0 = 298, 15 K and 1 bar), as in
Eq. 5.50:
0
∆S = sminer
al −
X
0
selements
(5.50)
Note that this procedure does not have associated any error, since it is based on the
definition of ∆G f .
Example: for mineral bronzite FeM gSi2 O6 , the enthalpy and entropy of formation
is known from [309]: ∆H 0f = −2753, 38 kJ/mole and s0 = 149, 13 J/(mole K). The
entropy change of bronzite is calculated as:
∆s FeM gSi2 O6
= s0FeM gSi
2 O6
0
− (s0M g + s0Fe + 2 · sSi
+ 3 · sO0 )
2
= 149, 13 − (27, 09 + 32, 67 + 2 · 18, 81 + 3 · 205, 15)
= −563, 70 J/(mole.K)
7
Such as calorimetric or solubility measurements.
Prediction of Enthalpy and Gibbs free energy of formation of minerals
173
0
Where sel
are obtained from [284]. The Gibbs free energy of formation of
ements
bronzite can be finally calculated with Eq 5.49:
∆G 0f ,FeM gSi
2 O6
5.4.2
= −2753, 38 − 298, 15 ·
563, 70
1000
= −2585, 31 kJ/mole
The ideal mixing model
An ideal solid solution of i components with x i molar fractions obeys the equations:
∆H m = 0
(5.51)
and
∆Gm = +RT
X
(5.52)
x i l nx i
Where ∆H m and ∆Gm , are the enthalpy and Gibbs free energy of mixing. This
means that the ideal mixing will take place without any heat loss or heat production.
Moreover, the different cations will be fully interchangeable [254]. The enthalpy
and Gibbs free energy of formation of the solid solution is calculated then with Eqs.
5.53:
∆H 0f ,solut ion =
X
x i ∆H 0f ,i
i
∆G 0f ,solut ion
=
X
x i ∆G 0f ,i
+ RT
X
x i l nx i
(5.53)
i
The error associated to the assumption of the mineral as an ideal solid solution varies
greatly with the mineral under consideration and decreases with the disorder among
components. We will assume a maximum error of ±1%.
Example: mineral tetradymite Bi2 Te2 S can be considered as a solid solution of
Bi2 Te3 , and Bi2 S3 , for which ∆H 0f and ∆G 0f are well known from [226] and [94]:
Bi2 Te2 S
⇔
2
1
Bi2 Te3 + Bi2 S3
3
3
Hence, ∆H 0f ,t et r ad y mi t e and ∆G 0f ,t et r ad y mi t e are calculated as follows with Eqs: 5.53:
174
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
∆H 0f ,t et r ad y mi t e
∆G 0f ,t et r ad y mi t e
5.4.3
5.4.3.1
=
2
1
· ∆H f ,Bi2 Te3 + ∆H f ,Bi2 S3
3
3
1
2
· (−78, 7) + (−143, 2)
=
3
3
= −100, 2 kJ/mole
=
2
1
2
2
1
1
· ∆G f ,Bi2 Te3 + ∆G f ,Bi2 S3 + RT
ln
+ ln
3
3
3
3
3
1
8, 314
· (−78, 3) + (−140, 7) +
· 298, 15(−0, 63)
=
3
3
1000
= −100, 6 kJ/mole
3
2
Assuming ∆G r and ∆H r constant
Thermochemical approximations for sulfosalts and complex oxides
Craig and Barton [67] developed an approximation method for estimating the thermodynamic properties of sulfosalts in terms of mixtures of the simple sulfides. The
ideal mixing model does not apply correctly to most sulfosalts, because the mixtures
of layers are rather ordered. The modified ideal mixing model of Craig and Barton
involves a mixing term (∆Gm ) in the estimation of the Gibbs free energy of formation of the sulfosalt per gram atom of S that is added to the weighted sum of free
energies of the simple sulfides:
∆Gm = (1, 2 ± 0, 8)(+RT
X
x i l nx i )
(5.54)
The mixing term can be divided into two parts, one estimated from the crystal structure as an entropy change, and the reminder as a non-ideal term. The non-ideal
term of this model was assumed to be constant for all sulfosalts. However, Vieillard
[387] showed that the properties of complex sulfides with respect to their simple
sulfides are a function of the electronegativity difference between the cations of the
sulfosalt.
The thermodynamic properties of sulfosalts may then be calculated by adding a term
(∆H r or ∆G r ) to the appropriately weighted sum of the enthalpies or free energies
of the simple component sulfides i (Eq. 5.55).
∆H f sul f osal t =
X
x i ∆H f i + nS sul f osal t ∆H r
∆G f sul f osal t =
X
x i ∆G f i + nS sul f osal t ∆G r
(5.55)
Prediction of Enthalpy and Gibbs free energy of formation of minerals
175
The reaction term, which is analogous to the mixing term of Craig and Barton is
associated to one atom of sulfur in the mineral (nS,sul f osal t ) and is obtained from a
sulfosalt for which its thermodynamic properties and those of its simple sulfides are
known. The calculated reaction terms can be applied to a family of sulfosalts formed
by the same cations and with partial element substitutions.
Example: mineral cubanite CuFe2 S3 can be decomposed into the sulfides CuFeS2
and FeS, for which the thermodynamic properties are provided [226]. The properties of cubanite can be calculated with Eq. 5.55, once ∆H r and ∆G r are known. The
reaction terms are obtained from mineral bornite Cu5 FeS4 as follows:
∆H r,Cu5 FeS4
=
=
∆H f ,Cu5 FeS4 − ( 25 ∆H f ,Cu2 S + 12 ∆H f ,Fe2 S3 )
4
(−371, 6) − [ 52 (−83, 9) + 12 (−279, 91)]
4
= −5, 48 kJ/mole S
∆G r,Cu5 FeS4
=
(−394, 7) − [ 52 (−89, 2) + 12 (−280, 75)]
4
= −7, 83 kJ/mole S
Where the properties of bornite and its constituents are provided in [284] and [241].
Hence, ∆H f and ∆G f of cubanite are calculated as:
∆H f ,CuFe2 S3
= ∆H f ,CuFeS2 + ∆H f ,FeS + 3 · ∆H r
= (−176, 8) + (−99, 98) + 3 · (−5, 48)
= −293, 22 kJ/mole
∆G f ,CuFe2 S3
= (−178, 49) + (−100, 40) + 3 · (−7, 83)
= −302, 38 kJ/mole
Vieillard et al. [387] demonstrated the analogy between the electronegativity scale
of cations with respect to sulfur and to oxygen. They showed that the methodology
of estimation of the thermodynamic properties of sulfosalts from simple sulfides can
be equally applied to complex oxides able to be decomposed into simple oxides. As
for sulfosalts, the reaction terms ∆H r and ∆G r (for this case denoted as ∆H ox and
∆Go x ) should be obtained for an oxide of the same family of the mineral under
analysis. The maximum error associated to this methodology is assumed to be ±1%.
176
5.4.3.2
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
The method of corresponding states
Similarly, the ∆H r and ∆G r can be assumed to be constant in the substitution reaction of minerals A-x and B-x into A-y and B-y, if A-x and B-y are isomorphous (Eq.
5.56). The associated error is assumed to be equal to the previous method, hence
±1%.
A − x + y → A − y + x (∆H r , ∆G r )
B − x + y → B − y + x (∆H r , ∆G r )
(5.56)
Consider mineral fluor-annite K Fe3 (Si3 Al)O10 (F )2 as an example, for which no
empirical thermodynamic values are available. Fluor-annite can be formed from
hydroxy-annite K Fe3 (Si3 Al)O10 (OH)2 as in the following reaction:
K Fe3 (Si3 Al)O10 (OH)2 + 2H F → K Fe3 (Si3 Al)O10 (F )2 + 2H2 O
Similarly, fluor-phlogopite can be formed from hydroxy-phlogopite. Since the thermodynamic properties of both substances are known, the reaction energy of substitution can be calculated:
K M g3 (Si3 Al)O10 (OH)2 + 2H F → K M g3 (Si3 Al)O10 (F )2 + 2H2 O
∆H r
= ∆H 0f ,K M g
3 (Si3 Al)O10 (F )2
+ 2∆H 0f ,H
2O
− ∆H 0f ,K M g
3 (Si3 Al)O10 (OH)2
− 2∆H 0f ,H F
= (−6375, 5) + 2 · (−285, 8) − (−6246, 0) − 2 · (−332, 6)
= −17, 9 kJ/mole H F
∆G r
= ∆G 0f ,K M g
3 (Si3 Al)O10 (F )2
+ 2∆G 0f ,H
2O
− ∆G 0f ,K M g
3 (Si3 Al)O10 (OH)2
− 2∆G 0f ,H F
= (−6030, 1) + 2 · (−237, 1) − (−5860, 5) − 2 · (−278, 8)
= −43, 11 kJ/mole H F
Where the thermodynamic properties are obtained from [391]. Fluor-annite can
now be calculated, assuming the same reaction energy calculated with phlogopite:
Prediction of Enthalpy and Gibbs free energy of formation of minerals
∆H 0f ,K Fe
3 (Si3 Al)O10 (F )2
= ∆H 0f ,K Fe
3 (Si3 Al)O10 (OH)2
+ 2∆H 0f ,H F − 2∆H 0f ,H
177
2O
+ 2∆H r
= (−5149, 3) + 2 · (−332, 6) − 2 · (−285, 8) + 2 · (−17, 9)
= −5278, 8 kJ/mole
∆G 0f ,K Fe (Si Al)O (F )
3
3
10
2
= ∆G 0f ,K Fe
3 (Si3 Al)O10 (OH)2
+ 2∆G 0f ,H F − 2∆G 0f ,H
2O
+ 2∆G r
= (−4798, 3) + 2 · (−278, 8) − 2 · (−237, 1) + 2 · (−43, 11)
= −4967, 9 kJ/mole
The thermodynamic properties of hydroxy-annite are obtained from [383].
5.4.4
The method of Chermak and Rimstidt for silicate minerals
The method proposed by Chermak and Rimstidt [55] predicts the thermodynamic
properties (∆G 0f and ∆H 0f ) of silicate minerals from the sum of polyhedral oxide and
hydroxide contributions. The technique is based on the observation that silicate minerals have been shown to act as a combination of basic polyhedral units. Chermak
[4]
and Rimstidt determined by multiple linear regression, the contribution of Al2 O3 ,
[6]
[6]
[4]
[6]
Al2 O3 , Al(OH)3 , SiO2 , M gO[6] , M g(OH)2 , C aO[6] , C aO[8−z] , N a2 O[6−8] ,
[6]
K2 O[8−12] , H2 O, FeO[6] , Fe(OH)2
[6]
and Fe2 O3
to the total ∆G 0f and ∆H 0f of a
selected group of silicate minerals 8 . The thermodynamic properties of the minerals
are calculated with Eqs. 5.57 and 5.58:
∆H 0f =
X
x i · hi
(5.57)
∆G 0f =
X
x i · gi
(5.58)
Where x i is the number of moles of the oxide or hydroxide per formula unit and hi
and g i are the respective molar enthalpy and free energy contribution of 1 mole of
each oxide or hydroxide component. Table A.17 in the appendix shows the values
of hi and g i for the different polyhedral components described in the methodology
[55].
The errors associated to the estimated vs. experimentally measured values can reach
±1% for ∆G 0f and ∆H 0f , depending on the nature of the compounds. Note that this
methodology can only be applied to those minerals able to be decomposed by the
oxides and hydroxides mentioned before.
8
The brackets next to the chemical formulas of oxides and hydroxides indicate the coordination
number of the polyhedral structure.
178
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
Example: the properties of mineral thomsonite N aC a2 Al5 Si5 O20 · 6H2 O are calculated as the sum of the g i and hi from its constituent oxides (N a2 O[6−8] , C aO[8−z] ,
[4]
[4]
Al2 O3 , SiO2 and H2 O):
∆H 0f ,N aC a
2 Al 5 Si5 O20 ·6H 2 O
5
hN a2 O[6−8] + 2hC aO[8−z] + hAl O[4] + 5hSiO[4] + 6hH2 O
2
2
2 2 3
1
5
=
(−683, 00) + 2(−736, 04) + (−1716, 4)
2
2
+5(−910, 97) + 6(−239, 91)
=
1
= −11543, 92 kJ/mole
∆G 0f ,N aC a
2 Al 5 Si5 O20 ·6H 2 O
=
1
5
(−672, 50) + 2(−710, 08) + (−1631, 32)
2
2
5 + (−853, 95) + 6(−292, 37)
= −12413, 65 kJ/mole
5.4.5
The ∆O−2 method
The linear additivity procedures based on the ∆O−2 parameter were developed by
Yves Tardy and colleagues [348], [349], [350], [351], [352], [347], [108], [380],
[383]. The parameter ∆O−2 , corresponds to the enthalpy ∆H O−2 or Gibbs free
energy ∆G O−2 of formation of a generic oxide M Ox (c) from its aqueous ion, where
z + is the charge of the ion and x the number of oxygen atoms combined with one
atom M in the oxide (x = z + /2):
∆H O−2 M z+ =
∆G O−2 M z+ =
1
x
1
x
z+
]
[∆H 0f M Ox(c) − ∆H 0f M(aq)
(5.59)
z+
]
[∆G 0f M Ox(c) − ∆G 0f M(aq)
(5.60)
For hydroxides, silicates, phosphates, nitrates and carbonates involving two cations,
it was found that the enthalpy and Gibbs free energy of formation of a given compound from its constituent oxides vary linearly with ∆O−2 and have the general
expressions [347]:
∆H o0x
= αH
and
∆Go0x
= αG
ni · n j
ni + n j
ni · n j
ni + n j
2−
z+
z+
j
Mi i (aq) − ∆H O2− M j (aq)
(5.61)
2−
z+
z+
j
Mi i (aq) − ∆G O2− M j (aq)
(5.62)
∆H O
∆G O
Prediction of Enthalpy and Gibbs free energy of formation of minerals
179
Being ∆H o0x and ∆Go0x :
∆H o0x [(Mi )ni (M j )n j ON ] = ∆H 0f [(Mi )ni (M j )n j ON ](c) − ni ∆H 0f Mi Ox i (c)
−n j ∆H 0f M j Ox j (c)
(5.63)
∆Go0x [(Mi )ni (M j )n j ON ] = ∆G 0f [(Mi )ni (M j )n j ON ](c) − n1 ∆G 0f Mi Ox i (c)
−n2 ∆G 0f M j Ox j (c)
(5.64)
z+
Where ni and n j are the numbers of oxygen ions linked, respectively, to the Mi i and
z+
j
M j cations; and N is the number of oxygens linked to the molecular structure of
the double oxide (N = x i + x j ). Parameters αH and αG are empirical coefficients
variable from one family of compounds to another one (αG is 0,84 for hydroxides,
1,01 for silicates, 1,15 for carbonates, 1,30 for nitrates, etc.).
Equation 5.62, yields a statistical deviation of 35 kJ/mole for the Gibbs free energy
of formation and depends on the family of compounds. We will assume a maximum
error associated to the ∆O2− general method of ±1%9 .
Example: for the silicate C a3 Si2 O7 , the α parameter was determined at -1,01 and
0
∆G O−2 C a2+ = −50, 31 and ∆G O−2 Si 4+ = −188, 08 kJ/mole [350]; so that ∆Gox
can be calculated with Eq. 5.64 as:
3·4
· [∆G O−2 C a2+ (aq) − ∆G O−2 Si 4+ (aq)]
3+4
= −238, 5 kJ/mole
∆Go0x (C a3 Si2 O7 ) = (−1, 01)
And
∆G 0f (C a3 Si2 O7 )(c) = 3∆G 0f C aO(c) + 2∆G 0f SiO2 (c)
0
+∆Gox
(C a3 Si2 O7 )(c)
= −3748, 1 kJ/mole
The value is close to ∆G 0f (C a3 Si2 O7 ) = −3760, 4 kJ/mole from Robie and Hemingway [284].
This methodology was later on improved by Vieillard ([380], [390], [381]) and Vieillard and
Tardy [389], by introducing a new empirical parameter representing the electronegativity of the cation
M z+ (comp).
9
180
THERMODYNAMIC
5.4.5.1
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
The ∆O−2 method for hydrated clay minerals and for phyllosilicates
Vieillard extended the methodology described above for the prediction of hydrated
clay minerals [382] and for phyllosilicates [383].
Hydrated clay minerals, have formulas expressed as:
(Ml1 , Ml2 , Ml3 ) (M g o1 , Feo2+ , Al o3 , Feo3+ ) (Si(4−t) Al t )O10 (OH)2 . Layer silicates can be
2
4
of two types: (a) 2:1 layer type, (Ml i , Mo j )(Si(4−t) Al t )O10 (OH)2 , with l i the number of interlayer atom which varies from 0 (pyrophyllite, talc) to 1 (micas, if
M = K + or N a+ , brittle micas, if M = C a2+ , or Ba2+ ) and (b) 2:1:1 layer type
(Mo j )Si(4−t) Al t )O10 (OH)2 · (M bk (OH)6 ), where bk is the number of brucitic cations.
Subscripts l, o, and t denote, respectively, the interlayer, octahedral, and tetrahedral
sites. The possible cations occupying each site of the mineral can be seen in table
A.18 for clays and phyllosilicates.
The Gibbs free energy of formation of a hydrated clay mineral or a phyllosilicate
composed by ns cations located in different sites and with ns (ns − 1)/2 interaction
terms is calculated as:
∆G 0f
=
i=n
Xs
0
(ni )∆G 0f (Mi Ox i ) + ∆Gox
(5.65)
i=1
0
The Gibbs free energy of formation from the oxides ∆Gox
is calculated with Eq. 5.66,
which is analogous to Eq. 5.64:

∆Go0x = −N

s −1 j=n
X
Xs
i=n

i=i
j=i+1
h
i
zj+
z+
X i X j ∆G O2− Mi i (cl a y) − ∆G O2− M j (cl a y)

where N is the total number of O atoms of all oxides; X i and X j are the molar
z+
zj+
fraction of oxygen related to the cations Mi i and M j in the individual oxides
Mi Ox i and M j Ox j , respectively (X i = (1/N )(ni x i ) and X j = (1/N )(n j x j )). Paramez+
zj+
ters Mi i (clay) and M j
zj+
z+
(clay) characterize the electronegativity of cations Mi i
and M j in a specific site and are calculated by minimizing the difference between
experimental Gibbs free energies and calculated ones from constituent oxides. Table
z+
A.18 in the appendix shows Mi i (clay) values for some of the main ions for hydrated
clays and phyllosilicates.
The predicted Gibbs free energy values showed an error between 0,0 and 0,6 %.
Prediction of Enthalpy and Gibbs free energy of formation of minerals
181
The ∆O−2 method for different compounds with the same cations
5.4.5.2
Tardy [347] showed that the Gibbs free energy of formation of a compound from
its two constituent oxides calculated per one oxygen in the formula was a parabolic
function of mean ∆O−2 compound. Subsequently, an expression for calculating the
Gibbs free energy of formation of a compound C intermediate in composition to two
compounds A and B, A + B → C was developed:
∆Go x,A+B→C = +αG
∆G O
2−
z+
Mi i
− ∆G O
2−
z+
j
Mj
nC (X iC − X iA)(X iC − X iB ) (5.66)
where nc designates the total number of oxygens of the compound C and X iA, X iB ,
z+
X iC the mole fractions of oxygen that balance cation Mi i in compounds A, B, and C
and α the correlation parameter for a given class of compounds, as in Eq. 5.62.
5.4.6
Assuming ∆S r zero
Helgeson et al. [134] showed that the entropy of formation of mineral B can be
determined, assuming that the entropy of the reaction involved in the formation of
the mineral is zero (Helgeson’s algorithm). Helgeson algorithm is useful when either
∆G 0f or ∆H 0f are known. Once the entropy of the mineral is known, ∆G 0f (or ∆H 0f )
can be calculated with ∆H 0f (or ∆G 0f ) through Eq. 5.49. The error associated to this
approximation is up to 5%.
Example:
T hSiO4 + UO2 → USiO4 + T hO2
0
0
s0 T hSiO4 = sUSiO
+ s0T hO − sUO
4
2
2
= 118, 0 + 62, 2 − 77, 0
= 106, 2
5.4.7
5.4.7.1
Assuming ∆G r and ∆H r zero
The element substitution method
In some cases, thermodynamic properties are available for a certain mineral (A),
belonging to the same family of the substance under consideration (B), but with
partial element substitutions. In such a case, the ∆H 0f and ∆G 0f of mineral B can
be calculated from mineral A, assuming that the reaction enthalpy or free energy
182
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
of formation of mineral B from A is zero. This approximation increases with the
magnitude of substitution and may yield to associated errors of up to 5%, although
it rarely exceeds ±2%. We will outline this method with an example.
Consider the mineral hydrosodalite N a8 Al6 Si6 O24 (OH)2 , for which no empirical
thermodynamic values are available. Hydrosodalite can be formed from sodalite
N a8 Al6 Si6 O24 (C l)2 as in the following reaction:
N a8 Al6 Si6 O24 (OH)2 + 2H C l → N a8 Al6 Si6 O24 (C l)2 + 2H2 O
Assuming that the energy of reaction is zero, ∆H 0f and ∆G 0f of hydrosodalite are
calculated as:
∆H 0f ,N a
8 Al 6 Si6 O24 (OH)2
= ∆H 0f ,N a
8 Al 6 Si6 O24 (C l)2
+ 2 · ∆H 0f ,2H
2O
− 2∆H 0f ,H C l
= (−13457) + 2 · (−285, 8) − 2 · (−167, 2)
= −13408, 5 kJ/mole
∆G 0f ,N a Al Si O (OH)
8 6 6 24
2
= ∆G 0f ,N a
8 Al 6 Si6 O24 (C l)2
+ 2 · ∆G 0f ,2H
2O
− 2∆G 0f ,H C l
= (−12703, 6) + 2 · (−237, 1) − 2 · (−131, 1)
= −12678, 2 kJ/mole
Where the thermodynamic properties of sodalite, H2 O and H F are obtained from
[187] and [391], respectively.
5.4.7.2
The addition method for hydrated minerals
Hydrated minerals have the ability to absorb nw water molecules, forming part of
their crystal structure:
A + nw · H 2 O → A · nw H 2 O
Usually, thermodynamic properties are available for the non-hydrated mineral. But
the enthalpy and Gibbs free energy of formation of the hydrated substance can be
0
estimated by addition of the hydration enthalpy and Gibbs free energy ∆Ghy
or
dr
∆Hh0y d r to those of the dehydrated substance, as in Eqs. 5.67.
∆H 0f ,A·n
w H2 O
∆G 0f ,A·n
w H2 O
0
= ∆H 0f ,A + nw · ∆Hhy
d r,A
0
= ∆G 0f ,A + nw · ∆Ghy
d r,A
(5.67)
Prediction of Enthalpy and Gibbs free energy of formation of minerals
183
If ∆Gh0y d r and ∆Hh0y d r are not available, one can assume that the enthalpy and
Gibbs free energy of the hydration reaction are zero (as in section 5.4.7.1). And
hence, the properties of the liquid water molecules contained in the hydrated sub0
0
stance must be added in place of ∆Ghy
and ∆Hhy
. This is not rigourously exact,
dr
dr
as demonstrated by Vieillard and Jenkins ([386], [384], [385]) and the error associated depends on the nature of the dehydrated component10 . We will assume an
associated error of ±5%, although it rarely exceeds ±2%.
Example: the contribution of tetrahedral silica Si 4+ to the hydration energy is
not known, so the enthalpy of opal SiO2 · 0, 5H2 O is calculated assuming that
the reaction energy of the hydration process is zero. Hence, ∆H 0f ,SiO ·0,5H O =
2
2
∆H 0f ,SiO +0, 5∆H 0f ,H O(l) = −901, 6 + 0, 5 · (−285, 8) = −1044, 5 kJ/mole. The en2
2
thalpy of formation of SiO2 (amorph.) and H2 O (l) are obtained from [284].
5.4.7.3
The decomposition method
If non of the previously described methods can be applied, the thermodynamic properties of a certain mineral can be estimated as the last resort by decomposing it into
its major constituents for which the enthalpy and Gibbs free energy of formation are
known. It will be assumed that the energy of reaction of the constituents to form
the mineral under consideration is zero. The error associated to this methodology is
significantly greater than with the substitution and addition methods, since in this
case we are not dealing with partial substitutions or additions of a known mineral,
but with the formation of a completely new mineral from its building blocks. The mineral under analysis will be decomposed into its most complex compounds (usually
double silicates). If this is not possible, most minerals can be decomposed into its
simple oxides, sulfides, carbonates, etc. We will assume that the decomposition
method throws an error of up to 10%.
Example: mineral pyroxene C aAl2 SiO6 can be decomposed into 1: C aO and
Al2 Si2 O5. Alternatively, into 2: C aO, SiO2 and Al2 O3 .
C aAl2 SiO6 → C aO + Al2 Si2 O5
→ C aO + Al2 O5 + SiO2
10
This methodology is not applied for hydrated clay minerals and phyllosilicates. In those cases,
the ∆O2− method is applied.
184
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
Hence, the Gibbs free energy of pyroxene is estimated as follows, with the help of
the thermodynamic properties tabulated in [94]:
∆G 0f ,C aAl
2 SiO6
= ∆G 0f ,C aO + ∆G 0f ,Al
2 Si2 O5
= (−603, 1) + (−2440, 1)
= −3043, 2 kJ/mole
or
∆G 0f ,C aAl SiO
2
6
= ∆G 0f ,C aO + ∆G 0f ,Al
2 O3
+ ∆G 0f ,SiO
2
= (−603, 1) + (−1583, 4) − (−856, 3)
= −3042, 8 kJ/mole
The measured Gibbs free energy of pyroxene reported in [94] is ∆G 0f = −3119, 7,
what gives an error of 2,4 and 2,5% of the estimated values with decompositions 1
and 2, respectively.
5.4.8
Summary of the methodologies
The described methodologies in the previous sections, will be used for calculating
the thermodynamic properties of the most abundant minerals in the earth’s upper
crust. Each methodology is given a number so as to specify in the next chapter,
which methodology has been used for determining the enthalpy or free energy of
formation of the minerals (see table 5.8). Additionally, the assumed maximum errors
associated to the estimation methods (± Error %) are given.
Table 5.8. Summary of the methodologies used to predict the thermodynamic properties of minerals
Method
Calculation of ∆H 0f or ∆G 0f from s0
The ideal mixing model
Thermochemical approximations for sulfosalts and complex oxides
The method of corresponding states
The method of Chermak and Rimstidt for silicate minerals
The ∆O−2 method
The ∆O−2 method for hydrated clay minerals and for phyllosilicates
The ∆O−2 method for different compounds with the same cations
Assuming ∆S r zero
The element substitution method
The addition method for hydrated minerals
The decomposition method
Nr.
1
2
3
4
5
6
7
8
9
10
11
12
±Error, %
0
1
1
1
1
1
0,6
1
5
5
5
10
Summary of the chapter
5.5
185
Summary of the chapter
This chapter has provided the thermodynamic tools required for the calculation of
natural resources, especially for minerals. We have seen, that the exergy of any
substance is always associated to a reference environment. The conditions of the
reference environment determine the final exergy value, therefore, the R.E. had to
be carefully selected. For that purpose, the different R.E. proposed so far have been
reviewed. It has been stated, that the best suitable R.E. for determining the exergy
of natural resources is the one based on Szargut’s criterion. The model developed
by Szargut has been adapted to our requirements with the help of new geochemical
information and the updates carried out by other authors. As a result, two different
R.E. have been proposed, the first one, taking into account the model of the continental crust developed in chapter 3, and the other one, considering the parameters
included in Grigor’ev’s model [127]. It has been stated, that the difference between
these R.E. and Szargut’s original environment, differ for both cases in less than 1%.
Nevertheless, when the whole continental crust is considered, these small numbers
become not so insignificant.
Next, the energy involved in the formation processes of a mineral deposit has been
shown. The most energy intensive processes are those related to the chemical formation of the mineral. The physical processes associated to the mixing and binding
of the crystal structure of the mineral are not so energy-intensive.
We have seen that the minimum exergy embedded in a mineral has two components:
the chemical and concentration components. The first parameter accounts for the
formation of the mineral from the R.E. The concentration exergy expresses the minimum energy that nature had to spend to bring the minerals from the concentration
in the reference state to the concentration in the mine. We have seen, that the latter
shows a negative logarithmic pattern with the grade. This means that as the ore
grade of the mine tends to zero, the exergy of the deposit approaches also zero and
the exergy required for replacing the mine tends to infinity.
Fossil fuels are a type of minerals, in which the concentration exergy is not so relevant. The chemical exergy of fuels is difficult to obtain with the formulas provided
for the rest of minerals, because of the complexity of their chemical structure. Hence,
special calculation procedures are applied. It has been seen, that the chemical exergy
of fossil fuels can be in many cases approximated to its HHV. Nevertheless, the different formulas developed by Valero and Lozano [369] have been provided, because
through them, we can calculate the effect of variations in the conditions of the ambient on the exergy of fuels.
The exergy values are very small, if compared to the real energy required for the
replacement of natural resources to their original state. In order to account for
the inefficiencies of man-made processes, the exergy values are multiplied by the
unit exergy replacement costs. These are dimensionless and measure the number
of exergy units needed to obtain one unit of exergy of the product. The resulting
186
THERMODYNAMIC
MODELS FOR THE EXERGY ASSESSMENT OF NATURAL RESOURCES
exergy costs represent the exergy required by the given available technology to return a resource into the physical and chemical conditions in which it was delivered
by the ecosystem. As opposed to exergy, exergy costs cannot be considered as a property of the resource, since unit exergy costs introduce to some extent an uncertain
factor to the calculation. Nevertheless, they can be used as a suitable indicator for
assessing the value of non-fuel mineral resources, as they integrate in one parameter,
concentration, composition and also the state of technology. Although unit exergy
replacement costs are considered in this PhD to be constant, in reality they vary with
time, as technology is being developed. The assessment of unit exergy replacement
costs as a function of time with the help of learning curves is a task that remains
open for further studies.
The chapter ends with the description of the twelve semi-theoretical models for the
calculation of enthalpies and Gibbs free energies of formation, required for the calculation of the chemical exergy of minerals.
All these tools, will allow us to assess in subsequent chapters, the exergy of the
substances that compose the earth, previously described in chapters 2, 3 and 4.
Chapter
6
The thermodynamic properties of
the earth and its mineral
resources
6.1
Introduction
This chapter is devoted to the calculation of the standard thermodynamic properties
of the earth (enthalpy, Gibbs free energy and exergy) focusing on each of its outer
layers: the atmosphere, hydrosphere and upper continental crust. For that purpose,
the geochemistry of our planet described in Part I is required, together with the
thermodynamic tools provided in chapter 5.
Additionally, a first approach to the chemical composition of the entropic earth is
provided.
Finally, the exergy of the mineral resources of the earth (of fuel and non-fuel origin)
will be calculated and added to the energy sources described in chapter 4. The
exergy of the natural resources will be analyzed and compared to the global chemical
exergy of the earth calculated before.
6.2
The properties of the earth
As we anticipated in previous chapters, the thermodynamic properties of the earth
are related to the species contained in it and not to their elements. In the model
developed in section 3.4.1, this implies that the average Enthalpy (∆H f ), Gibbs free
energy (∆G f ) or Chemical Exergy (b ch) of the earth expressed as kJ/g of earth, are
calculated as:
187
188
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
∆H f =
m
X
(ξi · ∆H f i )
(6.1)
i=1
∆G f =
m
X
(ξi · ∆G f i )
(6.2)
i=1
b ch =
m
X
(ξi · bch i )
(6.3)
i=1
Being ξi , the specific quantity of the species composing the earth, expressed in
mole/g, and ∆H f i , ∆G f i and bch i , their enthalpy, Gibbs free energy and chemical exergy in kJ/mole, respectively.
The enthalpy and Gibbs free energy of the substances are obtained either through
the literature or through the estimation methods described in section 5.4.
Remember also that the chemical exergy of the substance (bch i ) in kJ/mole is calculated with Eq. 5.1:
X
bch i = ∆G f +
r j,i bch j
j
where bch j is the standard chemical exergy of the elements that compose substance
i. In our case we will use the chemical exergy of the elements obtained with the R.E.
developed in this study and shown in table 5.4.
Since we have divided the earth into three subsystems, its average properties will
be first calculated separately for the atmosphere, hydrosphere and continental crust.
The average enthalpy, Gibbs free energy and exergy of the earth’s layers, can be
expressed in molar units by substituting ξi with the molar fraction x i for the i constituents of each sphere. Equation 6.4 relates both properties through the molecular
weight of the sphere considered (M Wspher e ):
x i = ξi · M Wspher e
(6.4)
Next, the specific and global standard properties of the substances composing the
atmosphere, hydrosphere and upper continental crust are shown.
6.2.1
The thermodynamic properties of the atmosphere
Table 6.1 shows the standard thermodynamic properties of the substances contained
in the atmosphere (on a dry basis), according to the composition provided in section
2.3.1. Values for ∆H 0f ,i and ∆G 0f ,i are taken from Weast et al. [400].
The properties of the earth
189
Table 6.1: Thermodynamic properties of the atmosphere. Va0
lues of ∆H 0f i , ∆G 0f i , bch
in kJ/mole
i
Substance
Nitrogen
Oxygen
Argon
Carbon dioxide
Neon
Helium
Methane
Hydrogen
Nitrogen oxides
Nitrous oxide
Ozone (troposphere)
Carbon monoxide
NMHC (assuming ethylene)
Ozone (stratosphere)
Hydrogen peroxide
Formaldehyde
Chlorofluorocarbon 12
Ammonia
Sulfur dioxide
Carbonyl sulfide
Chlorofluorocarbon 11
Hydrogen sulfide
Carbon disulfide
Carbon tetrachloride
Methylchloroform
Dimethyl sulfide
Hydroperoxyl radical
Hydroxyl radical
Sum
Formula
N2
O2
Ar
CO2
Ne
He
C H4
H2
N O2
N2 O
O3
CO
C2 H4
O3
H2 O2
C H2 O
C F 2C l2
N H3
SO2
OC S
C F C l3
H2 S
C S2
C C l4
C H3 C C l3
C H3 SC H3
HO2
OH
x i [-]
7,81E-01
2,09E-01
9,34E-03
3,60E-04
1,82E-05
5,24E-06
1,70E-06
5,50E-07
5,05E-07
3,10E-07
2,55E-07
1,25E-07
1,25E-08
5,25E-09
5,05E-09
5,50E-10
5,40E-10
5,05E-10
5,05E-10
5,00E-10
2,65E-10
2,53E-10
1,51E-10
9,80E-11
6,50E-11
5,50E-11
2,00E-12
5,00E-14
1,00
∆H 0f i
0,0
0,0
0,0
-393,7
0,0
0,0
-74,8
0,0
33,2
82,1
142,7
-137,2
52,3
142,7
-191,3
-117,2
-477,2
-46,1
-297,0
-142,2
-276,3
-20,6
117,4
-103,0
35,6
-45,8
20,9
39,0
∆G 0f i
0,0
0,0
0,0
-394,4
0,0
0,0
-50,8
0,0
51,3
104,2
163,3
-110,6
70,3
163,3
-131,9
-113,0
-439,5
-16,5
-300,3
-169,4
-238,6
-27,9
67,2
-60,7
51,9
-4,4
22,6
34,2
0
bch
i
0,72
3,97
11,7
19,9
27,2
30,4
831,7
236,1
55,7
106,9
169,2
301,7
1363,0
169,2
108,2
535,3
651,1
338,0
310,9
850,1
636,1
815,5
1692,0
598,1
1412,9
2131,7
144,6
154,3
According to table 6.1, the average standard enthalpy, Gibbs free energy and chemical exergy of the atmosphere can be obtained as:
190
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
0
m
X
(x i · ∆H 0f ,i ) = −1, 42E − 01 kJ/mole
0
m
X
=
(x i · ∆G 0f ,i ) = −1, 42E − 01 kJ/mole
(∆H f )at m =
i=1
(∆G f )at m
i=1
0
(b ch)at m
m
X
0
=
(x i · bch
i ) = 1, 51 kJ/mole
i=1
Obviously, the average properties are very close to those of N2 and O2 , for being both
the major constituents of the atmosphere.
6.2.2
The thermodynamic properties of the hydrosphere
In this section, the thermodynamic properties of the main constituents of oceans,
rivers, groundwaters and glacial runoff are provided. For all subsystems, values for
∆H 0f i and ∆G 0f i are taken from Weast et al. [400].
Table 6.2 shows the thermodynamic properties of the major substances that compose
seawater. The composition of the oceans is the one listed in table 2.5. The more
comprehensive composition given in table 2.6 could not be used, since although the
concentration of minor elements found in seawater are listed, their specific molecular formulas are not specified1 . It should be noted however, that the first composition
comprises more than 99% of the total substances included in seawater and hence,
its uncertainty cannot be compared to that of the continental crust, which had to be
estimated in this PhD.
Table 6.2: Thermodynamic properties of seawater. Values in
kJ/mole
Substance
H2 O
C l−
N a+
M g 2+
SO4−2
C a2+
K+
H CO3−
1
x i [-]
9,80E-01
9,98E-03
8,57E-03
9,65E-04
5,16E-04
1,88E-04
1,87E-04
3,20E-05
∆H 0f i
-286,0
-167,2
-240,2
-467,1
-909,7
-543,1
-252,5
-692,3
∆G 0f i
-237,3
-131,3
-262,0
-455,0
-745,0
-553,8
-283,4
-587,1
0
bch
i
0,79
-69,2
74,6
174,6
-129,8
170,0
83,2
-52,9
For instance, the concentration of vanadium is given, but this element could be in the form of
V + , V 3+ , etc. Obviously, the thermodynamic properties of the different forms of vanadium are
different.
V O2+ ,
The properties of the earth
191
Table 6.2: Thermodynamic properties of seawater. Values in
kJ/mole. – continued from previous page.
Substance
Br −
F−
B(OH)3
CO32−
B(OH)−
4
S r 2+
SUM
x i [-]
1,54E-05
1,24E-05
5,67E-06
4,93E-06
1,83E-06
1,64E-06
1,00
∆H 0f i
-121,6
-332,8
-1072,8
-677,5
-1344,7
-547,2
∆G 0f i
-104,0
-279,0
-969,3
-528,1
-1153,9
-560,0
bch i 0
-53,5
-0,9
19,4
-111,9
-45,1
198,8
The average standard enthalpy, Gibbs free energy and chemical exergy of seawater
(sw) can now be obtained as:
0
(∆H f )sw
= −284, 9 kJ/mole
0
(∆G f )sw
0
(b ch)sw
= −237, 0 kJ/mole
= 0, 87 kJ/mole
The average standard thermodynamic properties of rivers, according to the composition given by Livingstone [197] are shown in table 6.3.
Table 6.3: Thermodynamic properties of average rivers. Values
in kJ/mole
Substance
H2 O
H CO3−
C a2+
N a+
C l−
SiO2
M g +2
SO4−2
K+
N O3−
Fe2+
SUM
x i [-]
1,00E+00
1,72E-05
6,74E-06
4,93E-06
3,96E-06
3,92E-06
3,04E-06
2,10E-06
1,06E-06
2,90E-07
2,16E-07
1,00
∆H 0f i
-286,0
-692,3
-543,1
-240,2
-167,2
-911,4
-467,1
-909,7
-252,5
-207,5
-89,2
∆G 0f i
-237,2
-586,9
-553,5
-261,9
-131,0
-856,7
-454,8
-774,5
-283,3
-111,3
-78,9
0
bch
i
0,79
-52,9
170,0
74,6
-69,2
174,6
174,6
-129,8
83,2
-105,1
297,9
192
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
The average standard enthalpy, Gibbs free energy and chemical exergy of rivers (r w)
is then:
0
(∆H f ) r w
= −286, 0 kJ/mole
0
(∆G f ) r w
0
(b ch) r w
= −237, 2 kJ/mole
= 0, 79 kJ/mole
The average standard properties of glacial runoff, obtained from the composition
provided in section 2.4.3.1, are given in table 6.4.
Table 6.4: Thermodynamic properties of glacial runoff. Values
in kJ/mole
Substance
H2 O
N a+
H CO3−
C a+2
SO4−2
C l−
M g +2
K+
SUM
x i [-]
1,00E+00
1,44E-05
1,42E-05
5,71E-06
5,13E-06
3,92E-06
1,92E-06
9,13E-07
1,00
∆H 0f i
-286,0
-240,2
-692,3
-543,1
-909,7
-167,2
-467,1
-252,5
∆G 0f i
-237,2
-261,9
-586,9
-553,5
-774,5
-131,0
-454,8
-283,3
0
bch
i
0,79
74,6
-52,9
170,0
-129,8
-69,2
174,6
83,2
The average standard enthalpy, Gibbs free energy and chemical exergy of glacial
runoff (g l) is:
0
= −286, 0 kJ/mole
0
= −237, 2 kJ/mole
0
(b ch) gl
= 0, 79 kJ/mole
(∆H f ) gl
(∆G f ) gl
Since the composition of river waters and glacial runoff is very close, similar thermodynamic properties of both types of waters were expected, as corroborated by the
figures provided above.
The properties of the earth
193
Table 6.5. Thermodynamic properties of groundwaters. Values in kJ/mole
Substance
H2 O
H CO3−
C a2+
SO4−2
M g +2
SiO2
C l−
N a+
Al +3
N O3−
K+
Fe2+
SUM
x i [-]
1,00E+00
6,46E-05
3,95E-05
2,96E-05
2,13E-05
7,54E-06
6,98E-06
6,66E-06
2,05E-06
1,47E-06
9,67E-07
5,55E-07
1,00
∆H 0f i
-286,0
-692,3
-543,1
-909,7
-467,1
-911,4
-167,2
-240,2
-531,6
-207,5
-252,5
-89,2
∆G 0f i
-237,3
-587,1
-553,8
-745,0
-455,0
-857,1
-131,3
-262,0
-485,6
-111,4
-283,4
-78,9
0
bch
i
0,79
-52,9
170,0
-129,8
174,6
1,1
-69,2
74,6
308,7
-105,1
83,2
297,9
Table 6.5 shows the estimated average standard thermodynamic properties of
groundwaters on earth. The mean composition of groundwaters has been assumed
to be equivalent to the average of the compositions for granite, shale and serpentinite groundwaters given in table 2.10.
According to table 6.5, the average standard enthalpy, Gibbs free energy and chemical exergy of groundwater (g w) is then:
0
= −286, 0 kJ/mole
(∆G f ) g w
0
= −237, 4 kJ/mole
0
= 0, 80 kJ/mole
(∆H f ) g w
(b ch) g w
Summarizing, table 6.6 shows the standard thermodynamic properties of the hydrosphere. Since the ocean accounts for 97% of all earth’s waters, the global enthalpy,
Gibbs free energy and exergy of the hydrosphere can be approximated to that of seawater. It has been assumed, that the composition of lakes is equal to that of average
rivers.
It is remarkable in the hydrosphere’s tables presented above, that the specific exergy
of all negative ions is also negative. As explained in the previous chapter, the chemical exergy expresses the minimum work required for combining chemically the
reference substances dispersed in the reference environment to obtain the resource.
If the reference species are more stable than the considered substance, then its chemical exergy will be negative. In Ranz’s R.E. [276], this situation came up very
194
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
Table 6.6. Summary of the thermodynamic properties of the hydrosphere. Values in
kJ/mole
Reservoir
Oceans
Ice Caps and
Glaciers
Groundwater
Lakes
Streams and
Rivers
SUM
0
0
0
0
Volume (M km3 )
1370
29
xi
9,73E-01
2,05E-02
∆H f i
-284,9
-286,0
∆G f i
-237,0
-237,2
b ch i
0,87
0,79
x i .∆H f i
-2,77E+02
-5,86E+00
x i . ∆G f i
-2,30E+02
-4,86E+00
x i .b ch i
8,47E-01
1,63E-02
9,5
0,125
0,0017
6,80E-03
1,00E-04
1,00E-06
-286,0
-286,0
-286,0
-237,4
-237,2
-237,2
0,80
0,79
0,79
-1,94E+00
-2,86E-02
-2,86E-04
-1,61E+00
-2,37E-02
-2,37E-04
5,41E-03
7,93E-05
7,93E-07
1408,63
1,00
-284,9
-237,0
0,87
frequently, as she chose reference substances according to the abundance criterion.
In the R.E. developed in this PhD, which is based on partial stability, we have selected reference substances trying to avoid negative chemical exergies. However, in
the light of the hydrosphere’s results, we have not succeeded in that task.
A deeper analysis of the equilibrium substances found in seawater should be carried
out. A good starting point would be the work of Pinaev [266], [265]. Pinaev calculated the chemical exergy of elements, assuming that all reference substances are in
the ocean medium, with the exception of gas reference substances, which were the
same as in this PhD. As opposed to other methodologies, for Pinaev, the exergy of an
element is not obtained from a single reference substance. He takes into account not
only the dominant, but also the main secondary species found in the ocean medium
of each element, at the concentration ruled by their equilibrium constants. This
way, the exergy of an element is calculated as the sum of the exergy of the element
previously obtained with the dominant reference substance and the exergy of their
secondary species, obtained through their equilibrium concentrations.
Nevertheless, Pinaev’s element exergies generate also negative chemical exergies of
negative ions, as corroborated by the next example.
Example: standard chemical exergy of C l − , calculated from the standard chemical
0
exergy of the elements proposed by Pinaev [265]: (bch
= 60, 8 kJ/mole).
Cl
0
bch
C l−
0
= ∆G 0f ,C l − + bch
Cl
= −131, 3 + 60, 8 = −70, 5 kJ/mole
It is not the point of this PhD to show the exergy of all substances on earth calculated
with Pinaev’s R.E. But it has been stated, that the results are very close to ours. In
the example, Pinaev’s exergy of C l − is -70,5 kJ/mole, versus -69,2 kJ/mole obtained
here. That is because his methodology is based in outline on the conventional calculation procedures, also used in this PhD. This makes us to question the validity
of the conventional methodology, when the chemical exergy of the natural capital is
assessed.
The properties of the earth
6.2.3
195
The thermodynamic properties of the upper continental crust
Table 6.7 shows the standard thermodynamic properties of the major minerals that
compose the upper continental crust, according to the model developed in chapter 3.
Only the references (Re f .) of the experimental values of ∆H 0f i and ∆G 0f i are provided in the table. For those minerals where the latter values have been estimated
in this PhD, the method used for its estimation (M eth.)2 , as well as its associated
error (±" %) is given. The detailed calculations for the estimation of the mineral’s
properties is shown in the appendix (section A.5.3).
2
See table 5.8 for details about the different estimation methods.
-2587,4
-5932,5
-6841,0
-1118,3
-4117,7
-1237,2
-998,1
-10976,4
2,03E-04
1,42E-04
1,27E-04
9,25E-05
8,80E-05
8,00E-05
7,73E-05
6,15E-05
4,95E-05
3,88E-05
3,43E-05
3,24E-05
3,10E-05
2,95E-05
2,78E-05
2,54E-05
2,28E-05
2,09E-05
2,01E-05
2,01E-05
1,87E-05
1,84E-05
1,77E-05
N a0.6 C a0.4 Al1.4 Si2.6 O8
SiO2 · 0, 5H2 O
2+
Al0.4 T i0.1 Si1.9 O6
C a0.9 N a0.1 M g0.9 Fe0.2
N a0.5 C a0.5 Al1.5 Si2.5 O8
K(M g2,5 Fe0,5 )(Si3 Al)O10 (OH)1,75 F0,25
C aCO3
2+
Si3,5 O10 (OH)2
K0,6 (H3 O)0,4 Al2 M g0,4 Fe0,1
Al2 SiO5
N aAl3 Si3 O10 (OH)2
N a0.3 Fe23+ (Si3,7 Al0,3 )O10 (OH)2 · 4(H2 O)
Fe23+ Fe2+ O4
Al2 Si2 O5 (OH)4
Fe2+ T iO3
AlO(OH)
3+
(Si7 AlO22 )(OH)2
C a2 Fe42+ Al0,75 Fe0,25
KAl3 Si3 O10 (OH)1,8 F0,2
C aT iSiO5
Fe32+ Al2 (SiO4 )3
C
(M g3,75 Fe1,25 Al) (Si3 Al)O10 (OH)2 (OH)6
C a2 Fe3+ Al2 (SiO4 )3 (OH)
C
Al(OH)3
C aM gSi2 O6
N a0,33 Al2,33 Si3,67 O10 (OH)2
2+
C aFe0,6
M g0,3 M n2+
0,1 (CO3 )2
N aFe3+ Si2 O6
Al2 SiO5
M g Fe2+ Si2 O6
Fe3+ O(OH)
N aC l
AlO(OH)
N a0.2 C a0.8 Al1.8 Si2.2 O8
1,40E-05
-3031,2
1,39E-05
-5691,6
1,36E-05
-2076,8
1,32E-05
-2585,5
1,25E-05
-2590,4
1,17E-05
-2757,4
1,17E-05
-559,4
1,01E-05
-386,3
9,65E-06
-988,1
9,08E-06
-4186,8
Continued on next page . . .
-3026,3
-5317,2
-1923,1
-2417,2
-24443,0
-2594,6
-489,2
-384,4
-914,1
-3960,7
-5616,6
-2455,1
-4969,8
0,0
-7788,2
-6076,3
N.A.
-1155,8
-2441,0
-5557,6
-5447,7
-1015,9
-3796,0
-1163,5
-917,6
-10303,7
-763,7
-967,9
-3026,8
-769,8
-5706,7
-1129,0
-5499,1
∆G 0f i ,
kJ/mole
-857,2
-3704,5
-750,9
-3752,1
[284]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[284]
[94]
[94]
[94]
[94]
[94]
Reference
3
12
7
4
1
3
1; 7
5
2; 4
11
1
Method
1
10
0,6
1
0
0,6
1
1
5
0
±ε, %
47,4
39,4
96,6
16,5
9,7
132,2
9,7
14,3
2,2
10,5
-13,1
37,2
335,7
410,3
175,2
43,1
N.A.
-1,4
11,7
-15,7
738,2
122,6
-9,0
123,7
-1,3
398,5
3076,6
9,3
-446,9
3103,2
78,6
11,0
325,2
1,0
4,8
3023,9
-12,8
bch i ,
kJ/mole
THE
-5991,3
-2597,1
-5305,5
0,0
-8429,2
-6466,1
N.A.
-1282,2
-808,9
-1044,5
-3201,5
-815,0
-6079,4
-1207,7
-5886,2
3,81E-03
5,14E-04
4,49E-04
4,22E-04
SiO2
N aAlSi3 O8
N a0.8 C a0.2 Al1.2 Si2.8 O8
KAlSi3 O8
Quartz
Albite
Oligoclase
Orthoclase/ Kfeldspar
Andesine
Opal
Augite
Labradorite
Biotite
Calcite
Hydromuscovite/ Illite
Sillimanite
Paragonite
Nontronite
Magnetite
Kaolinite
Ilmenite
Diaspore
HornblendeFe
Muscovite
Titanite
Almandine
Graphite
Ripidolite
Epidote
C org
Hydragillite/
Gibbsite
Diopside
Beidellite
Ankerite
Aegirine
Andalusite
Hyperstene
Goethite
Halite
Boehmite
Bytownite
∆H 0f i ,
kJ/mole
-911,6
-3927,6
-796,0
-3977,5
Formula
Mineral
ξi ,
mole/g
Table 6.7: Thermodynamic properties of the upper continental crust
196
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
8,99E-06
7,82E-06
7,63E-06
7,33E-06
6,52E-06
C a3 (PO4 )2
N a2 Al2 Si3 O10 · 2(H2 O)
C aM g(CO3 )2
M g3,75 Fe1,25 Al2 Si3 O10 (OH)8
N a0,165 C a0,084 Al2,33 Si3,67 O10 (OH)2
Phosphate
rock
Natrolite
Dolomite
Clinochlore
Montmorillonite
Lawsenite
Riebeckite
Hematite
Sepiolite
Hydrobiotite
-5722,1
-2327,9
-8435,5
-5523,8
∆H 0f i ,
kJ/mole
-3886,6
C aAl2 Si2 O7 (OH)2 · H2 O
6,36E-06
-4812,8
6,14E-06
-10087,1
N a2 Fe32+ Fe23+ (Si8 O22 )(OH)2
Fe2 O3
6,05E-06
-826,1
M g4 Si6 O15 (OH)2 · 6(H2 O)
5,67E-06
-10123,7
3+
Al0,1 )(Si2,8 Al1,2 ) O10 ((OH)1,8 F0,2 ) ·
5,26E-06
-7362,2
(K0,3 C a0,1 )(M g2,3 Fe0,6
3(H2 O)
5,21E-06
-1489,4
Ulvöspinel
T iFe22+ O4
Distene/Kyanite Al2 SiO5
4,37E-06
-2593,7
Cummingtonite/ M g7 (Si8 O22 )(OH)2
3,73E-06
-12070,0
Anthopyllite
Glaucophane
N a2 (M g3 Al2 )Si8 O22 (OH)2
3,65E-06
-12080,6
Celestine
SrSO4
3,65E-06
-1454,1
Prehnite
C a2 Al2 Si3 O10 (OH)2
3,58E-06
-6197,3
Rutile
T iO2
3,41E-06
-945,4
Barite
BaSO4
3,04E-06
-1470,4
Niter
K N O3
2,96E-06
-495,0
Nitratine
N aN O3
2,96E-06
-468,2
Pennine
(M g3,75 Fe1,25 Al) (Si3 Al)O10 (OH)2 (OH)6
2,87E-06
-8429,2
Actinolite
C a2 M g3 Fe2 Si8 O22 (OH)2
2,82E-06
-11519,4
Pyrite
FeS2
2,75E-06
-175,0
Sanidine
K0,75 N a0,25 AlSi3 O8
2,67E-06
-3860,7
2+
3+
Hastingsite
N aC a2 Fe4 Fe (Si6 Al2 O22 )(OH)2
2,60E-06
-11926,3
2+
Ferrosilite
Fe M gSi2 O6
2,32E-06
-2757,4
Zircon
Z rSiO4
2,11E-06
-2034,8
2+
Siderite
Fe CO3
2,08E-06
-742,3
Spodumene
LiAlSi2 O6
2,06E-06
-3056,8
Pigeonite
M g1,35 Fe0,55 C a0,1 (Si2 O6 )
1,99E-06
-1535,4
Leucoxene
C aT iSiO5
1,90E-06
-2591,6
2+
Pyrrhotite
Fe S
1,79E-06
-105,5
2+
3+
Lepidomelane/
K Fe2,5 M g0,5 Fe0,75 Al0,25 Si3 O10 (OH)2
1,78E-06
-4995,0
Annite
Bronzite
M g FeSi2 O6
1,77E-06
-2753,4
Anhydrite
C aSO4
1,73E-06
-1435,1
Continued on next page . . .
ξi ,
mole/g
Formula
Mineral
-2585,3
-1322,7
-11346,7
-1341,6
-5823,0
-890,1
-1361,9
-395,2
-367,1
-7788,2
-10801,5
-163,3
-3715,9
-11343,4
-2594,6
-1919,5
-671,1
-2882,9
-1448,8
-2454,8
-100,5
-4642,3
-1392,9
-2442,0
-11343,0
-4510,6
-9399,5
-742,2
-9257,8
-6238,9
-5316,6
-2167,9
-7796,6
-5354,5
∆G 0f i ,
kJ/mole
-3878,2
[94]
[94]
[94]
[178]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[284]
[94]
[94]
1
3
2
3
7
3
12
1; 7; 10
3; 11
1
3
2
0
1
1
1
0,6
1
10
5
5
0
1
1
141,5
16,3
-78,8
32,4
35,7
18,3
18,8
-22,3
-24,2
175,2
405,9
1428,1
15,9
289,2
132,2
20,0
122,0
24,6
1401,1
37,5
883,6
284,8
273,1
10,7
181,6
2,2
318,9
17,4
1284,5
46,2
3,8
18,0
166,8
39,6
bch i ,
kJ/mole
[94]
[94]
±ε, %
32,4
Method
[94]
Reference
Table 6.7: Thermodynamic properties of the upper continental crust. – continued from previous
page.
The properties of the earth
197
1,53E-06
1,39E-06
1,20E-06
1,14E-06
2+
(SiO4 )
M g1,6 Fe0.4
2+
M n2+
K N a2 LiFe1,5
0,5 T i2 Si8 O24
Z nS
N aAlSi2O6 ∆(H2 O)
C aAl2 Si2 O8
M nCO3
Fe2+ C r2 O4
C aSO4 · 2H2 O
C a5 (PO4 )3 (OH)0,33 F0,33 C l0,33
Fe2+ Al9 Si4 O23 (OH)
M g3 Si4 O10 (OH)2
C aCO3
C a2 Al3 (SiO4 )3 (OH)
M g3 Si4 O10 (OH)2 · 2(H2 O)
M n2+
2 (SiO4 )
N aC a2 Al5 Si5 O20 · 6H2 O
C a2 Al3 Si3 O12 (OH)
M nO2
T iO2
4+
Ba2 M n2+
2 M n3 O10 · 2H 2 O
N a0,75 K0,25 Al(SiO4 )
M g2 SiO4
3+
N aAl0,9 Fe0,1
(Si2 O6 )
M n2 + 3Al2(SiO4)3
C e0,5 La0,25 N d0,2 T h0,05 (PO4 )
C a2 M g5 Si8 O22 (OH)2
N a2 M g2 Fe2+ Al2 (Si8 O22 )(OH)2
M n2+ M n3+
6 SiO12
CuFeS2
H3 BO3
M gCO3
2+
T i0,7 N b0,15 Fe0,225
O2
BaCO3
K0,8 Fe8 Al0,8 5Si11,1 O21 (OH)8 · 6H2 O
-2083,3
-3055,5
-1668,9
-7596,0
1,10E-06
-10724,6
1,02E-06
-206,1
1,01E-06
-3310,2
9,90E-07
-4274,4
9,48E-07
-894,7
8,83E-07
-1445,7
7,96E-07
-2024,0
7,91E-07
-6773,4
7,68E-07
-12066,8
7,67E-07
-5907,2
7,64E-07
-1207,9
7,51E-07
-6883,9
6,78E-07
-7018,8
6,30E-07
-1733,3
6,19E-07
-12413,7
5,68E-07
-6883,9
5,64E-07
-520,4
5,59E-07
-940,4
5,10E-07
-2569,1
5,09E-07
-2087,6
4,95E-07
-2175,5
4,78E-07
-2990,4
4,77E-07
-5646,3
4,29E-07
-2074,0
4,28E-07
-12367,8
4,06E-07
-11600,3
4,06E-07
-4260,0
3,62E-07
-194,6
3,60E-07
-1095,1
3,58E-07
-1114,1
3,22E-07
-864,6
3,04E-07
-1217,1
2,77E-07
-16655,5
Continued on next page . . .
1,64E-06
M g3 Si2 O5 (OH)4
Serpentine/
Clinochrysotile
Olivine
Enstatite
Corundum
ThuringiteChamosite
Neptunite
Sphalerite
Analcime
Anorthite
Rhodochrosite
Chromite
Gypsum
Apatite
Staurolite
Talc
Aragonite
Clinozoisite
Vermiculite
Tephroite
Thomsonite
Zoisite
Pyrolusite
Anatase
Psilomelane
Nepheline
Forsterite
Jadeite
Spessartine
Monazite (Ce)
Tremolite
Crossite
Braunite
Chalcopyrite
Sassolite
Magnesite
Ilmenorutile
Witherite
Stilplomelane
∆H 0f i ,
kJ/mole
-4363,4
-10061,3
-201,4
-3088,5
-4021,0
-817,1
-1358,4
-1798,6
-6386,9
-11215,6
-5543,0
-1128,6
-6483,9
-5957,2
-1632,1
-11543,9
-5416,5
-465,2
-883,7
-2347,2
-1972,4
-2057,8
-2812,1
-5326,3
-1943,3
-11639,3
-10925,8
-3944,7
-195,1
-969,0
-1030,2
-813,2
-1137,6
-15197,0
-1925,0
-2919,9
-1563,0
-6981,9
∆G 0f i ,
kJ/mole
-4035,4
[94]
[284]
[284]
[94]
[94]
[94]
[144]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
∆G 0f :
[94]
Reference
1
1; 2
1; 2
12
3
0
1
1
10
1
1
1
1
5
3
3
10
∆H 0f : 12
5
3; 10
10
0,6
1
1
5
0
±ε, %
∆H 0f : 5
12
7
∆H 0f :
1
Method
868,9
744,9
0,8
15,6
83,8
195,1
16,6
-23,2
269,1
22,6
11,4
53,0
1717,4
199,3
-49,1
1120,4
23,4
24,7
2103,1
28,1
63,6
-2,7
302,6
-43,3
73,7
133,0
325,8
1530,3
19,7
15,6
45,5
44,1
5459,7
95,3
59,6
31,5
-389,8
51,9
bch i ,
kJ/mole
THE
M g2 Si2 O6
Al2 O3
3+ 3+
Al0,5 ) (Si3 Al)O10 (OH)2
(Fe3 M g2 Fe0,5
ξi ,
mole/g
Formula
Mineral
Table 6.7: Thermodynamic properties of the upper continental crust. – continued from previous
page.
198
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
7,44E-08
7,19E-08
6,34E-08
6,18E-08
6,14E-08
5,99E-08
5,99E-08
5,24E-08
4,62E-08
4,23E-08
4,12E-08
4,09E-08
2+
N i4,5 S8
Fe4,5
N aC a(B5 O6 (OH)6 )· 5H2 O
N a4 Al3 Si9 O24 C l
2+
Fe1,2
M g0,6 M n2+
0,2 Al 4 Si2 O10 (OH)4
Cs0,6 N a0,2 Rb0,1 Al0,9 Si2,1 O6 · (H2 O)
C a2 B6 O11 · 5H2 O
Be3 Al2 Si6 O18
FeS2
C a3 Al2 (SiO4 )3
N iS2
M g5 Al2 (Si6 Al2 O22 )(OH)2
N aFe32+ Al6 (BO3 )3 Si6 O18 (OH)4
-6606,9
-3297,1
-6949,7
-9006,5
-154,9
-6631,1
-134,2
-12319,7
-14401,4
-778,3
-6762,2
-12197,4
∆H 0f i ,
kJ/mole
-2842,4
-4733,3
-1480,9
-1321,6
-910,1
-7148,6
-6292,8
-622,4
-1220,5
-307,1
-21175,8
-1237,4
-1660,9
-11926,3
-2281,0
-6003,2
-9114,7
-4104,9
-5632,5
-5984,4
-6481,6
4,08E-08
-1631,6
3,81E-08
-7657,8
3,09E-08
-3743,6
3,06E-08
-1602,1
Continued on next page . . .
2,75E-07
2,63E-07
2,34E-07
2,32E-07
2,06E-07
1,89E-07
1,58E-07
1,55E-07
1,44E-07
1,29E-07
1,20E-07
1,20E-07
1,16E-07
1,09E-07
1,07E-07
1,03E-07
9,52E-08
8,99E-08
8,93E-08
8,68E-08
7,81E-08
C aFe2+ Si2 O6
4+
Ba0,8 P b0,2 N a0,125 Fe1,3 Al0,2 Si0,1 M n2+
0,5 M n6 O16
Fe22+ SiO4
M n2+ SiO3
SiO2
C a2 M gAl2 (SiO4 ) (Si2 O7 )(OH)2 · H2 O
K M g3 AlSi3 O10 F (OH)
M nO(OH)
C aF2
Li0,75 N a0,25 Al(PO4 ) F0,75 (OH)0,25
C a10 M g2 Al4 (SiO4 )5 (Si2 O7 )2 (OH)4
3+
2+
2+
M n3+
Fe1,5
M n2+
0,5 O4
0,6 Fe0,3 M g
La(CO3 )F
N a3 Fe42+ Fe3+ (Si8 O22 )(OH)2
M gAl2 O4
K Li2 AlSi4 O10 F (OH)
M g2 Al4 Si5 O18
N a2 O · 2B2 O3 · 4H2 O
Al2 Si4 O10 (OH)2
C a5 (PO4)2,63 (CO3 )0,5 F1,11
C a(C e0,4 C a0,2 Y0,133 ) (Al2 Fe3+ )Si3 O12 (OH)
Hedenbergite
Hollandite
Fayalite
Rhodonite
Cristobalite
Pumpellyte
Phlogopite
Manganite
Fluorite
Amblygonite
Vesuvianite
Jacobsite
Bastnaesite
Arfvedsonite
Spinel
Lepidolite
Cordierite
Kernite
Pyrophyllite
Francolite
Orthite- Allanite
Pentlandite
Ulexite
ScapoliteMarialite
Chloritoid
Pollucite
Colemanite
Beryl
Marcasite
Grossular
Vaesite
Gedrite
TourmalineSchorl
Wollastonite
Clementite
Cryptomelane
Kieserite
C aSiO3
Fe32+ M g1,5 Al Fe3+ Si3 AlO12 (OH)6
2+
K8 (M n4+
7,5 M n0,5 ) O16
M gSO4 · (H2 O)
ξi ,
mole/g
Formula
Mineral
-1550,9
-7043,1
-3432,2
-1428,7
-6152,6
-3074,2
-6277,0
-8500,4
-156,6
-6281,0
-126,4
-11584,2
-13453,5
-766,2
-6151,5
-11504,2
∆G 0f i ,
kJ/mole
-2676,1
-4330,4
-1369,2
-1243,1
-855,5
-6672,5
-5902,2
-557,3
-1168,1
-282,7
-19948,7
-1137,5
-1527,8
-11201,5
-2172,5
-5654,7
-8603,9
-3713,1
-5257,6
-5698,1
-6055,4
[391]
[94]
[400]
[94]
[409]
[94]
[94]
[178]
[94]
[144]
[94]
[94]
[94]
[94]
[94]
Reference
Table 6.7: Thermodynamic properties of the upper continental crust. – continued from previous
page.
5
3
1
1
3
12
1; 6; 11
1
12
1
1
1; 3; 9
3
10
7; 4
1; 2; 9
1; 8; 10
10; 12
3
4
∆H 0f : 12
3
Method
1
1
0
0
1
10
5
0
10
0
0
1
1
5
1
5
5
10
1
1
10
1
±ε, %
33,1
504,6
3409,1
54,2
159,8
10,0
-796,8
56,9
1434,8
65,4
1320,6
149,9
377,6
6833,9
2855,3
22,5
8651,4
288,3
246,6
101,7
2,7
57,9
128,1
49,4
111,9
1992,6
219,0
711,5
160,8
-1146,5
53,6
126,7
139,2
440,8
7,6
714,3
32,3
bch i ,
kJ/mole
The properties of the earth
199
FeAsS
P bS
N a4 T i3,6 N b0,4 (Si2 O7 )2 O4 · 4(H2 O)
KC l
M g(OH)2
M g7 Si8 O22 (OH)2
Fe2+ N b2 O6
Arsenopyrite
Galena
Murmanite
Sylvite
Brucite
Anthophyllite
Ferrocolumbite
Covellite
Vernadite
Thorite
Nickeline
Sapphirine
Andradite
Chrysoberyl
Cassiterite
Violarite
Todorokite
Cubanite
Topaz
Glauconite
Garnierite
Molybdenite
Clinohumite
Tridymite
Euxenite
Gersdorffite
Jarosite
Humite
Scheelite
Kornerupine
Omphacite
Phenakite
Hisingerite
Uraninite
Malachite
Strontianite
Brookite
Perovskite
Yttrialite
∆H 0f i ,
kJ/mole
-41,9
-100,5
-9804,0
-437,0
-925,9
-12094,6
-2172,8
2,27E-08
-53,2
2,18E-08
-637,8
2,13E-08
-2160,5
2,04E-08
N.A.
2,04E-08
-10563,3
1,96E-08
-5764,4
1,80E-08
-2302,3
1,73E-08
-581,1
1,72E-08
-378,0
1,34E-08
-4037,4
1,33E-08
-293,7
1,29E-08
-3044,4
1,21E-08
-5150,3
1,18E-08
-3494,6
1,14E-08
-271,8
1,10E-08
-8966,4
1,05E-08
-909,7
1,02E-08
-2671,5
9,70E-09
N.A.
9,57E-09
-3521,7
9,46E-09
-6953,7
9,28E-09
-1646,2
9,24E-09
-9172,9
7,48E-09
-3075,5
7,31E-09
-2146,2
6,25E-09
-3229,6
5,60E-09
-1085,6
5,46E-09
-1052,1
5,34E-09
-1220,9
5,27E-09
-942,4
5,10E-09
-1662,2
4,64E-09
N.A.
Continued on next page . . .
2,89E-08
2,79E-08
2,78E-08
2,74E-08
2,71E-08
2,67E-08
2,40E-08
ξi ,
mole/g
-53,6
-571,4
-2048,8
N.A.
-9962,9
-5419,4
-2178,2
-519,6
-368,9
-3576,5
-302,8
-2875,2
-4785,6
-3267,1
-262,8
-8410,0
-855,9
-2506,3
-144,3
-3318,7
-6512,3
-1419,6
-8624,8
-2904,3
-2033,3
-2895,6
-1032,5
-906,0
-1140,1
-821,9
-1575,7
N.A.
∆G 0f i ,
kJ/mole
-50,2
-95,9
-9096,6
-410,2
-834,8
-11396,0
-2018,6
[94]
[383]
[94]
[94]
[94]
[94]
[94]
[94]
[205]
∆G 0f : [94]
[94]
[284]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
Reference
3
2
∆H 0f : 12
3; 10
12
10
1; 9
3
3
10
7
1; 7; 9
3
1; 9
12
12
Method
1
1
10
5
10
1
1
1
1
5
0,6
1
1
5
10
10
±ε, %
687,7
393,5
27,8
N.A.
2366,3
92,1
20,9
32,0
2902,0
742,6
2406,7
-11,4
52,1
25,9
1682,2
613,5
2,3
136,7
1189,5
208,5
504,3
139,8
173,8
38,7
34,1
1012,8
167,6
24,3
34,9
86,5
58,5
N.A.
1428,0
743,6
354,0
18,5
34,9
128,6
170,5
bch i ,
kJ/mole
THE
CuS
3+
M n4+
0,6 Fe0,2 C a0,2 N a0,1 O1,5 (OH)0,5 · 1, 4(H 2 O)
T hSiO4
N iAs
M g4 Al6.5 Si1.5 O20
C a3 Fe22+ (SiO4 )3
BeAl2 O4
SnO2
Fe2+ N i2 S4
3+
N a2 M n4+
4 M n2 O12 · 3H 2 O
CuFe2 S3
Al2 (SiO4 )F1,1 (OH)0,9
2+ 3+
3+
Al0,15 ) (Si3,8 Al0,2 )O10 (OH)2
M g0,4 Fe0,2
(K0,6 N a0,05 )(Fe1,3
(N i2 M g)Si2 O5 (OH)4
M oS2
M g6,75 Fe2,25 Si4 O16 (OH)0,5 F1,5
SiO2
Y0,7 C a0,2 C e0,1 (Ta0,2 )2 (N b0,7 )2 (T i0,025 )O6
N iAsS
K Fe33+ (SO4 )2 (OH)6
2+
M g5,25 Fe1,75
(SiO4 )3 F1,5 (OH)0,5
C aW O4
M g1,1 Fe0,2 Al5,7 (Si3,7 B0,3 )O17,2 (OH)
C a0,6 N a0,4 M g0,6 Al0,3 Fe0,1 Si2 O6
Be2 SiO4
Fe23+ Si2 O5 (OH)4 · 2(H2 O)
UO2
Cu2 (CO3 )(OH)2
Sr CO3
T iO2
C aT iO3
Y1.5 T h0.5 Si2 O7
Formula
Mineral
Table 6.7: Thermodynamic properties of the upper continental crust. – continued from previous
page.
200
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
-1430,8
-1429,4
1,45E-09
1,41E-09
1,38E-09
1,29E-09
1,06E-09
9,06E-10
8,27E-10
8,10E-10
8,01E-10
6,83E-10
6,36E-10
4,96E-10
4,81E-10
4,40E-10
4,30E-10
4,02E-10
3,96E-10
3,87E-10
3,82E-10
3,62E-10
K M gC l3 · 6(H2 O)
Y2 Fe2+ Be2 (Si2 O10 )
Y bPO4
N a8 Al6 Si6 O24 SO4
2+
M n0,5 W O4
Fe0,5
N a8 Al6 Si6 O24 (OH)2
P bCO3
S b2 S3
C dS
Cu2 S
Z nCO3
3+
U0,3 C a0,2 N b0,9 T i0,8 Al0,1 Fe0,1
Ta0,5 O6 (OH)
N a0,6 C e0,22 La0,11 C a0,1 T i0,8 N b0,2 O3
M g Fe23+ O4
2+
N a4 C a2 Fe0,7
M n0,3 Z r Si8 O22 (OH)1,5 C l1,5
Z rSiO4
M gC l2 · 6(H2 O)
Sn
P bSO4
N a2 T i2 Si2 O9
Continued on next page . . .
-11859,9
-2034,8
-2500,7
0,0
-920,0
-4360,1
-2946,7
-5220,0
-1868,6
-13936,7
-1246,2
-13408,5
-700,0
-175,0
-162,0
-79,5
-813,3
-2884,5
4,38E-09
3,90E-09
3,47E-09
3,38E-09
3,16E-09
2,80E-09
2,77E-09
2,76E-09
2,76E-09
2,65E-09
2,51E-09
2,36E-09
1,85E-09
1,84E-09
1,55E-09
1,45E-09
Cu3 (CO3 )2 (OH)2
Cu
N aC aN b2 O6 (OH)0,75 F0,25
Be4 Si2 O7 (OH)2
N a2 Fe52+ T iSi6 O20
K2 (UO2 )2 (V O4 )2 · 3H2 O
M gAlSi4 O10 (OH) · 4(H2 O)
C a2 (IO3 )2 (C rO4 )
C a(IO3 )2
Cu5 FeS4
N aAl(CO3 )(OH)2
N a3 Al F6
As2 S3
S8
Zn
M n4 Be3 (SiO4 )3 S
Azurite
Copper
Pyrochlore
Bertrandite
Aenigmatite
Carnotite
Palygorskite
Dietzeite
Lautarite
Bornite
Dawsonite
Cryolite
Orpiment
Sulphur
Zinc
Helvine/
Helvite
Carnallite
Gadolinite
Xenotime
Nosean
Wolframite
Hydrosodalite
Cerussite
Stibnite
Greenockite
Chalcocite
Smithsonite
Blomstrandite/ Betafite
Loparite - (Ce)
Pleonaste/
Magnesioferrite
Eudyalite
Sirtolite
Bischofite
Tin
Anglesite
Ramsayite/
Lorenzenite
∆H 0f i ,
kJ/mole
-1633,3
0,0
-2897,9
-4586,1
-8184,4
-4907,3
-6477,8
-2425,4
-1002,5
-334,5
-1965,3
-3311,3
-169,1
0,0
0,0
-5843,9
ξi ,
mole/g
Formula
Mineral
-11062,9
-1919,2
-2116,4
0,0
-784,5
-4103,9
-1343,6
-1351,0
N.A.
-4943,3
-1790,3
-13131,5
-1146,4
-12678,2
-627,5
-173,7
-156,5
-86,2
-731,9
-2683,8
∆G 0f i ,
kJ/mole
-1447,5
0,0
-2687,3
-4300,6
-7660,9
-4585,5
-5939,9
-2148,1
-839,3
-393,1
-1787,3
-3144,7
-168,7
0,0
0,0
-5532,4
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[388]
[132]
[391]
[94]
[94]
[94]
[94]
[94]
[94]
[191]
[94]
[94]
Reference
Table 6.7: Thermodynamic properties of the upper continental crust. – continued from previous
page.
12
1; 3; 10
12
12
10
2
3, 10
12
12
5
12
10; 12
1
12
Method
10
1
10
10
5
1
5
10
10
1
10
10
0
10
±ε, %
335,0
20,3
66,0
547,6
62,9
104,3
181,6
40,2
N.A.
299,7
24,2
115,0
120,0
193,1
20,9
2522,3
743,9
789,1
23,3
90,0
39,0
134,0
345,0
72,3
-164,8
792,4
440,4
78,7
71,4
3083,0
-0,1
327,9
2641,2
4858,2
339,0
1407,7
bch i ,
kJ/mole
The properties of the earth
201
Ag5 S bS4
Z rSiO4
Au
-142,2
-323,6
-1169,6
-99,9
-3004,3
-2549,9
-184,5
-1919,2
0,0
7,72E-12
-166,1
6,98E-12
-2034,8
6,47E-12
0,0
Continued on next page . . .
-1434,7
-9894,5
-40,3
-3925,1
-131,5
-307,3
-1227,2
-100,5
-3208,3
-2721,2
3,05E-11
2,76E-11
2,74E-11
2,59E-11
C aM oO4
3+
2+
Si4 O22
M g0,5 T i2,5 Fe0,5
C e1,7 La1,4 C a0,8 T h0,1 Fe1,8
Ag2 S
2+
N a1,1 C a0,9 M n2+
0,5 Fe0,5 Z r0,8 T i0,1 N b0,1 (Si2 O7 )
O0,6 (OH)0,3 F0,1
Ag3 S bS3
C o3 S4
T hO2
FeS
N a0,4 C a1,6 Ta2 O6,6 (OH)0,3 F0,1
Y0,7 C a0,2 C e0,12 (Ta0,7 )2 (N b0,2 )2 (T i0,1 )O5,5 (OH)0,5
2,38E-11
1,69E-11
1,56E-11
1,19E-11
8,71E-12
8,33E-12
-1542,4
-10499,8
-32,4
-4191,1
3,07E-10
3,05E-10
2,93E-10
2,80E-10
2,46E-10
2,38E-10
2,18E-10
2,05E-10
1,94E-10
1,93E-10
1,40E-10
1,30E-10
1,19E-10
1,03E-10
9,91E-11
9,91E-11
9,75E-11
8,08E-11
5,06E-11
5,06E-11
4,99E-11
4,20E-11
3,51E-11
3,18E-11
Fe2+ Ta2 O6
Pb
2+
(SiO4 )2 F1,5 (OH)0,5
M g3,75 Fe1,25
As2 O3
H gS
FeO
C a2,9 C e0,9 T h0,6 La0,4 N d0,2 Si2,7 P0,5 O12 (OH)0,8 F0,2
N a8 Al6 Si6 O24 C l2
Ag
C a2 Fe2+ Al2 BO3 Si4 O12 (OH)
As4 S4
Bi
Bi2 (CO3 )O2
C e0,75 La0,25 (PO4 ) · H2 O
Bi 2O3
Bi2 S3
Z rO2
N d0,4 C e0,4 Sm0,1 Y0,1 N bO4
C oAsS
C oAs2
Ag2 S
N a6 C a2 Al6 Si6 O24 (CO3 )2
SiC
T hSiO4
Ferrotantalite
Lead
Chondrodite
Arsenolite
Cinnabar
Iotsite
Britholite
Sodalite
Native silver
Axinite- Fe
Realgar
Bismuth
Bismutite
Rhabdophane
Bismite
Bismuthinite
Baddeleyite
Fergusonite
Cobaltite
Smaltite
Argentite
Cancrinite
Moissanite
UraniumThorite
Powellite
Chevkinite
Acanthite
Lavenite
∆G 0f i ,
kJ/mole
-2163,9
0,0
-4701,4
-579,1
-50,7
-251,5
-6666,9
-12703,6
0,0
-7180,9
-132,7
0,0
-888,7
-1821,9
-493,7
-140,6
-1043,3
-2631,2
N.A.
N.A.
-39,4
-14136,3
-60,3
-2048,8
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[94]
[391]
[94]
[94]
[94]
[94]
[94]
[187]
[94]
[94]
[94]
[94]
[94]
Reference
3
10; 12
12
9
10; 12
12
1; 9
12
12
3
12
2
12
1
10; 12
10; 5
12
Method
5
10
10
5
10
10
5
10
10
1
10
1
10
0
10
5
10
±ε, %
3030,3
20,3
51,5
2325,9
3032,2
48,8
884,2
315,1
54,6
27,6
1006,2
706,4
604,8
174,5
232,2
564,2
415,0
671,3
127,3
734,0
51,9
69,7
427,3
4272,6
274,8
81,1
325,0
61,9
2230,8
38,1
-717,4
N.A.
N.A.
707,3
101,8
1204,1
27,8
bch i ,
kJ/mole
THE
Pyrargirite
Linnaeite
Thorianite
Troilite
Microlite
Delorenzite/
Tanteuxenite
Stephanite
Naegite
Gold
∆H 0f i ,
kJ/mole
-2319,3
0,0
-5023,0
-659,8
-58,2
-272,1
-7057,3
-13457,0
0,0
-7640,4
-140,3
0,0
-968,0
-1964,9
-574,3
-143,2
-1101,3
-2808,3
-163,1
-61,5
-29,4
-14980,9
-62,8
-2160,5
ξi ,
mole/g
Formula
Mineral
Table 6.7: Thermodynamic properties of the upper continental crust. – continued from previous
page.
202
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
-4652,2
N.A.
N.A.
-8568,0
-2681,3
0,0
N.A.
-1023,7
-4170,0
-127,2
-602,2
-3279,4
-703,2
-53,6
-4608,4
-79,8
-11738,2
-4455,9
-1987,7
-1112,9
-85,7
-1968,6
-322,8
N.A.
-8020,8
-19,0
-444,9
-1909,5
-3740,2
-100,2
-9415,1
-5173,2
N.A.
N.A.
-9109,0
-2847,7
0,0
N.A.
5,61E-12
5,47E-12
3,77E-12
3,54E-12
3,52E-12
3,17E-12
2,59E-12
2,11E-12
2,00E-12
1,81E-12
1,68E-12
1,66E-12
1,30E-12
1,24E-12
1,14E-12
7,62E-13
7,20E-13
5,71E-13
5,29E-13
3,47E-13
2,71E-13
2,27E-13
2,25E-13
2,20E-13
1,57E-13
1,50E-13
1,33E-13
2,46E-14
1,54E-14
1,20E-14
2,12E-15
-1034,5
1,27E-15
-4439,7
End of the table
N a2 Sr BaT i3 Si4 O16 (OH)F
AgC l
M gO
Cu2 Si2 O6 (H2 O)4
2+
S b3 AsS13
Ag7,2 Cu3,6 Fe1,2
H gS
Fe3 (PO4 )2 (H2 O)8
P t 0,6 P d0,3 N i0,1 S
KC a2 C e3 Si8 O22 (OH)1,5 F0,5
Cu(UO2 )2(PO4 )2 · 8(H2 O)
Y PO4
P bM oO4
FeAs2
Cu10 Fe2 As4 S13
TeO2
Au0,75 Ag0,25 Te2
N a2,8 M n2+
0,2 Sr0,5 C a0,5 La0,33 C e0,6 Z n0,6 M g 0,4 Si6 O17
AuTe2
Ag4 M nS b2 S6
Cu10 Fe2 S b4 S13
Sc1,5 Y0,5 Si2 O7
Bi2 Te2 S
N a2 C a3 C e1,5 Y0,5 T i0,4 N b0,5 Z r0,1 (Si2 O7 )2 O1,5 F3,5
KAl3 (SO4 )2(OH)6
Os0.75 I r0.25
I r0.5 Os0.3 Ru0.2
Al6.9 (BO3 )(SiO4 )3 O2.5 (OH)0.5
Y0,5 C a0,1 C e0,1 U0,1 T h0,1 T i1,2 N b0,6 Ta0,2 O6
Pt
P t Fe
P b5 S b4 S11
N aC a2 Z r0,6 N b0,4 Si2 O8,4 (OH)0,3 F0,3
Lampro- phyllite
Chlorargirite
Periclase
Chrysocolla
Freibergite
Metacinnabar
Vivianite
Cooperite
Miserite
Tortbernite
Weinschenkite
Wulfenite
Loellingite
Tennantite
Tellurite
Sylvanite
Nordite
Calaverite
Samsonite
Tetrahedrite
Thortveitite
Tetradymite
Rinkolite/
Mosandrite
Alunite
Osmium
Iridium
Dumortierite
Polycrase (Y)
I-Platinum
Polixene/
Tetraferroplatinum
Boulangerite
Wohlerite
-109,9
-569,5
-2964,6
-727,5
-47,7
-4428,2
-73,8
-11035,1
-4129,8
-1871,1
-952,8
-80,2
-1999,6
-270,3
N.A.
-7532,2
-17,4
-463,5
-1939,7
-3540,6
-100,6
-8808,5
∆H 0f i ,
kJ/mole
-8401,2
ξi ,
mole/g
Formula
Mineral
∆G 0f i ,
kJ/mole
-7865,3
[94]
[135]
[94]
[94]
[94]
[191]
[94]
[94]
[94]
∆G 0f : [94]
Reference
Table 6.7: Thermodynamic properties of the upper continental crust. – continued from previous
page.
1; 9
10; 12
12
12
1
3
1
2; 9
2
10; 12
1
1
1
∆H 0f : 12
3
10; 12
∆H 0f :12
3
10; 12
Method
5
10
10
10
0
5
0
5
1
10
0
0
0
10
1
10
10
5
10
±ε, %
8565,5
466,6
127,3
342,1
N.A.
108,9
125,4
146,5
N.A.
22,0
62,1
-23,9
10786,0
674,3
457,4
688,3
1138,1
151,6
-35,2
17,8
1284,7
9965,1
60,0
N.A.
958,5
686,8
4817,9
9797,1
50,5
1709,0
1441,1
892,0
bch i ,
kJ/mole
The properties of the earth
203
204
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
According to table 6.7, the thermodynamic properties of the 291 main minerals included in the crust have been obtained. About a half of the properties (159) were
compiled directly from the literature. The remaining were obtained with the 12
different estimation methods described in section 5.4. From the latter, 18 minerals
were calculated with method 1, and hence without committing any associated error.
Five minerals were estimated with the method for hydrated clay minerals and for
phyllosilicates (M.7), committing a maximum error of ε < 0, 6%. Thirty-eight minerals were estimated with an error smaller than 1%, 20 substances with ε < 5%,
and 44 minerals with ε < 10%. Only the properties of 6 minerals3 : iridium, osmium4 , nickeline, polixene, sylvanite and yttrialite were not able to be estimated.
Additionally, the enthalpy of formation of gersdorffite and the Gibbs free energy of
smaltite are missing. Nevertheless, all together account for only 3, 5 × 10−6 % of the
continental crust.
The average standard enthalpy, Gibbs free energy and chemical exergy of the upper
continental crust, for an average molecular weight of the crust5 equal to M Wcr =
157, 7 g/mole is:
0
(∆H f )c r
m
X
=
(ξi · ∆H 0f ,i ) · M Wcr = −1958, 92 kJ/mole
i=1
0
(∆G f )c r
m
X
=
(ξi · ∆G 0f ,i ) · M Wcr = −1835, 82 kJ/mole
i=1
0
(b ch)c r
m
X
0
=
(ξi · bch
i ) · M Wcr = 372, 60 kJ/mole
i=1
As it happened to the hydrosphere, our R.E. generates some negative exergies of the
minerals, but far less than with Ranz’s R.E [276]. This is because, as stated above,
we chose our R.E. based on Szargut’s criterion of partial stability. According to this,
among a group of reasonable abundant substances, the most stable will be chosen
if they also complain with the “earth similarity criterion”. This criterium is different from that of Ahrendt’s [4] or Diederichsen [74], where complete stability was
assumed. As a consequence, the latter R.E. do not generate any negative exergies,
but the resulting environment is completely different from that of the current earth.
3
Excluding Cor g , since no exact composition can be applied.
The standard enthalpy and Gibbs free energy of iridium and osmium (Os0,5 I r0,3 Ru0,2 and
Os0,75 I r0,25 ) could be estimated considering the compunds as solid solutions of elements Os, I r, and
Re. Since for all three substances ∆G f =0 and ∆H f =0, the standard enthalpy of formation of iridium
and osmium would be also ∆H f =0, applying the solid solution method. Similarly, the standard Gibbs
free energy of formation would correspond to the entropy of the mixture. Hence, ∆G f =2,5 kJ/mole
for iridium and ∆G f =5,1 kJ/mole for osmium. We do not include these values in the table, since the
errors associated might be very significant.
5
As calculated in this study (section 3.6).
4
An approach to the chemical composition of the crepuscular earth
205
Our chosen R.E. obeys in principle the “earth similarity criterion”, but does generate some negative exergies. Hence, this leads us to question again the methodology
used and the proposed R.E.
6.2.4
The chemical exergy of the earth
In chapter 2, we described some physical properties of the bulk earth that are now
required for our calculations. According to Beichner [23], the earth has a mass of
around 5, 98 × 1024 kg. The earth’s relative mass proportions of each of the earth’s
spheres are according to Javoy [169]: core (35,5%), mantle (67%), oceanic crust
(0,072%), continental crust (0,36%), hydrosphere (0,023%) and atmosphere (0,842
ppm). The upper layer of the crust constitutes a mass of around 50% of the whole
continental crust [411]. With the information provided in the previous sections,
we are now able to calculate the chemical exergy of the outer layers of the earth,
namely the atmosphere, hydrosphere and upper continental crust. Table 6.8 shows
the standard chemical exergy of the aforementioned layers and their sum.
Table 6.8. The standard chemical exergy of the earth’s outer layers
Layer
Atmosphere
Hydrosphere
Upper continental crust
SUM
Mass, kg
5,04E+18
1,38E+21
1,08E+22
MW, g/mole
28,96
18,29
157,7
0
b ch, kJ/mole
1,51
0,87
372,60
0
B ch, Gtoe
6,27E+03
7,80E+05
1,21E+09
1,22E+09
The results of table 6.8 indicate that the standard chemical exergy of the earth’s
outer spheres is 1, 22 × 109 Gtoe. This can be considered as a rough number, and is
subject to updates, especially when a more appropriate R.E. is found. But the order
of magnitude is good enough for realizing the huge chemical exergy content of the
earth. From all layers, the upper continental crust is responsible for most of the
exergy (99,9%), due to its greater mass portion and specific exergy. Although the
relative proportion of the atmosphere and hydrosphere is small when compared to
the whole, their chemical exergies are also huge: 6, 27 × 103 Gtoe and 7, 80 × 105
Gtoe, respectively. Since the earth can be considered as a closed system, its chemical
exergy is considered as a non-renewable reservoir.
6.3
An approach to the chemical composition of the
crepuscular earth
As stated before, the crepuscular or entropic planet, is a completely degraded earth,
where all materials have reacted, dispersed and mixed. And this degraded earth is
206
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
not necessarily equivalent to the reference environments used so far. The crepuscular earth represents a planet towards we are inexorably approaching, as mineral
resources are extracted and dispersed, fossil fuels are burned, and waters are polluted by humankind. The model of crepuscular earth is composed by an atmosphere,
hydrosphere and continental crust, but differs from the current one in the absence
of concentrated minerals and freshwater. Furthermore, the atmosphere contains a
higher CO2 concentration due to the complete burning of fossil fuels.
According to table 4.10, the amount of the considered non-fuel mineral world resources by the USGS is in the order of 1015 kg. When the rest of minerals are
considered, the total quantity of concentrated minerals might increase in one or two
orders of magnitude, hence to around 1017 kg. The amount of possible available
fuels, according to table 6.19 is around 1016 kg6 . This means that all concentrated
mineral resources of fuel and non fuel origin only represent 0,001% of the total
mass of the earth’s upper crust. Therefore, we can state with no significant error,
that the upper continental crust of the entropic planet can be approximated to the
average mineralogical composition of the earth’s crust. And this in turn can be approximated to the composition estimated in this PhD (table 3.5), at least until it is
further improved with better geochemical information.
Concerning the hydrosphere, we saw that the amount of freshwater on earth stored
in the form of rivers, lakes, glaciers and groundwater represents only 3%. Therefore,
the final composition of the hydrosphere of the crepuscular planet when all waters
are mixed, can be very well approximated to that of seawater, which is well known
(tables 2.5 and 2.6).
Finally the atmosphere of the entropic planet will be composed of the same substances appearing in the current atmosphere (table 2.2), but presumably with a
higher concentration of CO2 and other anthropogenic gases. According to the IPCC
SRES report [160], in the worst scenario of emissions, where practically all available
conventional fossil fuels are burned, the CO2 concentration in the atmosphere will
increase to 710 ppm. Assuming that the ratio7 , of burned fuel to increase of CO2 concentration is 4 Gtoe/CO2 ppm, the burning of available unconventional fossil fuels
(around 2600 Gtoe), would imply an additional increase of 650 ppm in the atmosphere. Consequently, the final carbon dioxide concentration in the atmosphere of the
crepuscular planet would be around 1400 ppm. This value is only approximative,
since it has been assumed a linear relationship between the burning of fossil fuels,
and the increase of CO2 in the atmosphere. In fact, the processes that rule the carbon cycle and the earth’s climate are very complex and in many cases unpredictable.
It should be noted, that an increase of CO2 concentration would imply an equivalent reduction of the O2 content in the atmosphere. Hence, instead of being 20,94%
the volume fraction of oxygen in the atmosphere, this would be 20,83%, since 1100
6
This corresponds to around 300 Gtons of oil, 3000 Gtons of coal, 500 Gtons of natural gas and
7000 Gtons of unconventional fossil fuels.
7
According to the trends observed in the SRES report [160] for all six different scenarios analyzed.
The exergy of the mineral resources
207
ppm would be included in the molecules of the extra CO2 appearing in the entropic
earth. In addition to the latter, increases in the concentration of methane, nitrous
oxide, carbon monoxide, nitrogen oxides, chlorides, sulphides, etc. are expected in
the crepuscular planet, due to the anthropogenic action. But the latter figures cannot
be easily estimated and remain open for further studies.
With this preliminary model of crepuscular planet, together with the thermodynamic
properties of all its constituents estimated in this PhD, a new reference environment
could be proposed, for the calculation of the chemical exergies of the elements. A
model of degraded earth would not contain only a reference substance per element,
as it happens to the R.E. in which we have based our calculations. The new model
should calculate the chemical exergy of the elements, taking into account all the substances appearing in the planet that contain that element. Hence, we think that the
calculation procedures and even the philosophy for obtaining the chemical exergies
of the elements should be reviewed, since the selection of an appropriate R.E. is a
required but not a sufficient condition, as seen with Pinaev’s environment. But this
activity remains open for further studies in the future.
6.4
The exergy of the mineral resources
In the last sections, we have obtained the chemical exergy of the main substances
that compose the earth. We will now focus on a very small part of the earth’s constituents: the mineral resources.
For that purpose, the average exergy of the main fuel minerals (coal, oil and natural
gas) is obtained, so as to calculate the world’s proven fuel reserves. Additionally, the
exergy of the main non-fuel mineral reserves, reserve base and world resources is
obtained.
This information, together with the data provided in chapter 4 about other energy
sources, will allow us to analyze the current state of the main natural resources on
earth.
6.4.1
The exergy contained in fossil fuels
We saw in chapter 5, that the physical value of fuels is tightly related to its chemical
exergy content. Hence, the physical value of the world’s proven fuel reserves can
be approximated to their chemical exergy8 , which is obtained with the equations
provided in section 5.3.3. It must be remembered, that the exergy calculation of
fuels is undertaken with the models developed by Valero and Lozano [369] and not
with Eq. 5.1, due to the complexity and heterogeneity of the fuel’s composition.
8
It must be remembered that in chapter 4, an approximative exergy value in terms of Gtoe was
given for the proven reserves of coal, oil and natural gas.
208
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
Table 6.9. High heating value and elementary analysis (% by weight) considered in
the study of Valero and Arauzo [366] to define different types of coal.
RANK
Anthracite
Bituminous
Subbitum.
Lignite
HHV,
kJ/kg
30675
28241
23590
16400
O
H
C
N
S
Z
W
2,4
7,6
12,2
8,9
3,0
4,5
3,8
2,7
80,9
68,7
58,8
38,9
1,0
1,6
1,3
0,6
0,5
1,2
0,3
5,3
10,1
8,4
4,0
19,8
2,1
8,0
19,6
23,8
Table 6.10. Thermodynamic properties of the different types of coal. Values in
kJ/kg, except for s0 (kJ/kgK)
Type
Anthrac.
Bitum.
Subitum.
Lignite
HHV
30675
28241
23590
16400
∆H 0f
-136,2
-757,7
-1125,0
-662,7
s0
0,9
1,1
1,0
0,8
eI
29980,2
27083,4
22264,5
15241,9
eI I
30687,1
28262,1
23574,2
16413,9
eI I I
30739,9
28389,3
23606,0
16975,0
bI
31583,8
28950,6
24251,0
16930,2
bI I
31584,7
28952,1
24252,7
16931,6
bI I I
31624,2
29047,1
24276,5
17351,1
The calculations will be carried out, assuming an average composition of the different types of coal, oil and natural gas. A mean composition of the fuels, was already
studied by Valero and Arauzo [366], taking into account the conversion factors reported by the IEA assigned to the fuels in each country. Their analysis will be used in
this study. It must be pointed out, that although the latter analysis was carried out
with quite old data (statistics from 1989), and that the reserves figures have changed
since then, the average composition of the fuels should not have varied significantly.
6.4.1.1
Coal
The elementary analysis of each rank of coal chosen by Valero and Arauzo [366] is
shown in table 6.9.
The composition of the fuels listed in table 6.9, throw up the properties shown in
table 6.10, where ∆H 0f and s0 are the standard enthalpy and entropy of formation,
e I , e I I and e I I I , the chemical energy of the fuel corresponding to the R.E. I, II and III
from table 5.5, and b I , b I I and b I I I the chemical exergy for the three R.E., respectively.
As can be seen from the table, R.E. III produces the greatest exergy values, although
the difference between the three is very small (around 0,3% and a maximum of 2,5%
for lignite between I and III). Assuming an exergy content of coal equal to the HHV,
implies an associated error of about 3%, although for lignite, this could be up to 6%.
Next, the exergy of the proven reserves of coal is calculated. The main sources of
data for coal reserves come from BP and WEC. The WEC study complements the
The exergy of the mineral resources
209
BP Statistical Review and the World Energy Outlook. It collects these data from 96
WEC Member Committees worldwide. The difference of the proven reserve figures
between both entities (WEC and BP) is 7,3%. According to the Energy Watch Group
[89], the BP report just reproduces the data which are collected by the World Energy
Council. Therefore, we will take into account the figures of the WEC’s Survey of
Energy Resources 2007 [401].
The proven reserves data are provided for the different countries, reported as three
different types of coal: 1) anthracite and bituminous, 2) subbituminous and 3) lignite. Since we need to know the separate quantities of anthracite and bituminous in
order to calculate the exergy, we will assume that only hard coal9 coming from the
USA is anthracite10 .
The exergy values shown in table 6.11, are generated from R.E. III, which is the most
commonly used for fuel calculations (Lozano and Valero [202]).
Table 6.11: The exergy of the world’s coal proven reserves reported in [401]. Values in million tonnes if not specified
Country
Algeria
Botswana
Central
African Republic
Congo
(Democratic
Rep.)
Egypt (Arab
Rep.)
Malawi
Morocco
Mozambique
Niger
Nigeria
South Africa
Swaziland
Tanzania
Zambia
9
Anthracite
Bitumin.
59
40
Subbitum.
Lignite
3
Exegy, Mtoe
40,8
27,7
1,2
88
60,9
21
14,5
2
N.A.
212
70
21
169
48000
208
200
10
Continued on next page . . .
1,2
N.A.
146,6
48,4
112,2
33196,7
143,9
138,3
6,9
Hard coal is another name given to anthracite and bituminous, as opposed to brown coal, which
is given to subbituminous and lignite.
10
The conversion factors reported by the IEA [153] for coal in the different countries indicates that
US coal is the one with the highest heating capacity.
210
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
Table 6.11: The exergy of the world’s coal proven reserves reported in [401]. Values in million tonnes if not specified. –
continued from previous page.
Country
Zimbabwe
Total Africa
Canada
Greenland
Mexico
USA
Total
N.
America
Argentina
Bolivia
Brazil
Chile
Colombia
Ecuador
Peru
Venezuela
Total
S.
America
Afghanistan
China
India
Indonesia
Japan
Kazakhstan
Korea
(Democratic
People’s
Rep.)
Korea
(Republic)
Kyrgyzstan
Malaysia
Mongolia
Myanmar
(Burma)
Nepal
Pakistan
Anthracite
Bitumin.
502
49431
3471
860
112261
112261
4331
Subbitum.
Lignite
171
871
183
300
100086
101440
3
2236
51
30374
32661
424
1
31
6578
7068
1150
381
24
140
479
7229
66
62200
52240
1721
355
28170
300
9023
24
33700
18600
4258
798
Exegy, Mtoe
347,2
34286,5
3827,7
105,8
789,2
154926,6
159649,3
245,1
0,7
4085,4
686,2
4769,6
9,9
96,8
331,3
10224,9
300
45,6
70180,4
37888,2
2565,5
245,5
20775,4
380,9
135
78,0
1809
3130
812
4
335,5
2,8
2
1,4
1
1
167
Continued on next page . . .
1814
0,6
846,6
The exergy of the mineral resources
211
Table 6.11: The exergy of the world’s coal proven reserves reported in [401]. Values in million tonnes if not specified. –
continued from previous page.
Country
Philippines
Taiwan,
China
Thailand
Turkey
Uzbekistan
Vietnam
Total Asia
Albania
Bulgaria
Czech Republic
Germany
Greece
Hungary
Ireland
Italy
Montenegro
Norway
Poland
Portugal
Romania
Russian Federation
Serbia
Slovakia
Slovenia
Spain
Ukraine
United Kingdom
Total Europe
Iran (Islamic
Rep.)
Total Middle
East
Australia
Anthracite
Bitumin.
41
1
Subbitum.
170
Lignite
105
Exegy, Mtoe
170,0
0,7
1354
1814
2000
559,4
749,4
1517,8
103,7
136447,4
328,0
836,4
2756,9
1000
150
146251
36282
5
1673
63
2617
34685
794
1928
211
170
6556
3900
2933
152
199
14
10
5
6012
3
12
49088
6
2
2
97472
21
300
16577
13500
260
211
30
1945
5800,4
108,8
99,3
324,1
21001,9
107,2
72872
1386
117616
44649
136826,9
958,6
1386
0
0
958,6
37400
42322,9
200
15351
155
379
1490
33
408
10450
2813,5
1611,2
1447,6
9,7
5,8
0,0
2,9
4773,4
15,7
178,0
94606,2
37100
2100
Continued on next page . . .
212
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
Table 6.11: The exergy of the world’s coal proven reserves reported in [401]. Values in million tonnes if not specified. –
continued from previous page.
Country
New Caledonia
New Zealand
Total Oceania
Anthracite
TOTAL
WORLD
112261
Bitumin.
2
Subbitum.
Lignite
Exegy, Mtoe
1,4
33
37135
205
2305
333
37733
278,9
42603,1
318635
266837
149755
520996,7
End of the table
According to table 6.11, the exergy of coal proven reserves is 521 Gtoe, which is very
similar to the previous calculated value in chapter 4 (523 Gtoe). The 2006 production data in exergy terms is equal 3,3 Gtoe11 . Similarly, the WEC [401] estimated
additional resources amount in place and the estimated additional recoverable reserves are 1025,7 and 108,6 Gtoe, respectively.
It must be stressed, that different assumptions had to be made, such as considering
only four different classes of coal, with the same composition and high heating values. Nevertheless, the error introduced with the previous assumption is most likely
much smaller than the one made estimating the proven reserves. The Energy Watch
Group [89], after analyzing present and historical trends, stated that data quality of
coal reserves is poor, both on global and national levels. But there is no objective
way to determine how reliable the available data actually are.
6.4.1.2
Oil
The composition of the main types of fuel, according to the British standard
BS2869:1998 (see section 4.6.6.2), is listed in table 6.12. Only Fuels 1, 2 and 4
are considered, since they are the most commonly used.
The chemical composition of the fuels described above, throw up the thermodynamic
properties of table 6.13.
As it happened to coal, the energy and exergy of the fuels increase from R.E. I to III.
For the case of oil, the exergy can be approximated with no significant error to the
HHV of the fuel, since the maximum error introduced is 0,26%.
11
An average coal is considered to have an exergy content of 22692 kJ/kg and a HHV of 21876
kJ/kg.
The exergy of the mineral resources
213
Table 6.12. High heating value and elementary analysis (% by weight) of the different types of oil, according to the British standard BS2869:1998
RANK
Fuel-Oil 1
Fuel-Oil 2
Fuel-Oil 4
HHV, kJ/kg
46.365
45.509
43.920
O
0,2
0,2
0,4
H
13,2
12,7
11,9
C
86,5
86,4
86,1
N
0
0,1
0,2
S
0,1
0,6
1,4
Table 6.13. Thermodynamic properties of the different types of oil. Values in kJ/kg,
except for s0 (kJ/kgK)
Type
Fuel-Oil 1
Fuel-Oil 2
Fuel-Oil 4
HHV
46365
45509
43920
∆H 0f
-622,1
-763,7
-1279,1
s0
2,8
2,7
2,6
eI
43591,5
42859,4
41359,3
eI I
46475,6
45633,9
43958,9
eI I I
46486,2
45697,2
44107,1
bI
46247,4
45466,2
43888,4
bI I
46251,3
45469,8
43891,7
bI I I
46259,1
45517,4
44002,4
Next, the exergy of the world’s proven reserves of oil will be calculated (table 6.14).
For that purpose, the figures provided by BP in the Statistical Review 2007 will be
used [35]. The estimates of BP are compiled using a combination of primary official
sources, third-party data from the OPEC Secretariat, World Oil, Oil & Gas Journal
and an independent estimate of Russian reserves based on information in the public
domain. The WEC publishes regularly also reserve figures for oil in the Survey of
Energy Resources. Nevertheless, the latest WEC publication [401] includes reserve
values for the end of 2005 and not for 2006, as opposed to the BP report. The
classification of the world’s oil proven reserves into the different types of fuel (1, 2
and 4) is taken from the study of Valero and Arauzo [366].
Table 6.14: The exergy of the world’s oil proven reserves reported in [35].
Values in thousand million tonnes if not specified
Country
USA
Canada
Mexico
Total
North
America
Argentina
Brazil
Colombia
Ecuador
Peru
Trinidad & Tobago
Venezuela
Fuel-Oil 1
-
Fuel-Oil 2
3,7
2,4
1,7
7,8
Fuel-Oil 3
-
0,3
1,7
0,2
0,7
0,1
0,1
11,5
Continued on next page . . .
Exegy, Mtoe
3999,9
2586,0
1884,0
8469,9
294,7
1813,5
224,2
709,9
157,9
125,4
12494,6
214
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
Table 6.14: The exergy of the world’s oil proven reserves reported in [35].
Values in thousand million tonnes if not specified. – continued from previous
page.
Country
Other S. & Cent.
America
Total S. & Cent.
America
Azerbaijan
Denmark
Italy
Kazakhstan
Norway
Romania
Russian Federation
Turkmenistan
United Kingdom
Uzbekistan
Other Europe &
Eurasia
Total Europe &
Eurasia
Iran
Iraq
Kuwait
Oman
Qatar
Saudi Arabia
Syria
United
Arab
Emirates
Yemen
Other
Middle
East
Total
Middle
East
Algeria
Angola
Chad
Rep. of Congo
(Brazzaville)
Egypt
Equatorial
Guinea
Gabon
Libya
Nigeria
Sudan
Tunisia
Fuel-Oil 1
Fuel-Oil 2
0,2
Fuel-Oil 3
Exegy, Mtoe
195,6
-
14,8
-
16015,9
10,9
1039,2
167,5
113,9
5912,8
1231,4
64,6
11415,4
1,0
0,2
0,1
5,5
1,1
0,1
0,1
0,5
0,1
0,3
-
-
8,8
81,1
559,2
88,2
332,1
10,9
21005,3
18,9
15,5
14,0
0,8
2,0
36,3
0,4
13,0
0,0
20467,6
16819,3
15151,6
819,4
2162,8
39338,1
443,6
14038,5
0,4
0,1
404,8
54,2
101,2
-
1,5
109699,8
1,2
0,1
0,3
1702,0
1321,4
140,3
291,6
0,5
0,2
567,8
266,5
0,3
5,4
4,9
0,9
318,2
5851,1
5297,3
936,3
99,0
0,1
Continued on next page . . .
The exergy of the mineral resources
215
Table 6.14: The exergy of the world’s oil proven reserves reported in [35].
Values in thousand million tonnes if not specified. – continued from previous
page.
Country
Other Africa
Total Africa
Australia
Brunei
China
India
Indonesia
Malaysia
Thailand
Vietnam
Other Asia Pacific
Total Asia Pacific
TOTAL WORLD
Fuel-Oil 1
1,6
0,5
Fuel-Oil 2
0,1
13,9
Fuel-Oil 3
-
0,2
2,2
0,8
0,6
0,5
0,1
0,4
0,1
0,5
2,2
4,9
-
Exegy, Mtoe
85,2
16876,8
592,3
163,2
2409,0
851,8
644,7
595,8
63,8
456,8
116,5
5893,9
151,5
10,9
End of the table
177961,6
According to table 6.14, the world’s proven oil exergy reserves generated from R.E.
III are 177,9 Gtoe. This means, that the reserves of oil have around one third of the
coal’s exergy reserves. The 2006 production data in exergy terms of fuel-oil is equal
3,9 Gtoe12
It should be remembered, that in addition to the conventional oil reserves, a corresponding range of additionally recoverable resources in exergy terms between 40 and
150 Gtoe should be taken into account [211].
6.4.1.3
Natural gas
In the case of natural gas, Valero and Arauzo [366] took into account the average
standard composition of table 6.15.
Table 6.15. Standard volumetric composition of natural gas considered in [366]
HHV, kJ/N m3
42110
C H4
0,9225
C2 H6
0,0653
C3 H8
0,0055
C4 H10
0,0007
C5 H12
0,0001
CO2
0,0001
N2
0,0058
The chemical composition of the average natural gas described above, throw up the
thermodynamic properties of table 6.16.
12
An average fuel-oil is considered to have an exergy content of 45664 kJ/kg and a HHV of 45455
kJ/kg.
216
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
Table 6.16. Thermodynamic properties of natural gas. Values in kJ/N m3 , except for
∆H f (kJ/kg) and s0 (kJ/kgK)
N. Gas
HHV
42110
∆H 0f
-3117,4
s0
8,6
eI
38047,1
eI I
42108,7
eI I I
42108,7
bI
39388,6
bI I
39393,8
bI I I
39393,8
R.E. II and III generate for the case of natural gas, the same values of energy and
exergy, since no sulphur is contained in the fuel. The difference between the exergy
generated with I and III is very small, only 0,01%. For the case of natural gas,
assuming the exergy as the HHV, introduces an error of around 6,5%, and hence this
approximation should be taken with more precaution than for fuel-oil or coal.
The calculated proven exergy reserves of natural gas are given in table 6.17. The
values for the reserves are obtained from BP [35], because it presents more comprehensive and up-to-date data than the figures provided by the WEC.
Table 6.17: The exergy of the world’s natural gas proven reserves reported in
[35]
Country
Trillion N m3
USA
5,93
Canada
1,67
Mexico
0,39
Total North America
7,98
Argentina
0,42
Bolivia
0,74
Brazil
0,35
Colombia
0,12
Peru
0,34
Trinidad & Tobago
0,53
Venezuela
4,32
Other S. & Cent. America
0,07
Total S. & Cent. America
6,88
Azerbaijan
1,35
Denmark
0,08
Germany
0,16
Italy
0,16
Kazakhstan
3,00
Netherlands
1,35
Norway
2,89
Poland
0,10
Romania
0,63
Russian Federation
47,65
Turkmenistan
2,86
Ukraine
1,10
United Kingdom
0,48
Uzbekistan
1,87
Other Europe & Eurasia
0,45
Continued on next page . . .
Exegy, Mtoe
5557,3
1561,7
363,9
7482,9
389,2
694,1
326,3
115,4
318,9
497,1
4047,2
63,8
6452,0
1266,2
72,2
145,4
149,6
2813,8
1263,4
2712,5
97,5
589,0
44693,9
2682,5
1031,7
451,2
1754,0
424,8
The exergy of the mineral resources
217
Table 6.17: The exergy of the world’s natural gas proven reserves reported in
[35]. – continued from previous page.
Country
Total Europe & Eurasia
Bahrain
Iran
Iraq
Kuwait
Oman
Qatar
Saudi Arabia
Syria
United Arab Emirates
Yemen
Other Middle East
Total Middle East
Algeria
Egypt
Libya
Nigeria
Other Africa
Total Africa
Australia
Bangladesh
Brunei
China
India
Indonesia
Malaysia
Myanmar
Pakistan
Papua New Guinea
Thailand
Vietnam
Other Asia Pacific
Total Asia Pacific
TOTAL WORLD
Trillion N m3
64,13
0,09
28,13
3,17
1,78
0,98
25,36
7,07
0,29
6,06
0,49
0,05
73,47
4,50
1,94
1,32
5,21
1,21
14,18
2,61
0,44
0,34
2,45
1,08
2,63
2,48
0,54
0,80
0,44
0,30
0,40
0,34
14,82
181,46
End of the table
Exegy, Mtoe
60148,0
84,4
26384,4
2973,3
1669,5
919,2
23787,3
6634,1
272,0
5684,9
454,9
47,8
68911,9
4224,7
1819,6
1234,3
4886,7
1137,7
13303,1
2443,4
408,0
314,2
2297,0
1008,3
2468,7
2326,1
504,6
748,5
408,0
282,3
375,2
316,1
13900,4
170198,3
According to table 6.17, the exergy reserves of natural gas are around 170 Gtoe, as
opposed to the 163,4 estimated in chapter 4 with the conversion data provided by
BP. This indicates, that the natural gas exergy reserves are very close to those of fueloil. The 2006 production data in exergy terms of natural gas is equal 2,4 Gtoe13 . It
should be remembered, that additional available natural gas resources are estimated
13
An average natural gas is considered to have an exergy content of 51276 kJ/kg and a HHV of
54811 kJ/kg.
218
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
in exergy terms as between 210 and 520 Gtoe, according to the International Gas
Union [156] and to Gregory and Rogner [123].
6.4.2
The exergy of non-fuel mineral resources
As opposed to fossil fuels, non-fuel minerals are physically valued not only by their
chemical exergy content, but also by their concentration exergy. From the point of
view of man, the value of non-fuel minerals is also associated to the extraction costs.
A very abundant and concentrated mineral in the crust, such as iron, has a high
exergy value and a low exergy cost of extraction. On the contrary, a very dispersed
and scarce mineral such as gold, has a low exergy value, but a very high exergy cost
of extraction.
This is why the exergy replacement costs of minerals, explained in section 5.3.4
provide additional and interesting information for assigning a physical value to nonfuel minerals. Exergy costs are obviously closer to price than the minimum exergies.
In fact, the exergy cost could be considered as a fundamental ingredient of the final
price of non-fuel minerals.
In this section, the total minimum exergy B t and total exergy cost B ∗t of the mineral’s
reserve, base reserve and world resources compiled by the USGS and described in
chapter 4 are calculated (Table 6.18). The total minimum exergy B t is the sum of
the chemical Bch and concentration exergy Bc , which are calculated with Eqs. 5.1
and 5.10, from the R.E. developed in this PhD (section 5.2). The total exergy cost14 ,
which represents the exergy required for restoring the resource with the best available technology from the R.E. to the current conditions found in nature, is obtained
with Eq. 5.46. The unit exergy costs are the ones shown in table 5.7. The detailed
calculations for the chemical and concentration exergies of the mineral resources are
shown in table A.20 and A.21 in the appendix.
14
Remember that the application of exergy costs to fossil fuels has no sense, since it is impossible
with current technology to reproduce the photosynthetic process that once created the fuel resource.
Aluminium
Antimony
Arsenic
Barite
Beryllium
Bismuth
Boron oxide
Bromine
Cadmium
Cesium
Chromium
Cobalt
Copper
Feldspar
Fluorspar
Gallium
Germanium
Gold
Graphite
Gypsum
Hafnium
Helium
Indium
Iodine
Iron
Lead
Lithium
Magnesium
Production
Bt
B ∗t
2,39E+04
5,19E+05
1,22E+01
1,36E+02
9,78E+00
1,23E+02
4,09E+01
N.A.
7,75E-03
4,05E-01
1,94E-01
3,16E+00
1,57E+02
N.A.
8,24E+00
N.A.
1,27E+00
6,93E+01
0,00E+00
N.A.
1,63E+03
3,70E+03
8,73E+00
4,38E+02
9,01E+02
9,35E+04
5,06E+01
N.A.
2,33E+02
N.A.
1,29E-02
1,29E-02
1,67E-02
1,65E-02
1,91E-02
1,56E+03
8,70E+02
N.A.
4,02E+02
N.A.
N.A.
N.A.
5,09E+00
5,09E+00
5,52E-02
5,29E-01
4,67E-01
N.A.
1,42E+05
9,97E+05
9,99E+01
3,90E+03
N.A.
N.A.
4,33E+02
4,33E+02
Reserves
Bt
B ∗t
3,22E+06
6,99E+07
1,92E+02
2,13E+03
1,96E+02
2,46E+03
9,77E+02
N.A.
N.A.
N.A.
1,09E+01
1,77E+02
6,28E+03
N.A.
N.A.
N.A.
3,23E+01
1,76E+03
5,43E+00
5,09E+00
N.A.
N.A.
9,06E+02
4,55E+04
2,92E+04
3,04E+06
N.A.
N.A.
1,05E+04
N.A.
N.A.
N.A.
N.A.
N.A.
3,25E-01
2,66E+04
7,26E+04
N.A.
N.A.
N.A.
8,68E+01
N.A.
N.A.
N.A.
1,05E+00
1,00E+01
2,80E+02
N.A.
1,20E+07
8,40E+07
2,28E+03
8,88E+04
5,64E+03
2,11E+04
N.A.
N.A.
Continued on next page . . .
Reserve base
Bt
B ∗t
4,13E+06
8,95E+07
3,93E+02
4,37E+03
2,93E+02
3,69E+03
4,53E+03
N.A.
N.A.
N.A.
2,32E+01
3,77E+02
1,51E+04
N.A.
N.A.
N.A.
7,92E+01
4,31E+03
8,53E+00
8,00E+00
N.A.
N.A.
1,68E+03
8,44E+04
5,61E+04
5,82E+06
N.A.
N.A.
2,10E+04
N.A.
N.A.
N.A.
N.A.
N.A.
6,97E-01
5,71E+04
1,77E+05
N.A.
N.A.
N.A.
1,57E+02
N.A.
1,17E+03
1,17E+03
1,52E+00
1,46E+01
5,04E+02
N.A.
2,63E+07
1,84E+08
4,90E+03
1,91E+05
1,51E+04
5,66E+04
N.A.
N.A.
Table 6.18: The exergy and exergy cost of the mineral reserves, base reserve
and world resources. Values are expressed in ktoe
Resources
Bt
B ∗t
9,67E+06
2,10E+08
N.A.
N.A.
1,80E+03
2,26E+04
1,03E+04
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
3,96E+02
2,16E+04
N.A.
N.A.
1,06E+06
2,40E+06
1,94E+03
9,74E+04
1,79E+05
1,86E+07
N.A.
N.A.
2,19E+04
N.A.
1,77E+02
1,76E+02
N.A.
N.A.
N.A.
N.A.
6,76E+05
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
6,35E+02
N.A.
3,78E+07
2,65E+08
4,32E+04
1,69E+06
1,79E+04
6,69E+04
N.A.
N.A.
The exergy of the mineral resources
219
Reserves
Bt
B ∗t
1,00E+05
9,68E+05
7,82E-01
2,67E+02
1,59E+03
2,99E+04
6,72E+03
5,33E+05
6,36E+02
6,25E+02
1,55E+05
2,00E+05
1,43E+00
N.A.
8,89E+05
1,38E+06
2,66E+03
N.A.
1,91E-01
2,33E+01
9,37E+00
8,60E+00
4,82E+00
4,63E+03
1,44E+03
N.A.
2,84E+01
7,88E+03
1,33E+00
1,28E+00
1,34E+02
N.A.
6,96E+02
3,58E+04
4,43E+03
1,15E+05
4,48E+03
5,05E+04
3,20E+02
2,42E+04
2,33E+04
4,26E+05
3,89E+02
3,73E+05
1,65E+07
1,61E+08
End of the table
Reserve base
Bt
B ∗t
1,13E+06
1,09E+07
4,08E+00
1,39E+03
3,52E+03
6,61E+04
1,50E+04
1,19E+06
7,06E+02
6,94E+02
4,30E+05
5,56E+05
1,61E+00
N.A.
1,93E+06
2,99E+06
4,53E+03
N.A.
7,65E-01
9,31E+01
1,94E+01
1,78E+01
1,02E+01
9,78E+03
2,54E+03
N.A.
3,93E+01
1,09E+04
2,99E+00
2,87E+00
1,56E+02
N.A.
1,25E+03
6,46E+04
9,10E+03
2,36E+05
1,31E+04
1,48E+05
6,94E+02
5,26E+04
6,23E+04
1,14E+06
7,36E+02
7,07E+05
3,43E+07
2,98E+08
Resources
Bt
B ∗t
N.A.
N.A.
1,02E+01
3,48E+03
2,41E+03
4,52E+04
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
2,02E+00
N.A.
2,68E+07
4,16E+07
N.A.
N.A.
8,41E-01
1,02E+02
N.A.
N.A.
N.A.
N.A.
2,12E+05
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
1,21E+04
3,15E+05
2,17E+04
2,45E+05
N.A.
N.A.
2,46E+05
4,50E+06
N.A.
N.A.
7,67E+07
5,44E+08
THE
Manganese
Mercury
Molybdenum
Nickel
Niobium
Phosphate rock (as fosforite)
PGM
Potash (K2 O)
REE (as C e2 O3 )
Rhenium
Selenium
Silver
Strontium
Tantalum
Tellurium
Thorium
Tin
Titanium (T iO2 )
Vanadium
Wolfram
Zinc
Zircon (Z rO2 )
Sum
Production
Bt
B ∗t
2,59E+03
2,50E+04
2,51E-02
8,59E+00
3,41E+01
6,40E+02
1,58E+02
1,26E+04
1,05E+01
1,03E+01
1,22E+03
1,58E+03
1,05E-02
N.A.
3,12E+03
4,84E+03
3,72E+00
N.A.
3,61E-03
4,40E-01
1,76E-01
1,62E-01
3,61E-01
3,46E+02
1,24E+02
N.A.
3,03E-01
8,42E+01
8,39E-03
8,07E-03
N.A.
N.A.
3,45E+01
1,77E+03
3,52E+01
9,13E+02
1,94E+01
2,19E+02
1,00E+01
7,58E+02
1,30E+03
2,37E+04
1,21E+01
1,16E+04
1,80E+05
1,70E+06
Table 6.18: The exergy and exergy cost of the mineral reserves, base reserve
and world resources. Values are expressed in ktoe.– continued from previous
page.
220
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
The exergy of the mineral resources
221
According to table 6.18, the exergy of the mineral’s reserves, reserve base and world
resources studied is at least 16,5, 34,3 and 76,7 Gtoe, respectively. Their associated
exergy costs increase to 161, 298 and 544 Gtoe, respectively, what highlights how far
is our technology from reversibility. The exergy cost of the reserve base and world
resources are comparable to the exergy reserves of fossil fuels: 19%, 34% and 63%
of the total available fossil fuels in 2006 (869 Gtoe), while their exergy represent
only 2, 4 and 9%, respectively.
The latest consumption rate of non-fuel minerals recorded in terms of exergy cost
is 1,7 Gtoe/yr or around 0,6% (0,2 Gtoe/yr of exergy) of the total reserve base.
Only four minerals account for near 96% of the total exergy cost consumption: iron
(58,5%), aluminium (30,4%), copper (5,5%) and zinc (1,4%). However, the minerals which are consumed at the highest rates compared to the available reserves are
in decreasing order indium, silver, arsenic, antimony, tin and gold, with a rate of
between 3,5 and 2,5% of the reserves consumed yearly.
As opposed to fossil fuels, minerals do not lose their exergy when they are consumed.
In fact, through the process of refining and concentrating of ores, the exergy of the
final product increases. The problem arises when the already refined mineral is
dumped in landfills or becomes dispersed when the life cycle of the product has
finished. In that case, the demand for the mineral must be satisfied by extracting
new ore from the mine, thereby exhausting the resource and reducing the grade of
the mineral deposit. As stated before, the second law of thermodynamics, reflected
in Eq. 5.10 dictates that the effort required to separate the mineral from the mine
follows a negative logarithmic pattern with its ore grade. This means that as the ore
grade tends to zero, the energy needed to extract the mineral tends to infinity. This
is why recycling is essential to our society.
It must be stressed that neither reserves, nor reserve base are good indicators for
assessing the earth’s mineral capital. As stated by Highley [141], total world reserve
base of most mineral commodities are larger now than at any time in the past due
to wider geological information, more efficient technologies and price changes. The
world resources data would be the best approximation of numbers compiling the
mineral capital on earth. However, for being indeed the most comprehensive classification, the information is often scarce, inaccurate and incomplete, as can be seen
in table 6.18. The fact is that too little is still known about the earth’s crust, since
exploration costs are extremely high.
6.4.3
The exergy of the natural resources on earth
In the previous sections we have expressed all mineral resources of fuel and non-fuel
origin with the same units, using the property exergy. We are now in a position of
222
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
analyzing and comparing the global exergy resources of the earth, with the information of the rest energy resources15 provided in chapter 4.
Table 6.19 summarizes the results, showing the available exergy, potential exergy use
and current exergy consumption of natural resources on earth. As stated in chapter
4, with potential exergy, we mean probable exergy capacity using advanced technology, not necessarily developed nowadays. Consumption values are referred to the
end of 2006, except for geothermal, PV, wind, biomass and tidal energy, which are
2005 values. The information is divided into renewable (RW) and non-renewable
resources (Non-RW). For the group of renewables, the ratio between the current
exergy consumption and the potential exergy use (RW use %) is provided. For nonrenewables, the base reserve to production ratio (R/P, yrs) is given, as a measure of
the depletion degree of the considered mineral.
According to table 6.19, the available renewable resources on earth, which are the
sum of solar, tidal and geothermal energy is huge: around 32.537 Gtoe/year16 . Of
course this value is only theoretical, since currently and in the near future, there is
no way to technologically recover so much energy.
Nevertheless, the potential exergy use is not insignificant either: 62 Gtoe/year. This
means, that with a feasible improve of our technology, we could supply with renewable energy more than 6 times the energy consumption of the entire world nowadays
(10,9 Gtoe in 2006). The RW use indicator, shows that with the exception of water power, which is being used at 54% of its potential, the rest energy sources are
barely exploited. Geothermal electricity is using 7,5% of its potential17 , biomass 3%,
wind power 0,4%, tidal energy 0,2% and solar and ocean waves current energy use
is practically imperceptible with respect to their capacities. Therefore, there is an
enormous improving potential in the use of renewables.
For the case of non renewable resources, including nuclear energy, fossil fuels and
non-fuel minerals, the available exergy is at least around 114.000 Gtoe, from which
65% come from the not yet technologically developed fusion of deuterium and tritium. The potential exergy use of non-renewable resources is around 6.103 Gtoe.
In fact, with the exception of the different types of nuclear energies and unconventional fossil fuels, our technology is developed enough to extract the majority of the
available non-renewable resources on earth. And that is exactly what humankind
has been doing since especially the beginning of the industrialization period.
The R/P ratios show that there is enough uranium for at least 8667 years, coal for
156, natural gas for 63, oil for 42 and non-fuel minerals for 191, if the consump15
Note that the exergy of electrical energy is equivalent to its energy content. Hence, the figures of geothermal, solar, wind, water and oceans power are the same expressed in energy or exergy
terms. The rest energy sources: nuclear and unconventional fuels were already expressed in table 6.19
through its exergy content.
16
Note that wind, water, ocean and biomass power are sun-driven. Obviously, solar energy is only
accounted once.
17
The potential thermal use of geothermal energy is not quantified, but is presumably much higher
than its potential for electricity generation. Hence, global geothermal RW use indicator is even smaller.
The exergy of the mineral resources
223
tion rates of the commodities remain as in 2006. The total non-renewable energy
resources, would last for at least 595 years.
Taking up again the global chemical exergy of the earth obtained in section 6.2.4, we
can now compare the order of magnitude of the resources, with the whole chemical
exergy of our planet.
The chemical exergy of the atmosphere, hydrosphere and continental crust, is equivalent to the renewables potential during more than 38.000 years. This value allows
us to put into perspective the huge physical value of our planet.
In fact, non-renewable available resources contribute to a very small fraction of the
total chemical exergy of the earth: less than 0,01%. The exergy of conventional
fossil fuels and non energy mineral resources, constitute only 0,0001% of the upper
continental crust’s chemical exergy. And their exergy is equivalent to that of the
atmosphere, which is the layer with the least chemical exergy content.
The wealth of our planet is enormous, but man can only take advantage of a very
small part of it: the resources. With current technology, it is impossible to use the
chemical exergy of dispersed substances. Non-renewable resources are considered as
such, because they represent a stock of concentrated chemical exergy. Therefore, the
earth’s 1, 22 × 109 Gtoe of chemical exergy constitutes nowadays a useless reservoir
of exergy. Consequently, we should resign ourselves with only 0,01% of that amount.
The results obtained lead us to conclude that there is no energy scarcity, but mineral’s
scarcity. Vast amounts of energy are available on earth, much more than we could
ever use. The depletion of fossil fuels should not be a problem at least in the medium
term, as there are many energy alternatives. Obviously, the way of recovering them
needs to be developed, so as to be economically competitive. Hence we cannot speak
about energy crisis, but rather material’s and environmental crisis.
Unfortunately non-fuel minerals cannot be replaced by renewable resources. In the
short term, substitution among minerals will be possible with technological development, but this can only last whenever other mineral resources are available. Furthermore, the extraction of minerals produce a considerable quantity of waste rock, pollutant emissions and consume considerable amounts of water, energy and in many
cases toxic chemicals for refining processes. The consumption of these resources implies an even greater additional loss of natural resource wealth. Therefore, recycling
and especially, the search of a dematerialized society becomes essential.
Surprisingly, this fact that seems to be unquestionable has not really started the
alarms bells ringing regarding resources scarcity, at least for non-fuel minerals. Many
institutions, such as the European Commission, do not regard it as a prioritized issue
in their environmental action plan [88], and claim that the environmental impacts
of using non-renewable resources like metals, minerals or fossil fuels are of greater
concern than their possible scarcity. Probably the lack of information about resource
scarcity avoids assigning this problem the priority that deserves.
Tidal power
Solar PV
Solar thermal power
Water power
Wind power
Ocean thermal gradient
Ocean conveyor belt
Ocean waves
Biomass
Non renewable resources
Uranium - fission
Thorium - fission
Deutorium + Tritium (fusion)
Coal
Natural gas
Oil
Unconventional fuels
Non-fuel minerals
RW w/o ocean th. grad.
Non RW
Conv. fuels + Min.
AVAILABLE
POTENTIAL
TW
Gtoe/yr TW
Gtoe/yr
17,9
13,5
0,06
- 0,04
0,12 e
0,09 e
2,7
2
0,166
0,13
43200 32521
51,4
38,7
43200 32521
0,63 - 4,7
0,47 - 3,5
11
8,2
1,8
1,3
1000 753
14,5
10,9
1,4E+08 Gtoe
2.000 1506
3
2,3
0,5
0,4
92
70
19 - 56
14 - 42
Gtoe
Gtoe
27.100
5.200
7.500
74000
1549
521
380-690
170,2
220-330
177,9
∼ 2600
76,7
34,3
32537 Gtoe/yr
62Gtoe/yr
>114000 Gtoe
6103 Gtoe
∼2800 Gtoe
903 Gtoe
CURRENT
TW
Gtoe/yr
9,3E-03 e / 0,007 e /
0,03 th
0,02 th
3,00E-04
2,00E-04
0,003
0,002
0,00035 e
0,00026 e
0,92
0,7
0,06
0,045
7,50E-07
5,60E-06
1,7
1,3
Gtoe
0,6
3,3
2,4
3,9
0,07
0,18
1,33 Gtoe/yr
10,3 Gtoe
9,6 Gtoe
156
63
42
191
RW use: 1,9%
R/P: 595 yrs
R/P: 94 yrs
0,2
5,8E-03
7,4E-06
53,8
0,4
1,5E-04
3,0
R/P, yrs
8667
RW use %
7,5 e
THE
RESOURCE
Renewable resources
Geothermal
Table 6.19. Available exergy, potential exergy use and current exergy consumption of natural resources on earth. Letter e denotes
electrical consumption, while th thermal consumption.
224
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
Summary of the chapter
6.5
225
Summary of the chapter
In the first part of this chapter, the standard thermodynamic properties of the main
constituents of the outer earth’s spheres have been provided for the first time. That
is the standard enthalpy, Gibbs free energy and chemical exergy of more than 330
natural substances.
The enthalpies and Gibbs free energies, have been obtained either from the literature, or have been calculated with the 12 estimation methods described in section
5.4. The exergy of the substances has been calculated with the chemical exergies of
the elements, generated with the R.E. developed in this PhD.
The average thermodynamic properties of the atmosphere, hydrosphere (divided
into seawater, rivers, glacial runoff and groundwater) and upper continental crust
have been calculated with the molar fractions of the substances in each layer.
It has been stated, that all negative ions in the hydrosphere throw up negative chemical exergies. Additionally, some substances of the continental crust show also
negative exergy values. This is because the reference species of our R.E. are more
stable than the considered substance. This leads us to question the suitability of
the R.E. developed in this PhD, for natural resource accounting. Furthermore, this
R.E. differs substantially from the model of degraded earth (or entropic planet) that
should become.
A first approximation of the crepuscular planet has been provided. It has been stated,
that this degraded earth contains an atmosphere similar to the current one, but with
a higher CO2 concentration due to the burning of fossil fuels, a hydrosphere were
all fresh waters are mixed with salt water, and a continental crust without fossil fuels or concentrated mineral deposits. Since the relative quantity of freshwater with
respect to saltwater on earth is irrelevant, the hydrosphere of this hypothetical earth
has the same composition of the oceans. Something similar occurs with the continental crust, the abundance of mineral deposits and fossil fuels is negligible when
compared to the whole continental crust. Hence, the composition of the degraded
crust can be approximated to the model developed in this PhD. This preliminary
model of entropic planet, and the thermodynamic properties of the constituents of
each sphere, are the starting point of a new conception of reference environment for
the calculation of chemical exergies of the elements. But this task remains open for
further studies.
Despite of the limitations of the R.E. developed in this study, it still constitutes a tool
for obtaining chemical exergies. Since the mass of the earth and of its spheres is
known, we were able to calculate the absolute chemical exergy of the atmosphere,
hydrosphere and upper continental crust: 6, 27 × 103 , 7, 80 × 105 and 1, 21 × 109
Gtoe, respectively. Of course these are very rough numbers, and are subject to ulterior updates, especially when a more appropriate R.E. is found. But they are good
enough, for providing an order of magnitude of the huge chemical wealth of our
planet.
226
THE
THERMODYNAMIC PROPERTIES OF THE EARTH AND ITS MINERAL RESOURCES
The second part of this chapter has provided an inventory of the most important
resources on earth, expressed through a single unit of measure: exergy. The main
novelty introduced in the inventory is the combined assessment of energy resources
with non-fuel minerals, thanks to the use of the exergy indicator.
We have stated that there is a huge amount of energy sources on earth, of both
renewable and non-renewable nature. There are many energy alternatives that could
replace fossil fuels when they become depleted. But obviously the technology for
recovering these alternatives needs to be further developed.
Despite of the enormous chemical exergy of our planet, only 0,01% of that amount
can be considered as available for human use. With current technology, it is impossible to use the chemical exergy of dispersed substances. And only those minerals
that are concentrated, can be considered as resources.
In the short run, technological development will allow substitution among minerals,
but this can only last whenever other concentrated mineral stocks are available.
Hence, the scarcity problems that man could be facing are based on the use of materials, rather than on the use of energy sources. This is why recycling and especially,
the search of a dematerialized society becomes essential, in order to be consistent
with the sustainability doctrine.
Chapter
7
The time factor in the exergy
assessment of mineral resources
7.1
Introduction
The aim of this chapter is to include a new dimension in the exergy evaluation of
natural capital: time. A new concept called “Exergy distance” is presented. By means
of the Exergy distance, we will be able to measure the level of degradation of mineral
resources on earth and to evaluate the velocity of degradation of the mineral capital.
The degradation might be assessed for the entire earth, as well as for local areas in
the past, present and in the future with evolution models. This way, for example, we
will be able to see how climate change or the extraction of mineral resources affect
the degradation of the natural capital by the decrease of its exergy.
Additionally, the Hubbert peak model is proposed for evaluating the peaking production of mineral commodities. The model is applied to the exergy production and
not to the tonnage, thereby introducing the concentration factor not included in the
conventional estimations.
The theory behind the exergy distance and the Hubbert peak model applied to exergy
is described, and two case studies are presented: 1) the exergy loss of copper in the
US, and 2) the exergy loss of the main minerals in Australia.
7.2
The exergy distance
As explained in chapter 2, the earth can be considered as a closed system with a finite number of substances in it, regardless the occasional input of meteorites. There
is a constant mass and energy transfer among the different layers of the earth. These
kinds of transfers can be of natural or anthropogenic nature. Usually, mass transfers
227
228
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
of natural origin between the earth’s layers follow cycles that are stabilized by negative feedbacks. These are at a stationary state, from a planetary perspective. This
means that materials and energy flow from one system to another, but the systems
themselves do not change much because the different parts of the flow paths balance
each other. Most natural processes such as the hydrological cycle or photosynthesis
are essential for life and do not alter the ecological equilibrium on earth.
However human interactions with the environment may be changing the natural
fluxes. Industrial processes consume natural resources and return them to nature as
non-useful wastes mostly harmful for the ecosystem. A very clear case of this fact is
for instance the burning of fossil fuels and the emission of CO2 to the atmosphere.
The clearing of forests, intensive agriculture with massive additions of fertilizers to
the soil and the mining of ever-larger amounts of mineral resources are other cases
of human alterations of the planet. Furthermore, according to Skinner, [318] if
changes are made in one part of a closed system, the results of those changes will
eventually affect other parts of the system.
Following the conservation mass principle, it will be true that the total mass of the
elements (ε j ) in the atmosphere plus hydrosphere plus continental crust will remain
constant, at any situation of the planet. Considering two different situations of the
planet, (1) and (2), where (2) represents
a more degraded earth due to the human
P
action, and taking into account that r j,i · ξi = ε j (Eq. 3.1)1 , then:


X
X
X


r j,i · ξi )at m + (
r j,i · ξi )hy d r + (
r j,i · ξi )cr  =
(
j
j
j
1


X
X
X


r j,i · ξi )at m + (
r j,i · ξi )hy d r + (
r j,i · ξi )cr 
(
j
j
j
2
This means that regardless the human action, the total budget of elements in the
earth will be constant.
In the same way, the sum of the energy (ei ) contained in the three spheres of the
earth will be also conserved in both situations:


X
X
X
 (ξi · ei )at m +
(ξi · ei )hy d r +
(ξi · ei )cr ) =
i
i
i
1


X
X
X
 (ξi · ei )at m +
(ξi · ei )hy d r +
(ξi · ei )cr 
i
1
Remember that
elements ε j .
P
i
i
2
r j,i represents the stoichiometric coefficient matrix between species ξi and
The exergy distance
229
However, and regardless the small amount of solar energy that the earth converts
into biomass through photosynthesis (only a 0,023%), this is not true if the parameter measured is exergy (bi ):


X
X
X
 (ξi · bi )at m +
(ξi · bi )hy d r +
(ξi · bi )cr ) >
i
i
i
1

X
X
X
 (ξi · bi )at m +
(ξi · bi )hy d r +
(ξi · bi )cr 

i
i
i
2
In other words, even if mass and energy are conserved in all processes according
to the first law of thermodynamics, the second law states that as resources are consumed, the useful energy or exergy of the earth will decrease.
The degradation of a natural resource can come from three effects:
• an alteration of its composition,
• a change of its concentration2 ,
• a variation of the reference environment.
And all three effects can be detected by a decrease of its exergy. Hence, for instance,
when a fossil fuel is burned with oxygen, its chemical composition is transformed
into water, carbon dioxide and other gases, thereby, losing chemical exergy. In the
same way, when minerals are extracted from a deposit, the mine decreases its ore
grade, thereby losing concentration exergy. Therefore, the current exergy of the
earth and its exergy evolution over time can be an objective measure for the depletion degree of the planet.
We define the exergy distance (D) between two situations of the planet as the exergy
difference between both states, as in Eq. 7.1:
!
D=
X
i=1
ξi · bi
!
−
1
X
i=1
ξi · bi
(7.1)
2
The exergy distance can be applied on a global scale to the total quantity of substances on earth, or to a certain natural resource, if the aim is to assess its specific
degradation. In fact, due to the very small relative weight of what we consider resources with respect to the other substances on earth, it makes more sense to apply
2
Note that a decrease of its quantity is not considered as a degradation, since the conservation of
mass statement must be obeyed. The matter is not lost, it is either chemically transformed or dispersed.
230
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
the exergy distance concept to the resources only, separating them from the rest
components on earth.
Additionally, we define the exergy degradation velocity ( Ḋ) between two states as
the exergy distance between the states (D) divided by the period of time separating
them (∆t), as in Eq. 7.2:
Ḋ =
∆B
∆t
€P
=
i=1 ξi · bi
Š
−
1
€P
i=1 ξi · bi
Š
2
(7.2)
∆t
In the same way, the exergy distance and exergy degradation velocity can be applied
to the exergy replacement costs3 , obtaining the irreversible exergy distance (D∗ ) and
the irreversible exergy degradation velocity ( Ḋ∗ ). Through the exergy replacement
costs, we introduce the irreversibility factor not included in the exergy parameter,
since the latter only considers minimum energies.
!
∗
D =
X
ξi ·
bi∗
i=1
Ḋ∗ =
∆B ∗
∆t
€P
=
!
X
−
i=1
1
i=1 ξi
· bi∗
ξi ·
bi∗
Š
−
1
€P
∆t
(7.3)
2
i=1 ξi
· bi∗
Š
2
(7.4)
Figure 7.1 shows a conceptual diagram of the exergy distance and exergy degradation velocity terms of mineral reserves.
7.3
The tons of mineral equivalent
One of the drawbacks that could be attributed to exergy is that most people and
policy makers are not familiar with energy units for natural resource accounting.
So anybody can understand how much is a kg or a ton of a certain material, but
the equivalent amount in kJ or kcal does not give any practical information to the
majority of the population.
Fortunately exergy can be measured in different kinds of units, not only kJ or kcal,
but also in tons of oil equivalent -toe- (the exergy contained in one ton of oil).
Therefore, the same principle can be applied to non-fuel minerals as with oil. Since
the exergy of a resource, and particularly of a mineral deposit changes with the ore
grade and the reference environment, the unit of measure ton of mineral equivalent
has to be fixed to a specific year and a specific place. Hence, we define the parameter
ton of Mineral equivalent t M e as the exergy content of one ton of mineral in a certain
time and place, as in Eq. 7.5.
3
Explained in section 5.3.4
The tons of mineral equivalent
231
Degradation Exergy
Resources
D
.
D=dD/dt
Δt
Time
Figure 7.1. Conceptual diagram for the terms exergy distance and exergy degradation velocity
tMe =
BM
mM
(7.5)
t
Being B M the absolute exergy of mineral M , and m M the tonnage of mineral M
considered. Once the time and place has been specified and taken as reference
(situation 1), one can calculate the tons of Mineral equivalent of the mineral deposit
at another situation (2). Then the t M e of situation 2 will be:
(t M e)2 =
(B M )2
(t M e)1
(7.6)
Again, this concept can be applied either to exergy or to exergy replacement costs.
For the latter, the tons of Mineral equivalent will be calculated as:
‚
∗
tMe =
∗
BM
mM
Œ
(7.7)
t
The t M e can be also used for comparing the quality of different mineral deposits,
containing the same resource. This is clarified next through a simple example.
Mine A contains in year 2007 mA tons of gold and BA toe of exergy. If mine A is taken
as reference in that year, then one ton of gold equivalent has an exergy content of:
232
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
t Aue = BA/mA. Mine B has the same amount of gold than mine A (mA = mB ) but with
a worse quality (lower ore grade) than that of A (BB < BA). In mass terms, mine B
would be as good as mine A. But if we use the exergy indicator, mine B has less tons
of gold equivalent than the reference: (tAue)B = BB /(tAue) = mA · (BB /BA).
In the same way, the reserves of a certain mineral in a country could be expressed
in a practical and elegant way as tons of Mineral equivalent. This combines the
advantages of both indicators: on one hand the more comprehensive unit of measure exergy and on the other hand the more understandable unit of measure mass.
Nevertheless, as the property mass is involved in the calculation, the t M e loses the
additive capacity that characterizes the exergy indicator.
7.4
The R/P ratio applied to exergy
The resources to production ratio (R/P) is an estimative measure for assessing the
years until depletion of a certain resource. For that purpose, the tonnage of the
estimated reserves is divided into the production of the year under consideration.
Since both, production and reserves fluctuate throughout the years, R/P ratios may
increase or decrease accordingly. Remember that the reserves might increase if new
deposits are discovered or if technological development or mineral prices allow to
extract lower grade deposits not considered as profitable before. Therefore, the R/P
ratio should always be accompanied by the calculation year.
In this PhD, we calculate the resources to production ratio in exergy terms. This
allows to include additional information about the concentration of the deposit, not
taken into account with the conventional calculation in mass terms.
7.5
The Hubbert peak applied to exergy
M. King Hubbert ([146], [147]) found in the mid-fifties that the production of fossil
fuel trends had a strong family resemblance. The curves started slowly and then
rose more steeply tending to increase exponentially with time, until finally an inflection point was reached after it became concave downward. The observed trends
are based on the fact that no finite resource can sustain for longer than a brief period such a rate of growth of production; therefore, although production rates tend
initially to increase exponentially, physical limits prevent their continuing to do so.
So for any production curve of a finite resource of fixed amount, two points on the
curve are known at the outset, namely that at t = 0 and again at t = ∞. The production rate will be zero when the reference time is zero, and the rate will again be
zero when the resource is exhausted, after passing through one or several maxima.
The second consideration is that the area under the production curve must equal the
quantity of the resource available (R). In this way, the production curve of a certain
Production (P)
The Hubbert peak applied to exergy
233
Q=
R∞
Pdt
0
Time (t)
Figure 7.2. The Hubbert’s bell shape curve of the production cycle of any exhaustible
resource [146].
resource throughout history takes the ideal form of the bell-shape curve shown in
Fig. 7.2.
The model was successful in predicting the peak of oil extraction in the US lower
48 states and the subsequent decline in production. Recently, several authors used
Hubbert’s model to predict the evolution of crude oil extraction at the planetary
level (Deffeyes [72], Bentley [24], Campbell and Laherre [47], [46]). According to
these estimates, the corresponding production peak could take place within the first
decade of the 21st century or not much later. And as Campbell and Laherre [47]
argue, from an economic perspective, when the world runs completely out of fuels is
not directly relevant: what matters is when production begins to taper off. Beyond
that point, prices will rise unless demand declines commensurately.
It must be pointed out that the successful prediction of the model depends on many
factors, being the most important one, the reliability of the estimated reserves. Forrester/Meadows models [96], [218] are almost always asymmetric with the decline
much sharper than the growth. Bardi [18] showed that the bell-shaped curve may
turn out to be strongly asymmetric depending on extraction strategies. As Bartlett
argues [22], actual production curves will be probably modified by economic, geological, political, technological, and other factors, which may result in a deterioration
of the quality of the fit between the data and the Gaussian, but the role of these
important factors is limited to changing the quality of this fit.
Basically, the Hubbert model can be applied to those minerals, where the concentration factor is not important, i.e. to liquid and gaseous fossil fuels. Roberts and
Torrens [283] applied also the Hubbert model in 1974 to examine the production
cycle of copper. At that time, there was not so much information as today regarding
consumption rates or future reserve estimates, which are essential ingredients for
the methodology. Therefore, the model had to be applied making quite lot assump-
234
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
tions. Nowadays, the curve can be defined through more points and there are more
reliable estimations for mineral reserves (as for instance the data provided by the US
Bureau of Mines).
Furthermore, we think that the bell-shape curve is better suited to minerals, if it
is fitted with exergy over time instead of mass over time. Oil quality keeps nearly
constant with extraction, whereas other non-fuel minerals don’t (mineral’s concentration decreases as the mine is being exploited). Therefore exergy is a much better
unit of measure than mass, since it accounts not only for quantity, but also for ore
grades and composition. The well known bell-shaped curve can be fitted to the
exergy consumption data provided, in order to estimate when mineral production
will start declining. Next, the mathematical procedure for the application of the
model is explained.
Hubbert’s bell-shape curve can be described through the generic gaussian curve described in Eq. 7.8.
f (t) = y0 e
−

t−t 0
b0
‹
(7.8)
The integral of the gaussian curve is equal to the reserves (R) of the commodity:
Z
+∞
f (t)d t = R
(7.9)
−∞
And the integral of Eq. 7.8 is given by Eq. 7.10.
Z
∞
e
−

t−t 0
b0
‹
dt =
0
p
b0 π
2
(7.10)
Combining Eqs. 7.9 and 7.10, and taking into account that the curve is symmetric,
the reserves can be expressed as:
p
y0 b0 π = R
(7.11)
Hence, the model of the curve to be adjusted is given by Eq. 7.12:
R
−
f (t) = p e
b0 π

t−t 0
b0
‹
(7.12)
Where parameters b0 and t 0 are the unknowns.
In our case, we will represent the yearly exergy loss of the commodity vs. time.
With a least squares procedure, the points will be adjusted to the curve given by Eq.
7.12. The maximum of the function is given by parameter t 0 , and it verifies that
f (t 0 ) = b Rpπ .
0
The exergy loss of mineral deposits due to mineral extraction. The case of copper in
the US
235
7.6
The exergy loss of mineral deposits due to mineral
extraction. The case of copper in the US
Before explaining the exergy decrease of mineral deposits, it must be pointed out
that extraction does not necessarily mean that the inherent exergy of the mineral
is being lost. On the contrary, through the process of mining and concentrating
of ores, we are increasing the exergy per unit of resource and in fact, that exergy
will remain in wires, buildings, industrial machinery and other products were the
minerals are used. The problem arises when the objects made of the refined mineral
are disposed of in landfills at the end of their useful life. In that case, the demand
for the mineral must be satisfied by extracting new one from the mine, thereby
exhausting the resource and reducing the exergy of the mine (the mine contains a
lower quantity of mineral at a lower grade). Fortunately, recycling reduces the need
for so much new mineral to be extracted. Therefore, recycling is very important to
our society, by preventing dispersion once a material has been concentrated.
Hence, when we refer to the exergy loss of mineral deposits, we are indicating the
exergy that the mines are losing through mineral extraction. In practice, this exergy
is only lost when the refined mineral is dumped in landfills or becomes dispersed.
The calculation of the exergy loss of non-fuel minerals requires a great amount of
information: world trends of natural resources production and consumption, trends
of ore grades and mineral reserve projections. Unfortunately, these data is not always available and requires a lot of effort to gather it. The US Geological Survey,
British Geological Survey, British Petroleum and other entities publish periodically
new information about world mineral commodities. Nevertheless, the data is usually
insufficient, since for most commodities, ore grade trends are not studied.
In the next sections, we will present the application of the exergy analysis to the
assessment of the exergy loss of US copper mines. The calculations will be explained
in detail, so as to serve as an example for the Australian case, presented in section
7.7.
7.6.1
Copper mining features
Copper has been mined in the United States at an industrial scale, at least from
1709, in Simbsbury, Connecticut. The industrial revolution intensified the use of
copper in the mid of the nineteenth century, and consequently its production. The
USGS provides historical production and grades data since year 1900. The published
reserves and reserve base of US copper, as well as ore grade trends throughout the
20th century by the US Geological Survey [361], allow us to calculate the exergy
decrease of US copper mines in the last century.
Copper in mineral deposits is usually found in nature in association with sulfur, as
chalcopyrite (CuFeS2 ), but it can be also found as an oxide. The most important
236
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
Naturally occurring
chemical process
[xc]
Cu + 2SO4-2+1/2 Fe2O3
(0)
+2
[xc]
CuFeS2 + 19/2O2
(1)
Naturally
occurring
concentration
process
[xm]
CuFeS2
(2)
(0)
(1)
Dispersed
earth with
R.S.
Dispersed
earth with
minerals
Cu is dispersed on
Earth in form of Cu+2
(aq)
A chemical reaction takes
place, forming CuFeS2 from
their corresponding reference
substances
(2)
Minerals
concentrated in
mines
Actual
Earth
The dispersed CuFeS2 at
xc is concentrated into the
mines at xm.
Figure 7.3. Hypothetical processes involved in obtaining the mineral of copper from
the reference environment
copper ore deposits (the “porphyry coppers”) normally have quite low concentrations of copper (0,3 to 0,6% Cu) but this is compensated by their size (hundreds to
thousands of million tons of ore).
The production of pure copper from the ore can be summarized in two processes.
The first one is concerned with the mining and concentrating of low grade ores
containing copper mineral. The second one is fundamentally a chemical process
in which the concentrated ore is smelted and then refined through an electrolytic
process.
The hypothetical processes needed for replacing the mineral from the reference earth
to the conditions in the mine are outlined in Fig. 7.3. As a first approximation, it
has been assumed, that all the copper occurs in the mines as chalcopyrite. These
processes are needed to replace the mineral from the R.E.
At state 0, the earth is composed of only reference substances (R.S.) dispersed in
the three subsystems of the R.E.: continental crust, atmosphere and hydrosphere.
At state 1, the reference substances of the reference environment defined in this
PhD (section 5.2) composing the mineral (Cu+2 and SO4−2 from the hydrosphere
and Fe2 O3 from the continental crust), react to form CuFeS2 . Finally, at state 2,
the dispersed chalcopyrite is concentrated from x c to the ore grade of the mine x m .
The exergy loss of mineral deposits due to mineral extraction. The case of copper in
the US
237
The concentration of copper in the reference environment x c is assumed to be equal
to 2,8E-5 g/g, which is the average concentration of copper in the earth’s crust,
according to Rudnick and Gao [292].
The unit concentration cost of copper i.e. the energy required to concentrate copper
from x c to x m with today’s technology was estimated by Valero and Botero [371] as
kc = 385, 61. This value4 was obtained considering that the unit concentration cost
for the real process of mining and concentrating is the same as in the hypothetical
process of concentration between the R.E. and the mine conditions. The energy
requirement for mining and concentrating considered (ec ) was the one obtained
by Chapman and Roberts [53]: 66,7 GJ/ton for an ore grade of 0,5% Cu. The
ratio between the real energy required and the minimum exergy to concentrate the
mineral from the earth’s crust to the ore grade of the mine gives the unit exergy cost
mentioned before. The result obtained means that with current technology, we have
to invest 385,61 times more energy for concentrating copper from the R.E. to the
mine than in the reversible process. Martínez et al. [207] updated the value of kc
for copper with more recent information. The value obtained, which is the one used
for our calculations was: kc,Cu = 343, 1.
The real quantity of energy required for “refining” the mineral between the earth’s
crust (as in the Reference Environment) and the conditions in the mine is also usually
greater than the standard chemical exergy given by Eq. 5.1. As explained in section
5.3.4, Valero and Botero estimated the unit chemical exergy costs of sulfides as being
at least kch = 10. Martínez et al. [207] updated that value for copper, obtaining
kch,Cu = 80, 2. Remember that in chapter 5, table 5.7 shows the unit exergy costs of
selected minerals, according to Valero and Botero [371] and Martínez et al. [207].
7.6.2
Chemical exergy
The reserves and reserve base of copper in the US in year 2000 were 45.000 kt and
90.000 kt respectively [362].
The chemical exergy of copper mines will be calculated assuming that Cu is found in
the deposit as the metal. This approximation is used as there is a lack of information
about the amount of copper extracted from chalcopyrite and the other copper ores
such as oxides and other sulfides. Hence, our first goal is to obtain the exergy of
state 1 in
PFig. 7.3. The chemical exergy of Cu, calculated with Eq. 5.1 (bch i =
∆G f i + r j,i bch j ), being ∆G f Cu = −190, 9 kJ/mole and obtaining the chemical
exergy of the elements from the R.E. developed in this study and described in section
5.2.3.5 is: bch Cu = 134, 0 MJ/kmole.
Surprisingly, the chemical exergy of the mineral is higher than that of the pure element: bch CuFeS2 = 1534, 5 MJ/kmole (11,45 times greater). This is due to the fact
4
racy.
Although 5 significant figures are given for kc , the number cannot be considered with that accu-
238
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
that since stability (criterion taken partially by Szargut et al. [343] and in this study
for choosing the reference substances) does not coincide with abundance in a number of cases, some minerals that are quite abundant in nature, such as sulfides, have
a fairly high chemical exergy that can be considered as an exergy reservoir that the
earth provides us for free. This helps our technology to avoid the expenditure huge
amounts of commercial energy during the process of obtaining the corresponding
pure element.
The component of the minimum chemical exergy of a substance remains constant
over time, since it only depends on its chemical composition. Hence, in absolute
terms, the chemical exergy consumption of any substance is proportional to its production rate.
The chemical exergy decrease of copper mines in the United States in the 20th century (B), can be calculated by multiplying the molar copper primary production (ṁ)
with the exergy of copper obtained before: B = ṁ · b. The production of copper
in the US during the past century (see Fig. 7.4), was obtained from the Historical
Statistics for Mineral and Material Commodities in the United States [361], which is a
compilation of data from publications primarily of the USGS and USBM, such as the
Minerals Yearbook [363].
Figure
P 7.5 shows the cumulative chemical exergy decrease of copper mines in the
US ( Bch). At the end of year 2000, the total chemical exergy distance of copper
mines from the beginning of the century, was Dch = 5, 66 Mtoe. This exergy was
consumed at an average degradation velocity Ḋch = 56, 04 ktoe/year, although the
trend since the seventies shows an average degradation velocity of around 77,39
ktoe/year. The maximum velocity was attained in year 1998 (107,81 ktoe/year),
while the minimum was in 1900 (14,66 ktoe/year). Copper production has shown a
continuous growth, since it is strongly linked to the electrical and telecommunication
industries. The chemical exergy of copper reserves, calculated as pure copper at
the end of year 2000, was 2,27 Mtoe. If we add the cumulative chemical exergy
consumption to the exergy reserves at the end of year 2000, we obtain the exergy
reserves at year 1900: 7,93 Mtoe. Similarly, the chemical exergy of copper reserve
base at the beginning and end of the century were 10,19 and 4,53 Mtoe, respectively.
7.6.3
Concentration exergy
Next, the concentration exergy of the mine (step 3 in Fig. 7.3) will be obtained as the
difference between the concentration exergies obtained with the mineral concentration in a mine (x m ) and with the average concentration
in the earth’s crust
h
i (x c ). The
(1−x )
latter are calculated with Eq. 5.10 (bc i = −R̄T0 l nx i + x i l n(1 − x i ) ). Since no
i
ore grades are provided between years 1901 and 1905, it has been assumed that the
concentration of those years is the same as in 1900. The concentration exergy of the
mine, i.e. the minimum energy that nature had to spend to bring minerals from x c
to x m , is not constant over time, because it changes with the ore grade of the mine
The exergy loss of mineral deposits due to mineral extraction. The case of copper in
the US
239
120
140
100
120
100
80
60
60
40
40
20
bch,MJ/kmol
Bch, ktoe
80
20
0
0
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Year
Bch (ktoe)
bch (MJ/kmol)
Figure 7.4. Yearly chemical exergy consumption in the US of pure copper due to
copper production throughout the 20th century
6000
5000
ΣBch, ktoe
4000
3000
2000
1000
0
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Year
Figure 7.5. Cumulative chemical exergy decrease of copper mines in the US throughout the 20th century
(see Fig. 7.6). The mine has the greatest exergy concentration, when the ore grade
is at the maximum and becomes lower as the ore grade decreases. At the beginning
of the century, when the ore grades were at above 2% Cu, the concentration exergy
was the highest, namely bc Cu > 18 MJ/kmole. In the last years, the ore grades have
declined to values less than 0,45% Cu and hence the concentration exergy of the
mine has decreased accordingly: bc Cu < 15 MJ/kmole. Copper ore grade trends in
240
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
12,0
20
19
10,0
18
8,0
Bc, ktoe
16
4,0
15
2,0
14
0,0
1900
bc, MJ/kmol
17
6,0
13
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Year
Bc (ktoe)
bc (MJ/kmol)
Figure 7.6. Yearly concentration exergy consumption in the US of pure copper due
to copper production throughout the 20th century
the US are obtained from the work done by Ruth [295] and completed and updated
with information from the Minerals Yearbook [363].
Figure 7.7
Pshows the cumulative concentration exergy decrease of copper mines in
the US ( Bc ). The total concentration exergy distance of copper mines between
the beginning and end of the century was Dc = 628, 98 ktoe. This exergy was consumed at an average degradation velocity of Ḋc = 6, 22 ktoe/year. The maximum
degradation velocity was attained in year 2000 (10,56 ktoe/year), while the minimum in year 1906 (1,89 ktoe/year). The concentration exergy of copper reserves
and reserve base in year 1900 were 875,3 and 1121,71 ktoe respectively, while in
year 2000, 246,36 and 492,73 ktoe.
Figure 7.7 shows the cumulative concentration exergy decrease of copper mines in
the US.
7.6.4
Total exergy
We can now calculate the total exergy distance of US copper mines between the
beginning and end of the century:
D = (B t,1900 − B t,2000 ) = (Dch + Dc ) = (5660, 37 + 628, 98) = 6289, 35 ktoe.
Dividing this quantity into the years considered, we obtain the average exergy degradation velocity of US copper: Ḋ = 62, 2 ktoe/year.
As can be seen, the exergy concentration component is much lower than the chemical one. For more abundant minerals than copper, such as aluminium or iron,
The exergy loss of mineral deposits due to mineral extraction. The case of copper in
the US
241
700
600
ΣBc, ktoe
500
400
300
200
100
0
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Year
Figure 7.7. Cumulative concentration exergy decrease of copper mines in the US
throughout the 20th century
this fact is even more enhanced. The minimum thermodynamic energy required to
separate two substances such as sugar and salt for example, is equal to the energy
to mix them, which is in fact very low. This is of course not true and the exergy
required to separate substances is much greater than in the reversible case. In order
to overcome that problem, we need to resort to the exergy costs of the mine.
7.6.5
Exergy costs
Through unit exergy costs, reversible exergies are converted into real exergies with
Eq. 5.46 (B ∗t = kch · Bch + kc · Bc ). That equation assumes that exergy costs are constant over time. In fact this is not completely correct, because there are two factors
that must be taken into account. The first one is that technological development
improves the efficiency of mining and refining processes and thus costs tend to decrease (theory of learning curves). The second factor is that as extraction continues
and technology is being improved, lower quality resources can be extracted. However, the use of lower quality resources requires an increase in energy input, which
increases costs.
If we convert the total minimum exergy consumption into real exergy, making the assumption that the costs are constant, we obtain that the irreversible exergy distance
D∗ is:
D∗ = (B ∗t,1900 − B ∗t,2000 ) = Dch · kch + Dc · kc = 5660, 37 ∗ 80, 2 + 628, 98 ∗ 343, 1 =
669.764, 7 ktoe
And the average irreversible exergy degradation velocity Ḋ∗ = 6631, 3 ktoe/year.
242
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
Around 68% of the exergy costs are due to the chemical exergy of copper and 32%
to its concentration exergy. The cost represents the exergy consumed of US copper
mines during the 20th century and is equivalent to 71,3% of 2006 oil consumption
in the US (938,8 Mtoe [35]). This figure gives an idea of the huge amount of energy
that we are degrading by extracting minerals. It must be remembered, that this
study only applies to copper mines in the US.
Additionally, we can calculate the tons of copper equivalent (t Cue∗ ) associated to
the exergy costs of the reserves and reserve base. For that purpose, we take as
reference, the exergy cost B ∗t of the reserves in 1900 (5,95 toe/t of Cu extracted).
The M t Cue∗ is slightly lower than the tonnage due to the loss of concentration
exergy (44,7 M t Cue∗ vs 45 Mt for the reserves and 89,5 M t Cue∗ vs 90 Mt for the
reserve base).
7.6.6
The R/P ratio and the depletion degree of the deposits
The resources to production ratio for US copper, is calculated by dividing the reserve
base’s exergy in year 2000 (5027 ktoe), with the exergy of the metal produced in
that year (90,16 ktoe). The resulting R/P ratio indicates that if production of US Cu
remains as in year 2000, and the reserve base does not increase after that year, the
reserves would be completely depleted in 56 years.
The depletion degree of US copper deposits (%R loss and %R.B. loss) is calculated
as the ratio between the exergy distance D, and the total reserves of the commodity.
The latter are obtained as the published reserves or reserve base of the commodity in
2000, plus the exergy distance D from 1900 to 2000. Accordingly, copper production
in the US throughout the 20th century has leaded to the depletion of 71% and 56%
of its national copper reserves and reserve base, respectively.
7.6.7
The Hubbert peak model
We are now going to apply the Hubbert peak model to US copper mining, in order
to estimate its peak of production. For that purpose, the exergy production has to be
plotted against the corresponding years. At a first stage, we are going to adjust the
points to the gaussian curve, given by Eq. 7.8, i.e. without applying the constraint
about a fixed amount of reserves. The resulting curve represented in Fig. 7.8 is
described by Eq. 7.13:
f (t) = 107, 1e
− 12
t−2041
87,08
(7.13)
The maximum is reached at t = t 0 in year 2041. The integral of Eq. 7.13 represents
R +∞
the reserves: −∞ f (t) = 24.053, 4 ktoe. The regression of the curve is quite low:
RF = 0, 7532.
The exergy loss of mineral deposits due to mineral extraction. The case of copper in
the US
243
Therefore, the production behavior of US copper is associated to available reserves
equal to around 24 Mtoe, assuming that it follows the bell-shaped curve defined by
Hubbert.
120
2041
100
Bt
80
60
40
20
0
2.5
4
x 10
Integral Bt
2
1.5
1
0.5
0
1700
1800
1900
2000
2100
2200
2300
2400
Figure 7.8. The Hubbert peak applied to US copper production. Best fitting curve.
Values in ktoe.
Nevertheless, according to the USGS, the reserve base in year 2000 is equal to 5,02
Mtoe. Adding the already exergy extracted from 1900 to 2000, the base reserves increase to 11,3 Mtoe. Since no data is provided before 1900 and there were certainly
important amounts of copper extracted at least in the second half of the nineteenth
century, we will make the assumption, that Cu extraction from 1700 to 1900 followed the curve of Eq. 7.13. Hence, the 1700 reserve base are approximated to:
R1700 = R2000 +
2000
X
Bt +
1900
= 12549, 9ktoe
Z
1900
107, 1e
− 12
t−2041
87,08
= 5026, 7 + 6289, 4 + 1233, 8
1700
(7.14)
244
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
Therefore, instead of the 24 Mtoe of reserves obtained from the model without constraints, the US total base reserves amount to around one half of that: 12,55 Mtoe.
With the constraint of the reserves, we can now apply the Hubbert peak model,
adjusting the production points to Eq. 7.12.
Figure 7.9 shows the final curve, with again a low regression factor RF = 0, 7305.
According to the model, the production would have reached the peak in year 1994.
In fact, recent data about copper production in the US reveals that the peak was
reached in year 1998 with 2,1 Mt extracted. Since then production has decreased
more rapidly than it increased before reaching the peak. This indicates that the observations of Meadows [218], where production follows asymmetric curves with the
decline much sharper than the growth, apply better at least for US copper production.
Another conclusion that can be extracted from the application of the model is that if
the production curves are generally asymmetrical, the peak will be reached after the
year predicted by the Hubbert model. During a short period of time, the commodities
will be probably over-exploited and the production points will appear over the bellshaped curve. The compensation of the overproduction is the much sharper decrease
of production after the peak, instead of a gradual and steady reduction.
Applying the Hubbert peak model to production in mass terms, instead of exergy
terms gives 1993 as the peaking year for US copper. As can be seen, the difference
between both approaches is very small, since as stated before, in minimum exergy
terms, the concentration component is considerably less important than the chemical one. And it should be remembered, that as opposed to the concentration exergy,
the chemical exergy is proportional to the quantity of mineral extracted. The effect
of decreasing ore grades with production would be better observed if exergy costs,
rather than minimum exergies are used for the plotting. In such a case, the concentration and the chemical exergy terms are well balanced. However, in this study
we have assumed that unit exergy costs remain constant over time. For a correct
representation of exergy costs vs. time, we would require that the exergy costs are
calculated with the corresponding unit exergy costs of the period of time considered,
incorporating the learning curves of the technologies. But this task remains open for
further studies.
7.6.8
Summary of the results
Table 7.1 summarizes the results obtained, showing the exergy and exergy costs,
the exergy distance, average degradation velocity, the tons of mineral equivalent,
the R/P ratio, depletion degree of the reserves and reserve base (% R. loss and %
R.B. loss) and the estimated and real peak of production of US copper reserves and
reserve base during the 20th century.
The exergy loss of a country due to mineral extraction. The case of Australia
245
120
100
1994
Bt
80
60
40
20
0
14000
12000
Integral Bt
10000
8000
6000
4000
2000
0
1800
1900
2000
2100
2200
Figure 7.9. The Hubbert peak applied to US copper base reserves. Values in ktoe.
7.7
The exergy loss of a country due to mineral extraction.
The case of Australia
In the example above, we have applied the exergoecological method to a single
commodity of a country. Since exergy is an additive property, we can analyze the
exergy loss due to mineral extraction of all commodities in a region, country or even
in the entire world.
The objective now it to assess from the exergoecological point of view, the degradation of the main mineral resources of fuel and non-fuel origin of a country throughout its mining history.
Australia is the country chosen for our purpose for two reasons: 1) a comprehensive
analysis of Australian mining data was provided by Mudd [234], [232], [233] and
2) Australia is a major mineral producer and exports numerous commodities around
246
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
Table 7.1. Summary of the results of the exergy distance of US copper mines during
the 20th century.
Year
Bch
Bc
Bt
D
Ḋ, ktoe/yr
∗
Bch
Bc∗
B ∗t
D∗
Ḋ∗ , ktoe/yr
mCu , Mtons
M t Cue∗
R/P, yrs
% R. loss
Hubbert’s peak
Real peak
RESERVES
BASE RESERVE
1900
2000
1900
2000
Minimum exergy, Mtoe
7,93
2,27
10,19
4,53
0,86
0,25
1,11
0,49
8,79
2,51
11,30
5,03
6,28
62,25
Non-reversible exergy, Mtoe
635,77 181,81
817,58
363,62
300,33
84,53
384,86
169,05
936,10 266,34 1202,44 532,68
669,76
6631,33
157,36
45,00
202,36
90,00
157,36
44,77
202,13
89,54
56
71
56
1994
1998
the world. Furthermore, its resources are periodically updated and published in
Geoscience Australia [112].
The study of Mudd aims to shed light on the current debate on sustainable mining in
Australia, establishing the extent of the changes in ore grades for various minerals
and metals as well as quantifying the production of wastes. Mudd provides valuable information among others, about historical production data, ore grades and
economic demonstrated reserves. For some commodities such as copper, the information dates back to 1844.
Assimilating such a great amount of information for each commodity is not always
easy and not very useful for decision makers. However, all these data can be easily
processed and summarized in one indicator, namely the exergy indicator.
7.7.1
Non-fuel minerals
The aim of this section is to obtain the exergy and exergy cost of the main Australian metals throughout their mining history: Au, Cu, N i, Ag, P b, Z n and Fe.
The reversible and irreversible exergy distances D and D∗ , the exergy degradation
velocities Ḋ and Ḋ∗ , and the tons of mineral equivalent t M e∗ lost of the economic
demonstrated reserves are provided. The tons of mineral equivalent are calculated
as the average exergy cost B ∗t of one ton of mineral in the Australian mineral deposits
The exergy loss of a country due to mineral extraction. The case of Australia
247
in year 1900 (whenever data is available for that year). The reserves of the mine
at the beginning of the mining period are considered to be equal to the cumulated
production throughout the mining history until 2004, plus the published reserves in
2004 (the same principle is applied to the reserves in terms of exergy costs).
The peaking of mineral production is estimated with the application of the Hubbert
peak model described in section 7.5. Additionally, the R/P ratio assessed in exergy
terms is given as a measure of the estimated years until depletion of the different
commodities.
The same equations, data sources and ideas used for US copper mines are here applied. For calculating bch, Eq. 5.1 is used, taking as input the chemical exergies of
the elements generated from the R.E. defined in this study (Table 5.4). The concentration exergy bc is calculated with Eq. 5.10. The value of x c is taken from the latest
geochemical study of the earth’s continental crust from Rudnick and Gao [292]. Finally, the unit exergy costs applied are those obtained by Valero and Botero [371]
and updated by Martínez et al. [207].
Figures 7.10 through 7.22 show the cumulated minimum concentration and chemical exergy consumption over time on the left axis and the ore grade trend on the
right axis of the main base-precious metals extracted in Australia. As can be seen
from the figures, and as it happened to the case of copper in the US, the concentration exergy Bc is usually much smaller than the chemical one Bch. But this fact
∗
changes when the values are converted into exergy costs Bc∗ and Bch
, as shown in
tables 7.2 to 7.8. The graphs reveal as well that consumption of all commodities has
increased continuously, following a general exponential trend. The quality of Australian mines, or in other words, their ore grade trends, have been notably reduced
throughout the last century. This implies an even greater loss of the mine’s exergy
and an important production of waste rock.
For the sake of simplicity, the direct results are provided.
7.7.1.1
Gold
Gold has played an important role in Australia’s history, influencing the economic,
social, environmental and political life of the country. The decade of 1850’s is often
denoted as the gold rush decade and since then, great amounts of gold have been
extracted from all states. Australian gold industry is characterized as having continuous cycles of boom and bust. The most representative inflection points occurred
in the late 1800’s and around 1980. In both cases, the discovery of new fields caused
that production, which had gradually declined before those dates, rose to new highs
(see Fig. 7.10).
Gold’s ore grade has followed a general declining trend, even though there have
been various intermediate peaks coinciding with new discoveries. Ore grades have
descended from 37,27 g/t in 1859, to the current 2,02 g/t. The concentration exergy
costs of gold mines (bc∗ ) decreased respectively from 1,28 to 0,91 toe/kg.
248
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
100
40
35
80
30
70
25
60
50
20
40
15
30
Ore grade Xm, g/t
Cumulative total exergy Bt, toe
90
10
20
5
10
0
1859 1869 1879 1889 1899 1909 1919 1929 1939 1949 1959 1969 1979 1989 1999
0
Year
Bc
Bch
Xm
Figure 7.10. Ore grade and cumulated exergy consumption of Australian gold mines
The exergy distance (D) between Australian gold mines in 2004 and 1859 is equal
to 88,97 toe, while the irreversible exergy distance D∗ : 10.683 ktoe. The great
difference between the reversible and irreversible exergy distances are due to the
extremely high unit concentration costs for gold: 422.879 [207]. The average exergy
degradation velocity ( Ḋ) of Australian gold mines is 0,61 toe/year, ranging from
0,12 toe/year reached in 1929, to the last high of 2,64 toe/year in 1997. This figure
has fluctuated frequently due to changing gold prices, available resources, policy,
technology and socioeconomic factors. The average irreversible degradation velocity
Ḋ∗ is equal to 73,17 ktoe/year.
The ktons of gold equivalent in terms of exergy costs extracted in the mining period
from 1859 to 2004 was 11,06 ktAue∗ , being the reference actual exergy of one ton of
gold in year 1900 equal to 0,97 ktoe. The economic demonstrated reserves of gold
in year 2004 are estimated as 5,59 kt, or 5,30 ktAue∗ (B ∗t = 5118,61 ktoe), although
they might probably increase in the future, since exploration continues to take place
and technological development will probably allow to mine low grade deposits.
Note that since year 1900 was taken as reference for estimating the ktons of gold
equivalent, the ktAue∗ before that year will be greater than the tonnage, since the
ores were more concentrated. The contrary happens after the reference year.
The R/P ratio for Australian gold deposits is estimated as 22 years, being 2004 the
reference year for the calculations. Additionally, gold production in Australia has
depleted around 65% of its economic demonstrated reserves.
The Hubbert peak is applied for Australian gold deposits since year 1943. Previous
years are discarded in the analysis due to the fluctuation of the production rates,
as new gold fields were found. Since 1943, it is assumed that most of the reserves
The exergy loss of a country due to mineral extraction. The case of Australia
249
have been found. The value for R in that year is calculated as the sum of the exergy
reserves in 2004, plus the cumulated exergy between 1943 and 2004 (R1943 = 96, 02
toe). Accordingly, the production peak is reached in year 2006 (see Fig. 7.11), with
a regression factor of the fitting curve of RF = 0, 9014. This implies, that although
production in the last years has decreased, it was not caused by the resource limitation and rather by external factors such as company’s strategies.
3
2006
2.5
Bt
2
1.5
1
0.5
0
100
Integral Bt 1943
80
60
40
20
0
1940
1960
1980
2000
2020
2040
2060
2080
Figure 7.11. The Hubbert peak applied to Australian gold reserves. Values in toe.
The results for Australian Gold deposits is summarized in table 7.2.
7.7.1.2
Copper
Copper has been also a relevant contributor to the country’s richness, since Australia
is a major copper producer in the world. Their metal deposits were discovered and
worked on a significant and profitable scale from 1842. The production of copper
has been continuous ever since.
250
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
Table 7.2. Summary of the results of the exergy distance of Australian gold mines.
Year
Bch
Bc
Bt
D
Ḋ, toe/yr
∗
Bch
Bc∗
B ∗t
D∗
Ḋ∗ , ktoe/yr
t Au
∗
tAue1900
R/P, yrs
% R. loss
Year of the peak
Reserves
1859
2004
Minimum exergy, toe
98,62
34,91
37,37
12,10
135,99
47,02
88,97
0,61
Non-reversible exergy, ktoe
0,10
0,03
15801,82
5118,57
15801,92
5118,61
10.683,31
73,17
15.789
5.589
16.358
5.299
22
65
2006
Australian copper ore grades have declined from over 26% to 1,33%, accordingly, its
concentration exergy costs decreased from a maximum of 2,97E-3 toe/kg reached
in year 1849 to 1,97E-3 toe/kg in 2004. Despite the 33% of bc∗ decrease, Australian
copper ore grades are still greater than in other countries (according to the USGS
[363] in the US, the current ore grade is around 0,5%). Additionally, a significant amount of copper mines have been discovered throughout the past century and
prospects for the current scale of the Australian copper industry to continue remain
promising.
The exergy distance D from 1844 to 2004 is 956,12 ktoe, and the irreversible one
D∗ : 103,93 Mtoe. The exergy degradation velocity ( Ḋ) increased from less than 1
ktoe/year before year 1898, to 50,5 ktoe/year in 2001. On average the minimum
and irreversible exergy degradation velocities were Ḋ = 5, 94 and Ḋ∗ = 645, 5, respectively.
In the period of 1844 to 2004, Australian copper mines lost 17,2 M t Cue∗ (1900 reference exergy cost of 1 t Cue∗ is equal to 6,04 toe). The economic demonstrated reserves of copper in year 2004 are estimated as 42,1 Mt, or 41,88 MtCue (B ∗t = 253, 1
Mtoe). The resources to production ratio (R/P) is 48 years, and the percentage of
the economic reserves loss is about 29%.
The Hubbert peak model applied to Australian copper reserves is shown in Fig. 7.11.
Considering that the reserves of copper since 1884 are R = 3.319 ktoe, the peak is
reached in year 2021. The regression factor is RF = 0, 9336.
Table 7.3 shows a summary of the results.
The exergy loss of a country due to mineral extraction. The case of Australia
30
900
25
800
700
20
600
500
15
400
10
300
200
Ore grade Xm, %
Cumulative total exergy Bt, ktoe
1000
251
5
100
0
18
44
18
54
18
64
18
74
18
84
18
94
19
04
19
14
19
24
19
34
19
44
19
54
19
64
19
74
19
84
19
94
20
04
0
Bc
Year
Bch
Xm
Figure 7.12. Ore grade and cumulated exergy consumption of Australian copper
mines
60
2021
50
Bt
40
30
20
10
0
4000
Integral Bt
3000
2000
1000
0
1850
1900
1950
2000
2050
2100
2150
Figure 7.13. The Hubbert peak applied to Australian copper reserves. Values in ktoe.
252
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
Table 7.3. Summary of the results of the exergy distance of Australian copper mines.
Year
Bch
Bc
Bt
D
Ḋ, ktoe/yr
∗
Bch
Bc∗
B ∗t
D∗
Ḋ∗ , Mtoe/yr
M t Cu
∗
M t Cue1900
R/P, yrs
% R. loss
Year of the peak
7.7.1.3
Reserves
1844
2004
Minimum exergy, ktoe
2973,36
2120,87
345,65
242,02
3319,01
2362,89
956,12
5,94
Non-reversible exergy, Mtoe
238,46
170,09
118,59
83,04
357,06
253,13
103,93
0,645
58,98
42,10
59,08
41,88
48
29
2021
Nickel
The large-scale production of nickel is one of Australia’s most recent additions to
its mining industry. Although the earliest nickel production started in year 1913,
it was not until 1966, with the discovering of a large high grade deposit, when
N i production and exploration boomed. Since then, extraction has continued to
increase, even though in the period from 1977 to 1994, N i production suffered a
slight stagnation (see Fig. 7.14).
The ore grade has decreased from 4,57 to 1,16%. Accordingly, the concentration
exergy costs of N i mines (bc∗ ) decreased from 3,01 to 2,44 tep/t.
The exergy distance D between 1963 and 2004 is equal to 323,68 ktoe, while D∗ =
9, 46 Mtoe. The exergy degradation velocity Ḋ increased from 0,26 ktoe/year to
around the current 19 ktoe/year. On average, the minimum and irreversible exergy
degradation velocities of nickel mines are Ḋ = 8, 52 and Ḋ∗ = 683, 13 ktoe/year,
respectively.
The megatons of N i equivalent lost in the period 1967 to 2004 are equal to 3,27
M t N ie∗ (the reference year is in this case 1967, since there is no information for for∗
mer years; M t N ie1967
= 7, 93 toe). The economic demonstrated reserves of nickel
in year 2004 are estimated as 22,6 Mt, or 22,55 M t N ie∗ (B ∗t =178,8 Mtoe). The R/P
ratio of Australian nickel deposits, indicate that there is enough metal for at least
121 years. Additionally, the percentage of the economic reserves loss is around 13%.
The exergy loss of a country due to mineral extraction. The case of Australia
350
253
5,0
4,5
Cumulative total exergy, ktoe
300
4,0
250
3,0
2,5
150
2,0
1,5
100
Ore grade Xm, %
3,5
200
1,0
50
0,5
0
1967
0,0
1972
1977
1982
1987
1992
1997
2002
Year
Bc
Bch
Xm
Figure 7.14. Ore grade and cumulated exergy consumption of Australian nickel
mines
40
2040
Bt
30
20
10
0
3000
Integral Bt
2500
2000
1500
1000
500
0
1960
1980
2000
2020
2040
2060
2080
2100
2120
2140
Figure 7.15. The Hubbert peak applied to Australian nickel reserves. Values in ktoe.
Figure 7.15 shows the Hubbert peak model applied to Australian nickel reserves.
Considering that the reserves of nickel in 1967 are R1967 = 2.587, 6 ktoe, the peak is
reached in year 2040. The regression factor of the curve is RF = 0, 7549.
Table 7.4 shows a summary of the results.
254
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
Table 7.4. Summary of the results of the exergy distance of Australian nickel mines.
Year
Bch
Bc
Bt
D
Ḋ, ktoe/yr
∗
Bch
Bc∗
B ∗t
D∗
Ḋ∗ , ktoe/yr
M tN i
∗
M t N ie1967
R/P, yrs
% R. loss
Year of the peak
7.7.1.4
Reserves
1967
2004
Minimum exergy, ktoe
2442,76
2138,14
144,80
125,75
2587,57
2263,89
323,68
8,52
Non-reversible exergy, ktoe
142198,16
124465,18
62524,61
54298,66
204722,77
178763,84
25968,93
683,13
25,82
22,60
25,82
22,55
121
13
2040
Silver
Silver is usually found in mines containing also lead and zinc and hence their production rates are tightly connected. The establishment of major mining companies
in Australia was in the decade of the 1880’s.
The ore grades of silver have suffered a drastic reduction, passing from over 3000
g/t at the initial years, to less than 800 g/t in just one decade. Since 1931, the
ore grades have declined to less than 200 g/t, being the current ore grade equal to
133,5 g/t (see Fig. 7.16). This quality loss of silver mines is reflected in the actual
concentration exergy component: in year 1884, bc∗ was equal to 42,9 tep/t, while in
2004, 30,3 tep/t (30% of concentration exergy loss).
The exergy distance between the reserves in 1884 and 2004 are D = 1416, 91 toe
and D∗ = 2227, 4 ktoe. This minimum exergy was consumed at an average rate of
Ḋ = 11, 71 toe/year ( Ḋ∗ = 18.407 toe/yr), but since year 2000, the silver degradation velocity has increased to about Ḋ = 40 ( Ḋ∗ = 61.129) toe/year.
Silver mines in Australia lost throughout their mining history a total of 72,81 ktAg e∗
(being the 1900 reference exergy equal to 30,6 toe/t). The economic demonstrated
reserves of silver in year 2004 are estimated as 41,0 kt, or 40,8 ktAge (B ∗t = 1247, 4
ktoe). The R/P ratio indicates that the depletion of silver mines could occur in 19
years, if production remains as in 2004 and no further reserves are found. Sixtyfour of the economic reserves of silver in Australia have been already extracted, as
indicated by the %R loss ratio.
The exergy loss of a country due to mineral extraction. The case of Australia
1500
255
3500
1400
3000
1200
1100
2500
1000
900
2000
800
700
1500
600
500
1000
400
Ore grade Xm, g/t
Cumulative total exergy, toe
1300
300
500
200
100
0
18
84
18
89
18
94
18
99
19
04
19
09
19
14
19
19
19
24
19
29
19
34
19
39
19
44
19
49
19
54
19
59
19
64
19
69
19
74
19
79
19
84
19
89
19
94
19
99
20
04
0
Year
Bc
Bch
Xm
Figure 7.16. Ore grade and cumulated exergy consumption of Australian silver
mines
The Hubbert peak model applied to Australian silver reserves does not throw out
good results. The regression factor is very low (RF = 0, 577), considering the reserves in year 1884: R = 2226 toe. The maximum of the peak would have been
reached in year 2005 (see Fig. 7.17). It must be pointed out that silver is a special
mineral commodity in Australia, since it is extracted only as a by-product of other
minerals such as copper, lead zinc and to a lesser extent, gold [112]. Hence, the production patterns may not follow the general rules expected for other commodities.
Table 7.5 summarizes the results obtained.
7.7.1.5
Lead
Lead production has followed a general increasing trend since the beginning of its
mining industry. In deposits mined today, lead (in the form of galena, P bS) is usually
associated with zinc, silver and commonly copper, and is extracted as a co-product
of these metals [112].
As in the case of silver, lead ore grades decreased dramatically in a short period
of time. During the first 20 years of the lead industry, ore grades kept at around
60%. From that point, the quality of P b in the mines dropped to levels below 20%,
reaching the current level of 4,32%. The concentration exergy cost of P b in the
mines (bc∗ ) decreased from 0,63 toe/t at the highest point reached in 1877, to 0,49
toe/t in 2004 (see Fig. 7.18).
The exergy distance of lead between 1859 and 2004 is equal to D = 982, 10 ktoe,
and D∗ = 40, 74 Mtoe. The exergy degradation velocity of lead increased from
256
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
50
40
30
Bt
2005
20
10
0
2500
Integral Bt
2000
1500
1000
500
0
1900
1950
2000
2050
2100
2150
Figure 7.17. The Hubbert peak applied to Australian silver reserves. Values in toe.
Table 7.5. Summary of the results of the exergy distance of Australian silver mines.
Year
Bch
Bc
Bt
D
Ḋ, toe/yr
∗
Bch
Bc∗
B ∗t
D∗
Ḋ, ktoe/yr
t Ag
∗
tAg e1900
R/P, years
% R. loss
Year of the peak
Reserves
1880
2004
Minimum exergy, toe
1735,08
632,91
490,99
176,24
2226,07
809,15
1416,91
11,71
Non-reversible exergy, ktoe
17,35
6,33
3459,49
1241,07
3476,84
1247,40
2227,36
18,42
112399
41000
113588
40777
19
64
2005
1000
90
900
80
800
257
70
700
60
600
50
500
40
400
30
300
Ore grade Xm, %
Cumulative total exergy, ktoe
The exergy loss of a country due to mineral extraction. The case of Australia
20
200
10
100
0
1859 1869 1879 1889 1899 1909 1919 1929 1939 1949 1959 1969 1979 1989 1999
0
Year
Bc
Bch
Xm
Figure 7.18. Ore grade and cumulated exergy consumption of Australian lead mines
Ḋ = 0, 20 toe/year ( Ḋ∗ = 9 toe/year) to around 20 ktoe/year ( Ḋ∗ = 780 ktoe/year)
registered since year 2000. On average, Ḋ and Ḋ∗ are 6,73 and 279,04 ktoe/year,
respectively.
The megatons of lead equivalent lost in Australia’s mining history are equal to 34,12
M t P be∗ (being the 1900 reference actual exergy of one ton of lead equal to 0,766
toe). The economic demonstrated reserves of lead in year 2004 are estimated as 22,9
Mt, or 22,45 M t P be (B ∗t = 26, 81 Mtoe). According to the R/P ratio, the complete
degradation of Australian lead deposits would occur in 34 years, if the reference year
is 2004. Additionally, the percentage of the economic demonstrated reserves loss is
around 60%.
Figure 7.19 shows the Hubbert peak model applied to lead. The peaking year is
reached in 1997, considering that the economic demonstrated reserves are R1859 =
1646, 6 ktoe. The regression factor of the curve is RF = 0, 8691. And the production
points for the latest years (1998 - 2004) are not included under the curve. According
to the production data, the real peak might have been reached in year 2002. This
might indicate that, in the period between 1997 to 2002, there has been an overproduction of the reserves. Consequently an abrupt decrease of production rates is now
expected, as it happens with US copper. Nevertheless, the production pattern for
lead might not follow the general behavior of other commodities, as it is extracted
as a by-product, and the model cannot be applied satisfactorily.
Table 7.6 summarizes the results obtained for Australian lead mineral deposits.
258
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
25
20
1997
Bt
15
10
5
0
2000
Integral Bt
1500
1000
500
0
1850
1900
1950
2000
2050
2100
2150
Figure 7.19. The Hubbert peak applied to Australian lead reserves. Values in ktoe.
Table 7.6. Summary of the results of the exergy distance of Australian lead mines.
Year
Bch
Bc
Bt
D
Ḋ, ktoe/yr
∗
Bch
Bc∗
B ∗t
D∗
Ḋ, ktoe/yr
M tPb
M t ∗P be,1900
R/P
% R. loss
Year of the peak
Reserves
1859
2004
Minimum exergy, ktoe
1513,39
613,09
133,24
51,44
1646,63
664,53
982,10
6,73
Non-reversible exergy, ktoe
38394,47
15554,01
29156,24
11256,51
67550,71
26810,52
40740,19
279,04
56,53
22,90
56,57
22,45
34
60
1997
The exergy loss of a country due to mineral extraction. The case of Australia
6000
259
20
16
14
4000
12
10
3000
8
2000
6
Ore grade Xm, %
Cumulative total exergy, ktoe
18
5000
4
1000
2
3
3
8
3
8
3
8
3
8
3
8
3
8
3
8
3
8
3
8
8
20
0
19
9
19
9
19
8
19
8
19
7
19
7
19
6
19
6
19
5
19
5
19
4
19
4
19
3
19
3
19
2
19
2
19
1
19
1
19
0
19
0
18
9
3
0
8
0
Year
Bc
Bch
Xm
Figure 7.20. Ore grade and cumulated exergy consumption of Australian zinc mines
7.7.1.6
Zinc
Very little interest was shown in zinc until the beginning of the 20th century because
no known method for efficient Z n separation and recovery was found. At that time,
Z n was seen as a problem appearing in silver and lead mining. However, with the
new method of flotation, firstly applied in 1905, the Z n industry started to emerge.
The Z n grade of Australian mines has fluctuated strongly between 3 and 17%, especially until the late 1940’s. Since then, Z n grades tend to stabilize to around 8,5%
(bc∗ = 0, 82 toe/t).
The exergy distance since 1905 has been D = 5381 ktoe, and D∗ = 102 Mtoe.
The exergy has been extracted at an average rate of Ḋ=50 ktoe/year ( Ḋ∗ =950
ktoe/year). In the last 5 years, the yearly minimum and irreversible exergy degradation velocity of zinc ( Ḋ and Ḋ∗ ) has increased to about 178 and 3367 ktoe/year,
respectively.
The megatons of zinc equivalent lost in the mining period from 1898 to 2004 was
441,27 M t Z ne (M t Z ne1900 = 2, 46 toe). The economic demonstrated reserves of
zinc in year 2004 are estimated as 41 Mt, or 37,69 M t Z ne (B ∗t = 100, 90 Mtoe). The
R/P ratio of Z n economic reserves is estimated at around 30 years. The depletion
degree of the economic reserves is around 51%.
The Hubbert peak model applied to the Australian Z n reserves is shown in Fig. 7.21.
As zinc mining is closely related to the mining of lead and silver, a similar behavior
of the model to the latter minerals is expected. The latest production points are
not included under the curve (from 2000 to 2004). However, the adjusted curve
has a better regression factor than that of lead and silver, namely RF = 0, 8806.
260
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
200
2010
Bt
150
100
50
0
12000
Integral Bt
10000
8000
6000
4000
2000
0
1900
1920
1940
1960
1980
2000
2020
2040
2060
2080
2100
Figure 7.21. The Hubbert peak applied to Australian zinc reserves. Values in ktoe.
Table 7.7. Summary of the results of the exergy distance of Australian zinc mines.
Year
Bch
Bc
Bt
D
Ḋ, ktoe/yr
∗
Bch
Bc∗
B ∗t
D∗
Ḋ, ktoe/yr
M tZn
M t ∗Z ne,1900
R/P, yrs
% R. loss
Year of the peak
Reserves
1898
2004
Minimum exergy, ktoe
10188,07
5078,73
540,61
268,98
10728,68
5347,71
5380,97
50,3
Non-reversible exergy, ktoe
134494,54
67045,15
68057,12
33862,36
202552,16
100907,50
101644.,60
950,09
82,25
41,00
82,25
40.97
30
51
2010
The expected peaking year, assuming the economic demonstrated reservers R1898 =
10728, 7 ktoe is 2010.
Table 7.7 summarizes the results obtained for Australian zinc mineral deposits.
700000
70
600000
60
500000
50
400000
40
300000
30
200000
20
100000
10
0
1907
261
Ore grade Xm, %
Cumulative total exergy Bt, ktoe
The exergy loss of a country due to mineral extraction. The case of Australia
0
1917
1927
1937
1947
Bc
1957
Year
Bch
1967
1977
1987
1997
Xm
Figure 7.22. Ore grade and cumulated exergy consumption of Australian iron mines
7.7.1.7
Iron
Australia is the third iron ore production country in the world, after China and Brazil.
The economic demonstrated iron ore reserves have fluctuated throughout last century and accordingly, its associated ore grade. In addition to the discoveries of new
iron deposits, others have been reclassified as economic due to the increase of iron
prices. The available reliable data about grades and production trends for iron dates
back to 1907, although there are single figures for some years since 1850. There are
ore grades missing for the following year periods: 1930 - 1934; 1936 - 1940; 1946 1951; 1966 and 1994. For the latter, the same ore grade of the previous year, where
grade data was available, was assumed. The missing grades are represented hence
as a horizontal straight line in figure 7.22.
The abundance of iron rich deposits has allowed the ore grades to stabilize and even
increase throughout its mining history. Iron concentration in Australia rarely goes
down to 62%, equivalent to around bc∗ =0,29 toe/t (see Fig. 7.22).
The exergy distance between 1907 and 2004 has been D = 704 Mtoe, and D∗ =
4.901 Mtoe. The average exergy degradation velocity since 1907 was Ḋ = 7183
ktoe/year ( Ḋ∗ = 50.012 ktoe/year), although it increased sharply since the seventies
to near Ḋ = 40.000 ktoe/year ( Ḋ∗ = 265.000 ktoe/year).
The megatons of iron equivalent lost in the mining period from 1907 to 2004
was 4289 M t Fee∗ (The first available year was taken as the reference, 1907:
1t Fee∗ =1,14 toe). The economic demonstrated reserves of iron in year 2004 are
estimated as 14.600 Mt, or 14.556 M t Fee (B ∗t = 16665 Mtoe). Additionally, the
percentage of the economic demonstrated reserves loss is around 23%.
262
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
4
5
x 10
2026
4
Bt
3
2
1
0
3.5
6
x 10
3
Integral Bt
2.5
2
1.5
1
0.5
0
1900
1950
2000
2050
2100
2150
Figure 7.23. The Hubbert peak applied to Australian iron reserves. Values in ktoe.
The Hubbert peak model is satisfactorily applied to Australian iron reserves, as can
be seen in Fig. 7.23. The peaking year will be reached in 2026, considering that the
economic demonstrated reserves R1907 = 3100 Mtoe. The regression factor is very
acceptable: RF = 0, 9515.
Table 7.8 shows a summary of the results obtained for Australian iron mineral deposits.
7.7.2
Fuel minerals
In this section we are going to calculate the exergy degradation of Australian fuel
reserves, which are composed of vast amounts of coal and some oil and natural gas.
The exergy is calculated with the equations provided in section 5.3.3, with the
methodology developed by Valero and Lozano [369]. As stated in previous chapters,
the exergy of fuels is tightly related to its chemical exergy content (the concentration exergy component is insignificant). Note also that it has no sense of calculating
exergy costs of fossil fuels, as it is impossible to replace the photosynthesis process
with current technology.
As for the case of non-fuel minerals, R/P ratios, the depletion degree, and the year
estimation of maximum peaks of production are provided for Australian coal, oil and
natural gas.
The exergy loss of a country due to mineral extraction. The case of Australia
263
Table 7.8. Summary of the results of the exergy distance of Australian iron mines.
Year
Bch
Bc
Bt
D
Ḋ, ktoe/yr
∗
Bch
Bc∗
B ∗t
D∗
Ḋ, Mtoe/yr
M t Fe
M t ∗Fee,1907
R/P, yrs
% R. loss
Year of the peak
7.7.2.1
Reserves
1907
2004
Minimum exergy, Mtoe
3044,65
2353,31
55,50
42,86
3100,15
2396,17
703,98
7.183,45
Non-reversible exergy, Mtoe
16163,18
12493,08
5403,71
4172,74
21566,89
16665,82
4901,07
50,01
18.889,23
14.600,00
18.889,23
14.596,65
63
23
2026
Coal
Coal was first discovered in Australia in 1791 in New South Wales and the first coal
mining settlement was established there in 1801 [12].
Since then, coal production has increased dramatically. It is mined in every state
of Australia. Around 75% of the coal mined in Australia is exported, mostly to
eastern Asia. Consequently, Australia has become the fourth largest coal producer
in the world. Coal also provides about 85% of Australia’s electricity production The
relative abundance, reliability and low cost of coal have ensured that it remains the
most commonly used fuel source for electricity generation in Australia [164].
The main type of coal extracted in Australia is bituminous and to a lesser extent
lignite. Small amounts of subbituminous and traces of semi-anthracite are also produced. Table A.22 in the appendix, shows the production of the different types of
Australian coal in the period between 1913 and 2006. The data has been extracted
from the historical statistics compiled by the British Geological Survey and its preceding organizations. The exergies of the coal extracted in the mentioned period
are shown in figure 7.24. The specific exergies of anthracite, bituminous, subbituminous and lignite used are the ones listed in table 6.10 (b I I I ). According to BP [35],
Australian coal’s reserves are in 2006, around 38,6 Mtons of anthracite and bituminous, and 39,9 Mtons of subbituminous and lignite. The latter reserves expressed in
exergy terms, are equivalent to a total of 37,7 Gtoe.
264
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
Bt, ktoe
250000
Coal production in Australia
200000
Lignite
150000
100000
50000
Subbituminous
Bituminous
19
13
19
17
19
21
19
25
19
29
19
33
19
37
19
41
19
45
19
49
19
53
19
57
19
61
19
65
19
69
19
73
19
77
19
81
19
85
19
89
19
93
19
97
20
01
20
05
0
Year
Semi-anthracite
Bituminous
Subbituminous
Lignite
Figure 7.24. The exergy loss of Australian coal reserves. Values in ktoe.
The exergy loss of Australian coal reserves, i.e. the exergy distance D, between 1913
and 2006 has been around 5,6 Gtoe. This exergy was consumed at an average exergy
degradation velocity Ḋ of near 60 Mtoe/year, but since year 2000, the velocity has
increased to more than 200 Mtoe/year.
Assuming that the exergy reserves in 1913 were those of year 2006 plus the exergy
distance between 1913 and 2006, i.e. R1913 = 43, 4 Gtoe, the Hubbert’s bell-shaped
curve applied to Australian coal production reveals that the peak of production will
be reached in year 2048. As can be seen in fig. 7.25, the model has been very well
fitted, with a regression factor of 0,9883.
The resources to production ratio R/P in 2006, calculated as the ratio between the
exergy reserves in 2006 and the exergy production in the same year, indicates that it
will be enough coal for at least 153 years. The percentage of the economic reserves
loss is around 13%, what indicates that there are still large amounts of coal in the
country.
7.7.2.2
Oil
According to BP [35], Australia has around 0,54 Gtons of oil reserves. The majority
of these reserves are located off Western Australia in the Carnarvon basin and in the
Bass Strait off Southern Australia. Australian oil production does not cover internal
consumption and around 39% of total consumption needs to be imported. Oil production in Australia has increased gradually since 1980, peaking in 2000. Thereafter,
The exergy loss of a country due to mineral extraction. The case of Australia
265
5
x 10
2048
5
Bt
4
3
2
1
Integral Bt
0
7
x 10
5
4
3
2
1
0
1900
1950
2000
2050
2100
2150
2200
Figure 7.25. The Hubbert peak applied to Australian coal reserves. Values in ktoe.
Australia has experienced decreasing oil production due to oil producing basins such
as Cooper-Eromanga and Gippsland experiencing natural declines, coupled with a
lack of new fields coming online [82]. However, new exploration efforts, especially
offshore could help stabilize the country’s oil production over the next few years.
Historical data about Australian oil production is very fragmented. Reliable and
continuous information can only be found since the sixties. In fact, it was not until
those years, when the country started to produce considerable amounts of oil. It is
worth to mention that in addition to crude petroleum, oil shale5 has been extracted
in the past and might be taken up again in the future.
Table A.23 shows Australian oil production data from 1913 until 2006, published by
the British Geological Survey and its former organizations. With the specific exergy
of Fuel-oil Nr.1 (46259,1 kJ/kg - table 6.13), we obtain that the exergy distance D of
Australian oil production from 1964 to 2006 is equal to around 1 Gtoe. This exergy
was consumed at an average degradation velocity Ḋ of 21,7 Mtoe/year, reaching a
peak in 2000 of more than 40 Mtoe/year (see table 7.26).
The Hubbert peak model has been applied also for Australian oil production (see fig.
7.27). It has been assumed, that the total amount of exergy reserves are equal to
the current ones (0,59 Gtoe), plus the exergy degradation due to extraction in past
years (1,02 Gtoe), i.e. R = 1, 61 Gtoe. Our results throw up that the peak6 should
5
Oil Shales are sedimentary rocks containing a high proportion of organic matter (kerogen) which
can be converted to synthetic oil or gas by processing.
6
The fit has a regression factor of RF=0,853.
266
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
Oil production in Australia
Bt, ktoe
45000
40000
35000
30000
25000
20000
15000
10000
5000
6
2
4
20
0
20
0
8
0
20
0
20
0
4
6
19
9
19
9
0
2
19
9
19
9
6
8
19
9
19
8
2
4
19
8
19
8
8
0
19
8
19
8
4
6
19
7
19
7
0
2
19
7
19
7
6
8
19
7
19
6
2
4
19
6
19
6
19
6
19
6
0
0
Year
Figure 7.26. The exergy loss of Australian oil reserves. Values in ktoe.
4
4
x 10
1997
Bt
3
2
1
Integral Bt
6
0
x 10
2
1.5
1
0.5
0
1940
1960
1980
2000
2020
2040
2060
Figure 7.27. The Hubbert peak applied to Australian oil reserves. Values in ktoe.
have been reached in 1997. The real peak was however reached in year 2000, and
was followed by a sharp production decrease afterwards. This behavior is the same
found in US copper mines and in the models of Meadows et al. [218], indicating
that the symmetrical exponential curve of Hubbert might not be the best fit.
The exergy loss of a country due to mineral extraction. The case of Australia
267
The resources to production ratio for Australian oil production indicates that in less
than 26 years, oil reserves will be completely depleted, if no more deposits are found.
Additionally, around 60% of the economic reserves have been also exploited. As
stated before, this situation might change, since Australia is investing in oil exploration.
7.7.2.3
Natural gas
Australia has sizable natural gas reserves located in offshore basins, and in most of
all Australia’s states. The country is the fifth largest exporter of liquefied natural
gas (LNG) in the world. Natural gas production in Australia has increased steadily
over the last decade. In the same time period, consumption has grown as well. Australia is expected to maintain natural gas self-sufficiency for the ensuing decade at
a minimum. Additionally, recent natural gas exploration in Australia has resulted in
several important discoveries, mainly offshore. Further natural gas discoveries will
likely be made inadvertently as a byproduct of Australia’s recent surge in petroleum
exploration [82].
Historical data on Australian natural gas production dates back to 1961. Table A.24
shows production data compiled by the British Geological Survey. The 2006 Australian natural gas reserves are around 2,61 trillion of cubic meters, according to BP
[35]. The exergy loss of Australian natural gas reserves due to extraction is shown
in fig. 7.28. The specific exergy of natural gas assumed is 39393,8 kJ/N m3 (table
6.16). Accordingly, Australia has lost in the period between 1961 to 2006, 649 Mtoe.
This exergy was consumed at an average degradation velocity Ḋ of 13,8 Mtoe/year,
although it has increased to more than 30 Mtoe/year since the last decade (see fig.
7.28).
The application of the Hubbert bell shape-curve to Australian natural gas production, throws up a peak of production in year 2025. It has been assumed, that the
total reserves are equal to 3,1 Gtoe7 . The regression factor of the curve RF was
0,98. Assuming that production will stabilize to 2007 rates and that reserves will
not increase in the future, the R/P ratio of Australian natural gas reserves would be
equal to 67 years. Furthermore, about 21% of the natural gas reserves have been already extracted. Of course these numbers are only hypothetical and will presumably
increase, as new deposits are found.
7.7.3
Summary and discussion of the results
Table 7.9, summarizes the results obtained from this study, showing the year were
the peak of production is reached (Peak), the R/P ratio of the last recorded year,
7
The total reserves are obtained as the exergy reserves in 2006, plus the exergy distance between
1961 and 2006.
268
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
Natural gas production in Australia
Bt, ktoe
40000
35000
30000
25000
20000
15000
10000
5000
6
2
4
20
0
20
0
8
0
20
0
20
0
4
6
19
9
19
9
0
2
19
9
19
9
6
8
19
9
19
8
2
4
19
8
19
8
8
0
19
8
19
8
4
6
19
7
19
7
0
2
19
7
19
7
6
8
19
7
19
6
2
4
19
6
19
6
19
6
19
6
0
0
Year
Figure 7.28. The exergy loss of Australian natural gas reserves. Values in ktoe.
4
6
x 10
2025
5
Bt
4
3
2
1
Integral Bt
6
0
x 10
4
3
2
1
0
1940
1960
1980
2000
2020
2040
2060
2080
2100
2120
Figure 7.29. The Hubbert peak applied to Australian natural gas reserves. Values in
ktoe.
The exergy loss of a country due to mineral extraction. The case of Australia
269
Table 7.9. Summary of the results of the exergy assessment of the main Australian
minerals.
Mineral
∆t
Peak
Au
Cu
Ni
Ag
Pb
Zn
Fe
C oal
Oil
N .Gas
TOTAL
1859 - 2004
1844 - 2004
1967 - 2004
1884 - 2004
1859 - 2004
1897 - 2004
1907 - 2004
1913 - 2006
1964 - 2006
1961 - 2006
2006
2021
2040
2005
1997
2010
2026
2048
1997
2025
R/P,
yrs
22
48
121
19
34
30
63
153
26
67
% R
Loss
65
29
13
64
60
51
23
13
63
21
∆M t M e
D, ktoe
D∗ , Mtoe
Ḋ, ktoe, yr
Ḋ∗ , ktoe, yr
1,11E-02
17,2
3,3
7,28E-02
34,1
41,3
4292,6,
-
0,1
956,1
323,7
1,4
982,1
5381,0
703978,4
5637923,1
1019500,0
649045,8
8018091,5
10,7
103,9
26,0
2,2
40,7
101,6
4901,1
5186,3
6,1E-04
5,9
8,5
0,0
6,7
50,3
7183,5
59977,9
21691,5
13809,5
102733,8
73,2
645,5
683,1
18,4
279,0
950,1
50012,4
52661,8
the depletion degree of the commodities (% R. loss), the quantity of Metal extracted
(∆M t M e) in Mtons, the minimum and irreversible exergy distance (D and D∗ ) and
degradation velocities ( Ḋ and Ḋ∗ ) of the fuel and non-fuel mineral Australian reserves throughout the period of time considered (∆t). Thanks to the additive property of exergy, the total minimum and irreversible exergy distance of the mines in
Australia considered can be calculated.
The Hubbert peak model to the exergy reserves of the Australian minerals considered was satisfactorily applied to gold, copper, nickel, iron, coal, oil8 and natural gas.
That was not the case for commodities silver, lead and zinc were the regression factors of the curves were quite low and the latest production points were not included
under the bell-shaped curve. Probably the fact that the production of all three metals
are tightly connected, makes that their production patterns do not follow the general
behavior of other commodities. According to the economic demonstrated reserves
of the listed minerals, the Hubbert peak model applied in this study predicts that the
maximum production has been already reached for gold (2006), silver (2005), lead
(1997) and oil (1997). Zinc will reach the peak in 2010, copper in 2021, natural
gas in 2025, iron in 2026, nickel in 2040, and finally coal in 2048. The resources to
production data, informs us about the estimated years until depletion. Accordingly,
the most depleted commodities are in decreasing order: silver, gold, oil, zinc and
lead, with R/P ratios below 35 years. They are followed by the commodities of copper, iron, natural gas, nickel and finally coal, with R/P ratios of 48, 63, 67, 121 and
153 years, respectively. Of course these figures are only approximative, since they
depend strongly on production rates and reserves. The latter might increase as new
discoveries are found, or as technology or the increase of prices allows to extract
lower-grade deposits.
Although the quantity extracted of all commodities in terms of mass cannot be
summed up (gold and silver are extracted at rates of some tons per year, whereas the
8
Despite of the irregular oil production in Australia, the Hubbert peak model here applied has
predicted with only three years of difference the peaking of production.
270
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
other metals at rates of kilotons/year), the order of magnitude in terms of exergy
costs (B ∗ ) is similar for all commodities and its sum gives valuable information. The
irreversible exergy distance D∗ obtained for all metals in Australia listed in Table 7.9
is equal to 5186 Mtoe. The irreversible degradation velocity of the same metals is
on average 52,6 Mtoe/yr. This means that if we would like to replace the metals
extracted throughout Australia’s mining history, with current available technology,
we would require 154 times the 2006 primary energy consumption of that country
(33,7 Mtoe [35]). Moreover, each year Australia is degrading on average by the
extraction of metals the equivalent of 1,56 times its primary oil consumption. From
all metals, iron is responsible for 95% of the exergy consumption, due to the great
quantity of iron ore produced in Australia.
Figures 7.30 to 7.32 show the total consumption in exergy replacement costs terms
(B ∗t ) of all metals considered, from 1844 to 2004. In the first period illustrated in Fig.
7.30, the extraction of copper and gold contribute to most of the exergy consumed,
although lead acquires a relevant role from the last years of the 19th century. In the
second period, from 1907 to 1963 (Fig. 7.31), the extraction of zinc, lead and iron
represents the major exergy consumption. From 1950 to our days, iron dominates
clearly the non-fuel mineral exergy consumption in Australia.
700
B*t, ktoe
600
Zinc
500
Lead
400
300
Copper
200
100
Gold
Silver
18
44
18
46
18
48
18
50
18
52
18
54
18
56
18
58
18
60
18
62
18
64
18
66
18
68
18
70
18
72
18
74
18
76
18
78
18
80
18
82
18
84
18
86
18
88
18
90
18
92
18
94
18
96
18
98
19
00
19
02
19
04
19
06
0
Silver
Gold
Copper
Iron
Nickel
Lead
Zinc
Figure 7.30. Irreversible exergy consumption of the main non-fuel minerals in Australia in the period from 1884 to 1906
We have stated before, that calculating exergy costs of fuel minerals has no sense,
as it is impossible to replace them, at least with current technology. Nevertheless, its
chemical exergy is so large, that can be compared to the exergy costs of the metals
The exergy loss of a country due to mineral extraction. The case of Australia
271
10000
B*t, ktoe
9000
8000
7000
6000
Zinc
Lead
5000
4000
Iron
3000
2000
1000
Copper
19
07
19
09
19
11
19
13
19
15
19
17
19
19
19
21
19
23
19
25
19
27
19
29
19
31
19
33
19
35
19
37
19
39
19
41
19
43
19
45
19
47
19
49
19
51
19
53
19
55
19
57
19
59
19
61
19
63
0
Silver
Gold
Copper
Iron
Nickel
Lead
Zinc
Figure 7.31. Irreversible exergy consumption of the main non-fuel minerals in Australia in the period from 1907 to 1964
300000
B*t, ktoe
250000
200000
Zinc
150000
100000
Iron
50000
01
97
95
03
20
20
19
19
93
Lead
19
91
19
89
87
Nickel
19
19
85
Iron
19
83
81
Copper
19
19
77
75
73
71
69
79
Gold
19
19
19
19
19
19
19
65
67
19
19
Silver
99
Copper
0
Zinc
Figure 7.32. Irreversible exergy consumption of the main non-fuel minerals in Australia in the period from 1965 to 2004
272
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
80000
B*t, ktoe
70000
60000
50000
40000
Oil
30000
Coal
20000
10000
Iron
66
64
62
60
58
56
54
52
50
68
19
19
19
19
19
19
19
19
19
46
48
N.G.
19
19
42
44
Oil
19
38
40
Iron
19
19
36
34
32
30
28
26
24
20
22
16
Other metals
19
19
19
19
19
19
19
19
19
19
19
19
18
Other metals
19
19
14
0
Coal
Figure 7.33. Irreversible exergy consumption of the main fuel and non-fuel minerals
in Australia in the period of 1914 to 1968
studied. This way, we can estimate the exergy destruction of the global mineral
resources of a country.
We have divided the information into the commodities coal, oil, natural gas, iron
and other non-fuel metals. This is because the exergy cost of iron is significantly
greater than the rest of the metals and is comparable to that of the fuel minerals.
Furthermore, we have considered two periods of time: from 1914 to 1968 and from
1969 to 2004 (before and after the significant production of oil and natural gas).
As can be seen in figure 7.33, in the first period of time considered, the exergy consumption was clearly dominated by the extraction of coal and to a lesser extent of
iron, especially towards the end of the period. The global extraction trend increased
very rapidly, following an exponential-like behavior. This way, the exergy degradation velocity increased from around 10 Mtoe/year at the beginning of the period,
until the 70 Mtoe/year reached in 1968.
The coming out of significant reserves of oil and natural gas (cleaner and more handy
fuels than coal), lead to an important drop of coal’s production in the beginning of
the second period considered (see fig. 7.34). This resulted in a 25-year hegemony
of iron production in Australia. Nevertheless, the abundance of coal in the country,
together with the foreseeable depletion of oil, provoked a new increase of coal extraction. Since then, both coal and iron dominate the exergy destruction each year
of the mineral capital in Australia (see fig. 7.35).
Despite of the shifts in extraction trends among the different commodities, it is remarkable that the global behavior has continued to be exponential-like. In 2004,
the exergy degradation velocity exceeded 550 Mtoe/year (around 15% of current
The exergy loss of a country due to mineral extraction. The case of Australia
273
600000
B*t, ktoe
500000
400000
Coal
300000
N.G.
Oil
200000
Iron
100000
Other metals
Iron
Oil
N.G.
20
03
20
01
19
99
19
97
19
95
19
93
19
91
19
89
19
87
19
83
19
85
19
79
19
81
19
75
19
77
19
71
19
73
19
69
0
Coal
Figure 7.34. Irreversible exergy consumption of the main fuel and non-fuel minerals
in Australia in the period of 1969 to 2004
100
%, B*T
90
Coal
80
70
60
50
40
30
Iron
20
Oil
Other metals
10
N.G.
0
1914
1924
1934
1944
1954
1964
1974
1984
1994
2004
Year
Other metals
Iron
Oil
N.G.
Coal
Figure 7.35. Relative contribution of the extraction of fuel and non-fuel minerals to
the global exergy degradation of Australia in the period of 1914 to 2004
274
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
world’s oil consumption). And presumably, it will continue to increase exponentially
at least for 20 to 40 years, until the peaks of iron and coal are reached.
In figures 7.36 and 7.37, we have represented the Hubbert’s bell-shaped curves of
all mineral commodities considered in terms of their exergy replacement costs. This
type of representation will be named here as “Exergy countdown”, since it shows
in a very schematic way the amount of exergy resources available and the possible
exhaustion behavior that they will follow. It should be noted that representing B
vs t or B ∗ vs t brings up in our case similar results for the peaking year, as unit
replacement costs have been considered constant throughout the time considered.
The use of exergy replacement costs allows us to compare the exergy content of
fuels and non-fuel minerals. However, as stated before, a better fit should take into
account the change of technology, thereby using the appropriate unit exergy costs at
each period of time.
In figure 7.36, the bell shaped curves of all fuels plus those of iron and copper
are represented. As can be seen, in exergy cost terms, coal is the most abundant resource, followed by iron. Until the first decade of the 21st century, both commodities
will be extracted at similar rates. However, the coming of the peak of iron production in the second decade of the 21st century, will slow down the extraction of the
metal, while coal will clearly dominate the mineral extraction in Australia. Fig. 7.36
shows additionally the significant lower amount of the reserves of natural gas and
oil, with respect to iron and coal.
The same thing occurs with the rest of the metals considered, which are shown
in a separate figure (fig. 7.37). It is interesting to notice that although copper is
the most abundant commodity in exergy terms, the greater extraction rate of that
mineral will provoke a faster depletion of copper than of nickel. Similarly, although
the irreversible exergy reserves of zinc and nickel are similar, the greater extraction
rate of zinc, implies that the peaking year of that metal will be reached before that
of nickel. The graph also shows the smaller relative amount of the commodities of
lead, gold and silver, being the reserves of the latter commodity barely perceptible
in the figure.
The exergy countdown diagram of a country allows us to predict future mineral
productions and the depletion degree of the commodities. This way, for instance,
we can forecast according to our results, that in year 2050, about 64% of the total
considered mineral reserves in Australia will be depleted. Particularly, gold will be
depleted at 99,9%, copper at 90,3%, lead at 87%, zinc at 97,3%, nickel at 60,4%,
iron at 80%, coal at 52,4%, oil at 95,9% and natural gas at 85,2%.
It must be pointed out, that the latter minerals are not the only ones extracted in
Australia. Other non-fuel minerals such as uranium, alumina, manganese, tin, diamonds and industrial sands are also produced. The lack of information of especially
ore grade trends for the latter materials avoids us to complete the analysis. Nevertheless, the figures provided are good enough for giving an order of magnitude of
the depletion of Australian mineral reserves due to mineral extraction.
Conversion of exergy costs into monetary costs
275
Bt*, ktoe
Coal
500000
400000
Iron
300000
200000
100000
Natural gas
Oil
Copper
0
1890
1940
1990
2040
2090
2140
2190
Year
Figure 7.36. Exergy countdown of the main consumed minerals in Australia
7.8
Conversion of exergy costs into monetary costs
The conversion of exergy costs into monetary costs is a rather simple task through
conventional energy prices. It must be stated though, that this should not be necessarily the final objective, as the physical information is valuable by itself.
As an example, we will estimate the monetary cost of the main mineral reserve’s
depletion suffered in Australia in year 2004, due to mineral extraction.
The monetary value of fuel minerals, can be directly calculated by their corresponding prices in the year under consideration. For non-fuel minerals, we will consider
an average price of the energy mix consumed in the country. This is because the
exergy cost of non-fuel minerals represents the amount of energy required to restore
them with current technology.
According to the 2007 BP statistical report [35], the average price of coal9 in
2004 was 64,33 $US/t or 118,91 US$/toe, considering the specific exergy of coal.
The same report includes oil and natural gas prices10 : 40,83 $US/barrel (274,62
$US/toe), and 5,85 $US/million Btu (232,14 $US/toe), respectively.
According to ABARE [1], the 2004 primary consumption energy mix in Australia
was: 41% of coal, 35% of oil, 19% of natural gas and 5% of renewables. Assuming
zero the renewables cost, we obtain an average energy price in Australia of 189,0
$US/toe.
9
10
This price corresponds to the US Central Appalachian coal spot price.
The natural gas price corresponds to USA Henry Hub &.
276
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
7000
Bt*, ktoe
Copper
6000
5000
4000
3000
Zinc
Nickel
2000
1000
Lead
Gold
0
1890
Silver
1940
1990
2040
2090
2140
Year
Figure 7.37. Exergy countdown of metals copper, zinc, nickel, lead and silver in
Australia
Table 7.10 shows an estimation of the monetary costs associated to the depletion of
the main Australian mineral reserves due to mineral extraction in year 2004.
Table 7.10. Monetary costs of the main mineral reserves depletion suffered in Australia due to mineral production in year 2004
Mineral
Coal
Oil
N. Gas
Non-fuels
TOTAL
Exergy
Mtoe
231,3
22,6
33
274,7
561,6
extracted,
Mineral’s
US$/toe
118,9
274,6
232,1
189,0
price,
Monetary cost, Billion US$
27,5
6,2
7,7
51,9
93,3
According to the results obtained, Australia would have lost in 2004 an equivalent
of 93,3 billions of $US of its mineral capital, due to resource extraction. This corresponds to 15,2% of the 2004 Australian GDP (611,7 billions of $US [56], adjusted
for the countrie’s purchasing capacity11 ).
The same amount of physical capital lost, calculated with 2006 and 2008 energy
prices, would be equivalent to around 115 and 178 billions of $US, respectively
11
The Purchasing Power Parity takes into account how much an individual can buy within a country
along with the currency exchange rate between the individual country’s currency and the U.S. dollar.
Summary of the chapter
277
(19 and 29% of the 2004 Australian GDP12 ). This clearly indicates, that assessing
the loss of mineral capital in monetary costs is not very suitable, as the volatility
and arbitrariness of prices distorts the real physical value, which is absolute and
understandable worldwide.
However, monetary values provides us with an order of magnitude of the importance
of mineral extraction. The considerable amount of money just calculated as an example, is what Australia should pay the earth, for the amount of mineral extracted
only in year 2004. It should be stated, that less developed countries, whose economy
is mainly based on the extraction of their mineral capital could even obtain negative
GDP values. That maybe the case for countries like South Africa or Chile, but this
should be studied more carefully with detailed production data of those countries.
What is clear is that economy treats our planet as a reservoir of free goods. As
the earth becomes depleted, man slowly realizes the importance of conserving its
resources. And maybe in a not very distant future, we will have to take “Nature into
account”, as stated by Dieren’s book of the same name [75], and correct accordingly
the economic indices. As King argues in the book, if production is creating scarcity
rather than reducing it, economic growth is negative.
7.9
Summary of the chapter
We have seen in this chapter that neither mass, nor energy are appropriate indicators
for assessing the loss of mineral wealth on earth, as they are conservative properties.
In all physical transformations of matter or energy, it is always exergy that is lost.
Therefore, any degradation of the mineral capital which can come either from an
alteration in its composition, a decrease of its concentration, or a change in the
reference environment, can be accounted for with exergy.
Starting from the property exergy, we have built a series of indicators which should
measure the scarcity degree of the mineral reserves on earth. The exergy difference
between two situations of the planet has been named as exergy distance D. The
exergy degradation velocity Ḋ, calculated as the exergy distance divided by the period of time considered, should account for the rate of exergy destruction of a certain
resource.
We have also defined the ton of mineral equivalent (t M e), as the exergy content of
one ton of mineral in a certain time and place. The reference value of the ton of
mineral equivalent has to be established for each resource. The t M e is analogous
to the ton of oil equivalent, but it accounts for the tonnage, grade and chemical
composition of the substance. This new indicator allows us to assess the exergy
content of a certain deposit before and after extraction, and to compare the quality
12
For the following energy prices in 2006 and 2008, respectively: 116,4 and 167,7 $US/toe of coal;
438,2 and 807,1$US/toe of oil; 268,3 and 287,0 $US/toe of natural gas.
278
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
of different deposits containing the same mineral, but with a more understandable
unit of measure.
The estimated years until depletion of a resource are usually calculated with the R/P
ratio, which is obtained as the quotient between its reserves and its production in a
certain year in mass terms. We have proposed to calculate the R/P ratio in exergy
terms, thereby accounting for the concentration factor as well.
All indicators described above can be assessed either with minimum exergies, or
with exergy replacement costs. With the latter, the irreversibility factor present in all
real processes is taken into account.
Finally, we have proposed the application of the Hubbert peak model for the assessment of the production peak of non-fuel minerals. It has been stated that the
bell-shape curve is better suited to non-fuel minerals if it is fitted with exergy over
time, instead of mass over time. This way, we would not ignore the concentration
factor, which is very important for the case of solid minerals.
As a first case study, we have obtained the exergy decrease of US copper deposits
throughout the 20th century, and have applied all indicators described above. For
that purpose, the chemical and concentration exergy components of the mines, as
well as their associated exergy replacement costs have been obtained for the period
between years 1900 and 2000. It has been estimated, that the global exergy cost
associated to the degradation of US copper deposits in the 20th century was around
700 Mtoe, consumed at an average exergy degradation velocity of 6,6 Mtoe/year.
The R/P ratio of US copper deposits reveals for year 2000, that reserves would be
completely depleted after 56 years. Moreover, the application of the Hubbert peak
in exergy terms, gives as a result, that the peak was already reached in year 1994.
In fact the real peak was attained in year 1998. Although the exergy production
pattern did not perfectly fit in the bell-shaped curve, interesting conclusions have
been extracted. Generally, production follows asymmetric curves with the decline
much sharper than the growth. Hence, the real production peak is most probably
attained after the year predicted by the Hubbert model. During a short period of
time, the commodities will be probably over-exploited and the production points
will appear over the bell-shaped curve. The compensation of the overproduction is
the much sharper decrease of production after the peak, instead of a gradual and
steady reduction.
The second case study was aimed at assessing the exergy loss of a country due to
mineral extraction. Australia has been chosen for the analysis, because it is one of
the most important mineral exporting countries in the world and is the only one
with registered ore grade trends of its main minerals. The commodities analyzed
throughout their mining history until 2004 were gold, copper, nickel, silver, lead,
zinc, iron, coal, oil and natural gas. It has been stated, that generally, production
of all commodities has followed an exponential-like behavior. The most depleted
commodities are in decreasing order: silver, gold, oil, zinc and lead, with R/P ratios
Summary of the chapter
279
below 35 years. On the contrary, the reserves of copper, iron, natural gas, nickel and
finally coal will last at least for 48, 63, 67, 121 and 153 years, respectively.
The Hubbert peak model was satisfactorily applied for all commodities, with the
exception of the group lead-zinc-silver, whose production patterns differ from the
rest, as they are extracted together. The study predicts that the maximum production
has been already reached for gold (2006), silver (2005), lead (1997) and oil (1997).
Zinc will reach the peak in 2010, copper in 2021, natural gas in 2025, iron in 2026,
nickel in 2040, and finally coal in 2048.
By the extraction of metals, Australia has degraded the equivalent of 5,2 Gtoe (in
exergy replacement cost terms). This corresponds to 154 times the 2006 primary
energy consumption of that country. Moreover, each year Australia is degrading on
average by the extraction of metals the equivalent of 1,6 times its primary oil consumption. Adding the exergy loss of fossil fuels, the global degradation of the mineral reserves in Australia increase to 12,5 Gtoe. And this degradation is dominated
by the extraction of two commodities, coal and iron. In 2004, the global exergy
degradation velocity exceeded 550 Mtoe/year (around 15% of current world’s oil
consumption). And it will probably continue to increase exponentially at least for
20 to 40 years, until the peaks of iron and coal are reached.
A very practical representation of the mineral reserves available and the possible
extraction behavior of the commodities is through the “Exergy countdown” graphs.
In the latter, the different Hubbert peak models in terms of irreversible exergy are
shown in a single diagram. This has allowed us to compare the past, present and
possible future extraction rates and available reserves of fuel and non-fuel minerals
in Australia. With the exergy countdown, we have predicted that in year 2050,
about 64% of the main mineral commodities produced in Australia will be depleted.
Moreover, except for coal, iron and nickel, more than 85% of the mineral reserves
will be exhausted by then.
The exergy analysis together with the exergy countdown of minerals could constitute
a universal and transparent prediction tool for assessing the degradation degree of
non-renewable resources, with dramatic consequences for the future management
of the earth’s physical stock.
We additionally estimated the monetary cost of the main mineral reserve’s depletion
suffered in Australia in year 2004. This was carried out, by the conversion of exergy
costs into monetary costs through conventional energy prices. According to the results obtained, Australia would have lost an equivalent of 93,3 billions of $US of its
mineral capital, due to resource extraction in 2004. This corresponds to 15,2% of
the 2004 Australian GDP. However, if 2006 and 2008 energy prices are considered,
the same amount of physical stock extracted would correspond to 19 and 29% of
2004 Australian GDP. This indicates that monetary costs might not be a very suitable
indicator for assessing the mineral capital, as the volatility and arbitrariness of prices
distorts the real physical value. Nevertheless, it provides an order of magnitude of
the importance of the extraction of minerals to the economy.
280
THE
TIME FACTOR IN THE EXERGY ASSESSMENT OF MINERAL RESOURCES
It should be noted, that the results obtained are estimations and hence the numbers cannot be taken as final. More reserves could be found in the future, thereby
increasing the years until depletion and the peak of production of the commodities.
However, the huge amount of energy and its equivalent in money terms involved in
the degradation of minerals on earth, alerts us about the importance of conserving
our resources.
Chapter
8
The exergy evolution of planet
earth
8.1
Introduction
The aim of this chapter is to analyze the depletion of the exergy reservoir of minerals
on earth, due to the human action. For that purpose, the mineral exergy degradation
throughout the 20th century, will be studied. Furthermore, we will analyze the effect
of the emission of greenhouse gases in the exergy loss of fossil fuels. Finally, with
the help of scenarios, we will estimate the exergy depletion of mineral resources in
the next century.
8.2
The exergy loss of world’s mineral reserves in the 20th
century
As stated before, exergy is an accounting tool that allows us to assess resources of
single or aggregated commodities of a region, country or even of the whole world.
In chapter 7 we evaluated the exergy degradation of mineral capital of a country
and our aim now is to extrapolate the assessment to the entire planet.
This ambitious task is not free of difficulties. The first and most important problem
that we have to face is the lack of current and historical data of many commodities.
A few geological institutions, such as the USGS or BGS, compile world production
data of the most important minerals. But only the USGS provides estimations of
non-fuel mineral reserves. Furthermore, with the exception of copper in the US,
no ore grade trends of the commodities are compiled. The case of Australia is an
exceptional example of a country with available historical ore grades of the main
metals produced. And this was thanks to the own initiative of Mudd [232], [234].
281
282
THE
EXERGY EVOLUTION OF PLANET EARTH
To these limitations, we have to add that unit exergy replacement costs are available
for many important non-fuel mineral commodities, but not for all of them.
In order to overcome the difficulties mentioned before, we are obliged to make different assumptions at the expense of an important accuracy loss in the results. Firstly,
we will assume that the ore grade of non-fuel mineral commodities remains constant
and equal to the average ore grades estimated in this PhD (table 4.10). This implies
that the specific concentration exergy will not change over time. Consequently, the
calculation of tons of mineral equivalent has no practical sense anymore. Moreover,
the application of the Hubbert peak model in terms of exergy will ignore the concentration factor, which is quite significant in many non-fuel minerals. As it happened to
the previous case studies, unit exergy replacement costs are assumed to be constant.
In reality, unit costs are a function of the state of technology and hence vary with
time.
With the latter assumptions, we can make a rough estimate of the following variables
for fuel and non fuel minerals:
• The mineral exergy degradation on earth since the beginning of the 20th century (D),
• the earth’s exergy degradation velocity due to mineral extraction ( Ḋ),
• the depletion degree of the reserves and reserve base (% R. loss and % R.B.
loss),
• the years until depletion of the commodities (R/P), and
• the year where the peak of production is reached (Year of the peak)
8.2.1
Non-fuel minerals
With the help of the historical data compiled by the USGS [361], and the same
calculation procedures applied for US copper and the main metals in Australia, we
have calculated the exergy distances D and D∗ and the average exergy degradation
velocities Ḋ and Ḋ∗ of the main non-fuel mineral commodities throughout the 20th
century1 . Since production rates usually increase exponentially, it is interesting to
analyze the latest exergy degradation velocities registered. Therefore, we have additionally calculated the average degradation velocities of the last decade (from 2000
to 2006). The depletion degree of the commodities (% R and % R.B.) has been
obtained as the ratio between the exergy distance D, and the total reserves of the
commodity. The latter are obtained as the published reserves or reserve base of the
commodity in 2006, plus the exergy distance D from 1900 to 2006. Finally, the R/P
ratio applied to exergy is provided, as a measure of the years until depletion. It has
1
Some commodities have started to be extracted after the beginning of the century.
The exergy loss of world’s mineral reserves in the 20th century
283
been assumed that production remains as in year 2006, and that reserves do not
increase after that year.
The mineral of uranium has been included in the non-fuel mineral classification2 .
For that purpose, the world uranium statistics published by the World Nuclear Association [408] have been used (see table A.25). Current uranium assured reserves
were estimated by the OECD [248] as 3,804 Mtons, while the inferred reserves, as
4,742 Mtons. The average ore grade of U3 O8 is 0,33%, as calculated in this study
(table 4.9), or 0,28% of U).
Table 8.1 shows a summary of the results obtained for the 51 mineral commodities
taken into account.
As can be seen from the table and in figure 8.1, in reversible exergy terms, the
exergy degradation of the non-fuel mineral capital on earth is clearly dominated by
the extraction of two commodities: iron and aluminium, representing around 81 and
10% of the total exergy consumption. The exergy distance due to non-fuel mineral
extraction between 1900 and 2006 is at least3 5,68 Gtoe. As expected, the general
consumption pattern has followed an exponential-like behavior4 . This is reflected
in the drastic change of the exergy degradation velocity Ḋ, passing from around 10
Mtoe/year in 1910, to 180 Mtoe/year in 2006.
In irreversible terms, i.e. analyzing the exergy replacement costs (actual exergy) of
the commodities, we observe in fig. 8.2, that copper acquires a more important role.
Copper is responsible for 6% of the total exergy degradation costs on earth, while
iron and aluminium, 63 and 24%, respectively. The irreversible exergy distance D∗
of all analyzed commodities is at least 51 Gtoe. This means that with current technology, we would require a minimum of a third of all current fuel oil reserves on earth
(178 Gtoe [35]) for the replacement of all depleted non-fuel mineral commodities.
Excluding iron and aluminium, which eclipse the rest commodities, we observe in
fig. 8.3 that in decreasing order, the production of manganese, zinc, nickel, zirconium, lead, chromium, uranium, tin and gold contribute also significantly to the
planet’s non-fuel mineral capital degradation. Again, an exponential behavior of the
exergy costs of all commodities is observed. The average exergy cost degradation
velocity D∗ in the 20th century is at least 0,5 Gtoe/year. However in the last decade,
this velocity increased to 1,3 Gtoe/year.
2
The nuclear exergy of uranium, which is huge compared to its chemical exergy (see chapter 4),
has not been taken into account.
3
This value corresponds only to the 51 mineral commodities taken into account.
4
With the exception of uranium, whose production depends on other external factors, such as
political decisions.
D
5,64E+05
5,13E+02
5,75E+02
1,53E+03
6,88E-01
7,61E+00
4,04E+03
2,41E+02
6,51E+01
6,62E-02
4,53E+04
2,20E+02
2,96E+04
8,77E+02
9,95E+03
2,75E-01
6,52E-01
9,98E-01
3,26E+04
1,40E+04
1,32E+02
5,45E-01
1,12E+01
4,60E+06
6,01E+03
9,32E+03
1,01E+04
Mineral
Aluminium
Antimony
Arsenic
Barite
Beryllium
Bismuth
Boron oxide
Bromine
Cadmium
Cesium
Chromium
Cobalt
Copper
Feldspar
Fluorspar
Gallium
Germanium
Gold
Graphite
Gypsum
Helium
Indium
Iodine
Iron
Lead
Lithium
Magnesium
Ḋ∗
Ḋ
4,01E+05
1,31E+02
8,70E+01
N.A.
4,17E-01
2,50E+00
N.A.
N.A.
6,98E+01
N.A.
3,00E+03
2,86E+02
8,24E+04
N.A.
N.A.
N.A.
N.A.
1,58E+03
N.A.
N.A.
N.A.
N.A.
N.A.
7,26E+05
3,51E+03
1,22E+03
2,96E+02
1996-2006
Ḋ∗
5,27E+03
1,14E+05
1,85E+04
4,80E+00
5,34E+01
1,18E+01
5,37E+00
6,76E+01
6,91E+00
1,43E+01
N.A.
3,47E+01
6,43E-03
3,37E-01
7,97E-03
7,12E-02
1,16E+00
1,54E-01
3,78E+01
N.A.
1,69E+02
2,26E+00
N.A.
7,96E+00
6,08E-01
3,31E+01
1,28E+00
6,18E-04
N.A.
N.A.
4,23E+02
9,62E+02
1,32E+03
2,05E+00
1,03E+02
5,70E+00
2,76E+02
2,87E+04
7,94E+02
8,20E+00
N.A.
3,51E+01
9,30E+01
N.A.
2,03E+02
2,57E-03
N.A.
1,31E-02
6,09E-03
N.A.
1,24E-02
9,33E-03
7,64E+02
1,93E-02
3,05E+02
N.A.
7,13E+02
1,30E+02
N.A.
3,51E+02
1,23E+00
N.A.
4,11E+00
5,10E-03
N.A.
3,35E-02
1,05E-01
N.A.
3,86E-01
4,30E+04
3,01E+05
1,04E+05
5,62E+01
2,19E+03
8,99E+01
8,71E+01
3,26E+02
3,26E+02
9,45E+01
9,45E+01
2,96E+02
Continued on next page . . .
1900-2006
Ḋ
1,22E+07
5,71E+03
7,23E+03
N.A.
3,60E+01
1,24E+02
N.A.
N.A.
3,54E+03
N.A.
1,03E+05
1,10E+04
3,07E+06
N.A.
N.A.
N.A.
N.A.
8,17E+04
N.A.
N.A.
N.A.
N.A.
N.A.
3,22E+07
2,35E+05
3,49E+04
1,01E+04
D∗
14,9
72,8
74,6
61,0
N.A.
41,1
39,2
N.A.
66,8
1,2
N.A.
19,5
50,3
N.A.
48,6
N.A.
N.A.
75,4
31,0
N.A.
N.A.
34,3
3,8
27,7
72,5
62,3
N.A.
% R loss
Table 8.1: The exergy loss of the main mineral commodities in the world.
Values are expressed in ktoe
2006
% R. B. R/P, yrs
loss
12,0
135
56,6
16
66,2
20
25,2
24
N.A.
N.A.
24,7
56
21,1
40
N.A.
N.A.
45,1
25
0,8
N.A.
N.A.
N.A.
11,5
104
34,5
32
N.A.
N.A.
32,1
45
N.A.
N.A.
N.A.
N.A.
58,9
17
15,5
83
N.A.
N.A.
N.A.
N.A.
26,4
19
2,2
600
14,9
84
55,1
23
38,1
12
N.A.
N.A.
R.B./P,
yrs
173
32
30
111
N.A.
119
96
N.A.
62
N.A.
N.A.
193
62
N.A.
90
N.A.
N.A.
37
204
N.A.
N.A.
28
1080
185
49
33
N.A.
284
THE
EXERGY EVOLUTION OF PLANET EARTH
D
1,08E+05
9,24E+00
9,58E+02
4,48E+03
1,57E+02
5,47E+04
2,41E-01
1,30E+05
6,65E+01
6,10E-02
8,72E+00
1,76E+01
1,83E+03
4,71E+00
4,65E-01
1,58E+00
2,11E+03
2,47E+02
4,40E+02
3,01E+02
4,98E+04
3,03E+02
5,68E+06
Mineral
Manganese
Mercury
Molybdenum
Nickel
Niobium
Phosphate rock
PGM
Potash
REE
Rhenium
Selenium
Silver
Strontium
Tantalum
Tellurium
Thorium
Tin
Uranium
Vanadium
Wolfram
Zinc
Zirconium
SUM
1,01E+03
8,63E-02
8,95E+00
4,18E+01
1,46E+00
5,12E+02
2,25E-03
1,22E+03
6,22E-01
5,70E-04
8,15E-02
1,65E-01
1,71E+01
4,41E-02
4,35E-03
1,47E-02
1,97E+01
2,31E+00
4,11E+00
2,81E+00
4,65E+02
2,83E+00
5,31E+04
1900-2006
Ḋ
1,04E+06
3,16E+03
1,80E+04
3,55E+05
N.A.
7,08E+04
N.A.
2,02E+05
N.A.
7,43E+00
N.A.
1,69E+04
N.A.
1,31E+03
N.A.
N.A.
1,08E+05
7,29E+04
4,96E+03
2,28E+04
9,09E+05
2,91E+05
5,11E+07
D∗
Ḋ
1,76E+04
9,40E+00
4,92E+02
1,04E+04
N.A.
1,54E+03
N.A.
4,56E+03
N.A.
3,30E-01
N.A.
3,11E+02
N.A.
6,38E+01
N.A.
N.A.
1,51E+03
1,38E+03
1,76E+02
4,56E+02
2,06E+04
8,18E+03
1,29E+06
1996-2006
Ḋ∗
9,75E+03
1,82E+03
2,95E+01
2,75E-02
1,68E+02
2,62E+01
3,32E+03
1,31E+02
N.A.
6,90E+00
6,62E+02
1,19E+03
N.A.
8,35E-03
1,89E+03
2,94E+03
N.A.
2,85E+00
6,95E-02
2,71E-03
N.A.
1,77E-01
1,58E+02
3,24E-01
N.A.
8,52E+01
1,22E+01
2,30E-01
N.A.
7,03E-03
N.A.
N.A.
1,01E+03
2,92E+01
6,81E+02
4,68E+00
4,64E+01
1,56E+01
2,13E+02
6,02E+00
8,49E+03
1,13E+03
2,72E+03
8,52E+00
4,78E+05
1,34E+05
End of the table
Ḋ∗
51,9
92,2
37,5
40,0
19,8
26,1
14,4
12,8
2,4
24,2
48,2
78,5
56,0
14,2
25,8
1,2
75,2
34,8
8,9
48,5
68,1
43,8
25,6
% R loss
Table 8.1: The exergy loss of the main mineral commodities in the world.
Values are expressed in ktoe.– continued from previous page.
2006
% R. B. R/P, yrs
loss
8,7
39
69,4
31
21,4
47
22,9
42
18,1
61
11,3
127
13,0
137
6,3
285
1,4
715
7,4
53
31,0
53
63,4
13
41,9
12
10,7
94
13,5
159
1,0
N.A.
62,7
20
29,9
96
3,2
231
30,2
32
44,4
18
29,2
32
14,2
92
R.B./P,
yrs
437
162
103
95
67
352
154
619
1220
212
110
28
21
130
356
N.A.
36
120
675
69
48
61
191
The exergy loss of world’s mineral reserves in the 20th century
285
286
THE
EXERGY EVOLUTION OF PLANET EARTH
200000
BT, ktoe
180000
160000
140000
120000
100000
80000
60000
Iron
40000
20000
Aluminium
19
00
19
04
19
08
19
12
19
16
19
20
19
24
19
28
19
32
19
36
19
40
19
44
19
48
19
52
19
56
19
60
19
64
19
68
19
72
19
76
19
80
19
84
19
88
19
92
19
96
20
00
20
04
0
Uranium
Zirconium
Zinc
Wolfram
Vanadium
Tin
Thorium
Tellurium
Tantalum
Strontium
Silver
Selenium
Rhenium
REE
Potash
PGM
Phosphate rock
Niobium
Nickel
Molybdenum
Mercury
Manganese
Magnesium
Lithium
Lead
Iron
Iodine
Indium
Helium
Gypsum
Graphite
Gold
Germanium
Gallium
Fluorspar
Feldspar
Copper
Cobalt
Chromium
Cesium
Cadmium
Bromine
Boron oxide
Bismuth
Beryllium
Barite
Arsenic
Antimony
Aluminium
Figure 8.1. The exergy loss of the main non-fuel mineral commodities on earth in
the twentieth century
According to the depletion ratios (% R loss and % R.B. loss) in table 8.1, man has
depleted in just one century around 26% of its world non-fuel mineral reserves, and
around 14% of its reserve base. The estimated years until depletion of the total
reserves and reserve base are around 92 and 191 years, respectively. It must be
pointed out that these are only minimum numbers, as it has been assumed that no
more deposits are going to be found. However, as we observed before, extraction
follows an exponential behavior, what may lead that the finding of new deposits
does not compensate the increasing production rates.
According to fig. 8.4, the most depleted commodities are in decreasing order: mercury, with 92% of the reserves extracted, silver (79%), gold (75%), tin (75%), arsenic (75%), antimony (72%) and lead (72%). On the other hand, the minerals
of cesium, thorium, REE, iodine vanadium, PGM’s, tantalum, aluminium cobalt and
niobium are the least depleted commodities, having extracted less than 20% of their
respective world resources. The depletion degree of minerals depend on two factors:
the abundance of the considered mineral reserve, and its production rates. Usually,
the least depleted minerals coincide with those substances, for which no important
usefulness has been found until to date. Nevertheless, it can also be due to the
important abundance of the resource. That is the case for iodine, aluminium or iron.
The exergy loss of world’s mineral reserves in the 20th century
287
1800000
B*T, ktoe
1600000
1400000
1200000
1000000
800000
600000
400000
200000
Manganese
Iron
Copper
Aluminium
19
00
19
04
19
08
19
12
19
16
19
20
19
24
19
28
19
32
19
36
19
40
19
44
19
48
19
52
19
56
19
60
19
64
19
68
19
72
19
76
19
80
19
84
19
88
19
92
19
96
20
00
20
04
0
Uranium
Zirconium
Zinc
Wolfram
Vanadium
Tin
Thorium
Tellurium
Tantalum
Strontium
Silver
Selenium
Rhenium
REE
Potash
PGM
Phosphate rock
Niobium
Nickel
Molybdenum
Mercury
Manganese
Magnesium
Lithium
Lead
Iron
Iodine
Indium
Helium
Gypsum
Graphite
Gold
Germanium
Gallium
Fluorspar
Feldspar
Copper
Cobalt
Chromium
Cesium
Cadmium
Bromine
Boron oxide
Bismuth
Beryllium
Barite
Arsenic
Antimony
Aluminium
Figure 8.2. The actual exergy loss of the main non-fuel mineral commodities on
earth in the twentieth century
Despite of the intensive extraction of iron and aluminium throughout the 20th century, their respective abundances have avoided scarcity problems. Their reserve’s
depletion rates are around 28 and 15%, respectively. Unfortunately that is not the
case for copper, which has been and is still being massively extracted. More than
50% of the world’s copper reserves have been already depleted.
For the latter three minerals we have applied the Hubbert peak model, considering
their respective reserve base in year 19005 . Since unit exergy replacement costs
are assumed to be constant over time, plotting production versus time in minimum
exergy or in exergy replacement cost terms will not affect the final result. In this
case, the exergy replacement costs (B ∗t ) versus time and not the minimum exergies
(B t ) versus time have been plotted, because the production patterns obtained will
be later used for estimating exergy degradation costs of the reserves in the future.
Accordingly, it has been obtained that the peak of production of iron will be reached
in year 2068, of aluminium in 2057 and of copper in 2024 (see figs. 8.5, 8.6, and
8.7). It must be remembered, that the concentration factor has not been accounted
for.
5
The reserve base in year 1900 is calculated as the reserve base in year 2006 plus the exergy
distance in the period between 1900 and 2006.
288
THE
EXERGY EVOLUTION OF PLANET EARTH
200000
Uranium
B*T, ktoe
Zirconium
180000
Zinc
160000
Tin
Silver
140000
Nickel
120000
Mercury
Zirconium
Uranium
100000
Manganese
Tin
Magnesium
Zinc
80000
Nickel
Lead
Gold
Lead
60000
Gypsum
Manganese
Graphite
40000
Gold
Copper
20000
Gallium
04
96
92
Copper
Chromium
20
20
19
88
19
84
19
76
72
80
19
19
19
68
19
64
19
56
52
60
19
19
19
48
19
44
19
36
32
40
19
19
19
28
19
20
16
24
19
19
19
12
19
08
19
00
04
19
19
19
00
Chromium
0
Figure 8.3. The actual exergy loss of the main 15 non-fuel mineral commodities on
earth in the twentieth century, excluding iron and aluminium
100
%
Mercury
90
Silver
80
Gold
Arsenic
Antimony
70
Tin
Lead
Zinc
Cadmium
Lithium
Barite
60
Strontium
Manganese
Copper
Fluorspar
50
Wolfram
Selenium
Zirconium
Bismuth
Boron oxide
40
Nickel
Molybdenum
Uranium
Indium
Graphite
Iron
30
20
Phosphate rock
Rhenium
Tellurium
Niobium
Cobalt
Aluminium
PGM
Potash
Tantalum
Vanadium
10
Iodine
Cesium
REE
Thorium
0
Figure 8.4. Depletion degree in % of the main non-fuel mineral commodity reserves
The exergy loss of world’s mineral reserves in the 20th century
289
The results obtained should not be taken as definitive. They should be rather considered as an approximation of the state of non-fuel mineral reserves on earth. In
addition to the assumptions made, we should not forget that there are still many
places in the world that remain unexplored. Nevertheless, and despite that the numbers are only approximations, the results are pointing out that the rate of mineral
extraction in just one century has been excessive, when compared to past periods
of time. Moreover, many commodities are already suffering scarcity problems. In a
not very distant future, man will have to search for material alternatives of the most
depleted commodities. This has already occurred for some applications, for example
the shift away from copper to aluminium for conductors in wires and cables. But
substitution will be only possible, whenever other mineral resources are available.
5
x 10
15
2068
Bt*
10
5
8
0
x 10
2.5
Integral Bt*
2
1.5
1
0.5
0
1900
1950
2000
2050
2100
2150
2200
2250
Figure 8.5. The Hubbert peak applied to world iron production. Data in ktoe
290
THE
EXERGY EVOLUTION OF PLANET EARTH
5
10
x 10
2057
8
Bt
6
4
2
7
0
x 10
12
Integral Bt
10
8
6
4
2
0
1900
1950
2000
2050
2100
2150
2200
Figure 8.6. The Hubbert peak applied to world aluminium production. Data in ktoe
4
10
x 10
2024
8
Bt
6
4
2
6
0
x 10
10
Integral Bt
8
6
4
2
0
1900
1950
2000
2050
2100
2150
Figure 8.7. The Hubbert peak applied to world copper production. Data in ktoe
The exergy loss of world’s mineral reserves in the 20th century
8.2.2
291
Fuel minerals
The degradation of fuel minerals throughout history, requires historical production
data of coal, oil and natural gas. Historical statistics of world fuel minerals had to
be reconstructed from different information sources, being the most important ones
those from the British Geological Survey and its preceding organizations. Tables
A.26, A.27 and A.28 in the appendix show world production data of coal, oil and
natural gas, between years 1900 and 2006.
The exergy of the three types of fuel minerals has been obtained in the same way as
for the case of Australia, and assuming a single type of coal and oil6 , with the average
properties calculated by Valero and Arauzo [366]. This way, the exergy of average
coal and oil on earth are assumed to be 22.692 and 45.664 kJ/kg, respectively.
Table 8.2 summarizes the results obtained for world fuels throughout the 20th century.
Table 8.2. The exergy loss of coal, oil and natural gas in the 20th century.
Mineral
Coal
Oil
Natural gas
SUM
1900-2006
D, Mtoe
Ḋ, Mtoe/yr
1,45E+05
1,61E+05
7,60E+04
3,82E+05
1,37E+03
1,50E+03
1,74E+03
4,61E+03
1996-2006
Ḋ, M t oe/ y r
% R. loss
2006
R/P, yrs
2,73E+03
3,96E+03
2,34E+03
9,03E+03
27,9
47,5
30,9
30,5
156
42
63
114
Year of the
Peak
2060
2008
2023
2029
Figure 8.8 shows the exergy loss of coal, oil and natural gas deposits in the last
century. Although the most extracted fuel in the world is coal, as revealed by the
historical statistics included in tables A.26, A.27 and A.28, in exergy terms, the most
consumed fuel has been oil. Oil has accounted for 42% of the total fuel exergy degradation in the 20th century, while coal and natural gas for 38 and 20%, respectively.
The exergy distance between 1900 and 2006 (D), i.e. the total fuel’s exergy depleted
has been 382 Gtoe, corresponding to 30,5% of total world’s proven fuel reserves in
2006.
The exergy of fuels was consumed at an average exergy degradation velocity ( Ḋ)
of 4,6 Gtoe/year. However in the last decade, this velocity increased to around 9
Gtoe/year. From the latter figure, coal contributes to 2,7, oil to 4,0 and natural gas
to 2,3 Gtoe/year.
If we add the exergy loss of fossil fuels, to the exergy replacement costs of non-fuel
minerals, we obtain that man has depleted in the 20th century a total of 433 Gtoe,
which were consumed at an average velocity of around 4 Gtoe/year. However, the
6
Natural gas was already assumed to have a single composition, with a standard exergy of 39.394
kJ/N m3 (see section 6.4.1.3).
292
THE
12000000
12000
EXERGY EVOLUTION OF PLANET EARTH
B*t, Mtoe
10000000
10000
8000000
8000
N. Gas
6000000
6000
Oil
4000000
4000
Coal
2000000
2000
Iron
Copper
Aluminium
19
00
19
04
19
08
19
12
19
16
19
20
19
24
19
28
19
32
19
36
19
40
19
44
19
48
19
52
19
56
19
60
19
64
19
68
19
72
19
76
19
80
19
84
19
88
19
92
19
96
20
00
20
04
0
Figure 8.8. Actual exergy consumption of the world’s fuel and non-fuel minerals
throughout the 20th century
2006 mineral’s exergy degradation velocity increased to around 12 Gtoe. Most part
of this exergy degradation (82%) was due to the combustion of fossil fuels. The extraction of iron was responsible for 7,4% of the total exergy destruction, aluminium
for 2,8%, copper for 0,7% and the remaining minerals for 0,8% (see fig. 8.8).
Without exception, production of all fossil fuels have followed an exponential-like
behavior, what allows a satisfactorily application of the Hubbert’s bell-shaped curve.
Among all conventional fossil fuels, coal is the least depleted commodity (27,9%),
because of its large reserves worldwide. Assuming that no more coal reserves will
be found, and that the production rate remains as in 2006, the R/P ratio indicates
that there will be enough resource for 156 years. The Hubbert peak model applied
to the exergy consumption of coal (fig. 8.9), reveals that the peak will be reached in
year 20607 . Our study contradicts the recent estimate by the Energy Watch Group
(EWG), which reports that global coal production could peak in 2025 [89].
The reserves of natural gas are significantly more depleted than coal. In the period
between 1900 and 2006, natural gas consumption has leaded to the depletion of
30,9% of its exergy reserves. Its R/P ratio for 2006, reveals that there is enough
natural gas for 63 years. The peak of world’s natural gas production will be reached
in year 2023, according to the Hubbert peak model applied and represented in fig.
7
It has been assumed that the quantity of coal extracted in the period between 1800 and 1900
followed the same exponential behavior detected by the rest of the points. Hence, it has been assumed
that the total reserves in 1800 were 675 Gtoe.
The exergy loss of world’s mineral reserves in the 20th century
293
2060
4000
Bt
3000
2000
1000
5
0
x 10
8
Integral Bt
6
4
2
0
1800
1850
1900
1950
2000
2050
2100
2150
2200
2250
2300
Figure 8.9. The Hubbert peak applied to world coal production. Data in Mtoe
2023
3000
2500
Bt
2000
1500
1000
500
5
0
x 10
2.5
Integral Bt
2
1.5
1
0.5
0
1900
1950
2000
2050
2100
2150
Figure 8.10. The Hubbert peak applied to world natural gas production. Data in
Mtoe
8.10. Bentley estimated in year 2002 [24] that the global peak in conventional gas
production was already in sight, in perhaps 20 years. Hence, Bentley’s estimation
fits very well with the calculation carried out in this study.
Beyond doubt, oil is the most depleted commodity, having extracted almost half of
its resources (47,5%). The R/P ratio of oil indicates that there is enough fuel for only
294
THE
EXERGY EVOLUTION OF PLANET EARTH
5000
2008
4000
Bt
3000
2000
1000
0
3.5
5
x 10
3
Integral Bt
2.5
2
1.5
1
0.5
0
1900
1950
2000
2050
2100
Figure 8.11. The Hubbert peak applied to world oil production. Data in Mtoe
42 years, before complete depletion occurs. Hubbert’s bell-shaped curve applied to
world oil’s exergy (fig. 8.11) alerts that the peak is reached in year 2008. The latter
value fits very well with the predictions of other authors, such as Hatfield [133], Kerr
[183] or Campbell and Laherre [47], who estimated that the peak year of world oil
will be between 2004 and 2008. In fact, Campbell and Laherre’s prediction in 1998
that the world could see radical increases in oil prices ten years later, has turned out
to be completely right. The price of a barrel of crude oil increased by a 100% in just
one year, surpassing in January 2008, the psychological barrier of 100 $US. And the
observed tendency is that it will probably reach 200 $US by the end of year 2008 or
not much later.
Since exergy is an additive property, we can apply Hubbert’s bell-shape curve to the
sum of all three fuels. In fact, the depletion of one fossil fuel may lead to a greater
consumption of the others. This way, the fact that the peak of oil has been already
reached, will probably lead in the short and mid-run, to the consumption of more
natural gas and coal. Therefore, it is interesting to analyze all three fuels as a single
entity, making the assumption that they are mutually replaceable. If no more fuel
resources are found, and if the production rate remains as in 2006, the R/P ratio
indicates that in 114 years, all conventional fossil fuels will be completely depleted.
Moreover, as revealed by fig. 8.12, the peak of production of all conventional fossil
fuels would be reached in 2029. If this prediction is true, fuel prices will increase
sharply8 , putting at risk world economies. Hopefully other energy alternatives will
be ready by then and are able to supply the increasing world energy demand.
8
As it is happening already with oil and natural gas.
The exergy loss of world’s fossil fuel reserves due to the greenhouse effect
12000
295
2029
10000
Bt
8000
6000
4000
2000
Integral Bt
5
0
x 10
15
10
5
0
1900
1950
2000
2050
2100
2150
Figure 8.12. The Hubbert peak applied to the world’s conventional fossil fuel production. Data in Mtoe
Similarly, the Hubbert peak model can be applied to the exergy cost of non-fuel
minerals plus the exergy of fossil fuels. Taking into account the global extraction
of iron, aluminium, copper, coal, oil and natural gas, the peak of production would
be reached in year 2034, as shown in fig. 8.13. The same figure presents also the
derivative of the bell shape curve, i.e. the acceleration experienced in the production
processes throughout history. Accordingly, we observe that mineral production has
undergone acceleration until 1989. From that moment on, the velocity of extraction
rises until 2034, but at increasingly slower rates.
Figure 8.14 summarizes the results obtained in the previous sections, showing the
exergy countdown of the main minerals extracted on earth, of fuel and non-fuel
nature. As it can be seen, coal, iron and aluminium are the commodities having the
least scarcity problems. On the other end we find in decreasing order of scarcity
degree, oil, natural gas and copper. These values assume that no more resources
than the reserve base for non-fuel minerals, and the proven reserves for fuels will
be available in the future. Obviously the figures may change, as new discoveries are
made.
8.3
The exergy loss of world’s fossil fuel reserves due to
the greenhouse effect
The exergy of fossil fuel reserves may decrease either through extraction and subsequent burning, or through an alteration of the reference environment. This section
296
THE
15
EXERGY EVOLUTION OF PLANET EARTH
2034
Bt
10
5
0
1989
Derivative Bt
0.2
0.1
0
-0.1
-0.2
1900
1950
2000
2050
2100
2150
2200
Figure 8.13. The Hubbert peak applied to the world’s main minerals production.
Data in Mtoe
4500
Bt*, Mtoe
Oil
Coal
4000
3500
Natural gas
3000
2500
2000
Iron
1500
Aluminium
1000
500
Copper
0
1890
1940
1990
2040
2090
2140
2190
2240
2290
Figure 8.14. The exergy countdown of the main minerals extracted on earth
The exergy loss of world’s fossil fuel reserves due to the greenhouse effect
297
is devoted to analyze the exergy loss of fossil fuel reserves due to the increase of
greenhouse gases in the atmosphere (mainly CO2 ) and the subsequent temperature
rise.
A similar study was carried out for the first time in 1991 by Valero and Arauzo [366].
In their analysis, the exergy decrease of an “average fossil fuel” was determined,
assuming that CO2 concentration would double over the next hundred years.
In this section, the information provided by the latter authors will be updated with
recent GHG emission scenarios and the exergy loss of the reserves of coal, natural
gas and oil will be studied separately.
8.3.1
The carbon cycle and the greenhouse effect
The carbon cycle is a well-known natural flux occurring on earth. The mass transfer
of carbon takes place between the three spheres of our planet: hydrosphere, continental crust and atmosphere. According to Post [270], the annual natural flux of
carbon in the form of CO2 between terrestrial plus oceanic reservoirs and the atmosphere is about 200 Gt per year, from which 100-115 are exchanged between the
ocean and atmosphere, and 100-120 between earth biomasses and the atmosphere
(see Fig. 8.15).
On the other hand, the anthropic annual flux of CO2 from fossil fuel combustion
and modification of terrestrial ecosystems is estimated at 7-8 Gt C/year [296], or
only 3,5 to 4% of the natural flux. Nevertheless, the combined climate and biogeochemical systems that regulate the CO2 content of the atmosphere cannot handle
the anthropogenic perturbation without accumulating in the atmosphere in the near
term about half of the CO2 being released.
According to the IPCC’s forth assessment report [162], annual fossil carbon dioxide emissions increased from an average of 6,4 GtC (23,5 GtCO2 ) per year in the
1990s to 7,2 GtC (26,4 GtCO2 ) per year in 2000-2005. Accordingly, the annual
carbon dioxide concentration growth rate in the atmosphere was larger during the
years 1995-2005 (average: 1,9 ppm per year), than it has been since the beginning
of continuous direct atmospheric measurements (1960-2005 average: 1,4 ppm per
year). The record at Mauna Loa observatory shows that concentrations have increased from about 310 to the current 379 ppm since 1958. And preindustrial CO2
concentrations did not exceed 280 ppm.
Eleven of the twelve years between 1995 and 2006 rank among the 12 warmest years
in the instrumental record of global surface temperature (since 1850). The linear
warming trend over the last 50 years (0,13◦ C per decade) is nearly twice of that for
the last 100 years. The total temperature increase from 1850-1899 to 2001-2005 is
0,76◦ C [162].
There is considerable scientific consensus that the rapid buildup of CO2 is tightly related to the increase of atmospheric temperature, due to the well known greenhouse
298
THE
EXERGY EVOLUTION OF PLANET EARTH
Figure 8.15. Schematic presentation of the global carbon cycle as estimated by Post
et al. [270]
effect. Other gases cause the same or even a more enhanced greenhouse effect on
the atmosphere. The most important ones are methane C H4 (released from agriculture, waste and energy) and nitrous oxides N2 O (from agriculture and industry),
accounting for about 14 and 8% of the total greenhouse gas (GHG) emissions, respectively. The global warming impact of GHG gases is related to that of CO2 and is
measured in CO2 − eq units. The global warming impact of C H4 is 21 times of that
of CO2 , while that of N2 O is 310 greater.
According to the IPCC [162], atmospheric concentrations of CO2 (379 ppm) and
C H4 (1774 ppb) in 2005 exceeded by far the natural range over the last 650.000
years. Greenhouse gases are already having a major impact on the world climate
and sea level; and within 40 to 80 years atmospheric greenhouse gases will more
than double with alarming implications for world climate, agriculture, sea levels,
national economics, etc.
8.3.2
Scenarios
There is a great variety of scenarios published about national and world energy
consumptions. Two of the latest world scenarios are the ones carried out by the
The exergy loss of world’s fossil fuel reserves due to the greenhouse effect
299
World Energy Council in 2007 [44] and the International Energy Agency in 2006
[152].
The WEC report, more focused on political actions, takes into account four scenarios,
based on economic, population and policy aspects. The main conclusion of the study
is that to meet the energy demand of all households worldwide, energy supplies must
double by 2050.
The IEA considers two different scenarios: the reference and the alternative policy
scenario. In the latter one, governments take stronger action to steer the energy
system onto a more sustainable path. Globally, fossil fuels will remain the dominant
source of energy to 2030 in both scenarios. Primary energy demand in the reference
scenario is projected to increase by just over one-half between now and 2030 and
the associated carbon dioxide emissions increase by 55%. World primary energy
demand in 2030 is about 10% lower in the alternative policy scenario than in the
reference scenario, coming the biggest energy savings from coal. The carbon dioxide
emissions are cut by 16% in 2030 relative to the reference scenario.
The scenarios for GHG emissions most widely used are those of the IPCC published in
2000 for use in the Third Assessment Report (Special Report on Emissions Scenarios
- SRES - [160]). We will focus on the SRES scenarios, as they were constructed to
explore future developments in the global environment with special reference to the
production of greenhouse gases and aerosol9 precursor emissions.
The SRES defined four scenarios A1, A2, B1 and B2, describing the relationships
between the forces driving greenhouse gas and aerosol emissions and their evolution during the 21st century for large world regions and globally. Each scenario
represents different demographic, social, economic, technological, and environmental developments that diverge in increasingly irreversible ways. The scenarios are
summarized as follows:
• A1 scenario family: a future world of very rapid economic growth, global
population that peaks in mid-century and declines thereafter, and rapid introduction of new and more efficient technologies.
• A2 scenario family: a very heterogeneous world with continuously increasing global population and regionally oriented economic growth that is more
fragmented and slower than in other storylines.
• B1 scenario family: a convergent world with the same global population as
in the A1 storyline but with rapid changes in economic structures toward a
service and information economy, with reductions in material intensity, and
the introduction of clean and resource-efficient technologies.
• B2 scenario family: a world in which the emphasis is on local solutions to economic, social, and environmental sustainability, with continuously increasing
population (lower than A2) and intermediate economic development.
9
Aerosol emissions cause the opposite effect of greenhouse gases.
300
THE
EXERGY EVOLUTION OF PLANET EARTH
Figure 8.16. Scenarios for GHG emissions from 2000 to 2100 and projections of
surface temperatures [160]
Table 8.3. Projected global averaged temperature change (◦ C at 2090-2099 relative
to 1980-1999) at the end of the 21st century. After [160]
Scenario
Constant year 2000 concentrations
B1
A1T
B2
A1B
A2
A1FI
Temperature change
0,6
1,8
2,4
2,4
2,8
3,4
4,0
Six groups of scenarios were drawn from the four families: one group each in the
A2, B1 and B2 families, and three groups in the A1 family, characterizing alternative
developments of energy technologies: A1FI (fossil intensive), A1T (predominantly
non-fossil) and A1B (balanced across energy sources).
The SRES scenarios project an increase of global GHG emissions by 25-90% (CO2 eq) between 2000 and 2030 (Fig. 8.16), with fossil fuels maintaining their dominant
position in the global energy mix to 2030 and beyond.
According to those scenarios, the projected global averaged surface warming is the
one shown in table 8.3.
In order to stabilize the concentration of GHGs in the atmosphere, emissions would
need to peak and decline thereafter. Table 8.4 and figure 8.17 summarize the re-
The exergy loss of world’s fossil fuel reserves due to the greenhouse effect
301
Table 8.4. Characteristics of stabilization scenarios and resulting long-term equilibrium global average temperature rise above pre-industrial at equilibrium from
thermal expansion only. After [162]
Category
I
II
III
IV
V
VI
CO2 conc.
CO2 -eq conc.
ppm
350-400
400-440
440-485
485-570
570-660
660-790
ppm
445-490
490-535
535-590
590-710
710-855
855-1130
Peaking year
for CO2 emissions
year
2000-2015
2000-2020
2010-2030
2020-2060
2050-2080
2060-2090
Global aver. temp.
◦
C
2,0-4,0
2,4-2,8
2,8-3,2
3,2-4,0
4,0-4,9
4,9-6,1
Figure 8.17. CO2 emissions and equilibrium temperature increases for a range of
stabilization levels [162]
quired emission levels for different group of stabilization concentrations and the
resulting equilibrium global warming, according to the IPCC [162].
Combining the scenarios of table 8.3 and the stabilization temperatures of table 8.4,
we obtain the required variables to be introduced in the model of fossil fuels (table
8.5). The more energy intensive scenario, with an intensive use of fossil fuels (A1FI)
leads to the greatest CO2 concentrations and temperature increase. On the contrary,
scenario B1 is the most sustainable one in terms of CO2 emissions. Scenarios B2
and A1T throw out the same CO2 concentrations and temperature increase, since
the rapid economic growth assumed in A1T is mainly achieved through non-fossil
fuel technologies. Scenario A1B, which assumes a balanced use of fossil and nonfossil fuel energies, comes right after the latter scenarios in terms of CO2 emissions,
followed by scenario A2.
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Table 8.5. Temperature rise and CO2 concentration in the SRES scenarios
Scenario
∆T , ◦ C
CO2 , ppm
B1
1,8
350
A1T
2,4
400
B2
2,4
400
A1B
2,8
440
A2
3,4
620
A1FI
4
710
Table 8.6. Specific exergy (b in kJ/kg) and Exergy loss (%) of anthracite, bituminous, subbituminous, and lignite coal according to the different SRES scenarios
Scenario
0
B1
A1T
B2
A1B
A2
A1FI
8.3.3
Anthracite
b
loss,
%
31624,2 0,00
31603,6 0,07
31582,7 0,13
31582,7 0,13
31567,8 0,18
31511,4 0,36
31489,9 0,42
Bituminous
b
loss,
%
29047,1 0,00
29028,7 0,06
29010,7 0,13
29010,7 0,13
28997,8 0,17
28949,7 0,34
28931,0 0,40
Subbituminous
b
loss,
%
24276,5 0,00
24261,7 0,06
24246,5 0,12
24246,5 0,12
24235,7 0,17
24194,9 0,34
24179,3 0,40
Lignite
b
loss,
%
17351,1 0,00
17340,2 0,06
17329,5 0,12
17329,5 0,12
17321,9 0,17
17293,3 0,33
17282,3 0,40
The fossil fuel exergy decrease
With the help of the equations explained in section 5.3.3 and the fossil fuel’s reserves
data provided in section 6.4.1, we are able to calculate the fossil fuel exergy decrease
of the different scenarios of table 8.5, with respect to the current situation. For
that purpose, the exergy difference will be calculated for the four types of average
coal: anthracite, bituminous, sub-bituminous and lignite; for the three most common
types of average oil: fuel-oil 1, fuel-oil 2 and fuel-oil 4; and for natural gas10 . The
composition of the R.E. chosen for the calculations is number III, which contains the
following substances11 : O2 , N2 , CO2 , H2 O, C aSO4 · 2H2 O and C aCO3 .
Tables 8.6 through 8.8 and Figs. 8.18 to 8.20 show the exergy loss of the different
fuels, according to the SRES scenarios. Scenario “0” is the starting point, where the
R.E.’s temperature is assumed to be 298,15 K and the CO2 concentration, 300 ppm.
As can be seen from the figures and tables, the exergy loss increases with temperature and CO2 concentration. Therefore, the maximum exergy loss is achieved in
the scenario A1FI (rapid economic and population growth, intensive in fossil fuels),
with an exergy decrease of around 0,4%. This figure is very close to the one found
by Valero and Arauzo [366], where the exergy loss fell by approximately 0,31 to
0,38% if the CO2 concentration would double.
10
11
See section 6.4.1 for the properties of the different types of fuels.
See section 5.3.3 for more details about the different R.E. proposed for fossil fuels.
The exergy loss of world’s fossil fuel reserves due to the greenhouse effect
303
0,45
0,40
0,35
Exergy loss, %
0,30
0,25
0,20
0,15
0,10
0,05
0,00
300
360
420
480
540
600
660
720
CO2, ppm
Anthracite
Bituminous
Subbituminous
Lignite
Figure 8.18. Exergy loss of the different types of coal as a function of the CO2
concentration in the atmosphere
Table 8.7. Specific exergy (b) and Exergy loss (%) of fuel-oil 1, fuel-oil 2 and fuel-oil
4, according to the different SRES scenarios.
Scenario
0
B1
A1T
B2
A1B
A2
A1F1
T0
298,15
299,95
300,55
300,55
300,95
301,55
302,15
CO2 ,
ppm
300
350
400
400
440
620
710
Fuel-oil1
b, kJ/kg loss,
%
46259,1 0,00
46229,9 0,06
46205,2 0,12
46205,2 0,12
46187,4 0,16
46124,6 0,29
46099,3 0,35
Fuel-oil 2
b, kJ/kg loss,
%
45517,4 0,00
45488,2 0,06
45463,5 0,12
45463,5 0,12
45446,0 0,16
45383,4 0,29
45358,1 0,35
Fuel-oil 4
b, kJ/kg loss,
%
44002,4 0,00
43973,9 0,06
43949,6 0,12
43949,6 0,12
43931,9 0,16
43869,5 0,30
43844,5 0,36
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THE
EXERGY EVOLUTION OF PLANET EARTH
0,40
0,35
Exergy loss, %
0,30
0,25
0,20
0,15
0,10
0,05
0,00
300
360
420
480
540
600
660
720
CO2, ppm
Fuel-oil1
Fuel-oil 2
Fuel-oil 4
Figure 8.19. Exergy loss of the different types of fuel-oils as a function of the CO2
concentration in the atmosphere
Table 8.8. Specific exergy (b) and Exergy loss (%) of natural gas according to the
different SRES scenarios.
Scenario
0
B1
A1T
B2
A1B
A2
A1F1
T0
298,15
299,95
300,55
300,55
300,95
301,55
302,15
CO2 ,
ppm
300
350
400
400
440
620
710
Natural gas
b, kJ/N m3 loss,
%
39393,8
0,00
39355,7
0,10
39333,0
0,15
39333,0
0,15
39317,2
0,19
39269,3
0,32
39246,3
0,37
The exergy loss of world’s fossil fuel reserves due to the greenhouse effect
305
0,40
0,35
Exergy loss, %
0,30
0,25
0,20
0,15
0,10
0,05
0,00
300
360
420
480
540
600
660
720
CO2, ppm
Figure 8.20. Exergy loss of natural gas as a function of the CO2 concentration in the
atmosphere
Among all fuels, the different types of coal are the most sensible to CO2 concentrations, leaded by anthracite. Natural gas follows coal, while fuel-oils are the least
affected fossil fuels by the greenhouse effect.
Tables 8.9 through 8.11 show the exergy loss of the world’s 2006 coal, fuel-oil and
natural gas reserves, considering only the change of the conditions of the R.E. The
reserves for coal are the ones provided by the World Energy Council, while those
for fuel-oil and natural gas come from the statistics of BP12 . As can be seen from
the tables, the worst scenario A1F I would lead to an exergy loss of 2102,4 Mtoe of
coal, 623,7 Mtoe for fuel-oil and 637,3 Mtoe for natural gas. The global fossil fuel
exergy loss would amount to 3363,4 Mtoe, 84% of the 2006 USA oil reserves (4000
Mtoe). Obviously the real exergy loss would be much greater, since the consumption
of the resource in the different scenarios has not been taken into account. The latter
analysis is accomplished in the next section.
12
See the detailed reserves in tables 6.11, 6.14 and 6.17.
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Table 8.9. Exergy loss of the 2006 coal reserves due to the increase of GHG emissions, according to the different SRES scenarios. Values in Mtoe
Scen.
0
A1
A1T&B2
A1B
A2
A1F1
Africa
B
B
∆B
B
∆B
B
∆B
B
∆B
B
∆B
34286,5
34264,7
21,8
34243,5
43,0
34228,2
58,2
34171,4
115,05
34149,4
137,1
N. America
159649,3
159548,3
101,0
159445,7
203,6
159372,3
277,0
159095,8
553,50
158990,4
658,9
S. America
10224,9
10218,5
6,4
10212,2
12,7
10207,6
17,3
10190,5
34,34
10184,0
40,9
Asia
Europe
136447,4
136361,5
85,9
136277,0
170,4
136216,3
231,1
135989,9
457,59
135902,3
545,2
136826,9
136742,1
84,9
136657,0
169,9
136596,1
230,8
136367,9
459,00
136280,2
546,7
Middle
East
958,6
957,9
0,6
957,4
1,2
956,9
1,6
955,3
3,22
954,7
3,8
Oceania
WORLD
42603,1
42576,3
26,9
42549,9
53,2
42531,1
72,1
42460,6
142,56
42433,3
169,8
520996,7
520669,4
327,4
520342,8
654,0
520108,6
888,1
519231,5
1765,26
518894,3
2102,4
Table 8.10. Exergy loss of the 2006 fuel-oil reserves due to the increase of GHG
emissions, according to the different SRES scenarios
Scen.
A1
A1T&B2
A1B
A2
A1FI
B, Mtoe
∆B
B, Mtoe
∆B
B, Mtoe
∆B
B, Mtoe
∆B
B, Mtoe
∆B
N. America
S. & C.
America
8464,5
5,44
8459,9
10,03
8456,6
13,28
8445,0
24,94
8440,2
29,64
16005,6
10,28
15997,0
18,97
15990,8
25,11
15968,8
47,15
15959,9
56,06
Europe
& Eurasia
20991,7
13,55
20980,2
25,06
20972,0
33,33
20942,6
62,73
20930,8
74,52
Middle
East
Africa
Asia Pacific
WORLD
109629,4
70,40
109569,9
129,92
109527,8
172,02
109376,8
322,98
109315,8
383,95
16866,0
10,81
16856,8
19,96
16850,4
26,43
16827,2
49,62
16817,8
58,99
5890,1
3,78
5886,9
6,97
5884,7
9,23
5876,6
17,33
5873,3
20,60
177847,3
114,26
177750,7
210,90
177682,2
279,41
177436,8
524,76
177337,8
623,76
Table 8.11. Exergy loss of the 2006 natural gas reserves due to the increase of GHG
emissions, according to the different SRES scenarios
Scen.
A1
A1T&B2
A1B
A2
A1FI
B, Mtoe
∆B
B, Mtoe
∆B
B, Mtoe
∆B
B, Mtoe
∆B
B, Mtoe
∆B
N. America
S. & C.
America
7475,7
7,23
7471,4
11,54
7468,4
14,54
7459,3
23,64
7454,9
28,02
6445,8
6,24
6442,1
9,95
6439,5
12,54
6431,7
20,38
6427,9
24,16
Europe
& Eurasia
60089,8
58,14
60055,2
92,72
60031,1
116,90
59957,9
190,03
59922,7
225,23
Middle
East
Africa
Asia Pacific
WORLD
68845,3
66,61
68805,7
106,23
68778,0
133,93
68694,2
217,72
68653,9
258,04
13290,2
12,86
13282,6
20,51
13277,2
25,85
13261,1
42,03
13253,3
49,81
13886,9
13,44
13878,9
21,43
13873,4
27,02
13856,5
43,92
13848,3
52,05
170033,8
164,52
169935,9
262,37
169867,5
330,78
169660,6
537,73
169561,0
637,31
A prediction of the exergy loss of world’s mineral reserves in the 21st century
8.4
307
A prediction of the exergy loss of world’s mineral
reserves in the 21st century
Future consumption of minerals will be affected by many different factors, such as
economic, population, policy, or environmental aspects. In addition to the latter, mineral extraction will be obviously constrained by the amount of available resources.
We will explore seven different scenarios, for which the future mineral degradation
will be calculated: a scenario based on the Hubbert models developed in the last
sections, and the six scenarios included in the IPCC SRES report [160].
8.4.1
Hubbert scenario
At a first stage, we will suppose that the amount of available resources are those of
the reserve base for non-fuel minerals published by the USGS for year 2006 [362],
and the proven reserves of fuel commodities, published by BP [35] and WEC [401]
for the same year. It is assumed that no more resources are going to be found,
and that production of the commodities will follow the bell-shaped curves obtained
before. As we saw in section 8.2.1, iron, aluminium and copper dominate the world’s
non fossil fuel extraction, representing 93% of the total actual exergy degradation
in the 20th century. We will consider that the same behavior will be found in this
new century and hence only the latter three metals will be analyzed inside the nonfuels category. Moreover, the only fossil fuel minerals considered will be coal, oil
and natural gas, although the extraction of other types such as tar sands, oil shales,
natural bitumen or heavy crude oil might be economically competitive by then. In
order to be compared, the exergy of fuels (B) is added to the exergy costs (B ∗ ) of
non-fuel minerals13 .
Figure 8.21 shows the possible mineral reserve’s degradation in the 21st century
based on the latter assumptions.
According to fig. 8.21, if the reserves of the different commodities do not increase,
the peak of maximum mineral extraction will be reached in the decade of the 2020s,
exceeding 12 Gtoe/year. By then, production of all minerals would increase with
respect to 2010, with the exception of oil, which had reached the peak in 2008.
In the 2030s, the exergy consumption of conventional fossil fuels will come at approximately equal rates from all three fuels. From that moment on, oil will lose the
hegemony of exergy production in favor of coal.
In the middle of the 21st century, oil extraction will be reduced to more than a half
of the amount produced in 2010. Natural gas and copper production, which should
reach the peak in years 2023 and 2024, respectively, will be reduced to 23 and 13%
13
Remember that calculating exergy costs of fuel minerals has no sense, as it is impossible to replace them at least with current technology. Nevertheless, its chemical exergy is so large, that can be
compared to the exergy costs of the metals studied.
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EXERGY EVOLUTION OF PLANET EARTH
2050
2060
14
Bt*
12
Copper
Aluminium
Iron
10
N. Gas
8
6
Oil
4
2
Coal
0
1990
2000
2010
2020
2030
2040
2070
2080
2090
2100
Year
Coal
Oil
N. Gas
Iron
Aluminium
Copper
Figure 8.21. Actual exergy consumption of the main minerals in the 21st century
based on the Hubbert peak model. Values in Gtoe
of their respective extractions in 2010. On the contrary, iron, aluminium and coal
production will continue to increase exponentially. By the decade of 2070s, all considered minerals would have reached the peak, leading to production decelerations
also of the most abundant ones, i.e. of iron, aluminium and coal.
At the end of the 21st century, the exergy degradation velocity due to mineral extraction will be reduced to 5,3 Gtoe/year (a reduction of more than 50% with respect
to the peaking year). By then, 82% of the mineral’s exergy reserves available in
year 1900 will be depleted. Among all, the reserves of oil, natural gas and copper
will be almost completely exhausted (more than 99%). Aluminium, coal and iron
commodities will be depleted at 83%, 72% and 69% respectively. Table 8.12 shows
the exergy distance and the degradation degree of the reserves for the periods from
1900 to 2000 and from 1900 to 2100.
It should be noted however that future exploration efforts will result in the discovery
of new deposits. Moreover, technological development will likely allow to extract
mines that are economically unaffordable nowadays.
In the next scenarios, we will assume that the registered world resources by the
USGS [361] of the non-fossil fuel commodities, rather than the reserve base will
be available for extraction. This supposes that technology is enough developed and
mineral prices are high enough to extract resources that are currently not prifitable.
Accordingly, the peak of production of iron, aluminium and copper will be reached
in years 2087, 2089 and 2066, respectively (see figures A.1, A.2, and A.3 in the ap-
A prediction of the exergy loss of world’s mineral reserves in the 21st century
309
Table 8.12. Actual exergy degradation of the main extracted minerals in the 21st
century based on the Hubbert peak model
Mineral
Coal
Oil
Natural gas
Iron
Aluminium
Copper
SUM
1900
R.B., Gtoe
666,4
338,8
246,2
216,4
101,8
8,9
1578,4
1900 - 2000
D∗ , Gtoe % R.B. Loss
127,8
19,2
136,3
40,2
61,0
24,8
26,5
12,3
9,6
9,4
2,6
29,5
363,9
23,1
1900 - 2100
D∗ , Gtoe % R.B. Loss
480,2
72,1
333,9
98,6
243,9
99,1
145,1
67,0
84,7
83,2
8,9
99,7
1296,6
82,1
pendix). The extraction of coal, oil and natural gas is defined by the assumptions of
the IPCC SRES scenarios, which indirectly assume an increase of all proven reserves.
Tables A.29 through A.34 show the primary energy consumption and cumulative resources production assumed in each SRES scenario. Additionally, the exergy loss of
fossil fuels due to the greenhouse effect will be taken into account. We will assume
that this decrease will affect the fuels consumed from year 2050 on, letting CO2
emissions and temperatures stabilize in the atmosphere.
8.4.2
The IPCC’s B1 scenario
As stated before, IPCC’s B1 [160] scenario is characterized by a world toward a
service and information economy, with reductions in material intensity, and the introduction of clean and resource-efficient technologies. Among all SRES scenarios,
it is the most respectful with the extraction of fuel resources.
In addition to the exergy loss of the reserves due to mineral extraction, the exergy
degradation of fuels due to the greenhouse effect is taken into account. In scenario
B1, we obtained that the exergy loss of fuels was 0,06% for average coal and oil and
0,10% for natural gas.
Figure 8.22 shows the actual exergy consumption of the main minerals extracted in
the 21st century, based on the hypothesis of the B1 scenario for fuels. For non fuel
minerals it has been assumed that the extraction behavior follows Hubbert’s bellshaped curve, considering that the world resources published by the USGS [361]
are available for extraction.
According to B1 scenario, the peak of production of all considered fuels will be
reached in the decade of the 2040s with 13,2 Gtoe extracted each year, and declining
thereafter. Current relative consumptions of each fuel will be kept until the peak, i.e.
oil will dominate world’s extraction, followed by coal and finally natural gas. After
the peaking year, the relative consumption of coal will gradually decrease in favor of
the cleaner fuel natural gas. But oil will still dominate world’s fuel consumption.
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THE
EXERGY EVOLUTION OF PLANET EARTH
2050
2060
18
Bt*
Copper
16
Aluminium
Iron
14
N. Gas
12
10
8
Oil
6
4
Coal
2
0
1990
2000
2010
2020
2030
2040
2070
2080
2090
2100
Year
Coal
Oil
N. Gas
Iron
Aluminium
Copper
Figure 8.22. Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s B1 scenario. Values in Gtoe
The dynamic of the B1 scenario would imply an exergy degradation cost of minerals
in the 21st century of over 1300 Gtoe, from these, around 1050 come only from
the consumption of fossil fuels. With the exception of coal, the total exergy cost
degraded of all considered commodities is greater than in the previous Hubbert scenario. In order to meet the fuel consumption expectations of B1 scenario, the oil
proven reserves should increase by 69% and of natural gas by 52%. On the contrary,
current proven reserves of coal would suffice for meeting future world’s consumption. In fact, in year 2100, 64% of the current proven coal reserves will be depleted.
Obviously, the degradation of non-fuel minerals here is greater than in Hubbert’s
scenario, as the peaks are reached 20 to 40 years later, due to the greater available
resources considered. Moreover the depletion degree of the commodities would be
also smaller: 57% for iron, 58% for aluminium and 74% for copper.
Table 8.13 shows the irreversible exergy distance D∗ of the considered mineral resources in the period from 1900 to 2100, and the depletion degree of the commodities, according to the B1 scenario.
8.4.3
The IPCC’s A1T scenario
In the IPCC’s AIT scenario, the very rapid economic growth, and the rapid introduction of new and more efficient technologies is achieved with predominantly non-fuel
technologies.
A prediction of the exergy loss of world’s mineral reserves in the 21st century
311
Table 8.13. Actual exergy degradation of the main extracted minerals in the 21st
century based on the B1 scenario
Mineral
Coal
Oil
Natural gas
Iron
Aluminium
Copper
SUM
1900
W.R., Gtoe
666,4
338,8
246,2
297,0
222,0
21,6
1792,0
1900 - 2000
D∗ , Gtoe % W.R. Loss
127,8
19,2
136,3
40,2
61,0
24,8
26,5
8,9
9,6
4,3
2,6
12,1
363,9
20,3
1900 - 2100
D∗ , Gtoe %W.R. Loss
427,0
64,1
573,1
169,2
373,9
151,9
169,0
56,9
129,4
58,3
16,0
74,3
1688,5
94,2
According to the calculations carried out before, the exergy loss of fossil fuels due to
the greenhouse effect in the A1T scenario are: 0,12% for average coal and oil, and
0,15% for natural gas.
Taking into account the extraction of minerals, and the exergy decrease of fuels
due to the GHG emissions in the A1T scenario, we obtain that the peak of mineral
extraction is reached in the middle of the 21st century, with 19 Gtoe/year, coinciding
with the peak of population.
At the end of the century, the global irreversible exergy degradation velocity Ḋ∗
decreases to 10,4 Gtoe/year. Oil dominates world fuel consumption until the 2040s.
Thereafter, natural gas is the most extracted fuel, followed by oil and finally by coal
(see fig. 8.23).
The exergy cost degradation of the mineral reserves considered in the 21st century
amounts to more than 1500 Gtoe. And the extraction of fossil fuels is responsible
for around 80% of the global mineral depletion. Coal is the least depleted fuel
commodity, with a degradation degree of its proven reserves since 1900, of 59%.
On the other hand, the reserves of natural gas and oil should increase by 77% and
144%, in order to meet the world fuel requirements specified in scenario A1T. The
depletion degrees of the non-fuel mineral commodities are the same as for the latter
scenario, since the same assumptions have been taken into account (see table 8.14).
8.4.4
The IPCC’s B2 scenario
In the IPCC’s B2 scenario, a world with continuously increasing population and
intermediate economic development, mineral consumption increases continuously
throughout the century, although the rate of increase slows down in the decade of
the 2050s.
The exergy loss of fuels due to the greenhouse effect in the B2 scenario is identical
to the previous case, namely 0,12% for coal and oil, and 0,15% for natural gas.
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THE
EXERGY EVOLUTION OF PLANET EARTH
2050
2060
20
Bt*
Copper
18
Aluminium
Iron
16
14
N. Gas
12
10
8
Oil
6
4
Coal
2
0
1990
2000
2010
2020
2030
2040
2070
2080
2090
2100
Year
Coal
Oil
N. Gas
Iron
Aluminium
Copper
Figure 8.23. Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s A1T scenario. Values in Gtoe
Table 8.14. Actual exergy degradation of the main extracted minerals in the 21st
century based on the A1T scenario
Mineral
Coal
Oil
Natural gas
Iron
Aluminium
Copper
SUM
1900
W.R., Gtoe
666,4
338,8
246,2
297,0
222,0
21,6
1792,0
1900 - 2000
D∗ , Gtoe % W.R. Loss
127,8
19,2
136,3
40,2
61,0
24,8
26,5
8,9
9,6
4,3
2,6
12,1
363,9
20,3
1900 - 2100
D∗ , Gtoe %W.R. Loss
393,3
59,0
598,9
176,7
600,6
244,0
169,0
56,9
129,4
58,3
16,0
74,3
1907,2
106,4
According to figure 8.24, in year 2100, the global mineral degradation velocity will
reach near 20 Gtoe/year. By then, fuel demand will be satisfied at approxamtely
equal rates with natural gas and coal. Oil will reach the peak of production in
the 2040s. From that moment on, coal and natural gas production will increase,
compensating the lack of oil, although the peak of natural gas will be reached in the
2080s.
At the end of the century, the global exergy degradation cost of the mineral reserves
will be around 1580 Gtoe, slightly greater than in the A1T scenario. From these, 83%
correspond to the consumption of fossil fuels. Since 1900, coal extraction would
A prediction of the exergy loss of world’s mineral reserves in the 21st century
313
20
Bt*
18
Copper
16
Aluminium
Iron
14
12
N. Gas
10
8
6
Oil
4
2
Coal
0
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
Year
Coal
Oil
N. Gas
Iron
Aluminium
Copper
Figure 8.24. Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s B2 scenario. Values in Gtoe
Table 8.15. Actual exergy degradation of the main extracted minerals in the 21st
century based on the B2 scenario
Mineral
Coal
Oil
Natural gas
Iron
Aluminium
Copper
SUM
1900
W.R., Gtoe
666,4
338,8
246,2
297,0
222,0
21,6
1792,0
1900 - 2000
D , Gtoe % W.R. Loss
127,8
19,2
136,3
40,2
61,0
24,8
26,5
8,9
9,6
4,3
2,6
12,1
363,9
20,3
∗
1900 - 2100
D , Gtoe %W.R. Loss
417,6
62,7
567,4
167,5
644,8
261,9
169,0
56,9
129,4
58,3
16,0
74,3
1944,2
108,5
∗
lead to the degradation of 63% of the total reserves. However, the proven reserves of
natural gas and oil should increase by 63% and 167%, in order to meet the world fuel
requirements specified in scenario B2. Again, the same figures than in the previous
scenarios are obtained for non-fuel minerals, as the same assumptions have been
taken into account (see table 8.15).
314
8.4.5
THE
EXERGY EVOLUTION OF PLANET EARTH
The IPCC’s A1B scenario
In the A1B scenario, the rapid economic growth and rapid increase of new and more
efficient technologies is achieved with a balance between fuel and non-fuel energy
sources. It is assumed that since the decade of the 2030s, the consumption of fossil
fuels is dominated by natural gas.
The exergy loss of fossil fuels due to the greenhouse effect was calculated for A1B
scenario as 0,17% for average coal, 0,16% for average fuel, and 0,19% for natural
gas.
According to the hypothesis of the A1B scenario, the peaks of oil and coal production
are reached in the decades of 2030s and 2050s, respectively with around 5,7 Gtoe
of oil extracted per year and 4,6 Gtoe/year of coal. The global mineral production
peak is reached in the decade of 2070s, with around 24 Gtoe/year extracted (see fig
8.25).
25
Bt*
Copper
Aluminium
20
Iron
15
N. Gas
10
Oil
5
Coal
0
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
Year
Coal
Oil
N. Gas
Iron
Aluminium
Copper
Figure 8.25. Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s A1B scenario. Values in Gtoe
The global exergy degradation cost of all considered mineral reserves in the 21st
century exceeds 2000 Gtoe, from which 86% correspond to the extraction of fuels.
At the end of the 21st century, 74% of the total coal reserves would be depleted. The
A1B scenario assumes that oil and natural gas proven reserves should increase by
76% and 200%, respectively, in order to meet future fuel demands. The depletion
degree of non-fuel mineral reserves are identical to the previous cases, since the
same assumptions have been considered. Table 8.16 shows a summary of the results
for the A1B scenario.
A prediction of the exergy loss of world’s mineral reserves in the 21st century
315
Table 8.16. Actual exergy degradation of the main extracted minerals in the 21st
century based on the A1B scenario
Mineral
Coal
Oil
Natural gas
Iron
Aluminium
Copper
SUM
8.4.6
1900
W.R., Gtoe
666,4
338,8
246,2
297,0
222,0
21,6
1792,0
1900 - 2000
D∗ , Gtoe % W.R. Loss
127,8
19,2
136,3
40,2
61,0
24,8
26,5
8,9
9,6
4,3
2,6
12,1
363,9
20,3
1900 - 2100
D∗ , Gtoe %W.R. Loss
495,4
74,3
595,1
175,6
982,1
399,0
169,0
56,9
129,4
58,3
16,0
74,3
2387,1
133,2
The IPCC’s A2 scenario
The energy demand of the continuously increasing global population of IPCC’s A2
scenario is mainly satisfied by the increasing consumption of fossil fuels. World oil
consumption reaches the maximum of production in the 2020s, decreasing thereafter until its complete substitution towards the end of the century. Since the peaking of oil production, coal is the dominant fuel consumed in this scenario. It passed
from representing 25% of all fossil fuels consumed in the 2020s, to over 75% in year
2100.
To the exergy decrease of minerals due to extraction, we add the fuel’s exergy degradation due to the greenhouse effect, which is in the A2 scenario: 0,34% for average
coal, 0,29% for average fuel, and 0,32% for natural gas.
Accordingly the global peak of world mineral extraction in the 21st century is
reached in year 2100, with over 33 Gtoe/year extracted. In order to satisfy this
energy demand, the proven reserves of coal, oil, and natural gas should increase by
89%, 50%, and 140%, respectively (see fig. 8.26).
In table 8.17, the irreversible exergy distance between 1900 and 2100 is shown.
According to it, A2 scenario would imply a global exergy degradation in the 21st
century of over 2300 Gtoe (6,3 times more the exergy degraded in the previous
century). This implies the degradation of almost 150% of the global mineral resources available in 1900. Again, the same figures than in the previous scenarios
are obtained for non-fuel minerals, as the same assumptions have been taken into
account.
8.4.7
The IPCC’s A1FI scenario
In the IPCC’s A1FI scenario, the world’s rapid economic growth and rapid introduction of new and more efficient technologies is achieved through the intensive
316
THE
EXERGY EVOLUTION OF PLANET EARTH
2050
2060
35
Bt*
30
25
Copper
20
Aluminium
Iron
15
N. Gas
10
Oil
5
Coal
0
1990
2000
2010
2020
2030
2040
2070
2080
2090
2100
Year
Coal
Oil
N. Gas
Iron
Aluminium
Copper
Figure 8.26. Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s A2 scenario. Values in Gtoe
Table 8.17. Actual exergy degradation of the main extracted minerals in the 21st
century based on the A2 scenario
Mineral
Coal
Oil
Natural gas
Iron
Aluminium
Copper
SUM
1900
W.R., Gtoe
666,4
338,8
246,2
297,0
222,0
21,6
1792,0
1900 - 2000
D∗ , Gtoe % W.R. Loss
127,8
19,2
136,3
40,2
61,0
24,8
26,5
8,9
9,6
4,3
2,6
12,1
363,9
20,3
1900 - 2100
D∗ , Gtoe %W.R. Loss
1261,8
189,3
510,0
150,5
592,0
240,5
169,0
56,9
129,4
58,3
16,0
74,3
2678,2
149,5
consumption of fossil fuels. Consequently, it is the most mineral predatory scenario
taken into account.
The decrease of fuel’s exergy due to the greenhouse effect in the scenario A1FI obtained was: 0,4% for average coal, 0,35% for average fuel, and 0,37% for natural
gas.
According to figure 8.27, the peak of mineral production is reached in the decade of
the 2080s, coinciding with the peaks of oil and natural gas consumption. Thereafter,
the decrease of oil and natural gas production is compensated by an increase in the
world extraction. The global mineral degradation velocity in the eighties reaches
A prediction of the exergy loss of world’s mineral reserves in the 21st century
317
39,8 Gtoe/year, from which over 90% are due to the extraction of fossil fuels. It
should be remembered, that the consumption of non-fuel minerals has been assumed
to be identical to the previous cases.
45
Bt*
Copper
40
Aluminium
Iron
35
30
N. Gas
25
20
Oil
15
10
Coal
5
0
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
Year
Coal
Oil
N. Gas
Iron
Aluminium
Copper
Figure 8.27. Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s A1FI scenario. Values in Gtoe
The global mineral exergy degradation cost in the 21st century is in the A1FI scenario over 2750 Gtoe. This implies that man would have depleted 7,6 times more
mineral reserves than in the 20th century, and the degradation of around 174% of
the global mineral resources available in 1900 (see table 8.18). Furthermore, the
proven reserves of coal, oil and natural gas should increase at least by 56%, 140%
and 289%, in order to meet the fuel requirements of scenario A1FI.
8.4.8
Summary of the scenarios
Table 8.19 and figure 8.28 show a summary of the possible exergy degradation costs
of the main mineral reserves extracted in the period between 1900 and 2100, according to the different scenarios considered before. It should be noted that to the
obtained values, we should add the exergy loss of other minerals not accounted for
in this study. Additional non-fuel minerals could increase the global mineral exergy
consumption in 20% or more.
As can be seen from the table and the figure, the scenario that leads to the least
degradation degree of the mineral reserves, is the one based on the Hubbert model.
It should be remembered, that for this scenario it has been assumed that the only
available mineral resources for extraction are those of the reserve base, and that
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THE
EXERGY EVOLUTION OF PLANET EARTH
Table 8.18. Actual exergy degradation of the main extracted minerals in the 21st
century based on the A1FI scenario
Mineral
Coal
Oil
Natural gas
Iron
Aluminium
Copper
SUM
1900
W.R., Gtoe
666,4
338,8
246,2
297,0
222,0
21,6
1792,0
1900 - 2000
D∗ , Gtoe % W.R. Loss
127,8
19,2
136,3
40,2
61,0
24,8
26,5
8,9
9,6
4,3
2,6
12,1
363,9
20,3
1900 - 2100
D∗ , Gtoe %W.R. Loss
1036,9
155,6
811,3
239,4
955,6
388,2
169,0
56,9
129,4
58,3
16,0
74,3
3118,1
174,0
Table 8.19. Summary of the actual exergy degradation of the main extracted minerals in the period between years 1900 and 2100 based on the Hubbert and the
IPCC’s SRES scenarios
Scenario
D∗ 1900 - 2100
% Reserves lost
Hubbert
1297
82
B1
1689
94
A1T
1907
106
B2
1944
108
AIB
2387
133
A2
2678
149
A1FI
3118
174
no more resources will be found in the future. Accordingly, at the end of the 21st
century, man would have depleted around 82% of the reserve base available in 1900.
For the rest scenarios, it has been assumed that the non-fuel mineral reserves available for extraction, are those of the world resources published by the USGS [361].
Accordingly, the rate of extraction of non-fuel minerals is greater than in the previous
case, as more resources can be extracted.
In addition to the consumption of fossil fuels assumed in the different SRES scenarios, we have taken into account the exergy loss of fuels due to the emission
of greenhouse gases to the atmosphere. Depending on the scenario considered,
the greenhouse effect increases the global mineral exergy loss between 0,04% and
0,31%.
Among all SRES scenarios, A1FI implies the greatest degradation of mineral reserves,
leading to the depletion of more than 3100 Gtoe. On the other end, scenario B1 leads
to the least mineral degradation, with near 1700 Gtoe depleted. Nevertheless, all
IPCC’s scenarios involve greater degradation degrees of the mineral reserves than in
the case where the Hubbert behavior has been assumed. This indicates that for satisfying the energy consumption assumed in the SRES scenarios, the proven reserves
of coal, oil and natural gas should increase considerably.
New discoveries are indeed increasing the reserves of many mineral resources. A
recent case has been the discovery of the Carioca oil well in the Santos Basin off-
A prediction of the exergy loss of world’s mineral reserves in the 21st century
319
3500
Bt*, Gtoe
3000
2500
Copper
2000
Aluminium
Iron
1500
Natural gas
1000
Oil
500
Coal
0
Hubbert
B1
A1T
Coal
B2
Oil
Natural gas
A1B
Iron
Aluminium
A2
A1FI
Copper
Figure 8.28. Summary of the actual exergy degradation of the main extracted minerals in the period between years 1900 and 2100 based on the Hubbert and the
IPCC’s SRES scenarios
shore Brazil, which registered a test production of 2900 barrels/day of oil and 57000
m3 /day of gas.
But in the relatively mature oil industry, the quantity of additional reserves that remain to be discovered is unclear [160]. Ivanhoe and Leckie [165], Laherrere [190],
Campbell [45] or Hatfield [133] argue that few new oil fields are being discovered
and that most of the increases in reserves results from revisions of underestimating
existing reserves. However, optimistic views such as the one of Smith and Robinson [324], appeal to improvements in technology, which will increase recovery rates
from existing reservoirs and make profitable the development of fields previously
regarded as uneconomic.
In the case of natural gas, estimates of reserves and resources are being revised
continuously. Optimistic additional gas reserves are estimated as between 200, according to the International Gas Union [156] and 500 Gtoe, according to Gregory
and Rogner [123].
Coal proven reserves are larger than those of oil and natural gas. Furthermore,
according to the WEC [401] estimates of additional resources in place, the global
coal reserves could be multiplied by more than two. But as the EWG [89] argues,
the historical assessment of global resources has revealed substantial downgradings
over the last decades. Estimated coal resources have declined from 10 billion tons
coal equivalent ( 8300 Mtoe) to about 4,5 billion tons coal equivalent ( 3750 Mtoe),
a decline of 55% within the last 25 years. Moreover, this downgrading of estimated
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THE
EXERGY EVOLUTION OF PLANET EARTH
coal resources shows a trend supported by each new assessment. Therefore it is
possible that resource estimates will be further reduced in the future.
Hence, it remains to be seen whether the rate of discoveries and the reclassification
of mineral reserves as recoverable are sufficient to meet the demands of a rapidly
industrializing world.
8.5
8.5.1
Final reflections
The Limits to Growth to be reconsidered?
In the early seventies, Meadows et al. [218] raised the concern about the limits to
growth. Their conclusion was that if no immediate action is undertaken, the current
standard of living will not be sustained and world economies will eventually collapse. Pollution will increase and food and mineral commodities will suffer important shortages, leading to a reduction in population. The book constituted a world
shock and incited reflection about the urgent need for a sustainable development.
The Limits to Growth predicted oil running out in 1992 among other natural resources14 . Instead of shortages, the last two decades of the 20th century were
marked by a generalized excess. The world ended up enjoying significant declines
in almost all commodity prices. Consequently, the message of the Club of Rome was
soon discredited. But the lack of precise data and hence inexact and early predictions about future shortages does not excuse the reality of the message provided in
the Meadow’s book. It was also in the late eighties and early nineties when more
voices were raised on a global scale in favor of putting limits to growth, in view
of the systematic destruction of the environment. Clear examples of that were the
Brundtland report [398] in 1987 or the Earth Summit celebrated in Rio de Janeiro
in 1992. The beginning of the 21st century has been marked by a drastic increase of
mineral and food prices. In the period between may 2007 and may 2008 the prices
of wheat, soy or rice have increased by 62, 79 and 95%, respectively. Similarly, the
prices of aluminium, gold, natural gas or brent increased in the same period by 25,
36, 238 and 57%, respectively. These few examples can be extrapolated to other
commodities. The sharp increase of prices that we are currently facing, together
with the results offered in this PhD more than justify to reconsider the reflections
incited by the Club of Rome.
Obviously the aim of this PhD was not to reanalyze the truth or falseness of their
predictions, but to shed light on a more precise methodology that could improve
the capacity of the analysis, almost forty years later. The exergoecological analysis of fuel and non-fuel minerals could be extended to the loss of fertile soils and
14
The authors of the report offered also an upper value for the expiry time, as they accepted that
the known resources of minerals and energy could, and would, grow in the future, and consumption
growth rates could also decline. Assuming that the resources are multiplied by two, virtually all major
minerals and energy resources would expire within the following 100 years.
Final reflections
321
consequently to the analysis of the increasing world food demand and the carrying
capacity of the planet. If the demand of biofuels as an alternative to conventional oil
should compete with food production, one could question which will be the availability of food, biofuels and biodiversity in a world with increasing demands and
accelerated degradations. The analysis could be also extended to the growing freshwater requirements in a world with unpredictable climate changes.
On the other hand, the production of materials is still cheap, so even if they are partially recycled, extraction continues to increase. This indicates that mankind has put
neither energy nor mass limits to the extraction of minerals. Maybe the solution is
to establish some kind of global law stating that extraction should be limited to the
quantity of minerals that are naturally degraded through oxidation. This is, humanbeings should live with a certain amount of recyclable metals and materials and
should exploit only limited resources. Ulterior extractions should not be permitted,
except for extraordinary cases. This is, it should be stated that there has been extracted enough iron, aluminium, copper and other mineral commodities throughout
history, and mankind should learn to recycle and save materials, instead of promoting wasting. This new economy would be more focused toward use than toward
the consumption of raw materials. The dematerialization of a society could only be
achieved by limiting drastically the extraction of the earth’s resources. It should be
noted that this limitation would not avoid an increasing energy consumption. The
energy demand should be supplied through renewable resources for compensating
the exergy destruction associated to recycling.
It is not enough to establish conventional measures of energy efficiency, renewable
energies or more advanced energy technologies such as CO2 sequestration, fission or
fusion. We should propose a drastic limitation in the extraction of raw materials from
the earth. We should live from and with the already extracted materials, converting
their use and their recycling into an art that comes from the necessity. As long as
the “Great Mine Earth” continues providing cheap materials in which their value is
associated to extraction costs, rather than replacement costs, it will be always less
expensive to continue exhausting the planet, than to live with the available and
already extracted minerals. Society requires development, not growth.
However, as the former UK prime minister Tony Blair stated [84], “we cannot forget
that more than three and a half billion people live in countries rich in oil, gas or
minerals. These natural resources provide great opportunities to improve the lives
of poor people. But there are risks. Bad management and lack of transparency of
these resources can lead to poverty, conflict and corruption. However this is not
inevitably”.
If economic development of so many people in the world depends on the extraction
of their raw materials, limiting such activity is at the present time unfeasible and not
very practical. If this drastic limitation will surely come eventually, today the immediate and realistic requirement is to promote conservation measures of the resources
for the future use of coming generations and a more rational management of the
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extraction and use of minerals. The conservation of natural resources has worried
a number of renowned economists throughout the middle of the 20th century. Although this topic exceeds the objectives of this PhD, we want to shortly address this
problem.
As stated by Ciriacy-Wantrup [57], the economy is the study of the election between
alternative ways of action for solving scarcity. Conservation is interested in when
resources should be used. Conservation and its antithesis depletion are defined in
terms of the change in the intertemporal distribution of the use of resources. Such
changes lead to the comparison of two or more alternative temporal distributions
of resources extraction. According to Ciriacy-Wantrup, the optimum conservation
state is the temporal distribution of the use that maximizes the current value and
the income flux. An economic study of conservation should explain how a conservation state is produced and how it changes. In many practical situations, keeping a
minimum standard of living does not imply any abstention in the use of resources,
it rather implies a change in the technical ways (not in the quantity) of use.
8.5.2
The need for global agreements on the extraction and use of
natural resources
In the previous chapters, we have stated that there are two different types of accelerations appearing in the use of natural resources. One is the increasing demand of
minerals, and the other more subtle one is associated to the decline of ore grades.
This last phenomenon, corroborated throughout the 20th century for almost all minerals lead to increasing energy requirements per unit of mineral extracted.
The result is that not only the absolute quantity of energy increases for the extraction
of minerals in the planet, but also the energy per unit of mineral, as the ore grade
decreases. Currently, between 5 and 6% of the yearly world’s fossil fuel consumption
is used for the extraction and processing of iron, aluminium, copper and cement15 .
If the demand of minerals increase and at the same time ore grades decline, the
energy demand for extraction will likely suffer a doubly exponential increase in the
next decades. Although the recycling of materials, especially of metals has grown
in the last decades, these are far from reaching the accelerated extraction rate of
their precursors. It is still cheaper to continue extracting than to save materials. And
probably this trend will not change in the short run.
Therefore, global agreements are urgently required. Paraphrasing the words of the
e-Parliament16 [86], “We are burning oil, coal and gas and extracting minerals and
rocks at an ever increasing rate, while at the same time destroying our forests, our
biodiversity, our land and our mines. As a result, the earth is heating up fast. These
15
According to energy requirements data from the SimaPro 7.1 LCA software.
The e-Parliament is the first world institution whose members are elected by the people. It links
democratic members of parliament and congress into a global forum, combining meetings and electronic communication.
16
Final reflections
323
problems are global, but we are trying to solve them with an international system
of some 200 national interests. Each national capital makes policy decisions within
its own borders, with no easy way to learn from the experience of the others. The
governments have been trying for years to agree on what to do to protect the planet.
It isn’t working. To act in time, we need to create quickly a critical mass of lawmakers from all parties who understand the dangers, share a vision for a sustainable
world, and are ready to take the lead in their national parliaments. We need to invest not only in renewable energy, but in information for planet management and
political leadership. The only shortage we face is a lack of political will and political
leadership to make the transition to a sustainable world.”
It is surprising that the international worries are still very far removed from this
topic. Pancala and Socolow [256] have laid out a menu of 15 currently available
options for meeting the world’s energy needs over the next 50 years while stabilizing CO2 emissions near the current level of 7 billion tons of carbon per year. These
options include energy efficiency, renewable energies, CO2 capture and storage, new
generations of nuclear power plants, the massive use of hybrid and hydrogen vehicles and even a change in the energy model. Nevertheless, it has not been proposed
in a quantitative way what it may suppose a drastic world reduction and an appropriate management of the massive use of the extractive mining industry.
It seems though, that early birds in the sector are determined to improve public
transparency in their activities at least in economic terms. This way, the Extractive Industries Transparency Initiative (EITI) [84] came into being in 2002 at the
World Summit on Sustainable Development in Johannesburg. It brought together a
global coalition of governments, companies, civil society organizations and investors
to promote greater transparency in the payment and receipts of natural resource revenues. As a consequence, EITI is becoming the internationally accepted standard
for transparency in the oil, gas and mining sectors.
If EITI is an initiative that should be applauded, it is still not ambitious enough in
the physical frame. Indeed, we share with the EITI the following principles and most
relevant criteria [84]:
• We share the belief that the prudent use of natural resource wealth should
be an important engine for sustainable economic growth that contributes to
sustainable development and poverty reduction, but if not managed property,
can create negative economic and social impacts.
• We affirm that management of natural resource wealth for the benefit of a
country’s citizens is in the domain of sovereign governments to be exercised in
the interests of their national development.
• We recognize that the benefits of resource extraction occur as revenue streams
over many years and can be highly price dependent.
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• We recognize that public understanding of government revenues and expenditure over time could help public debate and inform choice of appropriate and
realistic options for sustainable development.
• We underline the importance of transparency by governments and companies
in the extractive industries and the need to enhance public financial management and accountability.
• In seeking solutions we believe that all stakeholders have important and relevant contributions to make, including governments and their agencies, extractive industry companies, service companies, multilateral organizations, financial organizations, investors and non-governmental organizations.
• Regular publication should be accomplished of all material oil, gas and mining
payments by companies to governments and all material revenues received
by governments from oil, gas and mining companies should be forwarded to
a wide audience in a publicly accessible, comprehensive and comprehensible
manner.
• Civil society is actively engaged as a participant in the design, monitoring and
evaluation of this process and contributes towards public debate.
Obviously, the global benefits obtained through a global EITI implementation would
be impressive. Underlying this work is the belief that more public accountability and
more transparency can raise the quality of public expenditure, cut corruption, reduce
poverty and raise the credibility and prestige of extractive companies. Moreover, it
provides the information that allows to decide on a global scale whether or not to
change extraction rates from an economic perspective.
Nevertheless, the EITI lays stress only on economic transparency, forgetting physical
parameters that are extraordinarily relevant for understanding the decline of benefits
or the extractive velocity in relation to its reserves. So EITI proposes transparency in
extraction, but after all it enhances extraction.
Physical and objective information about the amount of available resources, their
composition and quality, the ore grades, the quantity of energy and water required
for extraction, the amount of waste rock and other physical parameters that would
allow an objective analysis of the state of our mineral capital is rarely published. In
fact, in many cases this information is hidden or distorted by companies, institutions
or even governments for their own economic benefits. The EITI simply ignores this
issue. What really matters is the amount of money produced by a country through
the extraction of its mineral resources, for carrying out a more transparent and credible management in the international markets. In short, it is about where do the
profits from extraction go to and in any case, maximize them for a more universal
and fair benefit. But the possibility of reducing or stopping extraction is not even
questioned.
Final reflections
8.5.3
325
The need for an accountability theory of mineral resources. The
Physical Geonomics
On the other hand, it is surprising how the mineral’s wealth classification has been
carried out traditionally through purely qualitative criteria: the terms reserves or
resources are accompanied by adjectives like economically or technically feasible to
extract, hypothetical, identified, indicated, probable, etc. The definition is usually
imprecise and depends generally on those owning the data, who diminish or increase
the resources for their own interest.
The countries account economically for their increase of wealth through the GDP
indicator. However, the physical wealth, its decline and its eventual replacement
does not appear in any national account. The depletion of natural resources of a
country are seen as an asset that generates immediate wealth. Neither the associated pollution, nor the loss of wealth are considered in the national accounts of the
countries. It is as if we would sell the bricks of cathedrals to tourists, thereby increasing the wealth of local people. As stated by Seymour and Zadek [305], we need to
examine the underlying assumptions about energy and the environment on which
today’s governance and accountability systems have been built. Such an assessment
challenges us to develop a new generation of institutions with system of rules for
our economy and politics which incorporates energy, materials and water scarcity
and environmental fragility into its design. This will require dramatic innovations
moving forward in our understanding and practice of governance and accountability.
As long as there is not a unifying theory that allows to convert quantities, compositions and ore grades into non monetary units and thus not subject to variabilities
beyond mining extraction such as currency value, this physical and parallel accountability will probably remain in the level of dialectic speeches.
But this PhD, and in general, the development of the Exergoecology approach, could
break this theoretical barrier and provoke a global stream in favor of the physical accountability of the mineral wealth on a global and local scale and disaggregated by
mineral type, companies involved, etc. Hence, we propose a physical accountability
of mineral resources taking into account at least three physical properties: quantity,
composition and ore grade. Additionally, an estimation of the environmental impact
for the opening, exploitation and shutdown of mining activities in terms of energy,
water and material costs (not only in economic cost-effective terms) should be required. This is, mining resources should be evaluated in the same way as industrial
products, which can be assessed through the Life Cycle Assessment methodology. On
the other hand, the relationship between physical and monetary cost will be always
possible through energy prices. This could at the same time keep the objectivity of
physical data and the more intelligible meaning of monetary units.
In any case, more high quality data collection processes and better indicators are
required. Despite of the enormous currently available IT means, governmental agencies do not have the mineralogical information level attained until the seventies of
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last century. Those series and the critical mass built around the knowledge about
the mineralogical wealth of the countries and their yearly physical exploitation and
associated impacts, were progressively disappearing throughout the 20th century.
This was due to the neoliberal streams that transferred to the private initiative and
the markets, the responsibility of mineral extraction. The government agencies that
carried out the surveys through a network of experts were converted into research
institutes, leaving the systematic and controlled knowledge of the mineral and natural environment. Under this information and databases gap, it is impossible to
develop laws for improving the governance of national and global resources. Because in practical terms, current economy considers that we live in a planet full of
resources and it is only a matter of prices, i.e. of supply and demand, the solution of
the scarcity problem.
The theoretical principles of Exergoecology, stated in this thesis and in preceding
studies show the way. Nevertheless, it is necessary to work in the field and put
into practice these principles. This is already happening with the recent developed
methodology for water cost assessment called “Physical Hydronomics” developed
by Valero et al. [412], [372], which is based on the principles of Exergoecology.
Physical Hydronomics assesses the physical cost of a water body along its course
with a single unit of measure, exergy, which accounts for chemical quality, height,
temperature, velocity and flow. This way, any natural or human alteration of the
water body can be physically accounted for. Through the exergy replacement costs,
we have an objective tool for environmental cost assessment, allowing an alternative
management of water bodies for a certain region. The rules or accounting principles
are being developed thanks to specific experiences were problems are detected and
solved by the simple method of learning by doing.
In the same way, this thesis proposes as final corollary a new accounting tool for
the management of the mineral wealth on earth, including not only fossil fuels, but
also the much more complex and apparently less relevant information of non-fuel
minerals. We propose to call this tool “Physical Geonomics”. Obviously, the accounting principles on which it is based will be created through the learning by doing
technique. If Exergoecology considers that a mineral deposit is a thermodynamic
system that contains exergy because it is differentiated from its environment, the
accounting principles that allow to convert the theory into numbers should be further developed. And this should be carried out not only for exergy, but also for the
exergy replacement costs. The latter provide more significant numbers, but are more
arbitrary, since they depend on technologies and hence on international agreements.
Physical Geonomics should not only account for the minerals extracted from the
planet, but also for those that are being recycled. Consequently, we could obtain
a global accountancy of the planetary stocks of chemical elements available for
mankind in a certain period of time. This would allow to detect the quantity of
minerals that have been returned to the planet in a complete dispersed way. That
quantity is always positive, what tells us that the planet inexorably approaches the
degraded state. The assessment of that entropic planet will have to be further de-
Summary of the chapter
327
veloped in other studies for thinking over the degradation velocity of our planetary
resources.
Can we move to more efficient, equitable and cleaner use of the earth’s resources by
shifting conventional accountability practices into physical accounting systems? The
answer is not simply a clear “yes”, but we think that Physical Geonomics proposed
in this thesis can positively help in this task.
8.6
Summary of the chapter
This chapter has extrapolated at planetary level, the analysis of the exergy degradation of mineral reserves carried out before for Australia. For that purpose, many
assumptions had to be made at the expense of accuracy loss in the results. This
is because there is an important information gap about current and historical data
of many commodities. Bearing in mind these considerations, we have been able to
give a rough estimate of the mineral loss on earth since the beginning of the 20th
century, the earth’s degradation velocity, the depletion degree of the reserves and
reserve base, the years until depletion of the commodities, and the year where the
peak of production is reached for the main minerals extracted on earth.
According to our calculations, the irreversible exergy distance D∗ of the 51 non-fuel
mineral commodities analyzed is at least 51 Gtoe, consumed at an average exergy
degradation velocity Ḋ∗ of 1,3 Gtoe/year in the last decade. This means that with
current technology, the replacement of all depleted non-fuel commodities would
require a third of current world fuel oil reserves (178 Gtoe).
The exergy degradation of the non-fuel mineral reserves on earth is clearly dominated by the extraction of iron, aluminium and to a lesser extent of copper. Nevertheless, the latter three minerals are not the most depleted commodities. We have
stated that the reserves of mercury, silver, gold, tin, arsenic, antimony and lead are
suffering the greatest scarcity problems. On the other hand, the minerals of cesium,
thorium, REE, iodine, vanadium, PGM’s, tantalum, aluminium, cobalt and niobium
are the least depleted commodities.
For the most extracted non-fuel minerals on earth, we have applied the Hubbert
bell-shaped curve, assuming that only the reserve base published by the USGS [362]
are available for extraction. Accordingly, we have obtained that the peak of production for iron, aluminium and copper is reached in years 2068, 2057 and 2024,
respectively.
With respect to fossil fuels, we have stated that in exergy terms, oil has been the most
consumed fuel, accounting for 42% of the total fuel exergy degradation in the 20th
century (coal and natural gas accounted for 38 and 20%, respectively). The total
fuel’s exergy depleted between 1900 and 2006 is estimated at 382 Gtoe, consumed
at an average exergy degradation velocity of 9 Gtoe/year in the last decade. The
degradation corresponds to 30,5% of total world’s proven fuel reserves in 2006.
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Hubbert’s bell shaped curves applied to the exergy production of fossil fuels revealed
that the peak of coal will be reached in year 2060, of natural gas in 2023, and of oil
in 2008. The latter value fits very well with the predictions of other authors, who
estimated that the peak year of world oil will be between 2004 and 2008. Furthermore, it gives sense to the radical increase of oil prices registered recently. The price
of a barrel of crude has been doubled in just one year, surpassing in January 2008,
the psychological barrier of 100 $US.
If we add the exergy loss of fossil fuels to the exergy replacement costs of non-fuel
minerals, we obtain that man has depleted in the 20th century a total of 433 Gtoe.
In 2006, the exergy of mineral deposits was depleted at a degradation velocity of
around 12 Gtoe. Furthermore, considering all main mineral resources on earth, we
have estimated that the peak of production will be reached in year 2034.
The exergy of mineral reserves can be also affected by the conditions of the environment. With the help of the IPPC’s reference scenarios, we were able to estimate
the exergy loss of fuels due to the increase of GHG emissions in the atmosphere
and the temperature rise. According to our calculations, the exergy of fossil fuels
could decrease to up to 0,40%, if the current CO2 concentration in the atmosphere
doubles.
Finally, we have made an estimation of the possible depletion degree that mineral
reserves might suffer in the 21st century. For that purpose, we took into account
seven different scenarios.
In the first scenario, we assumed that production of the main mineral commodities
extracted, namely coal, oil, natural gas, iron, aluminium and copper, would follow
the bell-shaped curves calculated before. Accordingly, the global mineral exergy
decrease in the period between 1900 and 2100 would be near 1300 Gtoe. Furthermore, at the end of the 21st century, man would have depleted around 82% of the
reserve base available in 1900.
The other six case studies correspond to the IPPC’s SRES scenarios concerning fossil
fuel consumption. For non-fuel minerals, we assumed that world resources, rather
than the reserve base are available for extraction. Additionally, we have taken into
account the exergy loss of fuels due to the emission of greenhouse gases to the
atmosphere.
All IPCC’s scenarios involve greater degradation degrees of the mineral reserves than
in the case where the Hubbert behavior has been assumed. In the worst case, the
exergy of the mineral resources degraded exceeds 3100 Gtoe. This indicates that
for satisfying the energy consumption assumed in the SRES scenarios, the proven
reserves of coal, oil and natural gas should increase considerably. Although new
discoveries are indeed increasing the reserves of many mineral resources, it remains
to be seen whether the rate of discoveries and the reclassification of mineral reserves
as recoverable are sufficient enough to supply the huge future mineral demand.
Summary of the chapter
329
In the final reflections of this PhD, we have taken up again the ideas provided by
Meadows et al. [218] in their book “The Limits to Growth”. In view of the results
obtained in this study, we have stated that the message of the Club of Rome was
not as false as many claimed, even if the last decades of the 20th century indicated
the contrary. In fact, we have reached a point in which we might think about limiting radically extraction and living only with the already extracted materials. This
is recycling, rather than wasting should be promoted. But nowadays, this practice
would be impossible to undertake, as many economies are sustained by the extraction of resources. Hence, the realistic requirement now is to promote conservation
measures for assuring enough resources for coming generations and a more rational
management of the extraction and use of minerals.
We have stated that conventional measures of energy efficiency, renewable energies,
CO2 sequestration, etc., are not enough for achieving sustainability. We believe that
a drastic world reduction and an appropriate management of the massive use of
the extractive mining industry should be also required. For that purpose, global
agreements are a must.
An appropriate management should be based on a solid, transparent and objective
physical accountability system of resources. As final corollary of this PhD, we have
proposed a new accountability tool for the management of the mineral wealth on
earth, based on the Exergoecological principles stated in this study. We have proposed to call this tool “Physical Geonomics”. Obviously, the accounting principles on
which it is based will have to be further developed through the learning by doing
technique.
Chapter
9
Conclusions
9.1
Introduction
In this chapter, a synthesis of this PhD is accomplished and the main scientific contributions of the work are outlined. Finally, the perspectives of future interesting
studies that have arisen from this PhD are presented.
9.2
Synthesis of the PhD
The aim of this PhD has been the assessment of the resources available on earth and
their degradation velocity, due to human action. This has been accomplished under
the framework of the exergoecological analysis. The latter allows to value mineral
resources, according to the physical cost that would require to obtain them from
the materials contained in a hypothetical earth that has reached the maximum level
of deterioration. In other words, it quantifies the physical cost of restoring natural
resources from a degraded state in the so called reference environment to the conditions in which they are currently presented in nature. The exergoecology approach
uses the property exergy as the universal unit of measure. The main advantage of its
use with respect to other physical indicators is that in a single property, all the physical features of a resource are accounted for. Furthermore, exergy has the capability
of aggregating heterogeneous energy and material assets. This is not the case, if the
assessment is carried out in terms of mass, because we cannot add tons of oil with
tons of gold, for instance. Unlike standard economic valuations, the exergy analysis
gives objective information since it is not subject to monetary policy, or currency
speculation.
This PhD has been structured into two different parts. The first one, of an eminently
geological and geochemical character, has described and modeled the geochemistry
331
332
CONCLUSIONS
of the earth and its resources. The second part has developed and used the thermodynamic tools required for analyzing the state of our planet.
In chapter 2, a comprehensive analysis of the physical and geochemical features of
the earth has been undertaken as a starting point for determining its properties.
First, a coarse composition of the bulk earth with the relative mass proportions of
each sphere has been presented. This overview has given way to the more detailed
explanation of the geochemistry of the atmosphere, hydrosphere and upper continental crust, which are the layers of the earth with which man interacts.
It has been stated that the chemical composition of the atmosphere is rather uniform
to heights up to 100 km. Apart from the natural occurring gases, there are traces of
anthropogenic substances in the atmosphere that may alter the conditions on earth.
The hydrosphere is composed by the oceans (representing over 97% of the hydrosphere’s volume), renewable water resources (rivers, lakes and underground water),
ice, and atmospheric water. As it happens to the atmosphere, the composition of seawater is quite uniform. On the contrary, the composition of the rest hydrosphere’s
components may vary from place to place. Nevertheless, some examples and averages have been provided for all water reservoirs.
The continental crust is the outer layer of the solid earth, and is composed by the
core, mantle and crust. The crust is further divided into the lower, middle and
upper crust. We have focused our attention only in the upper part of it, as it is
the reservoir of the main minerals and other natural resources for mankind. The
chemical composition of the upper continental crust in terms of minerals is well
known, although it is still subject of numerous updates. However, its composition in
terms of minerals has been barely studied.
Since the determination of the thermodynamic properties of the upper continental
crust requires the knowledge of the minerals included in it, the aim of chapter 3 was
to obtain a model of its mineralogical composition.
For that purpose, a revision of the studies concerning the mineralogical composition
of the earth’s crust was carried out. It was stated, that the heterogeneity and complexity of the crust have hindered deep and accurate studies of its composition in
terms of minerals. In fact a single author N.A. Grigor’ev has been very recently the
first one in giving a comprehensive mineralogical composition of the upper crust.
We checked the satisfaction of the mass balance between the minerals proposed by
Grigor’ev and the better known chemical composition in terms of elements of the
upper crust. The no satisfaction of the mass balance, lead us to update Grigor’ev’s
composition. The methodology used minimizes the difference between Grigor’ev’s
and our target composition, under the constraint of assuring chemical coherence
with the average chemical composition of the earth’s crust in terms of elements.
Furthermore, the final composition includes important minerals not taken into account in Grigor’ev’s analysis. As a result, we obtained an estimate of the average
Synthesis of the PhD
333
mineralogical composition of the upper crust, consisting of the 307 most abundant
minerals.
The composition obtained should not be considered as final and closed, since many
assumptions had to be made. Nevertheless, it is the first step for obtaining a coherent
mineralogical composition of the crust.
Chapter 4 closes the analysis of the earth’s components (Part I of this report), by
undertaking a review of the different natural resources useful to man.
Generally, information is available for most of the energy resources. This is not the
case for non-fuel minerals, where the data is often scarce and inaccurate.
Hence at a first step, the revision was focused on the energy sources of renewable
and non renewable nature. With the most updated information sources, the available energy, potential energy use and current world energy consumption has been
provided. The energy resources studied were: geothermal, nuclear, tidal, solar, wind
and ocean power, as well as biomass, coal, natural gas, oil and unconventional fuels.
For the most important non-fuel minerals, the current production, and the available
reserves, reserve base and world resources has been obtained from the US Geological
Survey. But as opposed to fossil fuels, the abundance of minerals is not important
if these are dispersed throughout the crust. Therefore, the grade of the mineral
deposits is also required for assessing the state of mineral resources. From different
information sources, we were able to estimate world mineral average ore grades.
Part II of this PhD begins in chapter 5 with the description of the thermodynamic
models required for assessing the properties of the earth and its resources.
In order to obtain the exergy of any substance, a reference environment (R.E.)
should be defined. Therefore, the first aim of chapter 5 was to select an appropriate
R.E. for the exergy assessment of the mineral capital on earth.
For that purpose, the different R.E. proposed so far were reviewed. It was stated,
that the best suitable available R.E. for determining the exergy of natural resources
was the one based on Szargut’s criterion. Hence, Szargut’s R.E. [336], later modified
by Ranz [276], was updated and adapted to our requirements with the help of new
geochemical information and the model of continental crust developed in this PhD.
Next, we analyzed the energy involved in the formation processes of a mineral deposit from a defined R.E., and provided the equations required for the exergy calculation of minerals. We stated that the minimum exergy embedded in a mineral has
two components, one based on the chemical composition and the other one on its
concentration or ore grade. The first parameter accounts for the formation of the
mineral from the R.E. The concentration exergy expresses the minimum energy that
nature had to spend to bring the minerals from the concentration in the reference
state to the concentration in the mine. We saw, that the latter shows a negative logarithmic pattern with the grade. This means that as the ore grade of the mine tends
to zero, the exergy of the deposit approaches also zero and the exergy required for
replacing the mine tends to infinity.
334
CONCLUSIONS
In theory, the exergy of fossil fuels can be calculated with the general formulas provided for minerals. However, the complexity of their chemical structure, makes this
task very difficult and special calculation procedures are applied. It was stated that
the chemical exergy of fossil fuels can be in many cases approximated to its HHV. Nevertheless, we used the different formulas developed by Valero and Lozano [369],
since they take into account the conditions of the environment.
Generally, the minimum exergy values are very small, if compared to the real energy
required for the replacement of natural resources to their original state. In order to
account for the inefficiencies of man-made processes, the exergy values are multiplied by the unit exergy replacement costs. These are dimensionless and measure
the number of exergy units needed to obtain one unit of exergy of the product. The
resulting exergy costs represent the exergy required by the given available technology to return a resource into the physical and chemical conditions in which it was
delivered by the ecosystem. As opposed to exergy, exergy costs cannot be considered
as a property of the resource, since unit exergy costs introduce an arbitrary factor
to the calculation. Nevertheless, they can be used as a suitable indicator for assessing the value of non-fuel mineral resources, as they integrate in one parameter,
concentration, composition and also the state of technology.
The chapter ends with the description of the twelve semi-theoretical models for the
estimation of enthalpies and Gibbs free energies of formation, required for the calculation of the chemical exergy of minerals.
In chapter 6, the standard thermodynamic properties of the main constituents of
the outer earth’s spheres have been provided for the first time. That is the standard enthalpy, Gibbs free energy and chemical exergy of more than 330 natural
substances. The enthalpies and Gibbs free energies, have been obtained either from
the literature, or have been calculated with the 12 estimation methods described
in the previous chapter. The exergy of the substances has been calculated with the
chemical exergies of the elements, generated with the R.E. developed in this PhD.
Through the molar fractions of the substances in each layer, determined in part I
of this report, we were able to determine the average thermodynamic properties
of the atmosphere, hydrosphere (divided into seawater, rivers, glacial runoff and
groundwater) and upper continental crust.
It has been stated, that all negative ions in the hydrosphere throw up negative chemical exergies. Additionally, some substances of the continental crust show also
negative exergy values. This is because the reference species of our R.E. are more
stable than the considered substance. This lead us to question the suitability of the
R.E. developed in this PhD, for natural resource accounting. Furthermore, this R.E.
differs substantially from the model of degraded earth that should become.
The degraded earth could be assimilated to a dead planet, with an atmosphere similar to the current one, but with a higher CO2 concentration due to the burning
of fossil fuels, a hydrosphere were all fresh waters are mixed with salt water, and
Synthesis of the PhD
335
a continental crust without fossil fuels or concentrated mineral deposits. Since the
relative quantity of freshwater with respect to saltwater on earth is irrelevant, the hydrosphere of this hypothetical earth has the same composition of the oceans. Something similar occurs with the continental crust, the abundance of mineral deposits
and fossil fuels is negligible when compared to the whole continental crust. Hence,
the composition of the degraded crust can be approximated to the model developed
in this PhD.
From this model of degraded earth firstly defined in this PhD, we could recalculate
the chemical exergy of the elements. We think that the calculation procedures and
even the philosophy for obtaining the chemical exergies of the elements should be
reviewed, since the selection of an appropriate R.E. is a required but not a sufficient
condition. However, this activity remains open for further studies in the future.
Despite of the limitations of the R.E. developed here with Szargut’s methodology, it
still constitutes a tool for obtaining chemical exergies. Since the mass of the earth
and of its spheres is known, we were able to calculate the absolute chemical exergy
of the atmosphere, hydrosphere and upper continental crust: 6, 27 × 103 , 7, 80 × 105
and 1, 21 × 109 Gtoe, respectively. Of course these are very rough numbers, and are
subject to ulterior updates, especially when a more appropriate R.E. is found. But
they are good enough, for providing an order of magnitude of the huge chemical
wealth of our planet.
The second part of chapter 6 has provided an inventory of the most important energy
resources and non-fuel minerals on earth, expressed through a single unit of measure: exergy. We have stated that there is a huge amount of energy sources on
earth, of both renewable and non-renewable nature. There are many energy alternatives that could replace fossil fuels when they become depleted. But obviously the
technology for recovering these alternatives needs to be further developed.
Despite of the enormous chemical exergy of our planet, only 0,01% of that amount
can be considered as available for human use. With current technology, it is impossible to use the chemical exergy of dispersed substances. And only those minerals that
are concentrated, can be considered as resources. In the short run, technological development will allow substitution among minerals, but this can only last whenever
other concentrated mineral stocks are available.
Hence, we have stated that the scarcity problems that man could be facing are based
on the use of materials, rather than on the use energy sources. This is why recycling
and especially, the search of a dematerialized society becomes essential, in order to
be consistent with the sustainability doctrine.
In chapter 7, we have included the time dimension in the exergy evaluation of mineral capital on earth.
We stated that neither mass, nor energy are appropriate indicators for assessing the
degradation of mineral wealth on earth, as they are conservative properties. On the
contrary, in all physical transformations of matter or energy, it is always exergy that
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CONCLUSIONS
is lost. Therefore, any degradation of the mineral capital which can come either
from an alteration in its composition, a decrease of its concentration, or a change in
the reference environment, can be accounted for with exergy.
Starting from the property exergy, we have built a series of indicators which should
measure the scarcity degree of the mineral reserves on earth. The exergy difference
between two situations of the planet has been named as exergy distance D. The
exergy degradation velocity Ḋ, calculated as the exergy distance divided by the period of time considered, should account for the rate of exergy destruction of a certain
resource.
We have also defined the ton of mineral equivalent (t M e), which allows us to assess
the exergy content of a certain deposit before and after extraction, and to compare
the quality of different deposits containing the same mineral, but with a more understandable unit of measure.
Furthermore, we have proposed to calculate the resources to production ratio of
mineral deposits in exergy terms, thereby accounting for the concentration factor as
well.
All indicators described above can be assessed either with minimum exergies, or
with exergy replacement costs. With the latter, the irreversibility factor present in all
real processes is taken into account.
Finally, we have proposed the application of the Hubbert peak model for the assessment of the production peak of non-fuel minerals. It has been stated that the
bell-shape curve is better suited to non-fuel minerals if it is fitted with exergy over
time, instead of mass over time. This way, we would not ignore the concentration
factor, which is very important for the case of solid minerals.
As a first case study, we have obtained the exergy decrease of US copper deposits
throughout the 20th century, and have applied all indicators described above. It
has been estimated, that the global exergy cost associated to the degradation of US
copper deposits in the 20th century was around 700 Mtoe, consumed at an average
exergy degradation velocity of 6,6 Mtoe/year. The R/P ratio of US copper deposits
reveals for year 2000, that reserves would be completely depleted after 56 years.
Moreover, the application of the Hubbert peak in exergy terms, gave as a result, that
the peak was already reached in year 1994. In fact the real peak was attained in
year 1998.
Although the exergy production pattern did not perfectly fit in the bell-shaped curve,
interesting conclusions could be extracted. Generally, production follows asymmetric curves with the decline much sharper than the growth. Hence, the real production
peak is most probably attained after the year predicted by the Hubbert model. During a short period of time, the commodities will be probably over-exploited and the
production points will appear over the bell-shaped curve. The compensation of the
overproduction is the much sharper decrease of production after the peak, instead
of a gradual and steady reduction.
Synthesis of the PhD
337
The second case study was aimed at assessing the exergy loss of a country due to
mineral extraction. Australia has been chosen for the analysis, because it is one of
the most important mineral exporting countries in the world and is the only one
with registered ore grade trends of its main minerals. It has been stated that the
most depleted commodities are in decreasing order: silver, gold, oil, zinc and lead,
with R/P ratios below 35 years. On the contrary, the reserves of copper, iron, natural
gas, nickel and finally coal will last at least for 48, 63, 67, 121 and 153 years,
respectively.
The Hubbert peak model was satisfactorily applied for all commodities, with the
exception of the group lead-zinc-silver, whose production patterns differ from the
rest, as they are extracted together. The study predicts that the maximum production
has been already reached for gold (2006), silver (2005), lead (1997) and oil (1997).
Zinc will reach the peak in 2010, copper in 2021, natural gas in 2025, iron in 2026,
nickel in 2040, and finally coal in 2048.
By the extraction of minerals, Australia has degraded the equivalent of 12,5 Gtoe.
And this degradation is dominated by the extraction of two commodities, coal and
iron. In 2004, the global exergy degradation velocity exceeded 550 Mtoe/year
(around 15% of current world’s oil consumption). And it will probably continue
to increase exponentially at least for 20 to 40 years, until the peaks of iron and coal
are reached.
We additionally estimated the monetary cost of the main mineral reserve’s depletion
suffered in Australia in year 2004. This was carried out, by the conversion of exergy
costs into monetary costs through conventional energy prices. According to the results obtained, Australia would have lost an equivalent of 93,3 billions of $US of its
mineral capital, due to resource extraction only in year 2004. This corresponds to
15,2% of the 2004 Australian GDP.
It should be noted, that the results obtained are estimations and hence the numbers
cannot be taken as final. More reserves could be found in the future, thereby increasing the years until depletion and the peak of production of the commodities.
However, the huge amount of energy and its equivalent in money terms involved in
the degradation of minerals on earth, alerts us about the importance of conserving
our resources.
The last chapter of this PhD, chapter 8, has extrapolated at planetary level, the
analysis of the exergy degradation of mineral reserves carried out for Australia. For
that purpose, many assumptions had to be made at the expense of accuracy loss in
the results. This is because there is an important information gap about current and
historical data of many commodities. Bearing in mind these considerations, we have
been able to give a rough estimate of the mineral loss on earth since the beginning
of the 20th century, the earth’s degradation velocity, the depletion degree of the
reserves and reserve base, the years until depletion of the commodities, and the year
where the peak of production is reached for the main minerals extracted on earth.
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CONCLUSIONS
According to our calculations, the irreversible exergy distance D∗ of the 51 nonfuel mineral commodities analyzed is at least 51 Gtoe, consumed at an average
exergy degradation velocity of 1,3 Gtoe/year in the last decade. This means that with
current technology, the replacement of all depleted non-fuel commodities would
require a third of current world fuel oil reserves (178 Gtoe).
The exergy degradation of the non-fuel mineral reserves on earth is clearly dominated by the extraction of iron, aluminium and to a lesser extent of copper. Nevertheless, the latter three minerals are not the most depleted commodities. We have
stated that the reserves of mercury, silver, gold, tin, arsenic, antimony and lead are
suffering the greatest scarcity problems. On the other hand, the minerals of cesium,
thorium, REE, iodine vanadium, PGM’s, tantalum, aluminium cobalt and niobium
are the least depleted commodities.
For the most extracted non-fuel minerals on earth, we have applied the Hubbert
bell-shaped curve, assuming that only the reserve base published by the USGS [362]
are available for extraction. Accordingly, we have obtained that the peak of production for iron, aluminium and copper is reached in years 2068, 2057 and 2024,
respectively.
With respect to fossil fuels, we have stated that in exergy terms, oil has been the most
consumed fuel, accounting for 42% of the total fuel exergy degradation in the 20th
century (coal and natural gas accounted for 38 and 20%, respectively). The total
fuel’s exergy depleted between 1900 and 2006 is estimated at 382 Gtoe, consumed
at an average exergy degradation velocity of 9 Gtoe/year in the last decade. The
degradation corresponds to 30,5% of total world’s proven fuel reserves in 2006.
Hubbert’s bell shaped curves applied to the exergy production of fossil fuels revealed
that the peak of coal will be reached in year 2060, of natural gas in 2023, and of oil
in 2008. The latter value fits very well with the predictions of other authors, who
estimated that the peak year of world oil will be between 2004 and 2008. Furthermore, it gives sense to the radical increase of oil prices registered recently. The price
of a barrel of crude has been doubled in just one year, surpassing in January 2008,
the psychological barrier of 100 $US.
If we add the exergy loss of fossil fuels to the exergy replacement costs of non-fuel
minerals, we obtain that man has depleted in the 20th century a total of 433 Gtoe.
In 2006, the exergy of mineral deposits was depleted at a degradation velocity of
around 12 Gtoe.
The exergy of mineral reserves can be also affected by the conditions of the environment. With the help of the IPPC’s reference scenarios, we were able to estimate
the exergy loss of fuels due to the increase of GHG emissions in the atmosphere
and the temperature rise. According to our calculations, the exergy of fossil fuels
could decrease to up to 0,40%, if the current CO2 concentration in the atmosphere
doubles.
Synthesis of the PhD
339
Finally, we have made an estimation of the possible depletion degree that mineral
reserves might suffer in the 21st century. For that purpose, we took into account
seven different scenarios.
In the first scenario, we assumed that production of the main mineral commodities
extracted, namely coal, oil, natural gas, iron, aluminium and copper, would follow
the bell-shaped curves calculated before. Accordingly, the global mineral exergy
decrease in the period between 1900 and 2100 would be near 1300 Gtoe. Furthermore, at the end of the 21st century, man would have depleted around 82% of the
reserve base available in 1900.
The other six case studies correspond to the IPPC’s SRES scenarios concerning fossil
fuel consumption. For non-fuel minerals, we assumed that world resources, rather
than the reserve base are available for extraction. Additionally, we took into account
the exergy loss of fuels due to the emission of greenhouse gases to the atmosphere.
All IPCC’s scenarios involve greater degradation degrees of the mineral reserves than
in the case where the Hubbert behavior has been assumed. In the worst case, the
exergy of the mineral resources degraded exceeds 3100 Gtoe. This indicates that
for satisfying the energy consumption assumed in the SRES scenarios, the proven
reserves of coal, oil and natural gas should increase considerably. Although new
discoveries are indeed increasing the reserves of many mineral resources, it remains
to be seen whether the rate of discoveries and the reclassification of mineral reserves
as recoverable are sufficient enough to supply the huge future mineral demand.
In the final reflections of this PhD, we have taken up again the ideas provided by
Meadows et al. [218] in their book “The Limits to Growth”. In view of the results
obtained in this study, we have stated that the message of the Club of Rome was not
as false as many claimed, even if the last decades of the 20th century indicated the
contrary. In fact, we have reached a point in which we might think about stopping
extraction and living only with the already extracted materials. This is recycling,
rather than wasting should be promoted. But nowadays, this practice would be
impossible to undertake, as many economies are sustained by the extraction of resources. Hence, the realistic requirement now is to promote conservation measures
for assuring enough resources for coming generations and a more rational management of the extraction and use of minerals.
We have stated that conventional measures of energy efficiency, renewable energies,
CO2 sequestration, etc. are not enough for achieving sustainability. We believe that
a drastic world reduction and an appropriate management of the massive use of the
extractive mining industry should be also required.
An appropriate management should be based on a solid, transparent and objective
physical accountability system of resources. As final corollary of this PhD, we have
proposed a new accountability tool for the management of the mineral wealth on
earth, based on the Exergoecological principles stated in this study. We have proposed to call this tool “Physical Geonomics”. Obviously, the accounting principles on
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CONCLUSIONS
which it is based will have to be further developed through the learning by doing
technique.
9.3
Scientific contributions of the PhD
The main scientific contributions generated in this PhD are outlined next.
1. This PhD has provided average chemical compositions of the atmosphere, seawater, rivers, lakes, groundwater and glacial-runoff. Furthermore, the main studies
about the chemical composition in terms of elements of the upper continental crust,
have been compiled. Although this information is available in the literature, it is
rather dispersed in a significant number of different publications. The integration of
all these data accomplished in this work, provides a global overview of the geochemistry of our planet with special attention to the substances that compose the earth’s
outer spheres.
2. We have estimated for the first time the composition of the upper continental crust
in terms of minerals, through a procedure that assures chemical coherence between
species and elements.
The model of upper crust developed in this PhD is based on the recent and single
published study concerning the mineralogical composition of the upper crust, by the
Russian geochemist Grigor’ev [127]. He calculated the average contents of 265 rock
forming and accessory minerals in the upper part of the continental crust. Grigor’ev’s
model accounts for 56 elements, as opposed to the 78 included in the chemical
composition of the continental crust of Rudnick and Gao [292].
Since the earth and in particular the upper continental crust can be considered as a
closed system, the mass conservation principle dictates that the elements contained
in the minerals of the crust, must be equal to the chemical composition of the crust,
which is reasonably known. We stated that Grigor’ev’s mineralogical composition,
although comprehensive, does not fulfill the mass balance of the earth. Therefore,
we optimized Grigor’ev model, assuring the mass balance between species and elements. A rigorous analysis of the main minerals of each element was carried out,
and some important substances not included in Grigor’ev’s composition were considered in this model. As a result, we obtained a model of upper continental crust,
consisting of the 307 most abundant minerals. Furthermore, the new model takes
into account all 78 elements included in the chemical composition of Rudnick and
Gao [292].
Although the composition obtained should not be considered as definitive, since
different assumptions had to be made, it constitutes the first step for obtaining a
coherent and comprehensive mineralogical composition of the upper earth’s crust.
3. The full physical characterization of non-fuel mineral resources should be based
on at least two physical features: the tonnage and the grade of the deposits. Only the
Scientific contributions of the PhD
341
US Geological Survey provides world figures of the reserves for the most important
mineral commodities. However, average ore grades of the reserves are unknown.
This study has estimated the weighted average grades of the most important nonfuel mineral reserves. This was mainly accomplished basing on the the compendium
of the descriptive geologic models of Cox and Singer [66], who estimated pre-mining
tonnage’s grades from over 3900 well-characterized deposits all over the world.
With the published information about the reserves by the USGS, and the average ore
grade of the mineral commodities estimated here, we have been able to illustrate for
the first time in global terms, the quantity and quality of the main mineral deposits
on earth.
4. We have stated in this PhD, that the most appropriate of the reference environments published so far for assessing the chemical exergy of natural resources, is the
one based on Szargut’s methodology [336].
Ranz [276] and Rivero [281] made important contributions to the update of
Szargut’s R.E, proposing new reference substances. Nevertheless, it was stated
that the latter studies could be further adapted to our requirements. Consequently,
we have improved Szargut’s R.E., with the help of new geochemical information,
and the model of continental crust developed in this study. The criterion used for
choosing the reference substances of the R.E., which differs from Ranz’s and Rivero’s
models, is based on Szargut’s partial stability. This is, among a group of reasonable
abundant substances, the most stable will be chosen if they also fulfill the “earth
similarity criterion”. If the stability of the possible different reference substances for
a specific element (measured in terms of the formation Gibbs energy) is within a
certain threshold, then the most abundant R.S. will be chosen. If the differences
exceed this threshold, the most stable substance will be taken as R.S. as long as the
“earth similarity criterion” is not contradicted.
The new R.E. generates chemical exergies of the elements that differ on average in
only 1% with respect to the original environment. Nevertheless, when the whole
earth is considered, these small numbers become not so insignificant.
5. In this study a compendium of twelve different estimation methods for calculating
standard enthalpies and Gibbs free energies of substances are provided for the first
time. The calculation methodologies come from different thermochemical studies
published in the literature. The novelty introduced in this PhD is the compilation
of all procedures, the specification of their respective applications within the geochemical framework, and the estimation of the relative errors introduced with each
methodology.
This way, we have provided methodologies with estimation errors comprised between 0% and 10%. The first method is based on the definition of the Gibbs free
energy and therefore does not introduce any error in the calculation. The second
most accurate estimation procedure is Vieillard’s method for hydrated clay minerals
and for phyllosilicates, entailing an error of around ±0, 6%. Five further methods
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CONCLUSIONS
have associated an estimation error of ±1%. These are: the ideal mixing model;
the thermochemical approximations for sulfosalts and complex oxides; the method
of corresponding states; the method of Chermak and Rimstidt for silicate minerals;
the ∆O−2 method; and the ∆O−2 method for different compounds with the same
cations. The following three methods entail a maximum error of ±5%: assuming
∆S r zero; the element substitution method; and the addition method for hydrated
minerals. Finally, the estimation procedure proposed with the greatest associated
error (±10%) is the decomposition method.
6. We have developed for the first time a complete thermochemical data base of the
main substances that compose the atmosphere, hydrosphere and upper continental
crust. For that purpose, the standard Gibbs free energy, enthalpy of formation and
specific exergy of more than 330 natural substances has been provided. The enthalpy
and Gibbs free energy of the compounds have been compiled from the literature, or
have been calculated with the 12 estimation methods described previously. Generally, published thermochemical data is available for those substances with industrial
importance. Consequently, many components of the crust (a total of 125), lacked
of experimental thermochemical values and had to be estimated. From the Gibbs
free energy data and the chemical exergies of the elements generated from the R.E.
developed in this PhD, we were able to obtain the specific chemical exergy of the
considered substances.
7. With the relative abundance of the substances in each of the earth’s outer spheres
obtained in this PhD, and the thermochemical information, we were able to calculate
for the first time, the average Gibbs free energy, enthalpy of formation and chemical
exergy of the atmosphere, hydrosphere and upper continental crust.
Furthermore, since the mass of each layer of the earth is well known, we have obtained the first estimation of the earth’s specific chemical exergy: 1, 22 × 109 Gtoe.
We have stated that the upper continental crust is responsible for most of the exergy
(99,9%), due to its greater mass portion and specific exergy. Although the relative proportion of the atmosphere and hydrosphere is small when compared to the
whole, their chemical exergies are also huge: 6, 27 × 103 Gtoe and 7, 80 × 105 Gtoe,
respectively.
8. This PhD has provided the first model of degraded earth. It has been stated, that
this crepuscular planet is composed of an atmosphere similar to the current one, but
with a CO2 concentration of around 1400 ppm due to the complete burning of fossil
fuel resources. The composition of the hydrosphere is equivalent to that of seawater,
since in the degraded planet all fresh waters are mixed with salt water. We stated
that the freshwater contribution to the final composition of the seas is irrelevant,
due to their small relative volume. Finally, the continental crust of the degraded
planet is one in which no fossil fuels or concentrated mineral deposits exist. Since
the abundance of mineral deposits and fossil fuels is negligible when compared to
the whole continental crust (they account for about 0,001%), the composition of the
degraded crust can be approximated to the model developed in this PhD.
Scientific contributions of the PhD
343
9. This study has obtained an inventory of the most important renewable and nonrenewable resources on earth measured in exergy terms. The main novelty introduced in the inventory is the combined assessment of energy resources with nonfuel minerals. Since exergy is an additive property, we have been able to obtain the
total exergy of the non renewable energy resources, including nuclear, fossil fuels
and non-fuel mineral reserves. Furthermore we could estimate for all renewable resources, the rate of current consumption with respect to the available potential use.
Similarly, for non-renewables, we estimated the resource to production ratio.
We came to the important conclusion that vast amounts of energy resources are
available on earth, especially of renewable nature. However, we are currently using
less than 2% of its potential. On the other hand, we have estimated that the reserves
of concentrated fuel and non fuel minerals, which can be practically used by man,
represent only 0,01% of the chemical exergy of the earth. Furthermore, their global
R/P ratio excluding nuclear materials, is less than 100 years. Hence, humankind is
not facing an energy crisis, as many claim, but rather a material’s scarcity.
10. An important advance entailed in this PhD with respect to the works of Ranz
[276] and Botero [34] has been the inclusion of the time factor in the exergy assessment of natural resources. Consequently, we have been able not only to calculate
what is the exergy reservoir of the earth’s mineral capital, but also at which rate
these resources are being degraded by man. For that purpose, we defined several
indicators, aimed at quantifying the degradation degree of our planet. The exergy
distance (D) accounts for the total exergy degraded by man in a certain period of
time. Its derivative, the exergy degradation velocity ( Ḋ), measures the rate at which
the resources are being depleted. The resource to production ratio (R/P), usually
calculated in mass terms, is proposed to be assessed in exergy terms, thereby taking
also into account the concentration factor of the mineral deposits.
We have additionally defined a new indicator called the ton of mineral equivalent
(t M e), as the exergy content of one ton of mineral in a certain time and place.
The t M e is analogous to the ton of oil equivalent, but it accounts at the same time,
for the tonnage, grade and chemical composition of the considered mineral. This
indicator allows us to assess the exergy content of a certain deposit before and after
extraction, and to compare the quality of different deposits containing the same
mineral, but with a more understandable unit of measure.
11. This PhD has applied for the first time the Hubbert model to non-fuel minerals,
with the aim of estimating the year were the peak of production is reached. It
has been stated that the bell-shape curve is better suited to non-fuel minerals if
it is fitted with exergy over time, instead of mass over time. This way, we take
into account the concentration factor, which is very important for the case of solid
minerals. Consequently, we have developed the required equations for estimating
the Hubbert’s peak for all kinds of minerals in exergy terms.
12. With the help of the indicators previously defined, we were able to analyze the
exergy degradation of US copper during the 20th century, the average exergy degra-
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CONCLUSIONS
dation velocity, the R/P ratio, and the peak of US copper production. Among others,
it has been estimated, that the global exergy cost associated to the degradation of
US copper deposits in the 20th century was around 700 Mtoe, and that the peak of
production was reached in 1994. Since the real peak of production was reached in
1998, we came to the interesting conclusion that in fact production follows rather
an asymmetric curve with the decline much sharper than the growth.
13. This PhD has analyzed for the first time the degradation of the main mineral
deposits in a country, Australia. For that purpose, historical statistics of mineral
consumption and average ore grade trends have been taking into account of fuel
and non-fuel origin. We have been able to estimate the amount of exergy depleted
through mineral extraction, the rate at which that exergy is degraded, and the depletion degree of the commodities.
Furthermore, the application of the Hubbert peak model in exergy terms to all considered minerals has allowed us to establish the “Exergy countdown of the country”.
This is, in a single graphic, we have represented the bell-shaped curves of the production of Australian gold, silver, iron, zinc, lead, nickel, copper, coal, oil and natural
gas. Such a representation would be impossible if the analysis were carried out in
mass terms, as the orders of magnitude are radically different. The exergy countdown diagram provides in a simple and visual way a comparative of the available
reserves of the country, the year were the peak of production is reached, or the depletion degree of the different commodities. Furthermore it allows to predict future
mineral productions and the depletion degree of the commodities.
This way, for instance, we could forecast that in year 2050, about 64% of the total
considered mineral reserves in Australia will be depleted. Particularly, gold will be
depleted at 99,9%, copper at 90,3%, lead at 87%, zinc at 97,3%, nickel at 60,4%,
iron at 80%, coal at 52,4%, oil at 95,9% and natural gas at 85,2%.
The results obtained could lead to spectacular consequences in the future of Australian mining and its economic implications. Furthermore, the exergy countdown
of minerals could constitute a universal and transparent prediction tool for assessing
the degradation degree of non-renewable resources, with dramatic consequences for
the future management of the earth’s physical stock.
14. The physical analysis of the mineral degradation of a country has allowed us to
assess in monetary terms the value associated to mineral extraction. The conversion
of exergy into money is accomplished through conventional energy prices. The resulting monetary value represents the price that a country should pay the earth, for
degrading the resources that are being extracted.
This way, we have provided a first example of the contribution of mineral extraction
in the GDP of a country. Assuming 2004 energy prices, Australia would have lost
through mineral extraction in the same year, the equivalent of 15% of its 2004 GDP.
However, if 2006 or 2008 energy prices are considered, the corresponding monetary
cost associated to the same degradation of mineral capital would increase to 19 and
Scientific contributions of the PhD
345
29% of the Australian 2004 GDP, respectively. This ratifies that the physical cost is a
more objective and robust unit of measure than the monetary cost, which is highly
dependent on external factors. However, the monetary value provides us with an
order of magnitude of the importance of mineral extraction, which is understandable by the majority of the population. This procedure would allow to correct the
economic indices, taking nature into account, as stated by Dieren [75].
15. With the available information about world mineral historic statistics and available reserves, we have carried out the first diagnosis of the state of non-renewable
minerals on earth. This PhD has estimated through the exergy analysis, the degradation degree of the mineral commodities, detecting the ones being degraded at the
highest rates, and the ones facing important scarcity problems.
We have stated that iron and aluminium are the most extracted commodities but not
the most depleted ones, due to their crustal abundance. On the contrary, copper,
which is also being extracted at very high rates, is already suffering scarcity problems, with more than 50% of its world reserves depleted. Other commodities such
as mercury, silver, gold, tin, arsenic, antimony or lead are even more degraded, with
more than 70% of their reserves depleted.
Additionally, we have estimated the peak of production of the main mineral reserves.
Extensive literature is found on the application of the Hubbert peak model for local
and world oil production ([147], [133], [183], [47]). To our knowledge, there is
also at least one study about world coal production [89] and one about natural gas
[24]. The novelty introduced by our work is the application of the Hubbert peak
in exergy terms, what allows not only to obtain the peaking year of the separated
commodities, but also for the whole minerals. Our results fit very well with the
already published studies about the peaking of oil and natural gas, which are reached
in years 2008 and 2023, respectively. This is not the case with our prediction about
the peaking of coal, which is achieved according to this study in 2060. The Energy
Watch Group [89] reported recently that global coal production could peak in 2025.
If all fossil fuels are considered as a single entity, assuming that they are mutually
replaceable, the peaking of production will be reached in year 2029. Moreover the
R/P ratio reveals that there will be enough conventional fossil fuels for 114 years
more.
In addition to the analysis of fossil fuels, we have applied the Hubbert peak model to
world’s iron, copper and aluminium production. This task was never accomplished
before. According to our results, the peak of world iron production will be reached
in year 2068, of aluminium in 2057 and of copper in 2024.
Thanks to the use of the unit of measure exergy, we have been able to provide for the
first time the “the exergy countdown of the main minerals on earth”, representing
in a single graph the Hubbert peak curves for coal, oil, natural gas, iron, copper and
aluminium.
16. This PhD has assessed the loss of fossil fuel exergy due to the greenhouse effect.
This estimation was firstly carried out by Valero and Arauzo [366], for an average
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CONCLUSIONS
fuel composition that should account for the coal, oil and natural gas reserves, and
assuming that CO2 concentration in the atmosphere would double.
In our case, we have considered separately the world resources of each type of coal,
oil and natural gas. Furthermore, we have based our calculations on the IPCC’s SRES
scenarios of future CO2 concentration. According to our results, in the worst case,
the reserves of fossil fuels would be decreased by 0,4%.
17. In addition to the global overview of the state of our mineral resources in the
past and in the present provided before, this PhD has estimated the possible exergy
degradation of minerals throughout the 21st century. This was carried out considering 7 different scenarios.
In the first scenario, the production of minerals was constrained by the current available reserves (i.e. base reserves for non-fuel minerals and proven reserves for fossil
fuels). Accordingly if the 2006 reserves do not increase, at the end of the 21st century man would have depleted around 82% of the reserve base available in 1900.
The remaining 6 scenarios are based on the IPCC’s SRES models, which indirectly
assume a considerable increase of fossil fuel reserves. To the fossil fuel consumption
estimated by the IPCC, we have included as a novelty the possible consumption
of the main non-fuel minerals, namely iron, aluminium and copper, assuming that
the world resources, rather than the reserve base published by the USGS [362] are
available for extraction. This way, we have provided a global perspective of future
mineral production. According to our results, for satisfying the demand of fossil
fuels in the SRES scenarios, the reserves of fossil fuels should double and in some
cases, they should be multiplied by a factor of four. Consequently, we think that the
fuel consumption estimations of the SRES scenarios should be reviewed.
18. This PhD has proposed an accounting tool for the management of the mineral
wealth on earth, including not only fossil fuels, but also the much more complex and
apparently less relevant information of non-fuel minerals. This tool has been named
here as “Physical Geonomics”. It should take into account all physical changes of
the mineral stock on earth, considering both the extracted and recycled materials.
The concrete accounting procedures of Physical Geonomics should be created with
the learning by doing technique. But the principles on which it is based have been
already developed in this PhD and in other exergoecological studies. Physical Geonomics should help to achieve a more rational management of the extraction and
use of minerals.
9.4
Perspectives
This PhD has opened the way for assessing the exergy resources of the earth and
their degradation rate, providing the theoretical tools required for filling the existing
knowledge gap on that field. Obviously it is subject to further improvements and
refinements in future studies, with the help of better statistics, geochemical updates
Perspectives
347
and especially, the conception of a new model of degraded earth. Next, the ideas
and calculations that have arisen throughout the accomplishment of this PhD but
that have remained undone, are discussed.
The first thing that we realized when we embarked on the adventure of assessing
the state of the earth’s resources was that there is a huge information gap about our
mineral capital. It is incredible that in this high developed and ironically named
“knowledge society”, the mineralogical composition of the earth’s continental crust
is unknown. Similarly, data on the available mineral resources or the average ore
grade of the deposits on earth is uncertain.
An efficient management of our resources should be based on global and reliable
information sources. Hence, more data bases, better global statistics, the opening
of global information channels and impartial and serious interpretations of the information are urgently required. But for that purpose, we think that at least the
following data should be compiled worldwide for all mineral commodities:
• Yearly production data.
• Ore grade trends of all mineral deposits.
• Energy, water and raw material consumption.
• Production of waste rock.
• Tonnage and grade of available reserves.
In many cases, this information is hidden or distorted by companies or even governments for their own economic benefits. We cannot forget that the earth and its
resources are a common good. Consequently the state of our planet should be of
global knowledge.
This work has been based on many different and partially fragmented information
sources. Furthermore, the lack of some data needed for the calculations, lead us to
make important assumptions at the expense of accuracy loss in the results.
This way, for instance, the first step for determining the mineralogical composition
of the earth’s crust has been accomplished. Now is the turn of world geologists and
geochemists to update the model with better geochemical information.
Something similar occurs with the exergy assessment of the mineral reserves on
earth and their degradation velocity, carried out in this PhD. With the help of improved statistical data, an update of the results would be expected.
But the results of our study cannot only be improved with better data bases. We have
stated that some calculation procedures could be further developed and adapted to
the requirements of the study.
348
CONCLUSIONS
The main activity that has remain undone and that is crucial for an appropriate natural resource assessment, is a deeper analysis of the entropic earth towards we are
approaching. Moreover, the establishment of a methodology able to calculate the
chemical exergies of the elements from a realistic degraded reference environment
is still missing. In this PhD, we have stated that the R.E. based on Szargut’s criterion gives some problems when calculating the exergy of certain natural substances.
With the help of the model of continental crust developed in this PhD and the well
known average compositions of the atmosphere and seawater, we have been able
to develop the first model of a realistic degraded earth (or entropic planet). However, the selection of an appropriate R.E. is a required but not a sufficient condition.
Hence, the calculation procedures and even the philosophy for obtaining the chemical exergies of the elements should be reviewed. But this activity remains open for
further studies in the future.
In this PhD, we have stated that exergy replacement costs represent a suitable indicator for assessing the value of non-fuel mineral resources, as they integrate in one
parameter, concentration, composition and also the state of technology. Exergy costs
are calculated through unit exergy replacement costs, which are a function of the
state of technology and hence vary with time.
Nevertheless, in this work, we have considered unit exergy replacement costs to
be constant. A more exact determination of the exergy costs of minerals throughout
history would imply changing unit exergy replacement costs, according to the corresponding energy requirements. Generally, historical information of energy of extraction is usually unavailable for most commodities. But future energy requirements
could be assessed with the help of the theory of learning curves. With learning-bydoing, increases in material and energy efficiency increase with cumulative production.
The assessment of unit exergy replacement costs as a function of time remains open
for further studies. However, it should be noted that with appropriate historical and
future unit exergy replacement costs, the Hubbert peak model could be applied to
exergy replacement costs, rather than to minimum exergies, thereby introducing the
technological factor. This would provide a more accurate prediction of the peaking
year of mineral commodities.
Finally, we have stated that a gaussian model applied to the behavior of world mineral production might not be the perfect fit. We have seen, that generally production
follows asymmetric curves with the decline much sharper than the growth. Hence
other types of curves should be analyzed for improving the accuracy of the results.
In summary we have stated that with the required information, the exergoecological
approach used here could constitute a universal and transparent tool for assessing
natural resources. The study could be extended to the loss of fertile soils and consequently to the analysis of the increasing world food demand and the carrying
capacity of the planet. Similarly, it could be also extended to the growing freshwater
requirements in a world with unpredictable climate changes.
Perspectives
349
From the principles of the exergoecological approach, a new physical accounting tool
could be developed. This proposed tool, that we have called “Physical Geonomics”,
would account for all physical changes in the mineral stock on earth. Furthermore,
the conversion of physical into monetary costs with the procedure shown in this
PhD, would allow to keep at the same time the objectivity of physical data and the
more intelligible meaning of monetary units. But the specific accounting principles
of Physical Geonomics need to be developed with the help of the learning by doing
technique. In fact, the materialization of the proposal would require the formation
of international working groups participated by governments, the scientific community, industry and civil society organizations, allowing international agreements on
the methodological principles. Obviously, that would require a firm political will of
extending the current economic criteria.
In short, the Exergoecology method and its corollary, Physical Geonomics, could help
decision makers for an appropriate management of the earth’s physical stock.
Appendix
A
Additional calculations
A.1
Input data. Mineralogical composition of the earth’s
crust
This section shows vectors ε̂i , ξi and matrix R[ j × i] required for the calculation of
the mineralogical composition of the earth’s crust, according to Eq. 3.1. Additionally,
the resulting vector ξ̂i is presented.
Table A.1 shows vector εˆj from Rudnick and Gao [292] and ε j , obtained applying Eq.
3.1 to Grigorev’s mineralogical composition (ξi ) [127]. Table A.2, shows vectors ξi
and the resulting ξ̂i . Finally, tables A.3 and A.4 show the transposed of the coefficient
matrix R [ j × i]. R0 of dimensions [307 × 78] is given rather than R [78 × 307] in
order to make easier its representation. Additionally, the matrix is divided into two
tables because of lack of space.
Table A.1: Vector ε̂ j [78×1], according to Rudnick and Gao [292] and vector
ε j [78 × 1], obtained from Grigor’ev [127]. Values in mole/g
Element
Au
Te
Cs
Na
Rb
Al
Si
O
H
Ge
Y
Sc
j
1
2
3
4
5
6
7
8
9
10
11
12
εˆj
7,62E-12
3,92E-11
3,69E-08
1,19E-03
9,83E-07
3,02E-03
1,10E-02
εj
Element
j
9,14E-13 Ag
40
4,54E-13 Sb
41
0
Bi
42
8,65E-04 Os
43
0
Ir
44
2,60E-03 Ru
45
1,02E-02 Pt
46
2,97E-02 Pd
47
2,11E-03 Ni
48
1,93E-08
0
Rh
49
2,36E-07 1,12E-08 Sm
50
3,11E-07 4,07E-13 Pr
51
Continued on next page . . .
351
εˆj
4,91E-10
3,29E-09
7,66E-10
1,63E-13
1,14E-13
3,36E-12
2,56E-12
4,89E-12
8,01E-07
5,83E-13
3,13E-08
5,04E-08
εj
2,82E-11
4,14E-12
1,07E-11
0
0
0
2,51E-14
4,83E-15
6,94E-09
0
8,08E-12
0
352
ADDITIONAL
CALCULATIONS
Table A.1: Vector ε̂ j [78×1], according to Rudnick and Gao [292] and vector
ε j [78×1], obtained from Grigor’ev [127]. Values in mole/g – continued from
previous page.
Element
Ga
Re
Tb
Dy
Ho
Er
Eu
Tm
Gd
Lu
Hf
Cd
S
Hg
Ca
I
Cr
In
N
K
Se
Tl
W
Fe
Mn
Yb
P
j
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
εˆj
2,51E-07
1,06E-12
4,40E-09
2,40E-08
5,03E-09
1,38E-08
6,58E-09
1,78E-09
2,03E-08
1,77E-09
2,97E-08
8,01E-10
1,93E-05
2,49E-10
6,40E-04
1,10E-08
1,77E-06
4,88E-10
5,93E-06
5,95E-04
1,14E-09
4,40E-09
1,03E-08
7,02E-04
1,41E-05
1,13E-08
2,11E-05
εj
Element
0
Nd
0
Ce
0
Nb
0
Pb
0
Sn
0
Sr
0
C
0
Ba
0
F
0
Ti
0
B
0
Mg
1,91E-05 Li
2,57E-12 Mo
9,64E-04 U
0
Th
1,70E-08 V
0
Ta
0
Cu
6,22E-04 Be
0
Zr
0
Cl
2,52E-10 La
6,41E-04 Zn
1,10E-06 Co
1,38E-09 As
8,15E-06 Br
End of the table
j
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
εˆj
1,87E-07
4,50E-07
1,29E-07
8,20E-08
1,77E-08
3,65E-06
1,66E-04
4,57E-06
2,93E-05
8,01E-05
1,57E-06
6,15E-04
3,46E-06
1,15E-08
1,13E-08
4,53E-08
1,90E-06
4,97E-09
4,41E-07
2,33E-07
2,12E-06
1,04E-05
2,23E-07
1,02E-06
2,94E-07
6,41E-08
2,00E-08
εj
1,09E-08
5,84E-08
1,28E-09
2,34E-09
1,70E-10
9,28E-09
6,85E-04
4,26E-08
5,73E-05
3,13E-05
1,34E-07
9,24E-04
8,15E-11
7,52E-10
2,51E-10
4,68E-09
0
8,87E-11
7,30E-09
1,07E-08
5,46E-07
3,37E-05
2,82E-08
4,75E-09
5,06E-11
1,23E-09
0
Table A.2: Vector ξi [324 × 1], according to Grigor’ev [127] and vector ξ̂i
[324 × 1] obtained in this study
Mineral
Gold
Calaverite
Sylvanite
Pollucite
Dispersed Ge
Thortveitite
Dispersed Sc
Dispersed Ga
Dispersed Re
Dispersed Tb
Dispersed Dy
i
ξi , mole/g
1
9,14E-13
2
0
3
0
4
0
5
0
6
2,71E-13
7
0
8
0
9
0
10
0
11
0
Continued on next page . . .
ξ̂i , mole/g
6,47E-12
5,71E-13
7,62E-13
6,14E-08
1,93E-08
2,71E-13
3,11E-07
2,51E-07
1,06E-12
4,40E-09
2,40E-08
Input data. Mineralogical composition of the earth’s crust
353
Table A.2: Vector ξi [324 × 1], according to Grigor’ev [127] and vector ξ̂i
[324 × 1] obtained in this study – continued from previous page.
Mineral
i
ξi , mole/g
Dispersed Ho
12
0
Dispersed Er
13
0
Dispersed Eu
14
0
Dispersed Tm
15
0
Dispersed Gd
16
0
Dispersed Lu
17
0
Hf in Zr ores
18
0
Greenockite
19
0
Metacinnabar
20
3,27E-14
Cinnabar
21
2,54E-12
Lautarite
22
0
Dietzeite
23
0
In in ZnS
24
0
Nitratine
25
0
Niter
26
0
Se in copper ores
27
0
Dispersed Tl
28
0
Scheelite
29
2,26E-10
Wolframite
30
2,57E-11
Xenotime
31
1,38E-09
Yb in monazite
32
0
Native silver
33
1,11E-11
Samsonite
34
3,04E-14
Tetradymite
35
2,27E-13
Tellurite
36
0
Te in Cu ores
37
0
Iridium
38
0
Osmium
39
0
Polixene/ Tetraferroplatinum
40
1,20E-14
I-Platinum
41
1,54E-14
Cooperite
42
1,61E-14
Pt in Ni-Cu ores
43
0
Pd in Ni-Cu ores
44
0
Rh in Ni-Cu ores
45
0
Ru in Ni-Cu ores
46
0
Fergusonite
47
8,08E-11
Sm in Monazite and Bastnasite
48
0
Pr in Monazite and Bastnasite
49
0
Stibnite
50
1,30E-13
Boulangerite
51
2,12E-15
Sb in galena
52
0
Tin
53
3,71E-12
Cassiterite
54
1,66E-10
Lamprophyllite
55
5,61E-12
Celestine
56
9,26E-09
Strontianite
57
1,35E-11
Tourmaline
58
4,09E-08
Kornerupine
59
9,24E-09
Axinite -Fe
60
1,93E-10
Continued on next page . . .
ξ̂i , mole/g
5,03E-09
1,38E-08
6,58E-09
1,78E-09
2,03E-08
1,77E-09
2,97E-08
8,01E-10
3,17E-12
2,46E-10
2,76E-09
2,76E-09
4,88E-10
2,96E-06
2,96E-06
1,14E-09
4,40E-09
9,28E-09
1,06E-09
1,38E-09
9,95E-09
1,94E-10
5,29E-13
2,27E-13
1,14E-12
3,49E-11
1,50E-13
1,57E-13
1,20E-14
1,54E-14
2,11E-12
1,27E-12
4,25E-12
5,83E-13
3,33E-12
8,08E-11
3,12E-08
5,04E-08
8,10E-10
2,12E-15
1,62E-09
3,87E-10
1,73E-08
5,61E-12
3,65E-06
5,34E-09
4,09E-08
9,24E-09
1,93E-10
354
ADDITIONAL
CALCULATIONS
Table A.2: Vector ξi [324 × 1], according to Grigor’ev [127] and vector ξ̂i
[324 × 1] obtained in this study – continued from previous page.
Mineral
i
ξi , mole/g
Dumortierite
61
1,33E-13
Sassolite (natural boric acid)
62
0
Colemanite
63
0
Kernite
64
0
Ulexite
65
0
Psilomelane
66
5,25E-09
Barite
67
3,13E-08
Witherite
68
0
Bismutite
69
2,16E-12
Bismuthinite
70
1,79E-12
Bismuth
71
2,34E-12
Bismite
72
0
Spodumene
73
5,16E-11
Neptunite
74
2,75E-11
Amblygonite
75
3,24E-12
Staurolite
76
6,28E-07
Chromite
77
8,49E-09
Molybdenite
78
7,50E-10
Powellite
79
2,00E-12
Wulfenite
80
1,09E-13
Uraninite
81
2,44E-10
Blomstrandite/ Betafite
82
2,17E-11
Metatorbenite
83
7,89E-14
Polycrase (Y)
84
1,07E-15
Carnotite
85
0
Beryl
86
2,98E-09
Phenakite
87
3,63E-10
Bertrandite
88
1,68E-10
Helvine/ Helvite
89
7,21E-11
Chrysoberyl
90
0
Gadolinite
91
7,03E-11
Zircon
92
5,46E-07
Naegite
93
1,80E-12
Sirtolite
94
1,04E-10
Eudialyte
95
1,11E-10
Baddeleyite
96
2,52E-11
Lavenite
97
6,68E-12
Rinkolite/ Mosandrite
98
5,80E-14
Wohlerite
99
3,29E-16
Ferrotantalite
100
5,06E-12
Microlite
101
1,44E-13
Delorenzite/ Tanteuxenite
102
1,37E-13
Bastnasite
103
1,46E-08
Loparite - (Ce)
104
6,08E-11
Rhabdophane-Ce
105
1,31E-11
Chevkinite
106
3,48E-12
Monazite (Ce)
107
5,41E-08
Britholite
108
2,75E-11
Thorite
109
1,76E-09
Continued on next page . . .
ξ̂i , mole/g
1,33E-13
3,60E-07
5,99E-08
8,99E-08
7,19E-08
5,78E-07
3,44E-06
3,44E-07
1,19E-10
9,91E-11
1,30E-10
9,91E-11
2,06E-06
1,10E-06
1,29E-07
7,70E-07
8,83E-07
1,14E-08
3,05E-11
1,66E-12
5,60E-09
4,96E-10
1,81E-12
2,46E-14
2,80E-09
5,99E-08
7,31E-09
3,38E-09
1,45E-09
1,80E-08
1,41E-09
2,11E-06
6,98E-12
4,02E-10
4,30E-10
9,75E-11
2,59E-11
2,25E-13
1,27E-15
3,07E-10
8,71E-12
8,33E-12
1,16E-07
4,81E-10
1,03E-10
2,76E-11
4,29E-07
2,18E-10
2,13E-08
Input data. Mineralogical composition of the earth’s crust
355
Table A.2: Vector ξi [324 × 1], according to Grigor’ev [127] and vector ξ̂i
[324 × 1] obtained in this study – continued from previous page.
Mineral
i
ξi , mole/g
Uranium- Thorite
110
2,63E-12
Yttrialite
111
3,83E-10
Thorianite
112
1,29E-12
Dispersed V
113
0
Halite
114
3,25E-05
Apatite
115
2,55E-06
Scapolite
116
2,05E-07
Sylvite
117
8,85E-08
Carnallite
118
4,68E-09
Sodalite
119
6,60E-10
Bischofite
120
1,28E-09
Diadochic Nd
121
0
Sphalerite
122
4,74E-09
Zinc
123
7,19E-12
Smithsonite
124
2,95E-12
Cobaltite
125
5,06E-11
Smaltite
126
0
Linnaeite
127
0
Dispersed Co
128
0
Arsenopyrite
129
5,40E-10
Orpiment
130
3,45E-11
Realgar
131
2,62E-12
Fahlerz Group: Tennantite
132
2,31E-14
Lollingite
133
2,43E-14
Nickeline
134
3,82E-10
Gersdorffite
135
1,81E-10
Arsenolite
136
0
Pentlandite
137
1,09E-09
Garnierite
138
1,73E-10
Violarite
139
2,52E-10
Vaesite
140
6,19E-10
Diadochic Ni
141
0
Galena
142
7,94E-10
Lead
143
8,69E-12
Cerussite
144
2,36E-11
Anglesite
145
1,09E-11
Murmanite
146
2,26E-10
Ferrocolumbite
147
1,95E-10
Pyrochlore
148
2,83E-11
Ilmenorutile
149
2,62E-09
Euxenite
150
1,68E-10
Miserite
151
2,00E-12
Diadochic Ce
152
0
Weinschenkite
153
1,68E-12
Francolite
154
1,70E-07
Vivianite
155
2,59E-12
Biotite
156
1,73E-04
Muscovite
157
4,99E-05
Hydrobiotite
158
1,03E-05
Continued on next page . . .
ξ̂i , mole/g
3,18E-11
4,64E-09
1,56E-11
1,90E-06
1,01E-05
7,91E-07
6,34E-08
2,74E-08
1,45E-09
2,05E-10
3,96E-10
1,01E-07
1,02E-06
1,55E-09
6,36E-10
5,06E-11
5,06E-11
1,69E-11
2,93E-07
2,89E-08
1,85E-09
1,40E-10
1,24E-12
1,30E-12
2,04E-08
9,70E-09
2,80E-10
7,44E-08
1,18E-08
1,72E-08
4,23E-08
3,35E-07
2,79E-08
3,05E-10
8,27E-10
3,82E-10
2,78E-08
2,40E-08
3,47E-09
3,22E-07
1,02E-08
2,00E-12
2,02E-07
1,68E-12
8,68E-08
2,59E-12
8,80E-05
2,54E-05
5,26E-06
356
ADDITIONAL
CALCULATIONS
Table A.2: Vector ξi [324 × 1], according to Grigor’ev [127] and vector ξ̂i
[324 × 1] obtained in this study – continued from previous page.
Mineral
i
ξi , mole/g
Phlogopite
159
3,10E-07
Clinohumite
160
2,16E-08
Fluorite
161
2,82E-07
Humite
162
1,86E-08
Topaz
163
2,52E-08
Chondrodite
164
5,76E-10
Cryolite
165
0
Orthite-Ce/ Allanite
166
7,81E-08
Diadochic Y
167
0
Phosphate rock
168
0
Chalcopyrite
169
5,99E-09
Cubanite
170
2,21E-10
Covellite
171
3,77E-10
Azurite
172
7,25E-11
Bornite
173
4,38E-11
Malachite
174
9,04E-11
Copper
175
6,45E-11
Chalcocite
176
1,13E-11
Chrysocolla
177
5,87E-14
Diodochic Rb
178
0
Lepidolite
179
0
Ankerite
180
1,50E-06
Rhodochrosite
181
1,04E-07
Chloritoid
182
6,81E-09
Pyrolusite
183
6,21E-08
Todorokite
184
1,48E-09
Vernadite
185
2,40E-09
Spessartine
186
5,25E-08
Orthoclase
187
3,52E-04
Hydromuscovite/ Illite
188
6,45E-05
Glaukonite
189
3,04E-06
Lepidomelane/ Annite
190
1,48E-06
Sanidine
191
2,22E-06
Stilpnomelane
192
2,31E-07
Nepheline
193
4,24E-07
Jarosite
194
7,99E-09
Alunite
195
1,83E-13
Calcite
196
3,98E-04
Dolomite
197
3,80E-05
Graphite
198
9,99E-05
Siderite
199
1,04E-05
C org
200
9,16E-05
Aragonite
201
3,80E-06
Magnesite
202
1,78E-06
Dawsonite
203
1,25E-08
Cancrinite
204
2,09E-10
Moissanite
205
1,75E-10
Augite
206
5,12E-05
Ilmenite
207
1,25E-05
Continued on next page . . .
ξ̂i , mole/g
1,58E-07
1,10E-08
1,44E-07
9,46E-09
1,29E-08
2,93E-10
2,36E-09
7,81E-08
2,09E-07
8,99E-06
3,62E-07
1,33E-08
2,27E-08
4,38E-09
2,65E-09
5,46E-09
3,90E-09
6,83E-10
3,54E-12
9,77E-07
1,03E-07
1,31E-05
9,14E-07
5,96E-08
5,44E-07
1,29E-08
2,10E-08
4,60E-07
4,22E-04
7,73E-05
3,65E-06
1,78E-06
2,67E-06
2,77E-07
5,09E-07
9,57E-09
2,20E-13
8,05E-05
7,69E-06
2,02E-05
2,10E-06
1,86E-05
7,69E-07
3,60E-07
2,53E-09
4,23E-11
3,54E-11
1,27E-04
3,10E-05
Input data. Mineralogical composition of the earth’s crust
357
Table A.2: Vector ξi [324 × 1], according to Grigor’ev [127] and vector ξ̂i
[324 × 1] obtained in this study – continued from previous page.
Mineral
i
ξi , mole/g
Titanite
208
9,18E-06
Ulvöspinel
209
2,10E-06
Leucoxene
210
7,65E-07
Rutile
211
1,38E-06
Anatase
212
2,25E-07
Aenigmatite
213
1,28E-09
Perovskite
214
2,06E-09
Brookite
215
2,13E-09
Ramsayite/ Lorenzenite
216
1,46E-10
Kieserite
217
4,84E-08
Crossite
218
6,41E-07
Glaucophane
219
1,91E-08
Omphacite
220
1,18E-08
Clinochlore
221
1,16E-05
Cordierite
222
1,50E-07
Gedrite
223
6,51E-08
Palygorskite
224
4,38E-09
Pumpellyite
225
2,99E-07
Ripidolite
226
3,18E-05
Sapphirine
227
3,22E-08
Spinel
228
1,69E-07
Thuringite/ Chamosite
229
1,81E-06
Vermiculite
230
1,07E-06
Vesubianite/ Idocrase
231
1,90E-07
Actinolite
232
4,45E-06
Diopside
233
2,22E-05
Pigeonite
234
3,14E-06
Tremolite
235
6,77E-07
Anthophyllite
236
4,23E-08
Bronzite
237
2,80E-06
Brucite
238
4,29E-08
Cummingtonite
239
5,89E-06
Enstatite
240
2,19E-06
Forsterite
241
7,82E-07
Hypersthene
242
1,85E-05
Olivine
243
2,41E-06
Periclase
244
5,96E-12
Pleonaste/ Magnesioferrite
245
6,96E-10
Sepiolite
246
8,96E-06
Serpentine/ Clinochrysotile
247
2,60E-06
Talc
248
1,21E-06
Clementite
249
6,02E-08
Pyrite
250
5,25E-06
Anhydrite
251
3,31E-06
Pyrrhotite
252
3,41E-06
Gypsum
253
1,52E-06
Marcasite
254
1,00E-07
Sulphur
255
3,51E-09
Nosean
256
2,47E-09
Continued on next page . . .
ξ̂i , mole/g
2,28E-05
5,21E-06
1,90E-06
3,41E-06
5,59E-07
3,16E-09
5,10E-09
5,27E-09
3,62E-10
3,06E-08
4,06E-07
1,21E-08
7,49E-09
7,34E-06
9,52E-08
4,12E-08
2,77E-09
1,89E-07
2,01E-05
2,04E-08
1,07E-07
1,14E-06
6,78E-07
1,20E-07
2,82E-06
1,40E-05
1,99E-06
4,29E-07
2,68E-08
1,77E-06
2,71E-08
3,73E-06
1,39E-06
4,95E-07
1,17E-05
1,53E-06
3,77E-12
4,41E-10
5,67E-06
1,64E-06
7,68E-07
3,81E-08
2,64E-06
1,66E-06
1,71E-06
7,64E-07
5,03E-08
1,77E-09
1,24E-09
358
ADDITIONAL
CALCULATIONS
Table A.2: Vector ξi [324 × 1], according to Grigor’ev [127] and vector ξ̂i
[324 × 1] obtained in this study – continued from previous page.
Mineral
i
ξi , mole/g
Troilite
257
2,28E-11
Oligoclase
258
5,39E-04
Andesine
259
2,44E-04
Labradorite
260
1,11E-04
Montmorillonite
261
7,83E-06
Hastingsite
262
3,13E-06
Bytownite
263
1,09E-05
Thomsonite
264
7,44E-07
Anorthite
265
1,19E-06
Clinozoisite
266
9,02E-07
Epidote
267
2,25E-05
Grossular
268
5,55E-08
Hornblende (Fe)
269
3,34E-05
Prehnite
270
4,30E-06
Zoisite
271
6,82E-07
Andradite
272
2,36E-08
Hedenbergite
273
3,31E-07
Wollastonite
274
4,91E-08
Albite
275
1,52E-04
Nontronite
276
1,15E-05
Riebeckite
277
1,82E-06
Beidellite
278
4,11E-06
Aegirine
279
3,90E-06
Natrolite
280
2,31E-06
Analcime
281
3,00E-07
Arfvedsonite
282
3,23E-08
Jadeite
283
1,41E-07
Hydrosodalite
284
2,68E-10
Fayalite
285
1,91E-07
Ferrosilite
286
1,89E-06
Goethite
287
9,57E-06
Hematite
288
4,95E-06
Hisingerite
289
5,11E-09
Magnetite
290
2,81E-05
Iotsite
291
1,95E-10
Almandine
292
1,71E-05
Andalusite
293
3,89E-06
Boehmite
294
3,00E-06
Corundum
295
3,73E-07
Diaspore
296
9,17E-06
Distene/ Kyanite
297
1,36E-06
Hydragillite/ Gibbsite
298
5,51E-06
Kaolinite
299
1,01E-05
Pyrophyllite
300
2,78E-08
Sillimanite
301
1,91E-05
Cristobalite
302
2,16E-07
Opal
303
1,49E-04
Quarz
304
3,99E-03
Tridymite
305
1,10E-08
Continued on next page . . .
ξ̂i , mole/g
1,14E-11
4,49E-04
2,03E-04
9,24E-05
6,52E-06
2,60E-06
9,08E-06
6,19E-07
9,90E-07
7,51E-07
1,87E-05
4,62E-08
2,78E-05
3,58E-06
5,68E-07
1,96E-08
2,75E-07
4,08E-08
5,14E-04
3,88E-05
6,14E-06
1,39E-05
1,32E-05
7,82E-06
1,01E-06
1,09E-07
4,78E-07
9,06E-10
2,35E-07
2,32E-06
1,17E-05
6,06E-06
6,27E-09
3,44E-05
2,39E-10
2,09E-05
1,25E-05
9,65E-06
1,20E-06
2,95E-05
4,37E-06
1,77E-05
3,24E-05
8,93E-08
6,15E-05
2,06E-07
1,42E-04
3,81E-03
1,05E-08
Input data. Mineralogical composition of the earth’s crust
359
Table A.2: Vector ξi [324 × 1], according to Grigor’ev [127] and vector ξ̂i
[324 × 1] obtained in this study – continued from previous page.
Mineral
Dispersed Br
Acanthite
Argentite
Stephanite
Pyrargirite
Chlorargirite
Freibergite
Tetrahedrite
Nordite
Hollandite
Jacobsite
Cryptomelane
Manganite
Tephroite
Braunite
Rhodonite
Pennine
Lawsenite
Paragonite
i
ξi , mole/g
306
0
307
1,57E-12
308
2,87E-12
309
4,43E-13
310
1,37E-12
311
3,14E-13
312
2,02E-13
313
3,47E-13
314
7,20E-13
315
7,50E-09
316
1,32E-08
317
3,40E-09
318
1,71E-08
319
6,93E-08
320
4,47E-08
321
2,56E-08
322
4,54E-06
323
7,64E-06
324
1,47E-05
End of the table
ξ̂i , mole/g
2,00E-08
2,74E-11
4,99E-11
7,72E-12
2,38E-11
5,47E-12
3,52E-12
3,47E-13
7,20E-13
2,63E-07
1,15E-07
2,98E-08
1,49E-07
6,07E-07
3,91E-07
2,24E-07
2,87E-06
6,35E-06
4,95E-05
i\ j
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
1
2
1
0
1
2
0,75 2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0,6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0,2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0,1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0,9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2,1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
7
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
10
0
3
3
0
0
4
4
4
0
0
0
0
2
0
0
0
0
0
0
0
9
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0,5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
1,5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17 18 19 20 21 22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table A.3: Matrix R0 [324 × 78] (Part 1)
24
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
25
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
1
0
26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
27
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
33
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
36
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,5
0
0
0
0
0
0
0
0
0
1
0
0
0
37
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,5
0
0
0
1
0
0
0
0
0
0
0
0
0
38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
39
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
40
0
0
0,25
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
360
ADDITIONAL
CALCULATIONS
i\ j
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0,25 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
5,7
2
6,9
0
0
0
0
0
0
0
0
0
0
0
1
0
1
9
0
0
0
0
0
0,1
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
4
0
0
6
3,7
4
3
0
0
0
0
0
0
0
0
0
0
0
2
8
0
4
0
0
0
0
0
0
0
0
0
6
8
9
10
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
17 1
0
4
0
0
3
0
0
31 4
0
18,2 1
0
16 1
0
18 0,5 0
3
3
0
16 10 0
11 8
0
17 16 0
12 4
0
4
0
0
3
0
0
5
0
0
0
0
0
0
0
0
3
0
0
6
0
0
24 0
0
4,25 0,25 0
24 1
0
4
0
0
0
0
0
4
0
0
4
0
0
2
0
0
7
1
0
20 16 0
6
0
0
15 6
0
18 0
0
11
0
0
0
0,1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,5
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17 18 19 20 21 22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
24
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
25
0
0
0
0
0
0
3
11
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
27
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0,2
0
0,1
0
0
Table A.3: Matrix R0 [324 × 78] (Part 1). – continued from previous page.
28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
33
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
36
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0,2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1,5
0
2
1
0
0
0
0
0,1
0
0
0
0
37
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0,5
0
0
0
0
0
0
0
0
0
0
0
0
38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
39
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
40
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Input data. Mineralogical composition of the earth’s crust
361
i\ j
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
4
0
1,1
2
1
0
0,4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
8
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
6
0
0
0
0
0
0
0
0
0
0
7
1
2
3
0
2
1
1
1
8
0
2
4
2
0
0
0
0
0
0
4
0
2,7
1
1
2
0
0
0
0
9
0
0
6
0
0
0
0
0
0
0
0
0
0
8
9
10
4
0
0
9
2
0
12 0
0
4
0
0
10 0
0
4
0
0
4
0
0
4
0
0
23,5 1,5 0
2
0
0
7,9 0,3 0
15,5 0
0
8,7 0,3 0
6
0
0
6,9 0,3 0
6
0,5 0
3
0
0
3
0
0
5
2
0
22 0
0
4
0
0
13,8 1,8 0
4
0
0
4
0
0
7
0
0
2
0
0
0
0
0
0
0
0
12,3 0,33 0
24 0
0
0
0
0
6
12 0
24 0
0
6
12 0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
2
0
0
0
0
0
0
0,5
0
0
0
0,7
0
0
0
0
0
0
0
0
1,5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17 18 19 20 21 22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
24
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
25
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
1
26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
27
0
0
0
0
0
0
0
0
2
0
0,9
3
2
0
1,6
0,2
0,1
0
0
0,8
0
2,9
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
Table A.3: Matrix R0 [324 × 78] (Part 1). – continued from previous page.
28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
33
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
36
0
0
0
0
1
0
0
0
0,7
0
0,5
0
0
0
0
0
0
0
0
2,3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
37
0
0
4
0
0
0
0
0
0,3
0
0,5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
39
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0,5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
40
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
362
ADDITIONAL
CALCULATIONS
i\ j
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1,3
1
0
0
0
2
0
1
2
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
8
0
0
0
0
3
3
2,8
3
4
0
3
1
2
0
3
0
0
0
0
0
0
8
9
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
9
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
22 8
0
6
0
0
6,75 0,75 0
2
0
0
6
0
0
23,5 1,5 0
0
0
0
6
4
0
12 0
0
16 16 0
11,8 1,75 0
11,8 1,8 0
14,8 7,8 0
11 1
0
16,5 0,5 0
0
0
0
12,5 0,5 0
4,9 0,9 0
8,5 0,5 0
0
0
0
13 1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
8
2
0
11 12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,7 0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,1330
1
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17 18 19 20 21 22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
24
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
25
3
4
13
0
0
1
0
8
0
4
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
27
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0,2
2
0
0
5
0
0
0
0,1
0
0
1
0
0
0
0
1,2
0
3
0
0
0
0
Table A.3: Matrix R0 [324 × 78] (Part 1). – continued from previous page.
28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0,3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
33
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
36 37
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4,5 0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0,23 0
0
0
0
0
0
0
0
0
0
0
3
0
0,5 0
0
0
0,6 0
0
0
2,25 0
0
0
1,75 0
0
0
1,25 0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
39 40
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2,63 0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
Input data. Mineralogical composition of the earth’s crust
363
i\ j
173
174
175
176
177
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180
181
182
183
184
185
186
187
188
189
190
191
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193
194
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196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0,25 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0,1 0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
7
8
9
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
10 8
0
0
0
0
1
4
11 1
0
0
6
0
0
0
3
0
4
2
14 4
0
0
2
0
0
0
15 6
0
0
3,4 3,3
2
3
12 0
1
3
8
0
2
3,5 12,4 3,2
0,3 3,8 12 2
0,25 3
12 2
1
3
8
0
0,8 11,1 35 20
1
1
4
0
0
0
14 6
3
0
14 6
0
0
3
0
0
0
6
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
3
0
1
0
5
2
6
6
30 0
0
1
0
0
0,4 1,9 6
0
0
0
3
0
0
1
5
0
0
0
4
0
0
1
5
0
0
0
2
0
0
0
2
0
0
6
20 0
0
0
3
0
0
0
2
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17 18 19 20 21 22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
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0
0
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0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
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0
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0
0
0
0
0
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0
0
0
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0
0
0
0
0
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0
0
0
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0
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0
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0
0
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0
0
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0
0
0
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0
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0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
24
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
25
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
27
0
0
0
0
0
0
0
1
0
0
0
0
0,2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0,9
0
1
0
1
0
0
0
1
0
Table A.3: Matrix R0 [324 × 78] (Part 1). – continued from previous page.
28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32 33
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0,6 0
0,6 0
1
0
0,75 0
0,8 0
0,25 0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
36 37
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0,6 0,1
0
1
1,2 0,2
0
1
0
6
0,2 0,6
0
3
0
0
0,1 0
1,5 0
3,25 0
0
0
8
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0,2 0
1
0
0
0
5
0
0
0
0
0
0
0
5
0
0
0
0
0
38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
39
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
40
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
364
ADDITIONAL
CALCULATIONS
i\ j
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
2
0,4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0,8
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
2
0,3
2
4
4
1
2
2
8
2
1,5
0
5,5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
1,4
7
2
0
8
8
2
3
5
6
4
3
3
2
0
3
4
9
8
2
2
8
8
2
0
8
2
1
2
1
0
0
6
2
4
3
0
0
0
0
0
0
6
0
2,8
8
9
9
0
5
2
24 2
24 2
6
0
18 8
18 0
24 2
15 9
14 4
18 8
20 0
4
0
12 2
14 6
37,5 4,5
24 2
6
0
6
0
24 2
24 2
6
0
2
2
24 2
6
0
4
0
6
0
4
0
1
0
4
0
23 14
9
4
12 2
18 6
0
0
4
0
0
0
6
4
0
0
0
0
28 0
0
0
8
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17 18 19 20 21 22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
24
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
25
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
8
1
1
0
26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
27
0
0
0
0
0,6
0
0
0
0
2
0
0
0
0
0
9,5
2
1
0,1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0,2
Table A.3: Matrix R0 [324 × 78] (Part 1). – continued from previous page.
28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
33
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
36 37
0
0
0
0
1
0
0
0
0,1 0
1,25 0
0
0
0
0
0
0
0
0
1,25 0
0
0
0
0
3,5 0
0
0
0
0
2
0
0
0
0,55 0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0,4 0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
39
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
40
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Input data. Mineralogical composition of the earth’s crust
365
i\ j
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
5
0,6 0
0,5 0
0,17 0
1
0
0,2 0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0,3 0
2
0
0,33 0
1
0
2
0
1
0
3
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
7
1
2,6
1,5 2,5
2,4 3,7
2
6
1,8 2,2
5
5
2
2
3
3
2
3
2
3
0,75 7
2
3
3
3
0
3
0
2
0
1
1
3
0,3 3,7
0
8
2,3 3,7
0
2
2
3
1
2
0
8
0,9 2
6
6
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
3
2
1
1
0
2
0
1
0
2
1
1
0
2
2
2
4
2
1
8
8
8
12
24
8
26
8
13
13
12
24
12
13
12
6
3
8
16
24
12
6
12
7
24
6
26
4
6
2
3
11
4
1
12
5
2
3
2
5
3
9
12
5
9
0
0
2
2
0
12
0
1
1
0
2
2
1
0
0
0
0
10
2
2
0
4
2
2
0
2
0
0
1
0
4
0
0
0
0
1
0
1
0
3
4
2
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17 18 19 20 21 22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
24
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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0
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0
0
0
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0
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0
0
0
0
25
0
0
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0
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0
0
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0
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26
0
0
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0
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0
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0
0
0
0
0
0
0
27 28
0,4 0
0,5 0
0,08 0
2
0
0,8 0
2
0
1
0
2
0
2
0
1
0
2
0
2
0
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table A.3: Matrix R0 [324 × 78] (Part 1). – continued from previous page.
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
33
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
36 37
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
4,25 0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
5
0
0,1 0
0
0
2
0
2
0
1
0
2
0
2
0
3
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
39
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
40
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
366
ADDITIONAL
CALCULATIONS
i\ j
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
i\ j
1
2
3
4
5
6
7
8
9
10
11
12
13
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
41
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
42
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
43
0
0
0
0
0
0
0
0
0
0
0
0
0
44
0
0
0
0
0
0
0
0
0
0
0
0
0
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2,8 0
0,13 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
45
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0,2
0
0
0
0
0
0
2
2
3
46
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
1
1
1
0
0
0
0
0
0
0
0
6
0,1
0
0
0
1
1
1
3
2
3
47
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
3,5
2
2
0
0
0
0
0
0
0
0
17
16
4
16
2
4
12
3
18
10
12
48
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
8
4
2
49
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
50
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
51
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
52
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
53
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
54
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
18 19 20 21
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
End of the table
22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
55
0
0
0
0
0
0
0
0
0
0
0
0
0
56 57 58 59 60 61
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
62
0
0
0
0
0
0
0
0
0
0
0
0
0
Table A.4: Matrix R0 [324 × 78] (Part 2)
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
63
0
0
0
0
0
0
0
0
0
0
0
0
0
24
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
64
0
0
0
0
0
0
0
0
0
0
0
0
0
25
0
0
0
0
0
1
1
4
3
0
13
13
0
0
0
0
0
0
0
0
0
0
0
65
0
0
0
0
0
0
0
0
0
0
0
0
0
26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
66
0
0
0
0
0
0
0
0
0
0
0
0
0
27
0
0
0
0
0
0
0
0
0
0
0
0
0,5
0
0
0
0
0
0
0
0
1
0
Table A.3: Matrix R0 [324 × 78] (Part 1). – continued from previous page.
67
0
0
0
0
0
0
0
0
0
0
0
0
0
28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
68
0
0
0
0
0
0
0
0
0
0
0
0
0
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
69
0
0
0
0
0
0
0
0
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
70
0
0
0
0
0
0
0
0
0
0
0
0
0
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
71
0
0
0
0
0
0
0
0
0
0
0
0
0
32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
72
0
0
0
0
0
0
0
0
0
0
0
0
0
33
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
73
0
0
0
0
0
0
0
0
0
0
0
0
0
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
74
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
75
0
0
0
0
0
0
0
0
0
0
0
0
0
76
0
0
0
0
0
0
0
0
0
0
0
0
0
36 37
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1,2 0
3
0
0
0,2
1,3 6,5
1,8 1,1
0
8
0
1
0
2
0
7
0
1
1,25 0
0
0
0
0
77
0
0
0
0
0
0
0
0
0
0
0
0
0
38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
78
0
0
0
0
0
0
0
0
0
0
0
0
0
39
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
40
0
0
0
0
0
2
2
5
3
1
7,2
0
0
0
0
0
0
0
0
0
0
0
0
Input data. Mineralogical composition of the earth’s crust
367
i\ j
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
42
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
43 44 45
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,3 0,5 0,2
0,75 0,25 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0,6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
47
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
49
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,1
1
0
0
0
0
0
0
0
0
51
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
52
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,4
0
0
0
0
0
0
0
0
0
53
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,4
0
0
0
0
0
0
0
0
0
54
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
56 57 58 59 60 61
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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0
0
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0
0
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0
0
0
0
0
0
0
0
0
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0
0
0
0
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0
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0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
3
0
1
0
0
0
0
Continued on next page . . .
62
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
63
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
64
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
65
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
66
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table A.4: Matrix R0 [324 × 78] (Part 2). – continued from previous page.
67
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
68
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
69
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
70
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
71
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
72
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
73
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
74
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
75
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
76
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
77
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
78
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
368
ADDITIONAL
CALCULATIONS
i\ j
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
42
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
43
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
44
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
45
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
49
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
51
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
52
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
53
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,1
0
0
0
0
0
0
0
0
0
0
0
0
0
1,5
0
54
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,9
0
0,6
0
0
0
0
0
0
0
0
0
0
0
0
0,1
0,5
0,4
55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
56 57 58 59 60 61
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0,75 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,8
0
0
0
0
0
0
0
0
0
0
0
1,2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,1 0,1
0
0
0
0
3,5 0,4
0
0
0
0
0,3 0
Continued on next page . . .
62
0
3
1,2
1
1
1
6
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
63
0
0
3,5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
64 65
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0,75 0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
66
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0,3
2
0,1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table A.4: Matrix R0 [324 × 78] (Part 2). – continued from previous page.
67
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
68
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
69
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,5
0
0,2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
70
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
71
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
4
3
1
2
0
0
0
0
0
0
0
0
72
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0,8
0,1
0,6
73
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,5
0
0
0
0
74
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
75
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
76
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
77
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
78
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Input data. Mineralogical composition of the earth’s crust
369
i\ j
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
42
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
43
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
44
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
45
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4,5
2
2
1
1
0
49
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
51
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
52
0
0
0
0
0
0
0
0,2
0,2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
53 54
0
0
0
0
0,1 0,3
0
0
0,22 0,2
0,75 0
1,7 0
0,5 0
0,9 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
56 57 58 59 60 61 62
0
0
0
0
0
0
0
0
0
0
0
0,1 0
0
0
0
0
0
0
0,05 0
0
0
1
0
1
0
0
0
0
0
0
0
0,8 0
0
0
0
0
0
0
0
0
0
0
0
0
2,5 0
0
0
0
0
0
0
0
0
0
0
0
0,2 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,33 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
63
0
0
0
0
0
0
0,5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
64
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
65
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
66
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table A.4: Matrix R0 [324 × 78] (Part 2). – continued from previous page.
67 68
0
0
0
0
0
0
0
0
0
0
0
0
0,1 0
0,05 0
0,6 0
1
0
1
0
0,5 0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
69
2
2
1,4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
70
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
71
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
72
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
73 74 75
0
0
0
0
0
0
0
0
0
0
1
0
0
0,11 0
0
0,25 0
0
1,4 0
0
0,25 0
0
0,4 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0,33 0
0
1
0
0
1
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
76
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
77
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
4
4
2
1
1
2
0
0
0
0
0
0
78
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
370
ADDITIONAL
CALCULATIONS
i\ j
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
42
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
43
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
44
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
45
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
49
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
51
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
52
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
53
0
0
0
0
0
0
0
0,1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0,4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
54 55
0
1
0
1
0
1
0,4 0
2
0
2
0
0,15 0
1,4 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
56 57 58 59 60 61 62
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3,6 0
0
0
0
0
0
0
0
0
0
0
0
0,25 0
0
0
0
0
0
0
0,7 0
0
0
0
0
0
0,05 0
0
0
0
0
0,5 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,5 0
1,11 0
0
0
0
0
0
0
0
0
0
0
0
0
0,25 0
0
0
0
0
0
0,2 0
0
0
0
0
0
0,2 0
0
0
0
0
0
1
0
0
0
0
0
0
1,5 0
0
0
0
0
0
2
0
0
0
0
0
0
1,5 0
0
0
0
0
0
1,1 0
0
0
0
0
0
1,5 0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
63 64
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2,5 0
0
0
2,3 0
3
0
6,75 0
0
0
5,25 0
0
0
3,75 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0,3 0
0
0
0,6 0
0
0
0
0
0
0
65
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
66
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table A.4: Matrix R0 [324 × 78] (Part 2). – continued from previous page.
67
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
68
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
69
0
0
0
0
0
0
0
0,4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
70
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
5
2
1
2
2
0
0
0
0
0
0
0
0
71
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
72
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
73
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
74
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
75
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
76
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
77
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
78
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Input data. Mineralogical composition of the earth’s crust
371
i\ j
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41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
42
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
43
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
44
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
45
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
49
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
51
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
52
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
53
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
54
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
56 57 58 59 60 61
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0,1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
62
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
63 64
0
0
0
0
0,4 0
0,4 0
0,5 0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0,9 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0,6 0
3,75 0
2
0
5
0
1
0
1
0
3,75 0
4
0
1
0
65
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
66
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table A.4: Matrix R0 [324 × 78] (Part 2). – continued from previous page.
67
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
68
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
69
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
70
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
71
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
72
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
73
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
74
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
75
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
76
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
77
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
78
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
372
ADDITIONAL
CALCULATIONS
i\ j
229
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271
41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
42
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
43
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
44
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
45
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
49
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
51
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
52
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
53
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
54
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
56 57 58 59 60 61
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Continued on next page . . .
62
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
63 64
2
0
3
0
1
0
3
0
1
0
1,35 0
5
0
7
0
1
0
1
0
7
0
2
0
2
0
1
0
1,6 0
1
0
1
0
4
0
3
0
3
0
1,5 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
65
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
66
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table A.4: Matrix R0 [324 × 78] (Part 2). – continued from previous page.
67
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
68
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
69
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
70
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
71
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
72
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
73
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
74
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
75
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
76
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
77
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
78
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Input data. Mineralogical composition of the earth’s crust
373
i\ j
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
4
0
42
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
43
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
44
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
45
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
49
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
51
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
52
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
53
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,6
54
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
55
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
56 57 58 59 60 61
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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0
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0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,5 0
0
0
0
Continued on next page . . .
62
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
63
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,4
64
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
65
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
66
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Table A.4: Matrix R0 [324 × 78] (Part 2). – continued from previous page.
67
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
68
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
69
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
70
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3,6
9
0
71
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
72
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
73
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
74 75
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,33 0,6
76
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
77
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
78
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
374
ADDITIONAL
CALCULATIONS
i\ j
315
316
317
318
319
320
321
322
323
324
41
0
0
0
0
0
0
0
0
0
0
42
0
0
0
0
0
0
0
0
0
0
43
0
0
0
0
0
0
0
0
0
0
44
0
0
0
0
0
0
0
0
0
0
45
0
0
0
0
0
0
0
0
0
0
46
0
0
0
0
0
0
0
0
0
0
47
0
0
0
0
0
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
0
49
0
0
0
0
0
0
0
0
0
0
50
0
0
0
0
0
0
0
0
0
0
51
0
0
0
0
0
0
0
0
0
0
52
0
0
0
0
0
0
0
0
0
0
53
0
0
0
0
0
0
0
0
0
0
54
0
0
0
0
0
0
0
0
0
0
55
0,2
0
0
0
0
0
0
0
0
0
56
0
0
0
0
0
0
0
0
0
0
57 58 59 60
0
0
0,8 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
End of the table
61
0
0
0
0
0
0
0
0
0
0
62
0
0
0
0
0
0
0
0
0
0
63 64
0
0
0,1 0
0
0
0
0
0
0
0
0
0
0
3,75 0
0
0
0
0
65
0
0
0
0
0
0
0
0
0
0
66
0
0
0
0
0
0
0
0
0
0
Table A.4: Matrix R0 [324 × 78] (Part 2). – continued from previous page.
67
0
0
0
0
0
0
0
0
0
0
68
0
0
0
0
0
0
0
0
0
0
69
0
0
0
0
0
0
0
0
0
0
70
0
0
0
0
0
0
0
0
0
0
71
0
0
0
0
0
0
0
0
0
0
72
0
0
0
0
0
0
0
0
0
0
73
0
0
0
0
0
0
0
0
0
0
74
0
0
0
0
0
0
0
0
0
0
75
0
0
0
0
0
0
0
0
0
0
76
0
0
0
0
0
0
0
0
0
0
77
0
0
0
0
0
0
0
0
0
0
78
0
0
0
0
0
0
0
0
0
0
Input data. Mineralogical composition of the earth’s crust
375
376
A.2
ADDITIONAL
CALCULATIONS
Calculation of average mineral ore grades
The average grade of the different mineral deposits analyzed by Cox and Singer [66]
is calculated with Eq. 4.4, taking into account the tonnage of each model and the
number of deposits (No. dep.) containing the mineral under consideration. Tables
A.5 through A.12 show the mean average grade and tonnage of each deposit type.
Table 4.9 in chapter 4 shows the final average grade obtained.
Table A.5. Summary statistics of grade-tonnage models-1. After [66]
Deposit type
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Mean
No.dep.
Placer Au-PGE
1,07
65
0,03
0,20
16
65
Mean
No.dep.
Placer PGE-Au
0,13
83
1,50
1588,55
13
83
8,38
10
82,22
21
0,03
23
Mean
No.dep.
Shoreline Placer
87,50
61
0,03
29
0,27
52
1,27
0,21
0,23
61
50
24
Calculation of average mineral ore grades
377
Table A.6. Summary statistics of grade-tonnage models-2. After [66]
Deposit type
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Mean
No.dep.
Komatiite Ni-Cu
1,72
31
Mean
No.dep. Mean
No.dep.
Dunitic Ni-Cu
Synorg-synvolc. Ni-Cu
28,25
22
2,00
32
0,06
1,51
0,14
8
31
21
0,03
0,99
0,04
3
22
12
0,05
0,76
0,48
3
32
29
338,61
201,05
11
5
139,19
5
98,86
31,05
3
2
71,61
9
15,07
5
0,04
10
0,02
5
0,11
3
Major podiform Cu
0,02
174
Carbonatite
59,84
20
0,10
5
0,64
44,03
7,291
3,48
14,32
13,06
78,34
220,80
16
12
14
9
7
W Skarn
1,04
28
Mean
No.dep.
Minor podiform Cr
0,00
435
42,13
435
4,70
30,83
8,11
65,31
189,67
31
33
69
38
29
Sn Scarn
5,94
4
20
0,66
28
0,31
4
378
ADDITIONAL
CALCULATIONS
Table A.7. Summary statistics of grade-tonnage models-3. After [66]
Deposit type
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Mean
No.dep.
Replacement Sn
5,25
6
Mean
No.dep. Mean
No.dep.
W veins
Sn Veins
0,56
16
0,24
43
0,91
0,80
Mean
No.dep.
Sn Greisen
7,20
10
16
6
1,27
43
0,28
10
Climax Mo
201,84 9
Porphyry Cu
144,21 208
Porphyry Cu skarn-related
79,62
18
Cu skarn
0,56
64
0,54
0,01
208
103
0,98
0,02
18
4
1,69
64
0,19
1,65
0,12
76
81
4,78
0,33
9
6
21,43
1,78
15
16
9
Calculation of average mineral ore grades
379
Table A.8. Summary statistics of grade-tonnage models-4. After [66]
Deposit type
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Mean
No.dep.
Zn-Pb skarn
1,42
34
Mean
No.dep.
Fe skarn deposits
7,21
168
49,61
Mean
No.dep.
Polymet. replacement
1,82
52
Mean
No.dep.
Replacement Mn
0,02
37
0,03
3
32,54
37
0,88
4
168
0,46
17
0,23
35
114,55
0,45
5,91
22
7
0,2709
193,20
0,71
3,92
45
35
51
3,22
30
5,06
52
Porphyry Cu-Au
101,16
40
Porphyry Cu-Mo
508,16
16
Porphyry Mo, Low -F
94,19
33
0,50
0,00
40
20
0,42
0,02
16
16
0,09
1,59
0,38
27
40
1,22
0,01
16
16
Polymetallic vein
0,01
75
0,19
33
866,96
0,62
2,78
74
54
60
8,97
75
33
380
ADDITIONAL
CALCULATIONS
Table A.9. Summary statistics of grade-tonnage models-5. After [66]
Deposit type
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Mean
No.dep.
Cyprus massive sulfide
1,27
49
Mean
No.dep.
Besshi massive sulfide
0,22
44
Mean
No.dep.
Volcanogenic Mn
0,05
93
0,09
8
38,80
93
Mean
No.dep.
Creede epith. vein
1,42
27
1,60
49
1,46
44
0,30
19
12,85
0,91
0,79
15
15
16
7,86
0,34
0,56
14
14
6
125,60
2,12
1,88
27
23
26
0,05
3
2,55
24
Comstock epith. vein
0,77
41
Sado epith. vein
0,30
20
Epith. quartz-alunite Au
1,58
8
Volcanogenic U
0,34
21
0,12
0,02
18
0,19
9
0,24
5
114,82
7,46
0,03
41
41
3
37,93
6,86
0,25
20
18
1
17,82
7,81
8
8
0,01
19
0,00
2
21
Calculation of average mineral ore grades
381
Table A.10. Summary statistics of grade-tonnage models-6. After [66]
Deposit type
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Mean
No.dep.
Epithermal Mn
0,02
59
30,59
Mean
No.dep.
Rhyolite-hosted Sn
0,00
132
Mean
No.dep.
Volcan.-hosted magnetite
39,99
39
0,40
36
53,72
39
Mean
No.dep.
Carbonate-hosted Au-Ag
5,08
35
59
21,88
2,57
0,39
Hot-spring Hg
0,01
20
0,34
20
132
Silica-carbonate Hg
0,03
28
0,39
5
34
Sb veins
0,00
81
Disseminated Sb
0,09
23
36,39
5,14
8
9
1,20
0,30
1
2
34,67
81
3,55
23
28
382
ADDITIONAL
CALCULATIONS
Table A.11. Summary statistics of grade-tonnage models-7. After [66]
Deposit type
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Mean
No.dep.
Kuroko mass. sulfide
1,50
432
Mean
No.dep.
Algoma and Sup. Fe
165,20
66
0,06
47
50,83
66
Mean
No.dep.
Sandstone-hosted Pb-Zn
5,36
20
1,26
432
28,77
0,78
2,81
284
238
330
11,22
9
0,59
14
0,75
184
2,15
20
Sedim. Exhal. Zn-Pb
14,69
45
Bedded barite
1,82
25
83,02
Missouri / Appalach. Pb-Zn
34,83
20
Mean
No.dep.
Sedim.-hosted Cu
21,93
57
0,24
10
2,15
57
Sedimentary Mn
7,28
39
25
0,19
11
43,32
37
4,67
10
5,65
45
4,05
20
2,78
45
1,23
16
0,12
13
31,38
39
Calculation of average mineral ore grades
383
Table A.12. Summary statistics of grade-tonnage models-8. After [66]
Deposit type
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Tonnage (Mton)
RE2O5 (%)
Monazite (%)
U3O8 (%)
Zircon (% ZrO2)
Nb2O5 (%)
Barite (%)
Al2O3(%)
P (%)
P2O5 (%)
Ilmenite (% TiO2)
Rutile (% TiO2)
Leucocite (% TiO2)
Cr2O3 (%)
Mn (%)
Fe (%)
Co (%)
Ni (%)
Cu (%)
Mo (%)
WO3 (%)
Pd (ppb)
Pt (ppb)
Rh (ppb)
Ir (ppb)
Ru (ppb)
Os (ppb)
Ag (g/t)
Au (g/t)
Zn (%)
Hg (%)
Sn (%)
Pb (%)
Sb (%)
Mean
No.dep.
Phosphate, upwell.
331,13
60
Mean
No.dep.
Phosphate, warm current
400,87
18
23,96
24,16
60
Unconformity U-Au
0,23
36
0,52
Mean
No.dep.
Low-sulfide Au-quartz veins
0,03
313
Mean
No.dep.
Homestake Au
0,94
116
4,97
15,96
1,62
9,22
18
Lateritic Ni
44,16
71
39
313
52
116
Laterite type bauxite
25,18
122
Karst type bauxite
23,23
41
44,97
49,18
36
0,07
1,36
12
71
122
41
384
ADDITIONAL
A.3
CALCULATIONS
Calculation of the R.E.
Tables A.13, A.14 and A.15, show the variables required for the calculation of the
chemical exergy of the elements and the results, according to the assumptions described in section 5.2.3 and the model of the earth’s crust developed in this PhD
(chapter 3) for gaseous, liquid and solid reference substances, respectively.
Table A.13. Chemical exergies of the elements for gaseous reference substances
Element
R.S.
State
Pi0 (kPa)
Ar
C
H2
He
Kr
N2
Ne
O2
Xe
Ar
CO2
H2 O
He
Kr
N2
Ne
O2
Xe
g
g
g
g
g
g
g
g
g
9,06E-03
3,35E-04
2,20E-02
4,85E-06
9,70E-07
7,58E-01
1,77E-05
2,04E-01
8,70E-08
bch,R.S.
(kJ/mole)
11,7
19,9
9,5
30,4
34,4
0,7
27,2
4,0
40,3
∆G f i
(kJ/mole)
0,0
-394,4
-228,6
0,0
0,0
0,0
0,0
0,0
0,0
bch j
(kJ/mole)
11,7
410,3
236,1
30,4
34,4
0,7
27,2
4,0
40,3
Table A.14: Chemical exergies of the elements for aqueous reference substances
Element
R.S.
State
z+
Ag
As
B
Bi
Br2
Cd
C l2
Cs
Cu
Hg
I2
K
Li
Mo
Na
Ni
P
Pb
Rb
S
Se
W
Zn
Ag C l2−
HAsO4−2
B(OH)3
BiO+
Br −
C d C l2
C l−
Cs+
Cu+2
H g C l4−2
IO3−
K+
Li +
M oO4−2
N a+
N i +2
H PO4−2
P bC l2
Rb+
SO4−2
SeO4−2
W O4−2
Z n+2
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
-1
-2
0
1
-1
0
-1
1
2
-2
-1
1
1
-2
1
2
-2
0
1
-2
-2
-2
2
γi
0,6
0,138
1
0,52
0,73
1
0,63
0,6
0,2
0,1
0,6
0,62
0,68
0,1
0,65
0,2
0,1
1
0,6
0,12
0,1
0,1
0,2
End of the table
mi
(mole/kg)
2,70E-09
2,10E-08
3,25E-04
1,00E-10
8,70E-04
6,90E-11
5,66E-01
2,30E-09
7,30E-10
3,40E-10
5,20E-07
1,06E-02
2,50E-05
1,10E-07
4,86E-01
1,20E-07
4,90E-07
4,20E-11
1,40E-06
2,93E-02
1,20E-09
5,60E-10
1,70E-08
∆G f i
-215,5
-714,7
-968,8
-146,4
-104,0
-359,4
-131,3
-282,2
65,5
-446,9
-128,0
-282,4
-294,0
-836,4
-262,1
-45,6
-1089,3
-297,2
-282,4
-744,6
-441,4
-920,5
-147,3
bch j
(kJ/mole)
69,7
494,1
628,6
274,8
101,1
293,2
124,2
404,5
134,0
114,8
175,0
366,5
392,9
730,5
336,6
232,5
861,6
232,2
388,8
607,3
346,7
827,7
339,0
Calculation of the R.E.
385
Table A.15: Chemical exergies of the elements for solid reference substances
Al
Au
Ba
Be
Ca
Ce
Co
Cr
Dy
Er
Eu
F2
εj
(mole/g)
3,02E-03
7,62E-12
4,57E-06
2,33E-07
6,40E-04
4,50E-07
2,94E-07
1,77E-06
2,40E-08
1,38E-08
6,58E-09
2,93E-05
Fe
Ga
Gd
Ge
Hf
Ho
In
Ir
La
Lu
Mg
7,02E-04
2,51E-07
2,03E-08
1,93E-08
2,97E-08
5,03E-09
4,88E-10
1,14E-13
2,23E-07
1,77E-09
6,15E-04
Mn
Nb
Nd
Os
Pd
Pr
Pt
Pu
Ra
Re
Rh
Ru
Sb
Sc
Si
Sm
Sn
Sr
Ta
Tb
Te
1,41E-05
1,29E-07
1,87E-07
1,63E-13
4,89E-12
5,04E-08
2,56E-12
6,20E-20
4,40E-15
1,06E-12
5,83E-13
3,36E-12
3,29E-09
3,11E-07
1,10E-02
3,13E-08
1,77E-08
3,65E-06
4,97E-09
4,40E-09
3,92E-11
Element
1,60E-03
9,63E-10
4,66E-04
1,09E-06
1,27E-02
1,41E-06
2,31E-07
1,39E-06
7,54E-08
4,33E-08
2,07E-08
2,30E-05
bch,R.S.
(kJ/mole)
16,0
51,5
19,0
34,0
10,8
33,4
37,9
33,4
40,7
42,0
43,9
26,5
∆G f i
(kJ/mole)
-2441,0
0,0
-1361,9
-2033,3
-1129,0
-1024,8
-1032,6
-1882,3
-1294,3
-1291,0
-1320,1
-12985,3
bch j
(kJ/mole)
794,3
51,5
765,5
602,6
723,8
1054,2
308,9
584,4
974,9
973,0
1003,9
556,1
5,95E-04
3,94E-07
6,37E-08
1,52E-07
2,33E-07
1,58E-08
1,92E-09
8,95E-14
7,00E-07
5,56E-09
1,15E-04
18,4
36,6
41,1
38,9
37,9
44,5
49,8
74,5
35,1
47,1
22,5
-742,2
-998,6
-1288,9
-521,5
-1027,4
-1294,8
-830,9
-185,6
-1319,2
-1259,6
-5543,0
376,8
514,6
969,9
556,5
1061,3
979,3
437,4
256,1
994,3
946,6
629,6
24,1
39,9
35,6
73,6
65,2
38,8
66,8
108,5
76,8
69,0
72,2
66,1
54,7
33,8
1,4
40,0
31,9
34,8
48,0
44,9
60,0
-465,2
-1766,4
-1294,3
-305,1
-82,5
-1285,1
-83,7
-995,1
-1364,2
-1067,6
-299,8
-253,1
-829,3
-1819,7
-856,7
-1314,0
-519,6
-1140,1
-1911,6
-1314,2
-270,3
484,6
900,2
969,8
370,8
145,7
963,8
146,5
1099,7
825,8
561,3
183,0
315,2
437,1
923,8
854,2
993,9
547,6
758,8
974,8
999,0
326,4
R.S.
State
cj
xi
Al2 SiO5
Au
BaSO4
Be2 SiO4
C aCO3
C eO2
C oFe2 O4
K2 C r2 O7
D y(OH)3
E r(OH)3
Eu(OH)3
C aF2 C a9
(PO4 )6
Fe2 O3
Ga2 O3
Gd(OH)3
GeO2
H f O2
H o(OH)3
I n2 O3
I rO2
La(OH)3
Lu(OH)3
M g3 Si4 O10
(OH)2
M nO2
N b2 O3
N d(OH)3
OsO4
P dO
P r(OH)3
P tO2
PuO2
RaSO4
Re2 O7
Rh2 O3
RuO2
S b2 O5
Sc2 O3
SiO2
Sm(OH)3
SnO2
S r CO3
Ta2 O5
T b(OH)3
TeO2
s
s
s
s
s
s
s
s
s
s
s
s
6,75E-03
8,05E-01
6,49E-01
5,95E-02
1,26E-01
0,02
0,005
0,01
0,02
0,02
0,02
0,01
s
s
s
s
s
s
s
s
s
s
s
1,08E-02
0,02
0,02
0,05
0,05
0,02
0,05
0,005
0,02
0,02
3,56E-03
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
s
2,66E-02
5,89E-05
0,01
1,01E-07
0,02
5,87E-07
0,005
1,28E-13
0,005
3,84E-12
0,02
1,58E-07
0,005
2,01E-12
0,01
9,73E-20
0,05
3,45E-14
0,01
8,32E-13
0,005
2,29E-13
0,005
2,64E-12
0,001
2,58E-10
0,05
1,22E-06
3,33E-01
5,75E-01
0,02
9,83E-08
9,27E-01
2,58E-06
1,39E-03
7,97E-07
0,01
3,90E-09
0,02
1,38E-08
0,005
3,08E-11
Continued on next page . . .
386
ADDITIONAL
CALCULATIONS
Table A.15: Chemical exergies of the elements for solid reference substances
– continued from previous page.
Element
Th
Ti
Tl
Tm
U
V
Y
Yb
Zr
A.4
εj
(mole/g)
4,53E-08
8,01E-05
4,40E-09
1,78E-09
1,13E-08
1,90E-06
2,36E-07
1,13E-08
2,12E-06
R.S.
State
cj
T hO2
T iO2
T l2 O4
T m(OH)3
UO3 · H2 O
V2 O5
Y (OH)3
Y b(OH)3
Z rSiO4
s
s
s
s
s
s
s
s
s
3,27E-04
2,33E-09
4,15E-02
5,22E-04
0,01
3,45E-09
0,02
5,59E-09
0,01
1,77E-08
0,01
1,49E-06
0,02
7,41E-07
0,02
3,55E-08
9,45E-01
3,15E-04
End of the table
xi
bch,R.S.
(kJ/mole)
49,3
18,7
48,3
47,1
44,2
33,3
35,0
42,5
20,0
∆G f i
(kJ/mole)
-1169,1
-889,5
-347,3
-1265,5
-1395,9
-1419,6
-1291,4
-1262,5
-1919,5
bch j
(kJ/mole)
1214,5
904,4
193,8
952,5
1196,1
721,5
966,3
944,9
1077,4
Calculation of the chemical exergy of gaseous fuels
Table A.16 shows coefficients a1 through a7 for ideal gases required for the calculation of h∗ (T ) and s∗ (T ) in Eqs. 5.43 and 5.45, according to Zelenik and Gordon
[413].
Table A.16. Coefficients a1 through a7 [413]
C H4
C2 H 6
C3 H 8
C4 H10
C5 H12
N2
CO2
A.5
A.5.1
a1
2,928
1,463
0,8969
1,522
1,878
3,704
2,401
a2
0,002569
0,01549
0,02669
0,03429
0,04122
-0,001422
0,008735
a3
7,844E-06
5,781E-06
5,431E-06
8,101E-06
0,00001253
2,867E-06
-6,607E-06
a4
-4,91E-09
-1,26E-08
-2,13E-08
-2,92E-08
-3,70E-08
-1,20E-09
2,00E-09
a5
2,04E-13
4,59E-12
9,24E-12
1,27E-11
1,53E-11
-1,40E-14
6,33E-16
a6
-10054
-11239
-13955
-17126
-20038
-1064
-48378
a7
4,634
14,43
19,36
18,35
18,77
2,234
9,695
Estimation of the thermodynamic properties of
minerals
Chermak’s methodology
Table A.17 shows the enthalpy and Gibbs free energy of the polyhedral units required
for the calculation of silicate minerals. The brackets next to the chemical formulas
indicate the coordination number.
Estimation of the thermodynamic properties of minerals
387
Table A.17. The g i and hi of each polyhedral type and the standard error (%) of the
estimate. Values in kJ/mol. [55]
Polyhedral unit
[4]
Al2 O3
[6]
Al2 O3
[6]
Al(OH)3
[4]
SiO2
M gO[6]
[6]
M g(OH)2
C aO[6]
C aO[8−z]
N a2 O[6−8]
K2 O[8−12]
H2 O
FeO[6]
[6]
Fe(OH)2
[6]
Fe2 O3
A.5.2
gi
Error
hi
Error
-1631,32
-1594,52
-1181,62
-853,95
-628,86
-851,86
-669,13
-710,08
-672,5
-722,94
-239,91
-266,29
-542,04
-776,07
13,3
15,3
13,2
4,6
10,6
10,2
5,9
7,2
26,0
27,4
5,7
6,8
24,6
33,0
-1716,24
-1690,18
-1319,55
-910,97
-660,06
-941,62
-696,65
-736,00
-683,00
-735,24
292,37
-290,55
-596,07
-939,18
11,0
15,9
12,2
3,2
7,9
9,1
5,2
7,1
18,4
21,1
4,6
5,4
8,2
35,6
Vieillard’s methodology for hydrated clay minerals
Table A.18 shows the values for ∆G O−2 M z+ (clay) for ions located in the interlayer
(l), octahedral (o), tetrahedral (t) and brucitic (b) sites. These values are required
for the calculation of the Gibbs free energy of formation of hydrated clays and phyllosilicates with Eqs 5.65 and 5.66.
A.5.3
Estimated values of the enthalpy and Gibbs free energy of
minerals
Table A.19, shows the estimated standard enthalpy and Gibbs free energy of formation of some of the minerals included in the model of the upper crust developed in
chapter 3. The number of the method used to estimate the values are outlined in column “Meth.” (see table 5.8 for the correspondence between methods and numbers).
The estimation error ±" is taken as the greatest associated error to the methodologies used for the determination of the mineral’s properties. This means that if there
is a substance, for which 2 or more estimation methods were used, only the error
associated to the most inaccurate one will be taken into account (the maximum is
then ±" = 10%).
In the determination of Gibbs free energies of formation from standard entropies
(method 1), references [284] and [391] were used for the required standard en-
388
ADDITIONAL
CALCULATIONS
Table A.18. Values of ∆G O−2 M z+ (clay) for ions located in different sites [382] for
hydrated clays and phyllosilicates. Values in kJ/mole
Ions
K + (l)
N a+ (l)
Li + (l)
M g 2+ (l)
C a2+ (l)
(N H4 )+ (l)
M n+2 (l)
Cu+2 (l)
C o+2 (l)
N i +2 (l)
C d +2 (l)
Z n+2 (l)
Al +3 (l)
La+3 (l)
Fe2+ (l)
Cs+ (l)
Rb+ (l)
Ba2+ (l)
S r 2+ (l)
H + (l)
Ions
Al 3+ (t)
Fe3+ (t)
Ga3+ (t)
Be2+ (t)
Si 4+ (t)
∆GO−2 M z+
(hydr. Clays)
425,77
267,19
77,54
-100
-32,34
-28,4
-88
-136,7
-110
-114,8
-102,6
-121
-143,3
-65,6
565,9
528,1
157,6
123,4
-154,2
∆GO−2 M z+
(hydr. Clays)
-197,31
∆GO−2 M z+
Phyllosil.
476
280
-110
-52
-76,3
-148,7
562,1
545,1
73,7
18,8
∆GO−2 M z+
Phyllosil.
-196
-261,7
-241,9
-193,9
-169
Ions
∆GO−2 M z+
(hydr. Clays)
∆GO−2 M z+
Phyllosil.
-50,71
-112
Li + (o)
M g 2+ (o)
C a2+ (o)
C r +3 (o)
M n+2 (o)
-158,6
-122,9
-35,2
-103
-74,4
-160,6
-119,1
C o2+ (o)
N i +2 (o)
-136,8
-132,2
-135,3
Z n+2 (o)
Al 3+ (o)
-140,3
-161,23
-139,3
-157
Fe2+ (o)
Fe3+ (o)
Ga3+ (o)
T i 4+ (o)
-134,4
-164,05
-141
-168,5
-167,6
-180,5
H + (o)
Ions
M g 2+ (b)
Fe2+ (b)
Al 3+ (b)
Fe3+ (b)
Li + (b)
M n2+ (b)
Z n2+ (b)
N i 2+ (b)
C o2+ (b)
C r +3 (b)
C a2+ (b)
H + (b)
Si 4+ (clay)
H + (clay)
∆GO−2 M z+
(hydr. Clays)
-220
∆GO−2 M z+
Phyllosil.
-30
-115
-171
-210
70
-87,3
-129,1
-120,8
-114,5
-173,1
4,7
-228
-166,09
-220
tropies of the elements in their reference state, according to Eq. 5.50. Most of the
properties of the simple oxides used for the estimations are also recorded in the same
references.
In column “M.2: Poles”, the poles that compose the mineral under analysis assuming
an ideal solid solution (method 2, Eq. 5.53) are given.
Estimation of the thermodynamic properties of minerals
389
Column “M.3; 4; 6; 8: Ref. Minerals” includes the reference mineral used to determine the properties of the substance considered. Remember that in method 3,
the reference mineral is decomposed either into its sulfides or oxides and the obtained ∆H r and ∆G r is added to the weighted sum of enthalpies and free energies
of the simple sulfides or oxides of the mineral under consideration (see Eq. 5.55).
In method 4, the same reaction energy involved in a substitution reaction is applied
for the mineral under analysis and for an isomorphous one. For methods 6 and 8
(the ∆O−2 method for the same family of compounds, and for different compounds
with the same cations, respectively), the reference minerals (at least 2) required for
the determination of parameter α in Eqs. 5.62 and 5.66 are given. If not specified,
the reference mineral will be used for the determination of both, ∆H 0f and ∆G 0f .
The properties of substances approximated with method 4 (the method of Chermak
and Rimstidt for silicate minerals) and 7 (the ∆O−2 method for hydrated clay minerals and for phyllosilicates), were obtained with the information provided in tables
A.17 and A.18, after decomposing the mineral into its constituent blocks.
Column “M.9; 10: Ideal reaction” shows the reaction that takes place to form the
mineral under analysis. Remember that in method 9 (assuming ∆S f zero), it is
assumed that the entropy of reaction is zero. In method 10 (the element substitution
method), the enthalpy and Gibbs free energy of reaction is approximated to zero. If
not specified, the reference mineral will be used for the determination of both, ∆H 0f
and ∆G 0f .
For those substances whose properties were estimated with method 11 (the addition
method for hydrated minerals), the weighted enthalpy or Gibbs free energy of liquid
water contained in the mineral was added.
The properties of minerals estimated with method 12 are obtained through the
weighted sum of the simple blocks (either oxides or sulfides) that compose the substance. The properties of the simple compounds are mainly obtained from Faure
[94] and Robie [284].
Formula
-4586,1
-9006,5
-6079,4
-968,0
-2884,5
-1034,5
-7057,3
Be4 Si2 O7 (OH)2
Be3 Al2 Si6 O18
K(M g2,5 Fe0,5 )(Si3 Al)O10
(OH)1,75 F0,25
Bi2 (CO3 )O2
U0,3 C a0,2 N b0,9 T i0,8 Al0,1
3+
Ta0,5 O6 (OH)
Fe0,1
P b5 S b4 S11
C a2,9 C e0,9 T h0,6 La0,4 N d0,2
Si2,7 P0,5 O12 (OH)1,8 F0,2
Bertrandite
Beryl
Biotite
Bismutite
Blomstrandite/
Betafite
Boulangerite
Britholite
-6606,9
-6152,6
-2585,3
-17,4
-14136,3
-9894,5
-4300,6
-8500,4
-5706,7
-5317,2
-1527,8
-7180,9
FeAl2 SiO5 (OH)2
K Fe3 (Si3 Al)O10 (F )2
from
K M g3 (Si3 Al)O10 (OH)2 and
K M g3 (Si3 Al)O10 (F )2
∆H f
C a0,167 Al2,33 Si3,67 O10 (OH)2
SmOH · CO3 · 0, 5H2 O;
N dOH · CO3 · 0, 5H2 O
C a2 Fe5 Si8 O22 (OH)2
M.3; 4; 6; 8: Ref. Minerals
Continued on next page . . .
K M g3 (Si3 Al)O10 (OH)2 ;
K M g3 (Si3 Al)O10 (F )2 ;
K Fe3 (Si3 Al)O10 (OH)2 ;
K Fe3 (Si3 Al)O10 (F )2
C a5 (PO4 )3 F ; C a5 (PO4 )3 C l;
C a5 (PO4 )3 OH
M.2: Poles
→
P b5 S b4 S11 → 5P bS + 2S b2 S3
C a2,9 C e0,9 T h0,6 La0,4 N d0,2
Si2,7 P0,5 O12 (OH)0,8 F0,2 + 0, 2H2 O
→
C a2,9 C e0,9 T h0,6 La0,4 N d0,2
Si2,7 P0,5 O12 (OH)2 + 0, 2H F
La(CO3 )F + 1, 5H2O → LaOH ·
CO3 · 0, 5H2 O + H F
C a10 (PO4 )6 C l2
+2H F
C a10 (PO4 )6 F2 +2H C l
Li0,75 N a0,25 Al(PO4 )
F0,75 (OH)0,25
+
0, 75H2 O
→ Li0,75 N a0,25 Al(PO4 )(OH)2 +
0, 75H F
M.9; 10: Ideal reaction
3
1
1
12
12
1; 9
10;
12
12
12
1
1
2; 4
3
1; 8;
10
12
12
∆H f :
5
3; 10
3
12
10;
12
Meth.
[94] [284]
[284][94]
[284][94]
References
[94] [284]
[136]
[136]
[284][391]
[222][391]
[223]
[284]
[94] [284]
1
0
0
10
10
[94] [284]
[309][284]
[255]
[94]
[284][94]
5 [67] [284]
10 [284][94]
10 [284][94]
10 [284][94]
0
0
1
1
5
10 [284][94]
5
10 [284][94]
1 [55]
±",
%
1
10
10
ADDITIONAL
Chloritoid
-2753,4
-19,0
-14980,9
-10499,8
-5691,6
N a0,33 Al2,33 Si3,67 O10 (OH)2
Beidellite
M g FeSi2 O6
AuTe2
N a6 C a2 Al6 Si6 O24 (CO3 )2
C e1,7 La1,4 C a0,8 T h0,1
2+
3+
Fe1,8
M g0,5 T i2,5 Fe0,5
Si4 O22
2+
Fe1,2
M g0,6 M n2+
0,2
Al4 Si2 O10 (OH)4
-1023,7
-6666,9
-1660,9
La(CO3 )F
Bronzite
Calaverite
Cancrinite
Chevkinite
-888,7
-2683,8
-7640,4
AxiniteFe
Bastnaesite
-6386,9
-6773,4
C a5 (PO4 )3 (OH)0,33
F0,33 C l0,33
C a2 Fe2+ Al2 BO3 Si4 O12 (OH)
Apatite
-1923,1
-4021,0
-2076,8
-4274,4
-10801,5
-7660,9
-282,7
∆G 0f
2+
C aFe0,6
M g0,3 M n2+
0,1 (CO3 )2
C aAl2 Si2 O8
-11519,4
-8184,4
-307,1
∆H 0f
Ankerite
Anorthite
Actinolite
C a2 M g3 Fe2 Si8 O22 (OH)2
Aenigmatite N a2 Fe52+ T iSi6 O20
Amblygonite Li0,75 N a0,25 Al(PO4 )
F0,75 (OH)0,25
Mineral
Table A.19: Estimations of the standard enthalpy and Gibbs free energy of minerals. Values in
kJ/mole
390
CALCULATIONS
-2721,2
-2425,4
-11859,9
Y0,7 C a0,2 C e0,12 (Ta0,7 )2
(N b0,2 )2 (T i0,1 )O5,5 (OH)0,5
C a2 (IO3 )2 (C rO4 )
2+
N a4 C a2 Fe0,7
M n0,3 Z r
Si8 O22 (OH)1,5 C l1,5
Delorenzite/
Tanteuxenite
Dietzeite
Eudyalite
Euxenite
Y0,7 C a0,2 C e0,1 (Ta0,2 )2
(N b0,7 )2 (T i0,025 )O6
Fergusonite N d0,4 C e0,4 Sm0,1 Y0,1 N bO4
Ferrocolum- Fe2+ N b2 O6
bite
-293,7
CuFe2 S3
Cubanite
-2506,3
-2631,2
-2631,2
-2671,5
-2808,3
-2172,8
-2148,1
-11062,9
-2549,9
-302,8
-3432,2
-3743,6
-14136,3
N.A.
-6277,0
-73,8
-10925,8
-14980,9
-163,1
-6949,7
-79,8
-11600,3
N a6 C a2 Al6 Si6 O24 (CO3 )2
C oAsS
C a2 B6 O11 · 5H2 O
-7796,6
-8410,0
-8435,5
-8966,4
P t 0,6 P d0,3 N i0,1 S
N a2 M g2 Fe2+ Al2
(Si8 O22 )(OH)2
2+
CryptomelaneK8 (M n4+
7,5 M n0,5 ) O16
Cooperite
Crossite
Cancrinite
Cobaltite
Colemanite
Chrysocolla Cu2 Si2 O6 (H2 O)4
Clementite Fe32+ M g1,5 Al
Fe3+ Si3 AlO12 (OH)6
Clinochlore M g3,75 Fe1,25 Al2 Si3 O10 (OH)8
Clinohumite M g6,75 Fe2,25 Si4 O16
(OH)0,5 F1,5
-4701,4
-2964,6
-7043,1
Chondrodite
∆G 0f
-3279,4
-7657,8
-5023,0
2+
(SiO4 )2
M g3,75 Fe1,25
F1,5 (OH)0,5
∆H 0f
Formula
Mineral
N a12 C a6 Fe32+
Z r3 Si24 O66 (OH)6
∆H 0f :N a0,033 Al0,02 K0,12
M n0,94 Fe0,0375 Sr0,016
Ba0,012 O2 ; ∆G 0f : M n3 O4
Cu5 FeS4
∆H 0f :FeAsS
3C aO · B2 O3 ; 2C aO · B2 O3 ;
C aO · 2B2 O3
P tS
M g5 Al2 Si3 O10 (OH)8
M.3; 4; 6; 8: Ref. Minerals
Continued on next page . . .
N a2 M g3 Al2 Si8 O22 (OH)2 ;
N a2 Fe32+ Al2 Si8 O22 (OH)2
M.2: Poles
2+
N a4 C a2 Fe0,7
M n0,3 Z r
Si8 O22 (OH)2
+
1, 5H C l
2+
→
N a4 C a2 Fe0,7
M n0,3 Z r
Si8 O22 (OH)1,5 C l1,5 + 1, 5H2 O
M g6,75 Fe2,25 Si4 O16
(OH)2 + 2, 25M gO
→
M g9 Si4 O16 (OH)2 + 2, 25FeO;
M g6,75 Fe2,25 Si4 O16 (OH)0,5 F1,5
+1, 5H F
→
M g6,75 Fe2,25 Si4 O16 (OH)2 +
1, 5H2 O
±", References
%
5 [55] [284]
[94]
12
12
12
12
1; 3;
10
12
3
3
12
3
1; 6;
11
3
1; 2
3
10
[94] [284]
[144][284]
[97] [94]
[284]
[94] [284]
[120][284]
10 [284][94]
10 [284][94]
10 [284][94]
10 [391]
1 [179][284]
1
[241][226]
[284]
10 [284][94]
1
1
1
10 [94]
1 [284][391]
5 [319][284]
1
1
∆H 0f :12 10 [94] [400]
5
1 [55]
5; 10
2+
M g3,75 Fe1,25
(SiO4 )2 F1,5 (OH)0,5 + 1, 5H2 O
2+
(SiO4 )2 (OH)2 +
→ M g3,75 Fe1,25
1, 5H F
Meth.
M.9; 10: Ideal reaction
Table A.19: Estimations of the standard enthalpy and Gibbs free energy of minerals. Values in
kJ/mole– continued from previous page.
Estimation of the thermodynamic properties of minerals
391
Formula
Ba0,8 P b0,2 N a0,125
4+
Fe1,3 Al0,2 Si0,1 M n2+
0,5 M n6 O16
-864,6
-813,2
-12678,2
-13408,5
+1, 75M gO
→
M g9 Si4 O16 (OH)2 + 1, 75FeO;
2+
M g5,25 Fe1,75 (SiO4 )3 F1,5 (OH)0,5
+1, 5H F
→
2+
M g5,25 Fe1,75
(SiO4 )3 (OH)2
+1, 5H2 O
3+
(K0,3 C a0,1 )(M g2,3 Fe0,6
Al0,1 )
(Si2,8 Al1,2 )O10 (OH)1,8 F0,2 )
·
3(H2 O)+
0, 2H F
→
3+
(K0,3 C a0,1 )(M g2,3 Fe0,6
Al0,1 )
(Si2,8 Al1,2 )O10 (OH)2 · 3(H2 O) +
0, 2H2 O
N a8 Al6 Si6 O24 C l2
N a8 Al6 Si6 O24 SO4 + 2H2 O →
N a8 Al6 Si6 O24 (OH)2 + H2 SO4
1; 2
3, 10
5
1; 7;
10
3; 10
3
M g9 Si4O16 (OH)2
3
12
1
7
12
1; 3;
9
3
12
1; 7;
9
Meth.
K0,005 M n0,82 Fe0,165
Ba0,09 P b0,02 O2 · 0, 09H2 O;
∆G 0f : M n3 O4
C a2 M g4 Al(Si7 AlO22 )(OH)2
2+
(SiO4 )3 (OH)2
M g5,25 Fe1,75
M.9; 10: Ideal reaction
∆H 0f :N a0,0125 Al0,029 Si0,01
(N i2 M g)Si2 O5 (OH)4
+
2M gO → M g3 Si2 O5 (OH)4 +
2N iO
Ag3 S bS3
C a10 (PO4 )6 F2
M.3; 4; 6; 8: Ref. Minerals
Continued on next page . . .
T iO2 ; N b2 O5 ; FeO
M.2: Poles
1
5
1
5
5
1
[227][94]
[284]
[187]
[55]
[382][143]
[284]
[144]
[320][284]
[97] [94]
[284]
10 [284][94]
0 [144]
0,6 [383]
5 [284]
10 [284][94]
1 [383][143]
[284]
±", References
%
10 [284][94]
1 [167][391]
ADDITIONAL
2+
Ilmenorutile T i0,7 N b0,15 Fe0,225
O2
-5499,1
-5886,2
2+
Hydromusco- K0,6 (H3 O)0,4 Al2 M g0,4 Fe0,1
vite
Si3,5 O10 (OH)2
HydrosodaliteN a8 Al6 Si6 O24 (OH)2
-6238,9
-6512,3
-6953,7
-7362,2
-10303,7
-4330,4
-4733,3
-10976,4
-5532,4
-5843,9
-11584,2
-4785,6
-727,5
-4943,3
-3267,1
-2163,9
-5698,1
∆G 0f
3+
Hydrobiotite (K0,3 C a0,1 )(M g2,3 Fe0,6
Al0,1 )(Si2,8 Al1,2 )
O10 ((OH)1,8 F0,2 ) · 3(H2 O)
3+
Hornblende- C a2 Fe42+ Al0,75 Fe0,25
Fe
(Si7 AlO22 )(OH)2
2+
(SiO4 )3
Humite
M g5,25 Fe1,75
F1,5 (OH)0,5
Helvine/
Helvite
Hollandite
-12319,7
-5150,3
M g5 Al2 (Si6 Al2 O22 )(OH)2
3+
(K0,6 N a0,05 )(Fe1,3
Gedrite
Glauconite
2+ 3+
Al0,15 )
M g0,4 Fe0,2
(Si3,8 Al0,2 )O10 (OH)2
M n4 Be3 (SiO4 )3 S
-703,2
-5220,0
-3494,6
2+
S b3 AsS13
Ag7,2 Cu3,6 Fe1,2
Y2 Fe2+ Be2 (Si2 O10 )
(N i2 M g)Si2 O5 (OH)4
-2319,3
-5984,4
∆H 0f
Freibergite
Gadolinite
Garnierite
Ferrotantalite Fe2+ Ta2 O6
Francolite
C a5 (PO4)2,63 (CO3 )0,5 F1,11
Mineral
Table A.19: Estimations of the standard enthalpy and Gibbs free energy of minerals. Values in
kJ/mole– continued from previous page.
392
CALCULATIONS
-3713,1
-3208,3
-11738,2
-2074,0
KC a2 C e3 Si8 O22 (OH)1,5 F0,5
C e0,5 La0,25 N d0,2 T h0,05 (PO4 )
Miserite
Monazite
(Ce)
-557,3
-622,4
N a0,4 C a1,6 Ta2 O6,6
(OH)0,3 F0,1
-80,2
-1721,8
-85,7
-1430,8
FeAs2
N a0,6 C e0,22 La0,11
C a0,1 T i0,8 N b0,2 O3
M nO(OH)
Microlite
-4642,3
-4995,0
3+
2+
M g0,5 Fe0,75
K Fe2,5
Al0,25 Si3 O10 (OH)2
Lepidomelane/
Annite
Loellingite
Loparite (Ce)
Manganite
-1943,3
-11035,1
-3004,3
-4510,6
-5654,7
-4812,8
-6003,2
C aAl2 Si2 O7 (OH)2 · H2 O
K Li2 AlSi4 O10 F (OH)
Lawsenite
Lepidolite
-3925,1
-4191,1
2+
N a1,1 C a0,9 M n2+
0,5 Fe0,5
Z r0,8 T i0,1 N b0,1 (Si2 O7 )
O0,6 (OH)0,3 F0,1
Lavenite
-7865,3
Kernite
-2812,1
-3318,7
-8401,2
-4104,9
N a2 O · 2B2 O3 · 4H2 O
Jadeite
Jarosite
-1137,5
-8624,8
-2990,4
-3521,7
3+
(Si2 O6 )
N aAl0,9 Fe0,1
K Fe33+ (SO4 )2 (OH)6
Jacobsite
∆G 0f
-9172,9
-1237,4
2+
2+
M n2+
0,6 Fe0,3 M g
3+
O
M n3+
Fe1,5
0,5 4
Kornerupine M g1,1 Fe0,2 Al5,7
(Si3,7 B0,3 )O17,2 (OH)
LamproN a2 Sr BaT i3 Si4 O16 (OH)F
phyllite
∆H 0f
Formula
Mineral
C aAl2 Si2 O2
K M g3 (Si3 Al)O10 (OH)2 ;
K M g3 (Si3 Al)O10 (F )2
K Fe3 AlSi3 O10 (OH)2
Al6,75 BSi3 O17,25 (OH)0,75
N aAlSi2 O6
M.3; 4; 6; 8: Ref. Minerals
Continued on next page . . .
M nFe2 O4 ; Fe2 O4 ; FeM n2 O4 ;
M g Fe2 O4 ;
M nM n2 O4 ;
M g M n2 O4
M.2: Poles
→
N a0,4 C a1,6 Ta2 O6,6 (OH)0,3 F0,1 +
0, 1H2 O → N a0,4 C a1,6 Ta2 O6,6
(OH)0,4 + 0, 1H F
KC a2 C e3 Si8 O22 (OH)1,5 F0,5
+
0, 5H2 O
→
KC a2 C e3 Si8 O22 (OH)2 + 0, 5H F
K Li2 AlSi4 O10 F (OH) + H2 O
K Li2 AlSi4 O10 (OH)2 + H F
N a2 Sr BaT i3 Si4 O16 (OH)F + H2 O
→ N a2 Sr BaT i3 Si4 O16 (OH)2 +
HF
2+
N a1,1 C a0,9 M n2+
0,5 Fe0,5
Z r0,8 T i0,1 N b0,1 (Si2 O7 )
O0,6 (OH)0,3 F0,1
+
0, 1H2 O
2+
→
N a1,1 C a0,9 M n2+
0,5 Fe0,5
Z r0,8 T i0,1 N b0,1 (Si2 O7 )
O0,6 (OH)0,4 + 0, 1H F
N a2 O · 2B2 O3 · 4H2 O → N a2 O +
2B2 O3 + 4H2 O
FeM n2 O4 + M nO → M nM n2 O4 +
FeO
M.9; 10: Ideal reaction
Table A.19: Estimations of the standard enthalpy and Gibbs free energy of minerals. Values in
kJ/mole– continued from previous page.
[135][284]
[284][94]
12
10;
12
10 [284][94]
10 [284][94]
10 [284][94]
10 [284]
∆H 0f :
12
10;
12
[94] [284]
[284][94]
[383][391]
0 [113]
10 [284][94]
1
5
1
10 [284][94]
10 [284][94]
1
5
±", References
%
5 [227][285]
[284]
[227]
[189]
[118]
1 [94] [284]
10 [94] [400]
1
12
3
3; 11
7; 4
10;
12
10;
12
3
3
∆H 0f :
12
10
1; 2;
9
Meth.
Estimation of the thermodynamic properties of minerals
393
N a0,75 K0,25 Al(SiO4 )
2+
M n2+
K N a2 LiFe1,5
0,5 T i2 Si8 O24
N a0.3 Fe23+ (Si3,7
Al0,3 )O10 (OH)2 · 4(H2 O)
N a2,8 M n2+
0,2 Sr0,5 C a0,5
La0,33 C e0,6 Z n0,6 M g0,4 Si6 O17
N a8 Al6 Si6 O24 SO4
2+
(SiO4 )
M g1,6 Fe0.4
Nepheline
Neptunite
Nontronite
Olivine
M g1,35 Fe0,55 C a0,1 (Si2 O6 )
Pyrargirite
C a2 M gAl2 (SiO4 )
(Si2 O7 )(OH)2 · H2 O
Ag3 S bS3
-3752,1
-5939,9
-766,2
-5902,2
-3977,5
-6477,8
-778,3
-6292,8
-2347,2
-2569,1
-131,5
-142,2
-6672,5
-2681,3
-2847,7
-7148,6
-3074,2
-3297,1
-1448,8
-967,9
-6055,4
-1044,5
-6481,6
-1535,4
-2904,3
-1925,0
-3075,5
-2083,3
-13131,5
-7532,2
-8020,8
-13936,7
-1972,4
-10061,3
-5447,7
-5616,6
-2087,6
-10724,6
-6841,0
-5991,3
-9096,6
-5354,5
-5523,8
-9804,0
∆G 0f
∆H 0f
M gSi2 O6 ;
Fe2 Si2 O6 ;
C a4 M gAl5 Si6 O21 (OH)7
4+
∆H 0f :Ba0,4 M n2+
0,4 M n0,6 O2
0, 4H2 O; ∆G 0f : M n3 O4
K M g3 (Si3 Al)O10 (OH)2 ;
K M g3 (Si3 Al)O10 (F )2
C a2 (Al2 Fe3+ )Si3 O12 (OH)
N aAlSiO4
K M g3 (Si3 Al)O10 (OH)2 ;
K M g3 (Si3 Al)O10 (F )2
M.3; 4; 6; 8: Ref. Minerals
Continued on next page . . .
C aSi2 O6 ;
M gSi2 O6 ;
N aFeSi2 O6 ;
C aSi2 O6 ; N aAlSi2 O6
C a0,167 Al2,33 Si3,67 O10 (OH)2 ;
N a0,33 Al2,33 Si3,67 O10 (OH)2
M.2: Poles
·
Ag3 S bS3 →
3
Ag2 S
2
+
1
S b2 S3
2
K M g3 AlSi3 O10 F (OH)+H2 O
K M g3 AlSi3 O10 (OH)2 +H F
N a8 Al6 Si6 O24 SO4 + 2H C l
N a8 Al6 Si6 O24 C l2 + H2 SO4
→
→
KAl3 Si3 O10 (OH)1,8 F0,2
+0, 2H2 O → KAl3 Si3 O10 (OH)2
+0, 2H F
M.9; 10: Ideal reaction
1
9
3
3
12
12
2
1
5
12
4
[284]
[55]
[187]
[284]
5
1
1
[284]
[144][284]
[97] [94]
[284]
10 [284][94]
10 [284][94]
1
5
1
[284]
[144][284]
[94]
0 [25]
1 [55]
10 [284][94]
1 [391][284]
1
5
5
2
11
3
[391][284]
1 [94] [284]
10 [284][94]
0,6 [382][143]
[284]
10 [284][94]
1
10 [284][94]
±", References
%
1 [94]
∆H 0f :
10
12
3
12
1; 7
4
12
2
Meth.
ADDITIONAL
Pumpellyte
Pollucite
Cs0,6 N a0,2 Rb0,1 Al0,9 Si2,1 O6 ·
(H2 O)
Polycrase
Y0,5 C a0,1 C e0,1 U0,1
(Y)
T h0,1 T i1,2 N b0,6 Ta0,2 O6
4+
Psilomelane Ba2 M n2+
2 M n3 O10 · 2H 2 O
Pigeonite
C a0,6 N a0,4 M g0,6 Al0,3
Fe0,1 Si2 O6
Opal
SiO2 · 0, 5H2 O
OrthiteC a(C e0,4 C a0,2 Y0,133 )
Allanite
(Al2 Fe3+ )Si3 O12 (OH)
Orthoclase KAlSi3 O8
Palygorskite M gAlSi4 O10 (OH) · 4(H2 O)
2+
N i4,5 S8
Pentlandite Fe4,5
Phlogopite K M g3 AlSi3 O10 F (OH)
Omphacite
Nosean
Nordite
Muscovite
N a0,165 C a0,084 Al2,33
Si3,67 O10 (OH)2
N a4 T i3,6 N b0,4 (Si2 O7 )2 O4
4(H2 O)
KAl3 Si3 O10 (OH)1,8 F0,2
Montmorillonite
Murmanite
·
Formula
Mineral
Table A.19: Estimations of the standard enthalpy and Gibbs free energy of minerals. Values in
kJ/mole– continued from previous page.
394
CALCULATIONS
Chamosite
Titanite
Todorokite
C aT iSiO5
3+
N a2 M n4+
4 M n2 O12 · 3H 2 O
3+ 3+
(Fe3 M g2 Fe0,5
Al0,5 )
(Si3 Al)O10 (OH)2
-2597,1
-4037,4
-7596,0
-3740,2
Thortveitite Sc1,5 Y0,5 Si2 O7
Thuringite-
-1999,6
-100,6
-1939,7
-11543,9
-2048,8
-1968,6
-100,2
-1909,5
-12413,7
-2160,5
-2455,1
-3576,5
-6981,9
-3540,6
-4035,4
-184,5
-15197,0
-4363,4
-166,1
-16655,5
-7788,2
-463,5
-3715,9
-11504,2
-8429,2
-444,9
-3860,7
-12197,4
(M g3,75 Fe1,25 Al)
(Si3 Al)O10 (OH)2 (OH)6
Ag4 M nS b2 S6
K0,75 N a0,25 AlSi3 O8
N a4 Al3 Si9 O24 C l
-4103,9
-132,7
-1821,9
-9399,5
-8808,5
-2687,3
∆G 0f
Samsonite
Sanidine
ScapoliteMarialite
Serpentine M g3 Si2 O5 (OH)4
Stephanite Ag5 S bS4
StilplomelaneK0 , 8Fe8 Al0,8 5Si11,1
O21 (OH)8 · 6H2 O
Tennantite Cu10 Fe2 As4 S13
Tetradymite Bi2 Te2 S
Tetrahedrite Cu10 Fe2 S b4 S13
Thomsonite N aC a2 Al5 Si5 O20 · 6H2 O
Thorite
T hSiO4
Ripidolite
-4360,1
-140,3
-1964,9
-10087,1
-9415,1
-2897,9
N aC aN b2 O6 (OH)0,75 F0,25
Pyrochlore
Ramsayite
N a2 T i2 Si2 O9
Realgar
As4 S4
RhabdophaneC e0,75 La0,25 (PO4 ) · H2 O
Riebeckite
N a2 Fe32+ Fe23+ (Si8 O22 )(OH)2
Rinkolite/
N a2 C a3 C e1,5 Y0,5
MosanT i0,4 N b0,5 Z r0,1 (Si2 O7 )2
O1,5 F3,5
drite
∆H 0f
Formula
Mineral
∆H 0f :M g0,19 M n3+
0,38
∆H 0f :Ag3 S bS3
KAlSi3 O8
∆H 0f :Ag3 S bS3
M.3; 4; 6; 8: Ref. Minerals
0
M n4+
0,62 O2 · 0, 75H 2 O; ∆G f :
M n3 O4
Continued on next page . . .
Y2 Si2 O7 ; Sc2 Si2 O7
Bi2 Te3 ; Bi2 S3
LaPO4 ; C ePO4
M.2: Poles
→
Sc2 Si2 O7 + Al2 O3 → Al2 Si2 O7 +
Sc2 O3 ; s0f :Y2 Si2 O7 + Al2 O3 →
Al2 Si2 O7 + Y2 O3
T hSiO4 + UO2 → USiO4 + T hO2
N a2 C a3 C e1,5 Y0,5
T i0,4 N b0,5 Z r0,1 (Si2 O7 )2
O1,5 F3,5 + 3, 5H2 O
N a2 C a3 C e1,5 Y0,5
T i0,4 N b0,5 Z r0,1 (Si2 O7 )2
O5 + 3, 5H F
N aC aN b2 O6 (OH)0.75 F0.25
+
0, 25H2 O → N aC aN b2 O6 (OH) +
0, 25H F
M.9; 10: Ideal reaction
Table A.19: Estimations of the standard enthalpy and Gibbs free energy of minerals. Values in
kJ/mole– continued from previous page.
1
3
7
2; 9
1
2
1
5
1; 9
1
3
1
3
3
1
7
12
1
2
1
10;
12
10;
12
Meth.
[284][94]
[312]
[364][388]
[94] [312]
[284][94]
[284]
[94] [284]
[186][284]
0
1
0
5
0
[94] [312]
[97] [284]
[94]
[25]
[284]
[210][210]
[284]
0 [303][284]
1 [226][94]
0 [303][284]
1 [55]
5 [298][192]
[284]
5 [62] [269]
[213]
[391]
[284]
0,6 [383]
5
1
0
0,6 [383]
10
0
1
0
10
±", References
%
10 [284][94]
Estimation of the thermodynamic properties of minerals
395
-6151,5
-1392,9
-5957,2
-14401,4
-6762,2
-1489,4
-7018,8
-637,8
-378,0
-4608,4
-4439,7
-1246,2
N aFe32+ Al6 (BO3 )3 Si6
O18 (OH)4
N aC a(B5 O6 (OH)6 )· 5H2 O
T iFe22+ O4
M g3 Si4 O10 (OH)2 · 2(H2 O)
3+
M n4+
0,6 Fe0,2 C a0,2
N a0,1 O1,5 (OH)0,5 · 1, 4(H2 O)
Fe2+ N i2 S4
Fe3 (PO4 )2 (H2 O)8
Y PO4
N aC a2 Z r0,6 N b0,4
Si2 O8,4 (OH)0,3 F0,3
2+
M n0,5 W O4
Fe0,5
TourmalineSchorl
Ulexite
Ulvöspinel
Vermiculite
Vernadite
Violarite
Vivianite
Weinschenkite
Wohlerite
Wolframite
-1987,7
-13453,5
-3044,4
Al2 (SiO4 )F1,1 (OH)0,9
Topaz
-1146,4
-4170,0
-1871,1
-4428,2
-368,9
-571,4
-2875,2
∆H 0f
Formula
Mineral
∆G 0f
FeW O4 ; M nW O4
M.2: Poles
End of the table
M n4+
0,6 O2 · 0, 4H 2 O;
M n3 O4
∆G 0f :
∆H 0f :Ba0,13 M nO2 · 0, 27H2 O
M.3; 4; 6; 8: Ref. Minerals
FeS
2
N i3 S4 + 13
3
Fe2 S3 +
N aC a2 Z r0,6 N b0,4
Si2 O8,4 (OH)0,3 F0,3 + 0, 3H2 O
→
N aC a2 Z r0,6 N b0,4
Si2 O8,4 (OH)0,6 + 0, 3H F
1
3
Fe2+ N i2 S4 →
Al2 (SiO4 )F1,1 (OH)0,9 +0,9H F →
Al2 SiO4 F2 +0,9H2 O
M.9; 10: Ideal reaction
Table A.19: Estimations of the standard enthalpy and Gibbs free energy of minerals. Values in
kJ/mole– continued from previous page.
2
10;
12
∆H 0f :
12
1
1; 9
1
12
∆H 0f :
12
3
1
10
Meth.
[107][284]
[255][79]
[241]
[284][94]
1
0
[284]
[364][345]
[284]
[391]
10 [284][94]
10 [284]
1
1
0 [293][284]
10 [284][94]
10 [284]
0
±", References
%
5 [94]
396
ADDITIONAL
CALCULATIONS
Exergy calculation of the mineral resources
A.6
397
Exergy calculation of the mineral resources
Table A.20 and A.21 show the chemical Bch and concentration Bc exergy, as well
∗
as their corresponding exergy cost (Bch
and Bc∗ ), of the world’s mineral production
in 2006, the reserve, base reserve and world’s resources, collected from the USGS
[362]. The specific chemical exergies of the substances bch are calculated with Eq.
5.1. The concentration exergies bc are calculated as the difference between the concentration exergies obtained with the average mineral concentration in the deposits
(x m ) and with the average concentration in the earth’s crust (x c ), both are calculated with Eq. 5.10. The exergy costs are obtained with Eq. 5.46, and the unit
exergy costs kch and kc from table 5.7. The average mineral concentration in the
crust and in the mineral deposits are expressed as x c and x m , respectively.
Aluminium
Antimony
Arsenic
Barite
Beryllium
Bismuth
Boron oxide
Bromine
Cadmium
Cesium
Chromium
Cobalt
Copper
Feldspar
Fluorspar
Gallium
Germanium
Gold
Graphite
Gypsum
Hafnium
Helium
Indium
Iodine
Iron
Lead
Lithium
Magnesium
Manganese
Mercury
Molybdenum
Nickel
Niobium
Phosphate rock (as fosforite)
PGM
Potash (K2 O)
REE (as C e2 O3 )
Rhenium
Selenium
Silver
Strontium
bch [kJ/mol]
794,30
437,10
494,10
18,40
24,30
274,80
84,12
50,56
293,15
404,46
584,40
308,89
134,03
35,02
112,64
514,61
556,48
51,50
410,25
17,92
1061,31
30,37
437,36
87,48
376,84
232,18
392,92
629,60
484,64
114,77
730,50
232,48
900,20
360,45
146,52
416,26
408,21
561,34
346,70
69,73
758,76
kch [-]
8
10
10
N.A.
1
10
N.A.
N.A.
10
1
1
10
80
N.A.
N.A.
1
1
1
N.A.
N.A.
1
1
10
N.A.
5
25
1
1
1
10
1
58
1
1
N.A.
1
N.A.
10
1
10
N.A.
Production
Reserves
∗
∗
Bch
Bch
Bch
Bch
2,38E+04
1,91E+05
3,20E+06
2,57E+07
1,15E+01
1,15E+02
1,80E+02
1,80E+03
9,42E+00
9,42E+01
1,88E+02
1,88E+03
1,50E+01
N.A.
3,58E+02
N.A.
4,15E-03
4,15E-03
N.A.
N.A.
1,79E-01
1,79E+00
1,01E+01
1,01E+02
1,23E+02
N.A.
4,91E+03
N.A.
8,24E+00
N.A.
N.A.
N.A.
1,20E+00
1,20E+01
3,05E+01
3,05E+02
N.A.
N.A.
5,09E+00
5,09E+00
1,57E+03
1,57E+03
N.A.
N.A.
8,45E+00
8,45E+01
8,77E+02
8,77E+03
8,20E+02
6,58E+04
2,66E+04
2,13E+06
4,63E+01
N.A.
N.A.
N.A.
1,84E+02
N.A.
8,27E+03
N.A.
1,29E-02
1,29E-02
N.A.
N.A.
1,65E-02
1,65E-02
N.A.
N.A.
1,54E-02
1,54E-02
2,62E-01
2,62E-01
8,40E+02
N.A.
7,02E+04
N.A.
1,74E+02
N.A.
0,00E+00
N.A.
N.A.
N.A.
8,64E+01
8,64E+01
5,09E+00
5,09E+00
N.A.
N.A.
5,29E-02
5,29E-01
1,00E+00
1,00E+01
4,12E-01
N.A.
2,47E+02
N.A.
1,40E+05
7,41E+05
1,18E+07
6,25E+07
9,29E+01
2,36E+03
2,11E+03
5,37E+04
4,50E+02
4,50E+02
5,54E+03
5,54E+03
4,26E+02
4,26E+02
N.A.
N.A.
2,51E+03
2,51E+03
9,69E+04
9,69E+04
2,02E-02
2,02E-01
6,29E-01
6,29E+00
3,35E+01
3,35E+01
1,56E+03
1,56E+03
1,49E+02
8,70E+03
6,34E+03
3,69E+05
1,03E+01
1,03E+01
6,25E+02
6,25E+02
1,21E+03
1,21E+03
1,54E+05
1,54E+05
9,29E-03
N.A.
1,27E+00
N.A.
3,07E+03
3,07E+03
8,76E+05
8,76E+05
3,65E+00
N.A.
2,61E+03
N.A.
3,40E-03
3,40E-02
1,80E-01
1,80E+00
1,62E-01
1,62E-01
8,60E+00
8,60E+00
3,12E-01
3,12E+00
4,17E+00
4,17E+01
1,21E+02
N.A.
1,41E+03
N.A.
Continued on next page . . .
Reserve base
∗
Bch
Bch
4,10E+06
3,29E+07
3,69E+02
3,69E+03
2,83E+02
2,83E+03
1,66E+03
N.A.
N.A.
N.A.
2,14E+01
2,14E+02
1,18E+04
N.A.
N.A.
N.A.
7,48E+01
7,48E+02
8,00E+00
8,00E+00
N.A.
N.A.
1,63E+03
1,63E+04
5,11E+04
4,09E+06
N.A.
N.A.
1,65E+04
N.A.
N.A.
N.A.
N.A.
N.A.
5,62E-01
5,62E-01
1,71E+05
N.A.
0,00E+00
N.A.
1,56E+02
1,56E+02
1,17E+03
1,17E+03
1,46E+00
1,46E+01
4,45E+02
N.A.
2,58E+07
1,37E+08
4,55E+03
1,15E+05
1,49E+04
1,49E+04
N.A.
N.A.
1,10E+06
1,10E+06
3,28E+00
3,28E+01
3,46E+03
3,46E+03
1,42E+04
8,26E+05
6,94E+02
6,94E+02
4,27E+05
4,27E+05
1,44E+00
N.A.
1,90E+06
1,90E+06
4,46E+03
N.A.
7,20E-01
7,20E+00
1,78E+01
1,78E+01
8,80E+00
8,80E+01
2,48E+03
N.A.
Table A.20: The chemical exergy and exergy cost of the 2006 world’s mineral production, mineral
reserves, base reserve and world resources. Values are expressed in ktoe if not specified
World resources
∗
Bch
Bch
9,61E+06
7,72E+07
N.A.
N.A.
1,73E+03
1,73E+04
3,77E+03
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
3,74E+02
3,74E+03
N.A.
N.A.
1,02E+06
1,02E+06
1,88E+03
1,88E+04
1,63E+05
1,31E+07
N.A.
N.A.
1,72E+04
N.A.
1,76E+02
1,76E+02
N.A.
N.A.
N.A.
N.A.
6,53E+05
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
5,60E+02
N.A.
3,71E+07
1,97E+08
4,02E+04
1,02E+06
1,76E+04
1,76E+04
N.A.
N.A.
N.A.
N.A.
8,20E+00
8,20E+01
2,36E+03
2,36E+03
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
1,79E+00
N.A.
2,64E+07
2,64E+07
N.A.
N.A.
7,92E-01
7,92E+00
N.A.
N.A.
N.A.
N.A.
2,07E+05
N.A.
398
ADDITIONAL
CALCULATIONS
Tantalum
Tellurium
Thorium
Tin
Titanium (T iO2 )
Vanadium
Wolfram
Zinc
Zircon (Z rO2 )
Sum
bch [kJ/mol]
974,85
326,36
1214,50
547,58
18,84
721,48
827,70
339,02
46,21
kch [-]
1
1
N.A.
1
1
1
1
13
1
Production
Reserves
∗
∗
Bch
Bch
Bch
Bch
2,97E-01
2,97E-01
2,78E+01
2,78E+01
8,07E-03
8,07E-03
1,28E+00
1,28E+00
0,00E+00
N.A.
1,32E+02
N.A.
3,33E+01
3,33E+01
6,72E+02
6,72E+02
3,27E+01
3,27E+01
4,11E+03
4,11E+03
1,90E+01
1,90E+01
4,40E+03
4,40E+03
9,77E+00
9,77E+00
3,12E+02
3,12E+02
1,24E+03
1,64E+04
2,23E+04
2,94E+05
1,06E+01
1,06E+01
3,40E+02
3,40E+02
1,77E+05
1,03E+06
1,63E+07
9,22E+07
End of the table
Reserve base
∗
Bch
Bch
3,85E+01
3,85E+01
2,87E+00
2,87E+00
1,54E+02
N.A.
1,21E+03
1,21E+03
8,45E+03
8,45E+03
1,29E+04
1,29E+04
6,78E+02
6,78E+02
5,95E+04
7,85E+05
6,45E+02
6,45E+02
3,37E+07
1,79E+08
Table A.20: The chemical exergy and exergy cost of the 2006 world’s mineral production, mineral
reserves, base reserve and world resources. Values are expressed in ktoe if not specified.– continued
from previous page.
World resources
∗
Bch
Bch
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
1,13E+04
1,13E+04
2,13E+04
2,13E+04
N.A.
N.A.
2,35E+05
3,11E+06
N.A.
N.A.
7,55E+07
3,19E+08
Exergy calculation of the mineral resources
399
Aluminium
Antimony
Arsenic
Barite
Beryllium
Bismuth
Boron oxide
Bromine
Cadmium
Cesium
Chromium
Cobalt
Copper
Feldspar
Fluorspar
Gallium
Germanium
Gold
Graphite
Gypsum
Hafnium
Helium
Indium
Iodine
Iron
Lead
Lithium
Magnesium
Manganese
Mercury
Molybdenum
Nickel
Niobium
Phosphate rock (as fosforite)
PGM
Potash (K2 O)
REE (as C e2 O3 )
Rhenium
Selenium
Silver
Strontium
x m [g/g]
4,60E-01
3,78E-02
1,00E-02
8,30E-01
1,00E-02
2,00E-03
2,00E-01
5,00E-03
1,00E-04
2,33E-01
4,35E-01
1,08E-03
5,80E-03
4,50E-01
2,50E-01
2,30E-05
5,00E-05
2,20E-07
5,00E-01
8,00E-01
6,00E-05
7,00E-02
1,40E-04
1,60E-04
5,11E-01
2,05E-02
4,00E-04
4,50E-01
3,15E-01
3,83E-03
3,10E-04
1,30E-02
6,38E-03
1,10E-03
8,02E-07
2,50E-01
9,70E-04
2,23E-04
2,50E-02
4,30E-06
3,40E-01
x c [g/g]
8,15E-02
4,00E-07
4,80E-06
4,13E-06
2,10E-06
1,60E-07
1,70E-05
5,00E-03
9,00E-08
4,90E-06
9,20E-05
1,73E-05
2,80E-05
1,45E-01
1,32E-06
1,75E-05
1,40E-06
1,50E-09
1,99E-03
1,08E-04
5,30E-06
7,00E-02
5,60E-08
1,40E-06
3,92E-02
1,70E-05
2,40E-05
1,50E-02
7,74E-04
5,00E-08
1,10E-06
4,70E-05
1,20E-05
4,03E-04
5,00E-10
2,32E-02
6,30E-05
1,98E-10
9,00E-08
5,30E-08
3,20E-04
kc [-]
2250
28
80
N.A.
112
90
N.A.
N.A.
804
N.A.
37
1262
343
N.A.
N.A.
N.A.
N.A.
422879
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
97
219
158
1
284
1707
947
432
N.A.
44
N.A.
39
N.A.
1939
N.A.
7042
0
Production
Reserves
Bc
Bc∗
Bc
Bc∗
1,46E+02
3,28E+05
1,97E+04
4,42E+07
7,48E-01
2,12E+01
1,17E+01
3,33E+02
3,61E-01
2,89E+01
7,23E+00
5,78E+02
2,60E+01
N.A.
6,19E+02
N.A.
3,59E-03
4,01E-01
N.A.
N.A.
1,52E-02
1,37E+00
8,56E-01
7,69E+01
3,44E+01
N.A.
1,37E+03
N.A.
N.A.
N.A.
N.A.
N.A.
7,13E-02
5,73E+01
1,81E+00
1,45E+03
N.A.
N.A.
3,40E-01
N.A.
5,81E+01
2,13E+03
N.A.
N.A.
2,80E-01
3,54E+02
2,91E+01
3,67E+04
8,10E+01
2,78E+04
2,63E+03
9,01E+05
4,34E+00
N.A.
N.A.
N.A.
4,97E+01
N.A.
2,24E+03
N.A.
1,69E-05
N.A.
N.A.
N.A.
2,63E-04
N.A.
N.A.
N.A.
3,69E-03
1,56E+03
6,30E-02
2,66E+04
2,96E+01
N.A.
2,47E+03
N.A.
2,28E+02
N.A.
N.A.
N.A.
N.A.
N.A.
4,89E-01
N.A.
N.A.
N.A.
N.A.
N.A.
2,34E-03
N.A.
4,44E-02
N.A.
5,53E-02
N.A.
3,32E+01
N.A.
2,63E+03
2,56E+05
2,22E+05
2,16E+07
7,05E+00
1,54E+03
1,60E+02
3,51E+04
N.A.
N.A.
9,84E+01
1,56E+04
6,15E+00
6,15E+00
N.A.
N.A.
7,93E+01
2,25E+04
3,07E+03
8,71E+05
4,91E-03
8,39E+00
1,53E-01
2,61E+02
6,41E-01
6,07E+02
3,00E+01
2,84E+04
8,97E+00
3,87E+03
3,80E+02
1,64E+05
1,78E-01
N.A.
1,08E+01
N.A.
8,34E+00
3,66E+02
1,06E+03
4,64E+04
1,16E-03
N.A.
1,59E-01
N.A.
4,58E+01
1,77E+03
1,31E+04
5,04E+05
6,07E-02
N.A.
4,34E+01
N.A.
2,09E-04
4,06E-01
1,11E-02
2,15E+01
1,45E-02
N.A.
7,72E-01
N.A.
4,88E-02
3,43E+02
6,52E-01
4,59E+03
2,83E+00
0,00E+00
3,29E+01
0,00E+00
Continued on next page . . .
Reserve base
Bc
Bc∗
2,52E+04
5,66E+07
2,40E+01
6,82E+02
1,08E+01
8,67E+02
2,87E+03
N.A.
N.A.
N.A.
1,82E+00
1,63E+02
3,31E+03
N.A.
N.A.
N.A.
4,43E+00
3,56E+03
5,34E-01
N.A.
N.A.
N.A.
5,40E+01
6,81E+04
5,04E+03
1,73E+06
N.A.
N.A.
4,47E+03
N.A.
N.A.
N.A.
N.A.
N.A.
1,35E-01
5,71E+04
6,04E+03
N.A.
N.A.
N.A.
8,83E-01
N.A.
N.A.
N.A.
6,46E-02
N.A.
5,97E+01
N.A.
4,86E+05
4,73E+07
3,45E+02
7,55E+04
2,64E+02
4,18E+04
N.A.
N.A.
3,47E+04
9,84E+06
7,97E-01
1,36E+03
6,62E+01
6,26E+04
8,51E+02
3,68E+05
1,20E+01
N.A.
2,94E+03
1,29E+05
1,79E-01
N.A.
2,83E+04
1,09E+06
7,40E+01
N.A.
4,43E-02
8,59E+01
1,60E+00
N.A.
1,38E+00
9,69E+03
5,81E+01
0,00E+00
Table A.21: The concentration exergy and exergy cost of the 2006 world’s mineral production,
mineral reserves, base reserve and world resources. Values are expressed in ktoe if not specified
World resources
Bc
Bc∗
5,90E+04
1,33E+08
N.A.
N.A.
6,65E+01
5,32E+03
6,52E+03
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
2,22E+01
1,78E+04
N.A.
N.A.
3,77E+04
1,38E+06
6,23E+01
7,86E+04
1,61E+04
5,52E+06
N.A.
N.A.
4,66E+03
N.A.
2,32E-01
N.A.
N.A.
N.A.
N.A.
N.A.
2,30E+04
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
7,52E+01
N.A.
6,98E+05
6,80E+07
3,05E+03
6,66E+05
3,12E+02
4,93E+04
N.A.
N.A.
N.A.
N.A.
1,99E+00
3,40E+03
4,53E+01
4,29E+04
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
2,24E-01
N.A.
3,93E+05
1,52E+07
N.A.
N.A.
4,87E-02
9,45E+01
N.A.
N.A.
N.A.
N.A.
4,84E+03
N.A.
400
ADDITIONAL
CALCULATIONS
Tantalum
Tellurium
Thorium
Tin
Titanium (T iO2 )
Vanadium
Wolfram
Zinc
Zircon (Z rO2 )
Sum
x m [g/g]
6,50E-03
1,00E-06
3,00E-02
4,80E-03
6,90E-03
2,00E-02
7,17E-03
4,06E-02
2,69E-03
x c [g/g]
9,00E-07
5,00E-09
1,05E-05
2,10E-06
3,84E-03
9,70E-05
1,90E-06
6,70E-05
1,93E-04
kc [-]
12509
N.A.
N.A.
1493
348
572
3105
126
7744
Production
Reserves
Bc
Bc∗
Bc
Bc∗
6,71E-03
8,39E+01
6,28E-01
7,86E+03
3,25E-04
N.A.
5,16E-02
N.A.
N.A.
N.A.
2,15E+00
N.A.
1,17E+00
1,74E+03
2,35E+01
3,52E+04
2,53E+00
8,80E+02
3,18E+02
1,11E+05
3,49E-01
2,00E+02
8,07E+01
4,61E+04
2,41E-01
7,48E+02
7,70E+00
2,39E+04
5,82E+01
7,33E+03
1,05E+03
1,32E+05
1,49E+00
1,16E+04
4,81E+01
3,73E+05
3,51E+03
6,69E+05
2,70E+05
6,92E+07
End of the table
Reserve base
Bc
Bc∗
8,70E-01
1,09E+04
1,16E-01
N.A.
2,50E+00
N.A.
4,25E+01
6,34E+04
6,53E+02
2,28E+05
2,36E+02
1,35E+05
1,67E+01
5,19E+04
2,79E+03
3,52E+05
9,12E+01
7,06E+05
6,04E+05
1,19E+08
Table A.21: The concentration exergy and exergy cost of the 2006 world’s mineral production,
mineral reserves, base reserve and world resources. Values are expressed in ktoe if not specified.–
continued from previous page.
World resources
Bc
Bc∗
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
N.A.
8,71E+02
3,03E+05
3,91E+02
2,24E+05
N.A.
N.A.
1,11E+04
1,39E+06
N.A.
N.A.
1,26E+06
2,25E+08
Exergy calculation of the mineral resources
401
402
A.7
A.7.1
ADDITIONAL
CALCULATIONS
Australian fossil fuel production
Coal
Table A.22 shows the Australian coal production from 1913 to 2006. The data has
been obtained from the British Geological Survey’s historical statistics [159], [157],
[52], [250], [154], [155], [30], [31] and [29].
Table A.22: Evolution of the Australian coal production. Values in ktons
Year
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
Anthrac.
Bitum.
12619
12657
11600
9971
10398
11126
10695
13178
13087
12498
12720
13980
13850
13465
13742
12032
10533
9686
8537
8725
9239
9734
11064
11555
12270
11869
14443
14612
14423
13944
13020
14000
14901
15022
14336
16816
Subbit.
Lign.
Year
Anthrac.
1960
51
1961
60
1962
70
1963
62
1964
74
1965
71
1966
47
1967
39
1968
30
1969
15
1970
119
1971
130
1972
891
1973
973
1974
1479
1975
1618
1976
1769
1977
1861
1978
2230
1979
2655
1980
2622
1981
2660
1982
2257
1983
3094
1984
3449
1985
3735
1986
1987
1988
4640
1989
2
5014
1990
5174
1991
35
5098
1992
42
5533
1993
138
5799
1994
196
6240
1995
6801
1996
7495
1997
7446
1998
Continued on next page . . .
Bitum.
20975
22347
22362
22629
24840
28685
30568
31806
37350
42349
46063
45841
59389
57355
66474
62417
69676
72679
74094
72679
76794
93405
99109
99828
116018
158256
170067
178399
176604
190085
162957
167472
179144
180045
182553
193534
198638
216690
222040
Subbit.
1908
1988
2433
2568
2891
3191
3297
3425
3542
3735
3482
3161
3300
3298
3975
3300
5008
5529
5733
5529
6365
7190
7992
8998
8288
Lign.
15210
16543
17415
18756
19341
20993
22136
23763
23346
23282
24175
23382
23697
24676
27303
23697
28178
29250
32860
29250
32597
32990
37821
34191
35166
36985
37604
44877
43450
48252
47725
52124
50228
48458
48582
50751
53604
58160
65600
Australian fossil fuel production
403
Table A.22: Evolution of the Australian coal production. Values in ktons–
continued from previous page.
Year
1951
1952
1953
1954
1955
1956
1957
1958
1959
A.7.2
Anthrac.
58
55
Bitum.
16373
18084
17119
18212
17979
18050
18596
18917
18877
Subbit.
1521
1635
1590
1871
1608
1536
1645
1798
1695
Lign.
Year
Anthrac.
7963
1999
8235
2000
8391
2001
9482
2002
10276 2003
10731 2004
10915 2005
11832 2006
13246
End of the table
Bitum.
232860
244840
266710
272560
280700
294810
308000
316000
Subbit.
Lign.
65820
67363
64958
66661
66809
66343
67152
67737
Oil
Table A.23 shows Australian oil production from 1913 to 2006. The data has been
obtained from the British Geological Survey’s historical statistics [159], [157], [52],
[250], [154], [155], [30], [31] and [29]. For the period between 1931 to 1940,
oil data corresponds only to the region of Victoria. Until 1964, the statistics include
crude petroleum plus oil shale.
Table A.23: Evolution of the Australian oil production. Values in ktons
Year
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
ktons
5,52
16,26
5,03
5,66
10,27
10,52
10,15
8,12
0,08
0,08
Year
ktons
Year
ktons
1937
0,04
1961
1938
0,03
1962
1939
0,02
1963
1940
0,02
1964
278
1941
1965
334
1942
1966
432
1943
1967
993
1944
1968
1818
1945
1969
2065
1946
1970
8541
1947
1971 14803
1948
0,12
1972 15685
1949
0,14
1973 20635
1950
0,16
1974 24559
1951
0,27
1975 21738
1952
1976 22122
1953
1977 22793
1954
1978 22976
1955
1979 23141
1956
1980 19451
Continued on next page . . .
Year
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
ktons
30447
27151
29076
27493
25908
30548
28835
28326
26300
28505
27031
28407
30000
28000
27000
37000
34000
33000
27000
20748
404
ADDITIONAL
CALCULATIONS
Table A.23: Evolution of the Australian oil production. Values in ktons.–
continued from previous page.
Year
1933
1934
1935
1936
A.7.3
ktons
0,08
0,02
0,02
0,02
Year
1957
1958
1959
1960
ktons
Year
1981
1982
1983
1984
End of the table
ktons
19799
18839
21209
26377
Year
2005
2006
ktons
21439
20831
Natural gas
Table A.24 shows Australian natural gas production from 1961 to 2006. The data
has been obtained from the British Geological Survey’s historical statistics [154],
[155], [155], [30], [31] and [29].
Table A.24: Evolution of the Australian natural gas production. Values in
millions of cubic meters
Year
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
A.8
A.8.1
M m3
0,34
1,6
2,7
3,0
4,0
4,0
4,3
6,1
265
1502
2274
3188
Year
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
M m3
4099
4677
5026
5929
6728
7320
8381
9567
11260
11565
11581
12600
Year
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
M m3
13470
14714
15023
15383
17806
20620
21694
23462
24457
28147
29761
29799
Year
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
M m3
29876
30361
30755
31165
32482
32606
33180
35224
37129
38883
World’s fuel production
Uranium
Table A.25 shows the production of uranium in western countries and the world
production from 1945 to 2006. Approximate data about uranium production in
western countries is extracted from the World Nuclear Association [408]. For world
production data, it has been assumed that western countries contribute to about 69
World’s fuel production
405
% of total world production. From 2002 to 2006, world production information is
directly provided by the WNA [408].
Table A.25: Production of uranium in western countries and in the world.
Values are expressed in tons
Year
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
A.8.2
Production
w. countries
[408]
500
500
500
1500
1500
3000
3000
2000
4500
6500
7500
10300
20000
30000
34000
32000
28000
25500
23000
22500
15300
15000
15400
17000
17000
18300
19000
20000
20000
19000
20000
World production
Year
725
725
725
2174
2174
4348
4348
2899
6522
9420
10870
14928
28986
43478
49275
46377
40580
36957
33333
32609
22174
21739
22319
24638
24638
26522
27536
28986
28986
27536
28986
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Production
w. countries
[408]
24000
29000
35000
39000
45000
45000
42000
36000
38000
35000
36500
34500
36000
33000
27500
26000
23000
22500
22500
25000
27500
28000
26500
22500
26500
27500
26000
25000
28000
World production
34783
42029
50725
56522
65217
65217
60870
52174
55072
50725
52899
50000
52174
47826
39855
37681
33333
32609
32609
36232
39855
40580
38406
32609
38406
39855
36063
35613
40251
41702
39429
Coal
Table A.26 shows the world’s coal production from 1900 to 2006. The data from
1981 to 2006 has been extracted from BP [35]. From 1900 to 1912 the information
has been obtained from the estimations done by Ortiz [253]. From 1913 to 1981,
406
ADDITIONAL
CALCULATIONS
the data was obtained from the British Geological Survey’s historical statistics [159],
[157], [52], [250], [154].
Table A.26: Evolution of the world’s coal production
Year
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
A.8.3
Mt coal
800,0
820,0
850,0
900,0
920,0
1000,0
1100,0
1080,0
1100,0
1190,0
1200,0
1210,0
1320,1
1160,0
1175,3
1258,7
1310,4
1234,3
1084,7
1302,0
1118,0
1210,0
1340,0
1340,0
1350,0
1340,0
Year
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
Mt coal
1450,0
1440,0
1540,0
1390,0
1240,0
1110,0
1150,0
1260,0
1310,0
1420,0
1510,0
1420,0
1550,0
1660,0
1745,0
1756,0
1770,0
1420,0
1324,0
1445,0
1622,0
1698,0
1670,0
1792,0
1570,0
1900,0
1930,0
Year
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
Mt coal
1940,0
2100,0
2220,0
2300,0
2400,0
2480,0
2590,0
2440,0
2510,0
2610,0
2710,0
2760,0
2790,0
2677,0
2702,0
2826,0
2944,0
2950,0
3041,0
3065,0
3107,0
3253,0
3349,0
3510,0
3558,0
3719,0
3806,0
Year
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Mt coal
3831,1
3980,1
3986,8
4191,5
4420,8
4528,8
4629,9
4735,7
4818,5
4718,6
4538,8
4500,2
4382,5
4470,5
4592,5
4667,7
4702,1
4555,7
4544,5
4606,6
4819,2
4852,3
5187,6
5585,3
5886,7
6195,1
Oil
Table A.27 shows the world’s oil production from 1900 to 2006. The data from 1965
to 2006 has been extracted from BP [35]. Until 1912, the information has been
obtained from the estimations done by Ortiz [253]. Between 1913 and 1965, the
data was obtained from the British Geological Survey’s historical statistics [159],
[157], [52], [250], [154].
World’s fuel production
407
Table A.27: Evolution of the world’s oil production
Year
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
A.8.4
Mt oil
0,0
4,5
9,0
13,6
18,1
22,6
27,1
31,7
36,2
40,7
45,2
49,8
54,3
56,0
59,0
62,7
67,4
71,8
69,1
79,3
99,8
113,1
124,1
146,9
146,1
154,1
157,4
Year
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
Mt oil
Year
181,7
1954
183,8
1955
207,0
1956
197,0
1957
190,5
1958
180,8
1959
199,1
1960
207,3
1961
228,6
1962
249,9
1963
283,5
1964
279,4
1965
289,9
1966
299,0
1967
310,6
1968
290,6
1969
320,6
1970
342,0
1971
361,9
1972
383,4
1973
423,2
1974
477,5
1975
475,1
1976
530,2
1977
600,9
1978
632,6
1979
668,5
1980
End of the table
Mt oil
699,0
774,5
842,7
888,4
910,8
984,0
1053,6
1131,8
1208,0
1303,5
1403,1
1500,6
1700,6
1824,7
1990,9
2141,2
2355,2
2492,6
2636,6
2866,6
2875,2
2734,4
2969,0
3073,2
3103,1
3233,1
3087,9
Year
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Mt oil
2910,0
2795,6
2759,2
2814,6
2792,1
2935,9
2947,1
3069,0
3102,9
3170,6
3160,5
3190,0
3188,6
3237,2
3281,0
3376,5
3480,5
3548,3
3482,9
3618,1
3602,7
3575,6
3701,3
3862,6
3896,8
3914,1
Natural gas
Table A.28 shows the world’s natural gas production from 1900 to 2006. The data
from 1970 to 2006 has been extracted from BP [35]. Until 1920, the information
has been estimated from US natural gas production, which is a compilation of data
from the “Espasa” encyclopedia [87] between years 1900 -1921. Between 1921 and
1970, the data was obtained from the British Geological Survey’s historical statistics
[159], [157], [52], [250], [154]. For years 1945-1947, a linear increasing rate has
been assumed, because of lack of data.
408
ADDITIONAL
CALCULATIONS
Table A.28: Evolution of the world’s natural gas production. Data in billion
of cubic meters
Year
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
A.9
World Prod.
3,5
5,0
5,9
6,7
7,3
7,5
10,8
11,5
11,2
13,4
14,6
14,7
15,8
16,2
16,5
17,6
21,0
22,1
20,3
21,0
22,4
19,8
22,8
29,8
33,7
35,3
38,9
42,7
45,6
56,4
57,6
49,3
47,0
47,4
54,6
Year
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
World Prod.
57,5
65,5
72,5
75,2
80,5
80,4
112,2
91,1
98,9
106,6
121,1
135,6
150,1
164,6
175,6
184,1
239,0
257,1
270,1
295,9
323,6
351,8
386,3
388,6
432,4
472,9
511,8
558,5
609,8
663,8
706,9
759,8
821,5
889,1
955,1
Year
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
World Prod.
1009,3
1073,8
1125,3
1180,2
1201,5
1203,3
1252,9
1301,5
1347,3
1438,0
1448,5
1475,8
1478,0
1483,2
1614,9
1666,7
1713,6
1798,7
1882,4
1943,3
1991,8
2023,7
2037,0
2073,1
2093,6
2134,7
2227,9
2231,5
2279,5
2343,7
2425,2
2482,1
2524,6
2614,3
2703,1
2779,8
2865,3
The Hubbert peak applied to world production of the
main non-fuel minerals
Figures A.1, A.2, and A.3 show the Hubbert model applied to the exergy costs of
world iron, aluminium and copper production. It is assumed that the total world
The Hubbert peak applied to world production of the main non-fuel minerals
409
5
x 10
15
2068
Bt*
10
5
8
0
x 10
2.5
Integral Bt*
2
1.5
1
0.5
0
1900
1950
2000
2050
2100
2150
2200
2250
Figure A.1. The Hubbert peak applied to the exergy cost of world’s iron production,
based on the world resources. Data in ktoe
6
2
x 10
2089
Bt*
1.5
1
0.5
8
0
x 10
2.5
Integral Bt*
2
1.5
1
0.5
0
1900
1950
2000
2050
2100
2150
2200
2250
2300
Figure A.2. The Hubbert peak applied to the exergy cost of world’s aluminium production, based on the world resources. Data in ktoe
mineral reserves are equal to the world resources of each mineral in 2006 published
by the USGS [362] plus the irreversible exergy distance D∗ from 1900 to 2006.
410
ADDITIONAL
CALCULATIONS
5
2
x 10
2066
Bt*
1.5
1
0.5
7
0
x 10
2.5
Integral Bt*
2
1.5
1
0.5
0
1900
1950
2000
2050
2100
2150
2200
2250
Figure A.3. The Hubbert peak applied to the exergy cost of world’s copper production, based on the world resources. Data in ktoe
A.10
Fuel consumption in the 21st century
Tables A.29 through A.34 show the primary energy consumption and cumulative
resources production assumed in each of the SRES scenarios.
Table A.29. Primary energy consumption and cumulative resources production in
the IPCC’s B1 scenario [160]
Year
Coal
Oil
Gas
1990
105
129
62
2000
109
141
71
2010
120
176
108
Coal
Oil
Gas
0,0
0,0
0,0
1,1
1,3
0,6
2,2
2,9
1,5
Primary Energy, EJ
2020
2030
2040
2050
2060
134
163
181
167
133
206
230
236
228
199
138
153
166
173
168
Cumulative Resources Production, ZJ
3,5
4,9
6,7
8,5
10,0
4,8
7,0
9,3
11,6
13,8
2,8
4,2
5,8
7,5
9,2
2070
101
167
154
2080
76
143
136
2090
58
119
121
2100
44
99
103
11,1
15,6
10,8
12,0
17,2
12,3
12,7
18,5
13,6
13,2
19,6
14,7
Fuel consumption in the 21st century
411
Table A.30. Primary energy consumption and cumulative resources production in
the IPCC’s A1T scenario [160]
Year
Coal
Oil
Gas
1990
91
128
71
2000
106
155
87
2010
125
172
124
Coal
Oil
Gas
0,0
0,0
0,0
0,9
1,4
0,8
2,0
3,0
1,6
Primary Energy, EJ
2020
2030
2040
2050
2060
151
180
153
119
87
193
223
241
250
236
166
231
288
324
344
Cumulative Resources Production, ZJ
3,2
4,7
6,5
8,1
9,3
4,7
6,6
8,9
11,3
13,8
2,9
4,5
6,8
9,7
13,0
2070
60
205
324
2080
53
143
291
2090
40
113
240
2100
25
77
196
10,1
16,1
16,4
10,7
18,2
19,6
11,3
19,6
22,6
11,7
20,8
25,0
Table A.31. Primary energy consumption and cumulative resources production in
the IPCC’s B2 scenario [160]
Year
Coal
Oil
Gas
1990
91
128
71
2000
91
168
84
2010
98
195
107
Coal
Oil
Gas
0,0
0,0
0,0
0,9
1,4
0,7
1,8
3,1
1,6
Primary Energy, EJ
2020
2030
2040
2050
2060
98
96
93
86
91
214
240
238
227
201
150
194
251
297
356
Cumulative Resources Production, ZJ
2,8
3,8
4,7
5,7
6,5
5,1
7,2
9,6
12,0
14,3
2,7
4,2
6,1
8,6
11,6
2070
119
146
390
2080
170
101
402
2090
231
72
385
2100
300
52
336
7,4
16,3
15,1
8,6
17,7
19,0
10,3
18,7
23,1
12,6
19,5
26,9
Table A.32. Primary energy consumption and cumulative resources production in
the IPCC’s A1B scenario [160]
Year
Coal
Oil
Gas
1990
93
143
73
2000
99
167
91
2010
134
209
147
Coal
Oil
Gas
0,1
0,1
0,1
1,1
1,7
0,9
2,2
3,6
2,1
Primary Energy, EJ
2020
2030
2040
2050
2060
163
179
182
186
165
238
239
226
214
188
196
298
372
465
519
Cumulative Resources Production, ZJ
3,7
5,4
7,0
9,1
10,5
5,8
8,2
10,2
12,7
14,4
3,8
6,3
9,3
13,9
18,2
2070
148
166
578
2080
126
149
604
2090
103
136
590
2100
84
125
576
12,2
16,3
23,9
13,6
18,0
29,8
14,7
19,4
35,5
15,9
20,8
42,2
412
ADDITIONAL
CALCULATIONS
Table A.33. Primary energy consumption and cumulative resources production in
the IPCC’s A2 scenario [160]
Year
Coal
Oil
Gas
1990
92
134
71
2000
90
172
74
2010
106
220
89
Coal
Oil
Gas
0,0
0,0
0,0
1,0
1,7
0,8
2,0
3,6
1,6
Primary Energy, EJ
2020
2030
2040
2050
2060
129
184
239
294
415
291
270
249
228
148
126
176
225
275
297
Cumulative Resources Production, ZJ
3,2
4,7
6,9
9,5
13,1
6,2
9,0
11,6
13,9
15,7
2,7
4,2
6,2
8,7
11,6
2070
536
69
319
2080
658
23
330
2090
781
12
331
2100
904
0
331
17,9
16,7
14,7
31,1
17,0
17,9
38,3
17,2
21,3
46,8
17,2
24,6
Table A.34. Primary energy consumption and cumulative resources production in
the IPCC’s A1FI scenario [160]
Year
Coal
Oil
Gas
1990
88
131
70
2000
115
136
85
2010
150
150
129
Coal
Oil
Gas
0,1
0,1
0,1
1,2
1,5
0,9
2,6
2,9
2,1
Primary Energy, EJ
2020
2030
2040
2050
2060
193
299
393
475
448
173
165
202
283
353
203
268
333
398
494
Cumulative Resources Production, ZJ
4,2
7,0
10,4
14,6
19,1
4,5
6,2
8,1
10,4
13,8
3,6
6,1
9,2
12,7
17,4
2070
432
416
573
2080
429
471
634
2090
518
359
606
2100
607
248
578
23,6
17,7
22,8
27,9
22,0
28,7
32,9
25,8
34,8
37,9
29,6
40,9
Nomenclature, Figures, Tables and
References
413
Nomenclature
Symbols
a1 − a7 : Experimental coefficients for the calculation of h∗ (T ) and s∗ (T ) [-]
a i : Effective diameter of the ion [m]
a j 1 : Intercept of the learning curve with the vertical axes for material’s use [-]
ae1 : Intercept of the learning curve with the vertical axes for energy’s use [-]
a j 2 : Parameter relating material inputs per unit output at time period t [-]
ae2 : Parameter relating energy inputs per unit output at time period t [-]
A1 : Constant in the Debye- Huckel equation with the value 0,51 kg1/2 mole−1/2 for water at 25o C
A2 : Constant in the Debye- Huckel equation with the value 3,287 * 109 kg1/2 m−1 mole−1/2 for water
at 25o C
b : Specific exergy [kJ/mole]
b0 : Full width at half maximum of the Gaussian peak [-]
bch : Specific chemical exergy [kJ/mole]
bc : Specific concentration exergy [kJ/mole]
B : Absolute exergy [kJ]
B∗ : Absolute exergy replacement cost (also named actual exergy) [kJ]
Bc : Absolute concentration exergy [kJ]
Bch : Absolute chemical exergy [kJ]
B t : Absolute total exergy [kJ]
c j : Fraction of the j-th element appearing in the form of reference species [-]
∆C p : Heat capacity [kJ/mole]
d1 : Moles of C contained in the fuel [mole/g]
D : Minimum exergy distance, equivalent to the exergy difference between two situations of the planet
[kJ]
D ∗ : Actual exergy distance, equivalent to the difference of the exergy replacement costs of two situations of the planet [kJ]
415
416
NOMENCLATURE
Ḋ : Minimum exergy degradation velocity [kW]
Ḋ ∗ : Actual degradation velocity in terms of exergy replacement costs [kW]
e 0 : Standard energy [kJ/mole]
e1 − e5 : Exponentials used to calculate the contribution of the entropy change for gaseous reference
substances [-]
e(t ) : Flow of energy used to perform a certain process [kJ]
f j : Elements of the atomic composition vector of the fuel f = [1, h, o, n, s]0 [-]
F : Fractal relationship of the deposit [-]
F1 − F7 : Coefficients for estimating x H2 O,00 [-]
gi : Free energy contribution of one mole of each oxide or hydroxide component of the substance,
according to the method of Chermak and Rimstid [55] [kJ/mole]
∆G f : Gibbs free energy of formation [kJ/mole]
∆Gm : Gibs free energy of mixing [kJ/mole]
0
∆Ghyd
: hydration Gibbs free energy [kJ/mole]
r
∆G O −2 : Gibbs free energy of formation of a generic oxide M Ox (c) from its aqueous ion [kJ/mole]
0
: Gibbs free energy of formation of a given compound as determined from the constituent oxides
∆Gox
[kJ/mole]
∆G r : Gibs free energy of the reaction [kJ/mole]
h : Moles of hydrogen per mole of carbon in the fuel [mole/mole]
hi : Enthalpy contribution of one mole of each oxide or hydroxide of the substance, according to the
method of Chermak and Rimstid [55] [kJ/mole]
h∗ (T ) : Enthalpy of Zelenik and Gordon [413] [kJ/mole]
H j,00 : Enthalpy of the elements in the dead state [kJ/mole]
∆H : Enthalpy change [kJ/mole]
∆H f : Enthalpy of formation [kJ/mole]
∆Hm : Enthalpy of mixing [kJ/mole]
0
∆Hhyd
: Hydration enthalpy [kJ/mole]
r
∆H O −2 : Enthalpy of formation of a generic oxide M Ox (c) from its aqueous ion [kJ/mole]
0
: Gibbs free energy of formation of a given compound as determined from the constituent oxides
∆Hox
[kJ/mole]
∆H r : Enthalpy of the reaction [kJ/mole]
I : Ionic strength of the electrolyte [mole/kg]
j(t ) : Flow of material used to perform a certain process [kg]
k c : Unit concentration exergy replacement cost [-]
k ch : Unit chemical exergy replacement cost [-]
l j : Number of the atoms of j-th element in the molecule of the reference species [-]
m : Mass [kg]
Nomenclature
417
m i : Conventional standard molarity of the reference substance i in seawater [mole/kg]
M : Tonnage of the deposit [k g]
Mc : Tonnage of the piece of land under consideration [kg]
M W : Molecular weight [mol e/g]
n : Moles of nitrogen per mole of carbon in the fuel [mole/mole]
n i : Number of moles of substance i [mole]. In section 5.4.5, the number of oxygen ions linked to the
Miz+ cations [-].
n s : Number of cations located in different sites of the hydrated clay mineral or phyllosilicate [-].
n w : Number of molecules of water [-]
N : Number of oxygens linked to the molecular structure of the double oxide [-]
o : Moles of oxygen per mole of carbon in the fuel [mole/mole]
∆O −2 : Enthalpy ∆H O−2 or Gibbs free energy ∆G O−2 of formation of a generic oxide M Ox (c) from its
aqueous ion [kJ/mole]
P : Pressure [kPa] and Production of a mineral commodity [ktoe/year]
P0i : Conventional mean ideal gas partial pressure of substance i in the atmosphere [kPa]
p H : Exponent of the concentration of hydrogen ion in seawater (pH=8,1) [-]
Q : Heat loss escaping the crust [W /m3 ]
Q B : Heat input at the base of the lithosphere due to mantle convection [W /m3 ]
QC : Radiogenic heat production of the crust [W /m3 ]
Q L : Radiogenic heat production in the mantle part of the lithosphere [W /m3 ]
Q M : Mantle heat flow [W /m3 ]
Q T : Long-term heat production transient due to cooling after a major tectonic or magmatic perturbation [W /m3 ]
r j,i : Amount of moles of element j in substance i [mole j/mole i]
rk,i : Number of molecules of additional elements k present in the molecule of reference substance i
[mole k/mole i]
R : Available reserves [ktoe]
R[ j × i] : Stoichiometric coefficient matrix between species i and elements j of dimensions [ j × i]
R̄ : Universal gas constant [8,314E-3 kJ/(mole K)]
RF : Regression factor of the fit [-]
R/P : Resources to production ratio [-]
s : Moles of sulphur per mole of carbon in the fuel [mole/mole]
s 0 : Standard entropy [kJ/mole]
s ∗ (T ) : Entropy of Zelenik and Gordon [413] [kJ/(mole K)]
∆S : Entropy change [kJ/(mole K)]
t : time [s, years]
t0 : Year where the peak of production is reached [yr]
418
NOMENCLATURE
T : Temperature [K]
t Me : Exergy content of one ton of mineral in a certain time and place [kJ]
t Me ∗ : Exergy replacement cost of one ton of mineral in a certain time and place [kJ]
w : Moles of water per mole of carbon in the fuel [mole/mole]
W : Moles of liquid water (moisture) in the fuel [mole]
x : Molar fraction [mole/mole]. In section 5.4.5, the number of oxygen atoms combined with one
atom M in the oxide [-].
x c : Concentration of the mineral in the earth’s crust [g/g]
x m : Concentration of the mineral deposit [g/g]
X : The molar fraction of oxygen related to the cations of a hydrated clay mineral or phyllosilicate [-]
y0 : Height of the Gaussian peak [-]
z : Moles of ashes per mole of carbon in the fuel [mole/mole]
z + : Number of elementary positive charges [-]
Z : Moles of ashes in the fuel [mole]
Greek letters
0
[-]
αG : Empirical coefficient variable for estimating ∆Gox
0
αH : Empirical coefficient variable for estimating ∆H ox
[-]
δ : Thickness of the crust [m]
γ : Activity coefficient (molarity scale) of the reference substance in seawater [-]
Γ(t ) : Cumulative production in period t [kg]
ε : Relative error [%]
ε j : Mean molar concentration of element j contained in the atmosphere, hydrosphere or continental
crust [mole/g]
µ j,00 : Chemical potential of the elements in the dead state [kJ/mole]
ρ15 : Density of the fuel at 15◦ C [kg/m3 ]
τ : Temperature [◦ C]
ξi : Mean molar concentration of substance i contained in the atmosphere, hydrosphere or continental
crust [mole/g]
Abbreviations
BGS : British Geological Survey
BP : British Petroleum
EWG : Energy Watch Group
HHV : High Heating Value
Nomenclature
IGU : International Gas Union
IPCC : Intergovernmental Panel on Climate Change
IWP&DC : The International Water Power & Dam Construction
LHV : Low Heating Value
PV : Photovoltaic energy
R.B. : Reserve Base
R.E. : Reference Environment
RE2 O5 : Rare earth’s oxides
R.S. : Reference Substances in the Reference Environment
RW : Renewable Energies
SRES : Special Report on Emission Scenarios
THC : Thermohaline Circulation
USBM : U.S. Bureau of Mines
USGS : U.S. Geological Survey
WEC : World Energy Council
W.R. : World Resources
Subscripts
0 : Conditions of the environment
00 : Conditions of the reference environment or dead state
at m: Atmosphere
bk : The number of brucitic cations
c r : Upper continental crust
e: Electrical consumption
g l: Glaciers
g w : Groundwater
h yd r : Hydrosphere
j : Index of the considered element. In section 5.4.5, also the index of the considered cation
i : Index of the considered species. In section 5.4.5, also the index of the considered cation
k : Index of the additional element appearing in the reference substance of element j
l i : The number of interlayer atom
L : Liquid fuel
F : Clean solid fuel
o : The octahedral site
t : The tetrahedral site
419
420
NOMENCLATURE
r w : River water
s p he r e: Considered sphere of the earth, either atmosphere, hydrosphere or upper continental crust
s w : Seawater
t : Total
t h: Thermal consumption
W : Moisture
Z : Ashes
Superscripts
∧ : Property calculated in this study
− : Average of the property
0 : Standard conditions
List of Figures
1.1
Conceptual diagram of the terms exergoecology and thermo-ecology .
11
2.1
The atmospheric layers. Source: http://www.atmosphere.mpg.de
(Max Plank Institute) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Earth’s cutaway. Source: USGS [397] . . . . . . . . . . . . . . . . . . . . .
22
38
2.2
Energy flow sheet for the surface of the earth [317] . . . . . . . . . . . .
The hydrologic cycle. Source: http://www.ec.gc.ca/water (Environment Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 A simplified summary of the path of the Thermohaline Ocean Circulation [274] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Primary world energy consumption by fuel type at the end of 2006.
Values in Mtoe [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Coal proved reserves at the end 2006. Values in thousand millions
tonnes (share of anthracite and bituminous coal in brackets) [35]. . . .
4.6 Coal production and consumption at the end of 2006. Elaborated from
data included in [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Oil proved reserves at the end 2006. Values in thousand millions of
barrels [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 Oil production and consumption at the end of 2006. Elaborated from
data included in [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9 Natural gas proved reserves at the end 2006. Values in trillion cubic
meters [35]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.10 Natural gas production and consumption at the end of 2006. Elaborated from data included in [35]. . . . . . . . . . . . . . . . . . . . . . . .
4.11 A classification of mineral resources and reserves [141]. . . . . . . . . .
4.12 Two possible relationships between ore grade and the metal, mineral,
or energy content of the resource base [316]. . . . . . . . . . . . . . . . .
4.1
4.2
5.1
Exergy required for separating a substance from a mixture, according
to Eq. 5.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
421
107
115
117
120
122
123
125
125
126
126
130
131
160
422
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14
7.15
7.16
7.17
7.18
7.19
7.20
7.21
7.22
7.23
7.24
7.25
7.26
7.27
7.28
7.29
7.30
7.31
LIST
OF
FIGURES
Conceptual diagram for the terms exergy distance and exergy degradation velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Hubbert’s bell shape curve of the production cycle of any exhaustible resource [146]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hypothetical processes involved in obtaining the mineral of copper
from the reference environment . . . . . . . . . . . . . . . . . . . . . . . .
Yearly chemical exergy consumption in the US of pure copper due to
copper production throughout the 20th century . . . . . . . . . . . . . .
Cumulative chemical exergy decrease of copper mines in the US
throughout the 20th century . . . . . . . . . . . . . . . . . . . . . . . . . .
Yearly concentration exergy consumption in the US of pure copper due
to copper production throughout the 20th century . . . . . . . . . . . . .
Cumulative concentration exergy decrease of copper mines in the US
throughout the 20th century . . . . . . . . . . . . . . . . . . . . . . . . . .
The Hubbert peak applied to US copper production. Best fitting curve.
Values in ktoe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Hubbert peak applied to US copper base reserves. Values in ktoe. .
Ore grade and cumulated exergy consumption of Australian gold mines
The Hubbert peak applied to Australian gold reserves. Values in toe. .
Ore grade and cumulated exergy consumption of Australian copper
mines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Hubbert peak applied to Australian copper reserves. Values in ktoe.
Ore grade and cumulated exergy consumption of Australian nickel mines
The Hubbert peak applied to Australian nickel reserves. Values in ktoe.
Ore grade and cumulated exergy consumption of Australian silver mines
The Hubbert peak applied to Australian silver reserves. Values in toe. .
Ore grade and cumulated exergy consumption of Australian lead mines
The Hubbert peak applied to Australian lead reserves. Values in ktoe. .
Ore grade and cumulated exergy consumption of Australian zinc mines
The Hubbert peak applied to Australian zinc reserves. Values in ktoe. .
Ore grade and cumulated exergy consumption of Australian iron mines
The Hubbert peak applied to Australian iron reserves. Values in ktoe. .
The exergy loss of Australian coal reserves. Values in ktoe. . . . . . . . .
The Hubbert peak applied to Australian coal reserves. Values in ktoe. .
The exergy loss of Australian oil reserves. Values in ktoe. . . . . . . . . .
The Hubbert peak applied to Australian oil reserves. Values in ktoe. . .
The exergy loss of Australian natural gas reserves. Values in ktoe. . . .
The Hubbert peak applied to Australian natural gas reserves. Values in
ktoe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Irreversible exergy consumption of the main non-fuel minerals in Australia in the period from 1884 to 1906 . . . . . . . . . . . . . . . . . . . .
Irreversible exergy consumption of the main non-fuel minerals in Australia in the period from 1907 to 1964 . . . . . . . . . . . . . . . . . . . .
231
233
236
239
239
240
241
243
245
248
249
251
251
253
253
255
256
257
258
259
260
261
262
264
265
266
266
268
268
270
271
List of Figures
7.32 Irreversible exergy consumption of the main non-fuel minerals in Australia in the period from 1965 to 2004 . . . . . . . . . . . . . . . . . . . .
7.33 Irreversible exergy consumption of the main fuel and non-fuel minerals
in Australia in the period of 1914 to 1968 . . . . . . . . . . . . . . . . . .
7.34 Irreversible exergy consumption of the main fuel and non-fuel minerals
in Australia in the period of 1969 to 2004 . . . . . . . . . . . . . . . . . .
7.35 Relative contribution of the extraction of fuel and non-fuel minerals to
the global exergy degradation of Australia in the period of 1914 to 2004
7.36 Exergy countdown of the main consumed minerals in Australia . . . . .
7.37 Exergy countdown of metals copper, zinc, nickel, lead and silver in
Australia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
8.16
8.17
8.18
8.19
8.20
The exergy loss of the main non-fuel mineral commodities on earth in
the twentieth century . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The actual exergy loss of the main non-fuel mineral commodities on
earth in the twentieth century . . . . . . . . . . . . . . . . . . . . . . . . .
The actual exergy loss of the main 15 non-fuel mineral commodities
on earth in the twentieth century, excluding iron and aluminium . . . .
Depletion degree in % of the main non-fuel mineral commodity reserves
The Hubbert peak applied to world iron production. Data in ktoe . . .
The Hubbert peak applied to world aluminium production. Data in ktoe
The Hubbert peak applied to world copper production. Data in ktoe . .
Actual exergy consumption of the world’s fuel and non-fuel minerals
throughout the 20th century . . . . . . . . . . . . . . . . . . . . . . . . . .
The Hubbert peak applied to world coal production. Data in Mtoe . . .
The Hubbert peak applied to world natural gas production. Data in Mtoe
The Hubbert peak applied to world oil production. Data in Mtoe . . . .
The Hubbert peak applied to the world’s conventional fossil fuel production. Data in Mtoe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Hubbert peak applied to the world’s main minerals production.
Data in Mtoe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The exergy countdown of the main minerals extracted on earth . . . .
Schematic presentation of the global carbon cycle as estimated by Post
et al. [270] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scenarios for GHG emissions from 2000 to 2100 and projections of
surface temperatures [160] . . . . . . . . . . . . . . . . . . . . . . . . . . .
CO2 emissions and equilibrium temperature increases for a range of
stabilization levels [162] . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exergy loss of the different types of coal as a function of the CO2 concentration in the atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . .
Exergy loss of the different types of fuel-oils as a function of the CO2
concentration in the atmosphere . . . . . . . . . . . . . . . . . . . . . . . .
Exergy loss of natural gas as a function of the CO2 concentration in the
atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
423
271
272
273
273
275
276
286
287
288
288
289
290
290
292
293
293
294
295
296
296
298
300
301
303
304
305
424
LIST
OF
FIGURES
8.21 Actual exergy consumption of the main minerals in the 21st century
based on the Hubbert peak model. Values in Gtoe . . . . . . . . . . . . .
8.22 Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s B1 scenario. Values in Gtoe . . . . . . . . . . . . . .
8.23 Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s A1T scenario. Values in Gtoe . . . . . . . . . . . . .
8.24 Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s B2 scenario. Values in Gtoe . . . . . . . . . . . . . .
8.25 Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s A1B scenario. Values in Gtoe . . . . . . . . . . . . .
8.26 Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s A2 scenario. Values in Gtoe . . . . . . . . . . . . . .
8.27 Actual exergy consumption of the main minerals in the 21st century
based on the IPCC’s A1FI scenario. Values in Gtoe . . . . . . . . . . . . .
8.28 Summary of the actual exergy degradation of the main extracted minerals in the period between years 1900 and 2100 based on the Hubbert
and the IPCC’s SRES scenarios . . . . . . . . . . . . . . . . . . . . . . . . .
A.1 The Hubbert peak applied to the exergy cost of world’s iron production,
based on the world resources. Data in ktoe . . . . . . . . . . . . . . . . .
A.2 The Hubbert peak applied to the exergy cost of world’s aluminium
production, based on the world resources. Data in ktoe . . . . . . . . . .
A.3 The Hubbert peak applied to the exergy cost of world’s copper production, based on the world resources. Data in ktoe . . . . . . . . . . . . . .
308
310
312
313
314
316
317
319
409
409
410
List of Tables
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
3.1
3.2
3.3
3.4
3.5
Composition of the main envelopes derived from direct sampling or
from a chemical translation of a direct measurement (density), in the
case of the core, and the corresponding whole earth composition [169].
Gaseous chemical composition of the atmosphere [272]. . . . . . . . . .
Inventory of water at the earth’s surface [263]. . . . . . . . . . . . . . . .
Volume of Oceans and Seas. Adapted from [85] . . . . . . . . . . . . . .
The composition of average seawater. Adapted from [224] . . . . . . .
Predicted Mean Oceanic Concentrations. Adapted from [273]. . . . . .
Renewable water resources and potential water availability by continents [311]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mean chemical contents of world river water [197] . . . . . . . . . . . .
The average concentrations of elements in filtered river water. Concentration in ppb. Adapted from Li [196]. . . . . . . . . . . . . . . . . . .
Constituents of ground waters from different rock types. Concentrations in µg/g [405]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Area of land surface covered by glaciers in different regions of the
world, together with estimates of volume and the equivalent sea level
rise that the volume implies [185]. . . . . . . . . . . . . . . . . . . . . . .
The concentration of major ions in glacial runoff from different regions
of the world. Concentrations are reported in mg/l. Adapted from [43]
Average composition of the upper continental crust according to different studies. Elements in g/g. . . . . . . . . . . . . . . . . . . . . . . . . .
Mineral classification based on Dana’s New Mineralogy [103] . . . . . .
Crustal abundance of minerals. Data in percent volume. . . . . . . . . .
Average mineralogical composition of the upper continental crust according to Grigor’ev [127]. Results are given in mass percentage. . . .
Comparison of Rudnick and Gao’s [292] chemical composition of the
upper earth’s crust and the one generated by Grigor’ev [127] according
to Eq. 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mineralogical composition of the earth’s crust according to the calculations of this study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
425
21
24
25
26
27
28
31
31
32
34
35
36
39
44
47
47
55
92
426
3.6
LIST
OF
TABLES
Crustal abundance of minerals according to this and Grigor’ev’s model
in mass % [127] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
101
World energy use in 1984 [130] . . . . . . . . . . . . . . . . . . . . . . . .
Estimates of bulk continental crust heat production from heat flow data
[168]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Estimated uranium resources in ores rich enough to be mined for use in
235
U power plants [317], together with estimated rates of production
for 2005 according to the BGS [139]. Data reported as ktons of metal
content. No distinctions are drawn between reserves and resources,
and no data for resources are reported by the former URSS countries. .
4.4 Specific exergy on a dry basis of representative biomass samples [138]
4.5 Rank of coal according to the norm ASTM D388. . . . . . . . . . . . . . .
4.6 Rank of oil according to the British standard BS2869:1998 . . . . . . .
4.7 Physical properties of different compositions of natural gas [34] . . . .
4.8 Available energy, potential energy use and current consumption of natural resources on earth. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9 Summary statistics of grade-tonnage models. After [66] . . . . . . . . .
4.10 Mineral world reserves, reserve base and world resources in 2006 . . .
4.1
4.2
5.1
5.4
5.5
5.6
5.7
5.8
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
Exergy difference of selected elements considering either as reference
species the most abundant or the most stable substances in the R.E.
[367] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Standard chemical exergies of the elements . . . . . . . . . . . . . . . . .
Composition of the three R.E. proposed . . . . . . . . . . . . . . . . . . .
Calculation of the chemical potential of the elements according to
three different R.E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exergy costs of selected substances [371] & [207] . . . . . . . . . . . . .
Summary of the methodologies used to predict the thermodynamic
properties of minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
106
109
111
118
121
122
123
128
132
136
144
154
164
166
170
184
Thermodynamic properties of the atmosphere. Values of ∆H 0f i , ∆G 0f i ,
0
bch
in kJ/mole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
i
Thermodynamic properties of seawater. Values in kJ/mole . . . . . . . .
Thermodynamic properties of average rivers. Values in kJ/mole . . . .
Thermodynamic properties of glacial runoff. Values in kJ/mole . . . . .
Thermodynamic properties of groundwaters. Values in kJ/mole . . . .
Summary of the thermodynamic properties of the hydrosphere. Values
in kJ/mole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thermodynamic properties of the upper continental crust . . . . . . . .
The standard chemical exergy of the earth’s outer layers . . . . . . . . .
High heating value and elementary analysis (% by weight) considered
in the study of Valero and Arauzo [366] to define different types of coal.
189
190
191
192
193
194
196
205
208
List of Tables
6.10 Thermodynamic properties of the different types of coal. Values in
kJ/kg, except for s0 (kJ/kgK) . . . . . . . . . . . . . . . . . . . . . . . . .
6.11 The exergy of the world’s coal proven reserves reported in [401]. Values in million tonnes if not specified . . . . . . . . . . . . . . . . . . . . .
6.12 High heating value and elementary analysis (% by weight) of the different types of oil, according to the British standard BS2869:1998 . . .
6.13 Thermodynamic properties of the different types of oil. Values in
kJ/kg, except for s0 (kJ/kgK) . . . . . . . . . . . . . . . . . . . . . . . . .
6.14 The exergy of the world’s oil proven reserves reported in [35]. Values
in thousand million tonnes if not specified . . . . . . . . . . . . . . . . . .
6.15 Standard volumetric composition of natural gas considered in [366] .
6.16 Thermodynamic properties of natural gas. Values in kJ/N m3 , except
for ∆H f (kJ/kg) and s0 (kJ/kgK) . . . . . . . . . . . . . . . . . . . . . . .
6.17 The exergy of the world’s natural gas proven reserves reported in [35]
6.18 The exergy and exergy cost of the mineral reserves, base reserve and
world resources. Values are expressed in ktoe . . . . . . . . . . . . . . . .
6.19 Available exergy, potential exergy use and current exergy consumption
of natural resources on earth. Letter e denotes electrical consumption,
while th thermal consumption. . . . . . . . . . . . . . . . . . . . . . . . .
Summary of the results of the exergy distance of US copper mines
during the 20th century. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Summary of the results of the exergy distance of Australian gold mines.
7.3 Summary of the results of the exergy distance of Australian copper
mines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Summary of the results of the exergy distance of Australian nickel mines.
7.5 Summary of the results of the exergy distance of Australian silver mines.
7.6 Summary of the results of the exergy distance of Australian lead mines.
7.7 Summary of the results of the exergy distance of Australian zinc mines.
7.8 Summary of the results of the exergy distance of Australian iron mines.
7.9 Summary of the results of the exergy assessment of the main Australian
minerals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.10 Monetary costs of the main mineral reserves depletion suffered in Australia due to mineral production in year 2004 . . . . . . . . . . . . . . . .
427
208
209
213
213
213
215
216
216
219
224
7.1
8.1
8.2
8.3
8.4
8.5
The exergy loss of the main mineral commodities in the world. Values
are expressed in ktoe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The exergy loss of coal, oil and natural gas in the 20th century. . . . . .
Projected global averaged temperature change (◦ C at 2090-2099 relative to 1980-1999) at the end of the 21st century. After [160] . . . . .
Characteristics of stabilization scenarios and resulting long-term equilibrium global average temperature rise above pre-industrial at equilibrium from thermal expansion only. After [162] . . . . . . . . . . . . .
Temperature rise and CO2 concentration in the SRES scenarios . . . . .
246
250
252
254
256
258
260
263
269
276
284
291
300
301
302
428
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
8.16
8.17
8.18
8.19
LIST
OF
Specific exergy (b in kJ/kg) and Exergy loss (%) of anthracite, bituminous, subbituminous, and lignite coal according to the different SRES
scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specific exergy (b) and Exergy loss (%) of fuel-oil 1, fuel-oil 2 and
fuel-oil 4, according to the different SRES scenarios. . . . . . . . . . . .
Specific exergy (b) and Exergy loss (%) of natural gas according to the
different SRES scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exergy loss of the 2006 coal reserves due to the increase of GHG emissions, according to the different SRES scenarios. Values in Mtoe . . . .
Exergy loss of the 2006 fuel-oil reserves due to the increase of GHG
emissions, according to the different SRES scenarios . . . . . . . . . . .
Exergy loss of the 2006 natural gas reserves due to the increase of GHG
emissions, according to the different SRES scenarios . . . . . . . . . . .
Actual exergy degradation of the main extracted minerals in the 21st
century based on the Hubbert peak model . . . . . . . . . . . . . . . . . .
Actual exergy degradation of the main extracted minerals in the 21st
century based on the B1 scenario . . . . . . . . . . . . . . . . . . . . . . .
Actual exergy degradation of the main extracted minerals in the 21st
century based on the A1T scenario . . . . . . . . . . . . . . . . . . . . . .
Actual exergy degradation of the main extracted minerals in the 21st
century based on the B2 scenario . . . . . . . . . . . . . . . . . . . . . . .
Actual exergy degradation of the main extracted minerals in the 21st
century based on the A1B scenario . . . . . . . . . . . . . . . . . . . . . .
Actual exergy degradation of the main extracted minerals in the 21st
century based on the A2 scenario . . . . . . . . . . . . . . . . . . . . . . .
Actual exergy degradation of the main extracted minerals in the 21st
century based on the A1FI scenario . . . . . . . . . . . . . . . . . . . . . .
Summary of the actual exergy degradation of the main extracted minerals in the period between years 1900 and 2100 based on the Hubbert
and the IPCC’s SRES scenarios . . . . . . . . . . . . . . . . . . . . . . . . .
A.1 Vector ε̂ j [78 × 1], according to Rudnick and Gao [292] and vector ε j
[78 × 1], obtained from Grigor’ev [127]. Values in mole/g . . . . . . .
A.2 Vector ξi [324 × 1], according to Grigor’ev [127] and vector ξ̂i [324 ×
1] obtained in this study . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.3 Matrix R0 [324 × 78] (Part 1) . . . . . . . . . . . . . . . . . . . . . . . . . .
A.4 Matrix R0 [324 × 78] (Part 2) . . . . . . . . . . . . . . . . . . . . . . . . . .
A.5 Summary statistics of grade-tonnage models-1. After [66] . . . . . . . .
A.6 Summary statistics of grade-tonnage models-2. After [66] . . . . . . . .
A.7 Summary statistics of grade-tonnage models-3. After [66] . . . . . . . .
A.8 Summary statistics of grade-tonnage models-4. After [66] . . . . . . . .
A.9 Summary statistics of grade-tonnage models-5. After [66] . . . . . . . .
A.10 Summary statistics of grade-tonnage models-6. After [66] . . . . . . . .
A.11 Summary statistics of grade-tonnage models-7. After [66] . . . . . . . .
TABLES
302
303
304
306
306
306
309
311
312
313
315
316
318
318
351
352
360
367
376
377
378
379
380
381
382
List of Tables
A.12
A.13
A.14
A.15
A.16
A.17
A.18
A.19
A.20
A.21
A.22
A.23
A.23
A.24
A.25
A.26
A.27
A.28
A.29
A.30
A.31
A.32
A.33
A.34
Summary statistics of grade-tonnage models-8. After [66] . . . . . . . .
Chemical exergies of the elements for gaseous reference substances . .
Chemical exergies of the elements for aqueous reference substances . .
Chemical exergies of the elements for solid reference substances . . . .
Coefficients a1 through a7 [413] . . . . . . . . . . . . . . . . . . . . . . . .
The g i and hi of each polyhedral type and the standard error (%) of
the estimate. Values in kJ/mol. [55] . . . . . . . . . . . . . . . . . . . . .
Values of ∆G O−2 M z+ (clay) for ions located in different sites [382]
for hydrated clays and phyllosilicates. Values in kJ/mole . . . . . . . . .
Estimations of the standard enthalpy and Gibbs free energy of minerals. Values in kJ/mole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The chemical exergy and exergy cost of the 2006 world’s mineral production, mineral reserves, base reserve and world resources. Values
are expressed in ktoe if not specified . . . . . . . . . . . . . . . . . . . . .
The concentration exergy and exergy cost of the 2006 world’s mineral
production, mineral reserves, base reserve and world resources. Values
are expressed in ktoe if not specified . . . . . . . . . . . . . . . . . . . . .
Evolution of the Australian coal production. Values in ktons . . . . . . .
Evolution of the Australian oil production. Values in ktons . . . . . . . .
Evolution of the Australian oil production. Values in ktons.– continued
from previous page. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Evolution of the Australian natural gas production. Values in millions
of cubic meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Production of uranium in western countries and in the world. Values
are expressed in tons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Evolution of the world’s coal production . . . . . . . . . . . . . . . . . . .
Evolution of the world’s oil production . . . . . . . . . . . . . . . . . . . .
Evolution of the world’s natural gas production. Data in billion of cubic
meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Primary energy consumption and cumulative resources production in
the IPCC’s B1 scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . . .
Primary energy consumption and cumulative resources production in
the IPCC’s A1T scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . .
Primary energy consumption and cumulative resources production in
the IPCC’s B2 scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . . .
Primary energy consumption and cumulative resources production in
the IPCC’s A1B scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . .
Primary energy consumption and cumulative resources production in
the IPCC’s A2 scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . . .
Primary energy consumption and cumulative resources production in
the IPCC’s A1FI scenario [160] . . . . . . . . . . . . . . . . . . . . . . . . .
429
383
384
384
385
386
387
388
390
398
400
402
403
404
404
405
406
407
408
410
411
411
411
412
412
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