UPPTEC ES13006
Examensarbete 30 hp
2012
Jules Verne or Joint Venture?
Investigation of a Novel Concept for
Deep Geothermal Energy Extraction
Henrik Wachtmeister
Abstract
Jules Verne or Joint Venture? Investigation of a Novel
Concept for Deep Geothermal Energy Extraction
Henrik Wachtmeister
Teknisk- naturvetenskaplig fakultet
UTH-enheten
Besöksadress:
Ångströmlaboratoriet
Lägerhyddsvägen 1
Hus 4, Plan 0
Postadress:
Box 536
751 21 Uppsala
Telefon:
018 – 471 30 03
Telefax:
018 – 471 30 00
Hemsida:
http://www.teknat.uu.se/student
Geothermal energy is an energy source with potential to supply mankind with both
heat and electricity in nearly unlimited amounts. Despite this potential geothermal
energy is not often considered in the general energy debate, often due to the
perception that it is a margin energy source bound to a few locations with favorable
geological conditions. Today, new technology and system concepts are under
development with the potential to extract geothermal energy almost anywhere at
commercial rates. The goal of these new technologies is the same, to harness the heat
stored in the crystalline bedrock available all over the world at sufficient depth. To
achieve this goal two major problems need to be solved: (1) access to the depths
where the heat resource is located and (2) creation of heat transferring surfaces and
fluid circulation paths for energy extraction.
In this thesis a novel concept and method for both access and extraction of
geothermal energy is investigated. The concept investigated is based on the earlier
suggested idea of using a main access shaft instead of conventional surface drilling to
access the geothermal resource, and the idea of using mechanically constructed
‘artificial fractures‘ instead of the commonly used hydraulic fracturing process for
creation of heat extraction systems. In this thesis a specific method for construction
of such suggested mechanically constructed heat transfer surfaces is investigated. The
method investigated is the use of diamond wire cutting technology, commonly used in
stone quarries.
To examine the concept two heat transfer models were created to represent the
energy extraction system: an analytical model based on previous research and a
numerical model developed in a finite element analysis software. The models were
used to assess the energy production potential of the extraction system. To assess
the construction cost two cost models were developed to represent the mechanical
construction method. By comparison of the energy production potential results from
the heat transfer models with the cost results from the construction models a basic
assessment of the heat extraction system was made.
The calculations presented in this thesis indicate that basic conditions for economic
feasibility could exist for the investigated heat extraction system.
Handledare: Peter Lazor, Institutionen för geovetenskaper
Ämnesgranskare: Therese Isaksson, Institutionen för teknikvetenskaper
Examinator: Kjell Pernestål, Institutionen för fysik och astronomi
ISSN: 1650-8300, UPPTEC ES13006
ACKNOWLEDGMENTS
I would like to express my sincere gratitude to my supervisor Professor Peter Lazor at the
Department of Earth Sciences, to my reviewer Therese Isaksson at the Department of
Engineering Sciences and to my examiner Kjell Pernestål at the Department of Physics and
Astronomy at Uppsala University for indispensable support and guidance throughout this
project.
I also want to thank Professor Jefferson W. Tester at Cornell University for introducing me to
the warm community of geothermal energy research. A special thanks to Dr. John Garnish,
former director of geothermal programs of the European Commission, for his advice and
encouraging correspondence. Gratitude also goes to Dr. Tony Batchelor, chairman and
managing director of GeoScience Ltd. and EarthEnergy Ltd., for providing much valuable
information.
Lastly,
special
thanks
to
Arne
Hallin,
Scandinavian
representative
of
Tyrolit
Schleifmittelwerke Swarovski K.G., for providing crucial diamond wire expertise, and to my
friend and co-researcher Christoffer Källberg for always sharing both work and happiness.
3
CONTENTS
1
2
3
4
5
INTRODUCTION ................................................................................................................................ 7
1.1
Background ................................................................................................................................... 7
1.2
Purpose of study ............................................................................................................................ 8
1.3
General assumptions and delimitations ......................................................................................... 9
1.4
Methodology ................................................................................................................................. 9
THEORETICAL FRAMEWORK .......................................................................................................11
2.1
The geothermal resource ..............................................................................................................11
2.2
Concepts of energy extraction ......................................................................................................14
2.3
Description of the investigated concept .......................................................................................21
2.4
Modelling of fractures and heat transfer ......................................................................................23
ANALYTICAL MODEL FOR ESTIMATION OF HEAT TRANSFER ............................................25
3.1
Introduction ..................................................................................................................................25
3.2
Estimation of the temperature distribution ...................................................................................27
3.3
Thermal and electric power ..........................................................................................................29
3.4
Thermal and electric energy .........................................................................................................29
3.5
Validation of the analytical model ...............................................................................................30
RESULTS FROM THE ANALYTICAL MODEL .............................................................................32
4.1
Base case parameter values ..........................................................................................................32
4.2
Base case initial study ..................................................................................................................33
4.3
Outlet temperature at different initial rock temperature ...............................................................37
4.4
Outlet temperature at different flow velocity ...............................................................................39
4.5
Outlet temperature at different rock thermal conductivity ...........................................................41
4.6
Optimal power and energy production .........................................................................................44
4.6.1
Introduction .........................................................................................................................44
4.6.2
Optimal thermal energy production.....................................................................................44
4.6.3
Optimal electric energy production .....................................................................................47
RESULTS FROM THE NUMERICAL MODEL ...............................................................................50
5.1
Introduction ..................................................................................................................................50
5.2
Comsol multiple fracture model...................................................................................................51
4
5.3
6
Comparison of results from the analytical and the numerical model ...........................................55
CONSTRUCTION OF HEAT EXCHANGE SURFACES .................................................................59
6.1
Introduction ..................................................................................................................................59
6.2
Diamond wire cutting...................................................................................................................59
6.3
Wire cut cost parameters ..............................................................................................................63
6.4
Total cut cost by selected parameter values .................................................................................64
6.5
Total cut cost by Monte Carlo simulation ....................................................................................65
6.6
Additional cut cost model ‘Quarry model’ ..................................................................................67
6.7
Power production installation cost ...............................................................................................70
7
DISCUSSION ......................................................................................................................................72
8
CONCLUSION ....................................................................................................................................78
9
FURTHER RESEARCH: UNDERGROUND THERMAL ENERGY STORAGE ............................79
REFERENCES ..............................................................................................................................................80
5
NOMENCLATURE
ηC
ηTRI
ηREAL
T0
TH
Thermal efficiency Carnot
Thermal efficiency triangular
Thermal efficiency real
Temperature ambient
Temperature heat source
K
K
T(x,z,t)
Tr,0
Tw,0
Tout
Temperature distribution function
Initial rock temperature
Water inlet temperature
Water outlet temperature
°C
°C
°C
°C
w
H
L
A
Half fracture width in x
Fracture height in z
Fracture depth/length in y
Area of rock fracture interface one side (A = HL)
m
m
m
m2
U
ṁ
ṁ/A
Water flow velocity
Water mass flow rate
Area normalized water mass flow rate
m/s
kg/s
kg/m2 s
kr
ρr
cp,r
Α
Thermal conductivity rock
Density rock
Specific heat capacity rock
Thermal diffusivity rock
W/m K
kg/m3
J/kg K
m2/s
kw
ρw
cp,w
β
Thermal conductivity water
Density water
Specific heat capacity water
Dimensionless parameter
W/m K
kg/m3
J/kg K
-
t
Time of the production phase
S
Pth
Pel
Power thermal
Power electric
W
W
Eth
Eel
Energy thermal
Energy electric
J
J
Pavg,th
Pavg,el
Average thermal power per fracture area
Average electric power per fracture area
W/m2
W/m2
kthd
Thermal drawdown
-
D
Distance between parallel fractures
m
δt
Thermal penetration depth estimation
m
6
1
INTRODUCTION
1.1
BACKGROUND
During this last century we have seen an incredible global economic development and a
significant increase in living standards. This fast development has been based on the
abundance of cheap and highly effective energy sources – the fossil fuels.
Today we know that our development has occurred on the expense of our environment. We
are also aware of the fact that oil is running out. We have already begun to see consequences
of these conditions: climate change, rising fuel prices and the impact of energy security in
international relations. To change these current developments, regardless of motivation, new
sustainable energy sources are necessary.
In everyday life we rarely think about what exists under our feet. Not often do we reflect on
the fact that Earth is a rotating orb of melted rock with a core temperature of 6 000 degrees
Celsius and with just a thin layer of solid crust to walk on. The large amounts of energy stored
and produced in the Earth’s interior is an energy source not often considered but with a
practically endless potential.
This thesis investigates a novel concept for extracting deep geothermal energy. The concept is
based on ideas presented in the report ‘Man-made Geothermal Energy Systems – MAGES’
published by the International Energy Agency (IEA) in 1979. These ideas have been further
developed by the two researchers active in this project: Henrik Wachtmeister (author of this
report) and Christoffer Källberg (author of the associated report). With new technology and
knowledge available today ideas suggested 30 years ago might be possible to realize.
The concept investigated in this thesis is based on the use of shafts instead of surface drilling
to access the geothermal resource. Shafts enable access for remote controlled machines and
even personnel at depth which allow new ways of extracting geothermal energy. In the
MAGES project (IEA 1979) the use of shafts in combination with mechanically constructed
heat transferring surfaces was considered as a futuristic option and alternative to the already
proved drilling and hydraulic fracturing approach. This thesis investigates a method for
creating such suggested mechanically constructed heat transferring surfaces. The method
investigated is the use of diamond wire cutting technology, commonly used in marble and
granite quarries for dimensional stone cutting. In the investigated concept diamond wire is
used for cutting channels with large heat transferring surfaces in the underground rock. Heat
is extracted by circulation of fluid through the constructed system. The channels act as
7
symmetrical artificial fractures transferring heat from the surrounding rock to the working
fluid.
During the research process Dr. John Garnish and Dr. Tony Bachelor, both active in the
MAGES project at the time, kindly pointed out that a proposal regarding a shaft based system
was put forth as long ago as in 1904 by the prominent Anglo-Irish engineer Sir Charles
Parsons, inventor of the steam turbine among many things. In the beginning of the 20th
century Parsons (1904) addresses the British Association for the Advancement of Science and
proposes the idea of constructing of a 12 km deep shaft for steam and power generation. In a
following address, published at the end of the Great War, Parsons (1919) comments the
immense horror and destruction seen in past years. He also identifies the remarkable
technological development during the war, and its integral role in it. Furthermore he
recognizes the fundamental significance of energy sources for both political and social
stability as well as for military power. He concludes that the power of the British Empire, and
its ability to survive the war, was primarily based on its early development of coal and its
following employment of oil. Foreseeing the inevitable exhaustion of coal reserves Sir
Parsons returns to the geothermal idea presented in 1904, stressing the importance of
deploying new energy sources for both economic development and for peace. In his
calculations the proposed 12 km deep shaft could be constructed at a cost equal to the
monetary cost of just a single day of the Great War, pinpointing the skewed allocation of
human efforts.
1.2
PURPOSE OF STUDY
The purpose of this thesis is to investigate and evaluate a specific method for mechanical
construction of heat transferring surfaces for deep geothermal energy production systems. To
evaluate the method the two following key questions need to be answered:

What is the energy production potential of a system constructed with the investigated
method?

What is the cost of constructing a system with the investigated method?
The aim of this project is to answer these questions by creating a heat transfer model for the
production system and a cost model for the construction method. The result from these
models will be compared and set in relation to each other to assess the viability of the
concept.
8
1.3
GENERAL ASSUMPTIONS AND DELIMITATIONS
This investigation is a theoretical estimation of the performance of an ideal system based and
conducted on the premise that the system is possible to construct. The study is based on the
assumption that shaft construction to required depths is technically achievable. Furthermore,
remote control and large scale implementation of wire saw technology is assumed. These
main assumptions require technology and methods not developed or proved today.
Several practical aspects have been disregarded. The impact of the extreme conditions at
depth in terms of temperature, pressure and rock stresses is not treated. Structural integrity of
the artificial fractures is assumed.
The study only investigates the heat extraction system. The results from this study, if positive,
must therefore in addition be able to cover the access cost and all other disregarded costs for
economic feasibility of a complete system concept. Furthermore, since the study only looks at
the possible performance of an ideal energy extraction system, pumping, conversion and other
losses are not included. The cost estimate of the construction method is based on basic cost
parameters identifiably for surface applications. Possible additional cost for underground and
remote control application is disregarded.
This being said, the construction of a shaft based concept must not necessary be considered
insurmountable. The deepest shaft today is 3.9 km in depth, and is located in the South
African TauTona gold mine (SPG Media Group PLC 2009). New shaft construction
technologies are under development that could make required deep shafts possible, as
example described by Chadwick (2010) and Ferreira (2005). It is also possible to assume an
alternative scenario where the proposed extraction system is constructed in already existing
locations, for example in abandoned mines as proposed by Hall, Scott, & Shang (2011) and
Rodriguez & Diaz (2009).
1.4
METHODOLOGY
To examine the possible energy production from the investigated system two different heat
transfer models were developed to represent the system. An analytical model was derived
from previous research and implemented in MATLAB and a numerical model was built in
COMSOL Multiphysics, a commercial finite element analysis simulation software. The
results from these two models were compared with each other and with other research for
validation.
9
To examine the construction cost of the heat extraction system a cost model for diamond wire
cutting was developed in a qualitative manner together with experts from the diamond wire
industry. Total cut cost were derived from identified cost parameters by two methods: (1)
selected parameter values and (2) Monte Carlo simulation. The qualitative model derivation
was complemented with a quantitative analysis of wire performance parameters by examining
proprietary data from 35 different stone quarries.
The feasibility of the energy extraction concept was investigated by comparing the estimated
potential energy production with the estimated construction cost of the system.
To estimate necessary dimensions of the system an additional numerical COMSOL model
was developed to examine thermal penetration and the effects of multiple parallel fractures.
All work and research was performed together by Henrik Wachtmeister and Christoffer
Källberg under the supervision of Professor Peter Lazor at the Department of Earth Sciences
at Uppsala University. The reporting of the results of the research was divided into two
separated reports. This report, written by Henrik Wachtmeister, focuses on the analytical
model whilst the second report, written by Christoffer Källberg, focuses on the numerical
model.
10
2
THEORETICAL FRAMEWORK
2.1
THE GEOTHERMAL RESOURCE
The heat within Earth originates from the creation of the planet and is also continuously
produced by decay of radioactive isotopes. The crust is cooled by space through the
atmosphere. The temperature difference between the hot interior and the cold crust has
established the ‘geothermal gradient’, the temperature distribution with respect to depth. The
geothermal gradient at near surface conditions has a global average of 25-30 °C/km but can
be several times higher in high-grade geothermal regions (Henkel 2006). In Figure 1
temperature at depth is given for four different geothermal gradients.
0
20 °C/km
-1
30 °C/km
40 °C/km
-2
50 °C/km
-3
Depth [km]
-4
-5
-6
-7
-8
-9
-10
0
100
200
300
Temperature [°C]
400
500
Figure 1.Temperature at depth at four different geothermal gradients.
The temperature difference causes a constant heat flow from the core to the surface. At the
crust surface the average heat outflow is 60 mW/m2 (Henkel 2006). This yields a world total
heat outflow of 30 TW, which is about two times more than the total global primary energy
supply (16 TW), and about 13 times the global average electric consumption (2.3 TW) (IEA
2011).
11
When looking at ways of using geothermal energy the continuous heat flow (60 mW/m2) is
not of main interest. The real potential of geothermal energy lies in extracting the massive
amounts of stored heat in Earth’s rock masses. The term ‘heat mining’ is often used to
describe this concept, a comprehensive account is given by Armstead & Tester (1987).
Energy is extracted by cooling a specific volume of rock, this volume loses its temperature
during extraction and after the extraction period production moves on and a new volume is
mined. The cooled rock mass will slowly regain its initial temperature due to heat conduction
by the surrounding rock supported by the continuous heat flow from the core.
To assess the scale of the heat resource in rock the following estimation can be made: a
volume of 1 km3 of granite rock with temperature 200 °C contains about 160 TWh of thermal
energy. Extracting 10 % of that energy, cooling it from 200 to 180 °C, yields 90 MW of
thermal power during 20 years. Extracting 50 % of the heat in place, cooling the rock from
200 to 100 °C, yields 450 MW of thermal power. See Figure 2 for a schematic representation
of scale.
Figure 2. Estimation of the geothermal resource.
A rock mass of temperature of 200 °C is on average located at depth of 6 km. This highlights
both the potential and the difficulties associated with geothermal energy; the resource is vast
but accessing it is difficult.
12
The energy extracted comes in the form of hot fluid, most common water is used as working
fluid. Energy in form of hot water can be transformed into electricity in steam cycles, using
ordinary steam turbines and electricity generators. The efficiency of this conversion is limited
by the Carnot efficiency. According to DiPippo (2007) the triangular cycle is more realistic to
use for binary geothermal plants since geothermal hot water is not a non-isothermal heat
source. Also other efficiency losses need to be taken into account resulting in a real efficiency
of thermal to electrical power of approximately 0.58 of the ideal triangular, see Equation 1, 2
and 3.
(1)
(2)
(3)
T0 is the ambient temperature and TH the temperature of the heat source, both in Kelvin. In
Figure 3 thermal efficiency is presented as a function of fluid temperature (the heat source)
according to Equation 1, 2 and 3. As seen in Figure 3 the conversion efficiencies for thermal
power to mechanical and electric power is low for the temperature levels associated with
geothermal energy. For large scale electricity production high mass flows are therefore
necessary.
0.7
Ideal Carnot
Ideal Triangular
0.6
Real (DiPippo, 2007)
Thermal efficiency [-]
0.5
0.4
0.3
0.2
0.1
0
50
100
150
200
250
Fluid temperature [°C]
300
Figure 3. Thermal power conversion efficiencies.
13
350
2.2
CONCEPTS OF ENERGY EXTRACTION
Several ways of extracting energy from deep impermeable crystalline rock has been proposed.
The goal of these different concepts is the same, to harness the heat stored in the crystalline
bedrock available almost everywhere on Earth at sufficient depth. To achieve this goal two
major problems need to be solved:

Access the depths were the heat resource is located

Create heat transferring surfaces and fluid circulation paths
Some concepts have more spectacular solutions to these problems than others. As an example,
according to Gringarten et al. (1975), in the 70’s scientist in both the United States and in the
Soviet Union were considering the use of sequentially fired and controlled nuclear explosives
to create highly fractured underground rock systems for water circulation and energy
extraction.
The most developed and successful concept so far is the use of conventional deep boreholes
for access and hydraulic fracturing for creation of heat transfer surfaces. These concepts are
referred to as Enhanced Geothermal Systems (EGS), also the earlier name Hot Dry Rock
(HDR) is used. Drilling to depth up to 12 km has been achieved (Kola Superdeep Borehole,
Soviet Union 1989), and drilling to 6 to 8 km is regular procedure in the oil and gas industry.
Hydraulic fracturing is also a technology with roots in the oil industry. It is a rock breaking
process where water is pumped down the borehole at high pressure. The high fluid pressure
opens preexisting joints and creates new ones in the rock system surrounding the injection
borehole. Depending on geology and the preexisting rock formations and stress fields the
results of hydraulic fracturing differs. The results of the fracture process are measured by
seismic instruments at the surface.
According to Duchande & Brown (2012) the idea of using hydraulic fracturing for geothermal
energy was first presented and tested by Los Alamos National Laboratory in 1973. The
original idea was to create discrete fractures, so called ‘penny shaped’ circular discs only
about a centimeter wide but up to a kilometer in diameter. This disc shaped fractures were
assumed to spread vertically around the injection borehole. Contemporary research and test
projects are primarily focused on geological areas where the rock has natural occurring
fractures and faults zones and where the hydraulic fracturing merely enhance and expand the
naturally occurring systems. These fracture systems created by hydraulic fracturing is often
referred to as geothermal reservoirs and are more cloud shaped than ‘penny shaped’. Two of
the most advanced geothermal projects using this approach are the EU-funded Soultz project
14
in France (Geothermie Soultz 2012), and the Cooper Basin project in Australia (Geodynamics
Ltd. 2012).
The development of EGS looks very promising but one remaining obstacle is the risk and
uncertainty associated with both drilling and hydraulic fracturing. Conventional drilling to
required depths is complicated and expensive and can sometimes fail leading to new
additional boreholes adding large unexpected costs to the projects. The creation of the
reservoir, and its productivity and lifetime, is also related to uncertainties. These obstacles
among others were identified by IEA (1979) and were partly the reason why an alternative
option was considered: the use of shafts for access and the use of mechanically constructed
surfaces for heat extraction at depth. Such a system would be closed in regard to fluid
circulation and controllable in regard to power production. Also the idea of shafts in
combination with underground boreholes was considered.
According to Dr. John Garnish (personal communication, 2012), former director of
geothermal programs of the European Commission and involved in the MAGES project at the
time, the purpose of the MAGES study was to ‘brainstorm’ and consider all possible concepts
for heat extraction from deep rock formations. The idea of a shaft based concept had at that
time not been subject of any preceding study. The concept was therefore treated only in a very
theoretical way.
In the final MAGES report by IEA (1979) some key positive properties of a shaft based
concept were identified as well as the many difficult and unknown practical aspect of such a
system. The major obstacle being the cost of a shaft deep enough and the extreme working
conditions at the relevant depths. The principal advantage of a shaft system is that it yields
access to the heat resource and enables implementation of controllable methods for
construction of heat transfer surfaces. Also, machines and personnel can work at depth,
installations can be maintained, repaired and refined. A main shaft from which several smaller
shafts and boreholes can be constructed eliminates the need of multiple boreholes all the way
from the surface. A surface borehole can only handle a limited mass flow, and is therefore
limited in potential power production, a single shaft can handle large mass flows by large
diameter pipes. A system based on a main access shaft, even though initially very expensive,
can be further expanded even under production. It is assumed in report that a shaft access
concept may be more cost effective for large scale systems due to the need of only one access
path, not several surface boreholes.
However, the conclusion and recommendation given in the MAGES study was clear: with the
technology available at the time the most promising direction for research was hydraulic
fracturing between multiple boreholes. Following this conclusion the member states of IEA
15
decided to develop the EGS concept. Within a few years the research was concentrated to a
single cite, Soultz, primary due to the high cost of deep drilling and the need of necessary
scale. Even after this concentration of effort it was not until 2005 that the system produced
electricity. According to Garnish it had been difficult enough to continue to get funding from
the various national bodies for the Soultz project, under no circumstances could funding have
been obtained for the far more challenging shaft concept, an no attempt was made to do so
either.
In the MAGES project (IEA 1979) the idea of constructing artificial fractures mechanically
was considered among other options as a mean of extracting energy. By constructing heat
transfer systems from design predictability and controllability can be achieved eliminating the
risk associated with contemporary hydraulic fracturing concepts. In this thesis a specific
technical method for constructing such artificial fractures is considered. The method
investigated is the use of diamond coated wire technology, a stone cutting method normally
used in stone quarries. A diamond wire saw creates a channel in the rock – an artificial
fracture – with width of around 11 mm. Diamond wire cuts can be executed in several ways
and in almost any kind of geometry. For heat transfer purposes extremely large cuts are
necessary for any substantial energy production potential. The artificial fractures must
therefore be constructed by several sub cuts. The heat extraction concept is described further
in chapter 2.3, details about diamond wire cutting is given in chapter 6.
EGS concepts can be referred to as open systems since the fluid flows freely in the rock
structure between injection boreholes and production boreholes. The shaft based concept can
be referred to as a closed system with fluid circulating in constructed paths and channels.
Except of shaft based concepts there are another additional type of closed system: borehole
heat exchanger systems. These concepts consist of boreholes only, either a single borehole or
multiple boreholes. A single borehole concept, 14 000 m in length, is proposed by Schulz
(2008). Another concept is developed by Norwegian company Rock Energy AS and is
described by Moe & Rabben (2001). In this later concept two main boreholes are drilled from
the surface. At depth a system of several heat extracting boreholes are drilled with directional
drilling technology between the two first main boreholes creating a underground closed heat
exchanging system.
Recently a similar shaft based concept (as investigated in this thesis) was proposed by an
Austrian workgroup consisting of researchers from Graz University of Technology,
Montanuniversität Leoben and from several private companies. The proposed concept
Geothermietiefenkraftwerk (GTKW) consists of a main access shaft and a tunnel systems at
depth from which several boreholes are drilled as heat exchanger system. The concept is
16
described in more detail by Hämmerle (2012). The GTKW concept came to the author’s
attention at a late stage in the research process. The original concept investigated in this report
was developed in parallel with GTKW and without knowledge of its existence. This is
interesting since the two research groups, although considering different heat extracting
methods, has reached similar conclusions and identified several similar important aspects in
many questions.
Figure 4. Concepts of geothermal energy extraction. Open systems (left): Hot Dry Rock (HDR) and
Enhanced Geothermal Systems (EGS). Closed systems (right): Borehole heat exchanger systems and Shaft
and artificial fractures concepts.
17
Figure 5. Example of HDR/EGS concept with surface boreholes and hydraulic fracturing (Tester et al.
2006).
Figure 6. Example of shaft concepts. Shaft in combination with underground boreholes (left). Shaft and
mechanically constructed heat transfer surfaces (right) (IEA 1979).
18
Figure 7. Example of shaft concepts. Geothermietiefenkraftwerk (GTKW), an Austrian shaft concept with
heat exchanger system based on tunnels and multiple boreholes, depth 6 000 m (Ehoch10
Projektentwicklungs GmbH 2012).
The GTKW heat extraction method is based on a tunnel system with multiple intersecting
boreholes for fluid circulation. According to Hämmerle (2012) the power output from such
boreholes is in the range of 150 to 250 W per m borehole at relevant depths. The GTKW
concept is planned to be deployed in the scale of gigawatts. Hämmerle (2012) describes a
plant consisting of a 6 000 m deep shaft, 25 km of tunnels and 40 000 km of heat extraction
boreholes. This system is estimated to produce 10 000 MW thermal and 1 000 MW electrical
power. The estimated construction cost is 13 billion euro.
According to Moe & Rabben (2001) the borehole heat exchanger system in the Rock Energy
AS concept will produce an average of 210 W per m borehole. This is consistent with the
stated power production of boreholes in the GTKW. The heat extracting boreholes in this
concept has a total length in the range of kilometers, and borehole diameter about 100 mm.
Moe & Rabben (2001) describes an example system consisting of four 2 000 m long heat
extracting boreholes expected to produce 1.7 MW of thermal power.
19
Figure 8. A 1.7 MW Borehole heat exchanger system by Rock Energy AS. In this concept directional
drilling is used to create a heat exchanger consisting of multiple intersecting boreholes at depth 3 000 - 6 000
m (Rock Energy AS 2012).
20
2.3
DESCRIPTION OF THE INVESTIGATED
CONCEPT
Figure 9 to Figure 12 shows schematic representations of the herein investigated concept. A
main access shaft gives access to the heat resource. A system of smaller construction shafts
and tunnels and necessary boreholes for cutting are established at depth. From this system
diamond wire cutting is used to create channels with large heat transferring surfaces. The
channels are constructed in modules creating separated large ‘artificial fractures’. Further
construction and expansion of the system is possible, in all directions, at the same time as the
first modules are producing energy.
Burj Dubai
Figure 9. Schematic representation of the investigated concept: Main access shaft and mechanically
constructed heat transfer surfaces with diamond wire saw technology.
21
Figure 10. A system of smaller construction tunnels and shafts are established at depth. From this system
necessary boreholes for wire cutting are drilled. Wire saws cuts channels between tunnels and boreholes
creating large heat transfering surfaces (red color in picture).
Figure 11. Energy production phase. Water is circulated through the channels transferring heat from the
surrounding rock to the water. Water travels to and from the surface in pipelines in the main access shaft.
Power conversion facilities (steam turbines and generators) are located at the surface.
22
Figure 12. Multiple channels or artificial fractures can be constructed next to each other at suitable distance
on the same level. The main shaft can continue deeper, with establishment of new channel systems on deeper
levels. Further construction and expansion can be performed while the first part of the system is producing
energy.
2.4
MODELLING OF FRACTURES AND HEAT
TRANSFER
Several authors have created models to study the heat transfer problem between injected
water and rock formation at depth. Two of the earliest works in this area was done by
Gringarten et al. (1975) and Wunder & Murphy (1978). The heat transfer problem addressed
in these works, and the analytical model of heat transfer in rock developed, has been
developed further by Tester et al. (2011).
In the model of Tester et al. (2011) a single rectangular, vertical fracture of constant width
separates two blocks of homogeneous, isotropic, impermeable rock. The rock is assumed to
extend horizontally to infinity. For simulating the heat extraction water is injected at the
bottom of the fracture at constant mass flow rate flowing upwards through the fracture to the
outlet. Although real geothermal reservoirs consist of complex networks of irregular fractures
the single fracture model adequately captures the rock to water heat transfer aspect and can be
used to represent a geothermal system. For the constructed artificial fracture investigated in
this report the heat transfer model described above is very accurate due to the symmetrical
geometry of the constructed fracture.
23
Tester et al. (2011) also develops a corresponding numerical model in THOUGH2, a general
purpose numerical simulation program for multi-dimensional non-isothermal flows of multiphase, multi-component fluid mixtures in fractured and porous media. In this project similar
numerical models were built in COMSOL Multiphysics. The single fracture numerical
COMSOL model developed is described in detail by Källberg (2012). An additional multiple
fracture model was developed and is described in chapter 5.2.
24
3
ANALYTICAL MODEL FOR ESTIMATION OF
HEAT TRANSFER
3.1
INTRODUCTION
The analytical heat transfer model was adapted from earlier works by Gringarten et al. (1975),
Wunder & Murphy (1978), Armstead & Tester (1981) and Tester et al. (2011).
The model describes a geometry representing a single rectangular vertical fracture of constant
width that separates two masses of homogeneous, isotropic, impermeable rock. The rock is
assumed to extend horizontally to infinity. Initially the system is at uniform temperature.
During heat extraction water is injected uniformly at the bottom of the fracture and is flowing
upwards to the outlet at constant mass flow rate. The heat transfer process to be solved is a
coupled problem of heat conduction in the rock and forced convection in the fracture. With a
set of assumptions and boundary conditions the heat transfer equations in this geometry can
be treated analytically for any case with uniform fluid flow and fixed inlet temperature. The
model geometry is given in Figure 13.
Figure 13. Geometry of analytical heat transfer single fracture model in three dimensions.
A Cartesian coordinate system is placed with the x = 0 plane at the rock-fracture interface.
Uniform geometry in y-direction makes it possible to reduce the model to two dimensions.
Symmetry in x-direction occurs around the mid-fracture plane x = -w. Under these
assumptions it is possible to reduce the mathematical problem to the two dimensional
geometry seen in Figure 14.
25
Figure 14. Analytical model in two dimensions.
The geometry seen in Figure 2 is used for solving the heat transfer problem. It represents the
half-width fracture w and one of the two the surrounding rock masses with temperature
distribution T(x,z,t). All constituent model parameters are presented in Table 1.
Table 1. List of analytical heat transfer model parameters.
T(x,z,t)
Temperature distribution function
°C
Tr,0
Initial rock temperature
°C
Tw,0
Water inlet temperature
°C
Tw,H
Water outlet temperature
°C
w
Half fracture width in x
M
H
Fracture height in z
M
L
Fracture depth/length in y
M
A
Area of rock fracture interface one side (A = HL)
m2
U
Water flow velocity
m/s
ṁ
Water mass flow rate
kg/s
ṁ/A
Area normalized water mass flow rate
kg/m2s
kr
Thermal conductivity rock
W/mK
ρr
Density rock
kg/m3
cp,r
Specific heat capacity rock
J/kgK
α
Thermal diffusivity rock
m2/s
ρw
Density water
kg/m3
cp,w
Specific heat capacity water
J/kgK
β
Dimensionless parameter
-
t
Time of the production phase
s
26
Initially at t = 0 the whole system is at uniform temperature Tr,0, the initial temperature of the
surrounding rock. During the production phase water is injected at z = 0 at constant
temperature Tw,0 and constant flow velocity U. The water flows upwards to the outlet at z = H.
The model is based on the following assumptions:

The variation of water temperature in x-direction in the fracture is neglected. The
fracture aperture is very small in relation to fracture height, w << H.

The heat transfer resistance at the rock-water interface is neglected. The water
temperature is equal to the rock temperature at x = 0 for every z.

Heat conduction in z-direction is neglected both in the fracture and in the surrounding
rock mass.

Heat conduction in y-direction is neglected both in the fracture and in the surrounding
rock mass.

Density and specific heat capacity is constant for both water and rock. Thermal
conductivity of rock is constant.

Single phase flow in in the fracture is assumed.
Under these assumptions heat transfer only occurs by conduction in the rock in x-direction
and by forced convection in the fracture in z-direction. In this manner fluid dynamics
equations can be disregarded altogether.
3.2
ESTIMATION OF THE TEMPERATURE
DISTRIBUTION
The time dependent heat conduction in x-direction within the rock is described by the
differential equation
(4)
Where α is the rock thermal diffusivity, i.e. the ratio of thermal conductivity kr and the
product of density ρr and specific heat capacity cp,r of rock
(5)
27
The boundary conditions at the rock-fluid interface gives
|
(6)
The initial rock temperature gives the initial condition
(
)
(7)
The far field rock temperature gives the boundary condition
(
)
(8)
The constant water temperature at the inlet gives the following additional boundary condition
(
)
(9)
The analytical solution to Eq. 4 under the boundary conditions Eq. 6-9 is based on the
solution of a classical transient heat transfer problem. The solution is presented in (Tester et
al., 2011).
(
)
(
)
[
√
]
(10)
where
(11)
Outlet temperature
With z = H and x = 0 Eq. 10 can be simplified to give the outlet water temperature T out at the
end of the fracture
(
)
[
√
28
]
(12)
3.3
THERMAL AND ELECTRIC POWER
Thermal power
The available thermal power from the artificial fracture system is calculated from the
temperature and mass flow of the fluid at the fracture outlet.
The thermal power Pth is calculated by
̇(
)
(13)
Where the mass flow ṁ is
̇
(14)
Electric power
Potential electricity production is calculated from thermal power using ideal Carnot
conversion efficiency according to
̇(
)(
)
(15)
For Carnot efficiency T needs to be in Kelvin.
3.4
THERMAL AND ELECTRIC ENERGY
Thermal energy
To assess the produced thermal energy over time the following integral needs to be solved
∫
(16)
This integral is solved numerically in MATLAB.
29
Electrical energy
To assess the produced electric energy over time the following integral need to be solved
∫
(17)
This integral is solved numerically in MATLAB.
3.5
VALIDATION OF THE ANALYTICAL MODEL
The analytical model was based on the same mathematical solution as presented and used by
Tester et al. (2011). Use of the same input parameter values should yield the same result in
both analytical models. This was investigated and confirmed. Figure 15 is the same as
presented by Tester et al. (2011) and shows outlet temperature at four different locations
along a 500 m long and 0.06 m wide fracture. Results from both the analytical model and the
numerical TOUGH2 model are presented.
The same input parameters values were used in our analytical model and in our numerical
COMSOL model. These results are presented in Figure 16. The results from our analytical
model and the analytical model by Tester et al. (2011) should be identical in this particular
case; this is confirmed by results shown in Figure 15 and Figure 16. The results from our
COMSOL model and the numerical TOUGH2 model should be similar; this is also confirmed
by results shown in Figure 15 and Figure 16.
The comparison of results from our two models with those of Tester et al. (2011) makes us
confident in the validity of our models. Results from our numerical COMSOL model are
presented in detail by Källberg (2012). In chapter 5.3 in this report a comprehensive
comparison of our analytical model and our numerical COMSOL model is presented and an
explanation to why the results differ is given.
30
Figure 15. Model validation: Outlet temperature at four locations along a fracture according to Tester et al.
(2011).
Analytical x=0 z=500 m
Analytical x=0 z=100 m
Analytical x=0 z=20 m
Analytical x=0 z=0 m
Numerical x=0 z=500 m
Numerical x=0 z=100 m
Numerical x=0 z=20 m
Numerical x=0 z=0 m
Dimensionless outlet temperature [-]
1
0.8
0.6
0.4
0.2
0
0
5
10
15
Time [y ears]
20
25
30
Figure 16. Model validation: Outlet temperature at four different locations along same fracture according
to developed models, analytical model in black and numerical COMSOL model in red.
31
4
RESULTS FROM THE ANALYTICAL MODEL
The analytical heat transfer model was implemented in MATLAB. A base case of parameter
values was selected for the model. The base case set of parameter values is referred to as just
the 'base case’.
The model solves the temperature distribution in the system over time. The main output from
the model is water outlet temperature Tout from the fracture over time. From outlet
temperature thermal power, electric power, produced thermal energy and produced electric
energy can be calculated.
To facilitate comparison between different fracture systems and model setups average power
per fracture area is calculated for each case. Average power is calculated from the aggregated
thermal and electric energy production, according to Eq. 16 and 17, divided on total
production time (30 years) and fracture area (1 000 000 m2), see Eq. 18 an 19.
(18)
(19)
Three major studies are presented in this report, preceded by an initial study of the base case.
0. Initial study of base case
1. Outlet temperature at different initial rock temperature
2. Outlet temperature at different water flow velocity
3. Outlet temperature at different rock thermal conductivity
All studies were based on the base case, altered parameter values are reported in each study.
4.1
BASE CASE PARAMETER VALUES
The geometry in the base case was determined by the most common cut width of diamond
wire, 11 mm, and an estimation of sufficient system size for producing energy in range of
megawatts, 1 km2. Material properties in the base case were set to the same values as used by
Tester et al. (2011) to facilitate comparison and validation of results. Production time of the
system was set to 30 years as commonly considered a relevant economic time scale in
previous studies. Numerical parameters values for the base case are presented in Table 2.
32
Table 2. Base case parameter values for analytical heat transfer model.
4.2
Tr,0
150
Initial rock temperature
°C
Tw,0
20
Water inlet temperature
°C
w
0.0055
Half fracture width in x
m
H
1000
Fracture height in z
m
L
1000
Fracture depth/length in y
m
A
1 000 000
Area of rock fracture interface one side (A=HL)
m2
U
0.005
Water flow velocity
m/s
ṁ
55
Water mass flow rate
kg/s
ṁ/2A
2.75e-05
Area normalized water mass flow rate
kg/m2s
kr
2.9
Thermal conductivity rock
W/mK
ρr
2700
Density rock
kg/m3
cp,r
1050
Specific heat capacity rock
J/kgK
α
1.02e-06
Thermal diffusivity rock
m2/s
ρw
1000
Density water
kg/m3
cp,w
4184
Specific heat capacity water
J/kgK
t
30 [years]
Time of the production phase
s
BASE CASE INITIAL STUDY
The model solves the temperature distribution in the system at position and time x, z and t.
The water flow path, the fracture, is located at x = 0. The rock extends in x-direction. Initial
rock temperature is 150 °C and water inlet temperature at x = 0, z = 0 is 20 °C. The water
flow velocity U is 0.005 m/s and constant during the whole production period. The water
mass flow depends on the geometry; at water flow velocity 0.005 m/s and fracture geometry
of 0.011 x 1000 x 1000 m the water mass flow equals 55 kg/s.
In Figure 17 a part of the solution to the temperature field for the base case is shown at three
different time instances: after 1, 15 and 30 years of production. Figure 17 illustrates the
cooling of the rock. We can see that the water outlet temperature at x = 0 and z = 1000 m at
these times instances are 150, 96 and 76 °C. After 30 years the “cold wave” has reached 100
m into the rock, even though the effect at this distance is small, it is observable. At the
distance of 60 m the cooling impact is getting significant.
33
z [m]
1000
980
960
940
920
900
880
860
840
820
800
780
760
740
720
700
680
660
640
620
600
580
560
540
520
500
480
460
440
420
400
380
360
340
320
300
280
260
240
220
200
180
160
140
120
100
80
60
40
20
0
150
150
150
150
149
149
149
149
149
149
148
148
148
147
147
146
146
145
144
143
142
141
140
138
137
135
133
131
128
126
123
120
116
113
109
105
101
96
91
86
81
76
70
64
58
52
46
39
33
27
20
0
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
149
149
149
149
149
149
148
148
148
147
147
146
146
145
144
143
142
141
140
138
136
135
132
130
128
125
122
10
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
149
149
149
149
149
149
148
20
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
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150
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150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
30
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
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150
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150
150
150
150
150
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150
150
150
150
150
150
150
150
150
150
150
150
40
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
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150
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150
150
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150
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150
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150
50
150
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150
150
150
150
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150
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150
150
150
150
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150
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150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
60
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
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150
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150
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150
150
150
150
150
150
150
150
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150
150
150
150
150
150
150
150
150
70
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
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150
150
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150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
80
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
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150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
90
z [m]
150
1000
150
980
150
960
150
940
150
920
150
900
150
880
150
860
150
840
150
820
150
800
150
780
150
760
150
740
150
720
150
700
150
680
150
660
150
640
150
620
150
600
150
580
150
560
150
540
150
520
150
500
150
480
150
460
150
440
150
420
150
400
150
380
150
360
150
340
150
320
150
300
150
280
150
260
150
240
150
220
150
200
150
180
150
160
150
140
150
120
150
100
150
80
150
60
150
40
150
20
150
0
100 x [m]
96
94
93
92
91
89
88
87
86
84
83
81
80
79
77
76
74
73
71
70
69
67
65
64
62
61
59
58
56
55
53
51
50
48
47
45
43
42
40
38
37
35
33
32
30
28
27
25
23
22
20
0
116
116
115
114
113
112
111
110
109
108
107
106
105
104
102
101
100
99
98
97
95
94
93
92
91
89
88
87
85
84
83
81
80
78
77
76
74
73
71
70
68
67
65
64
62
61
59
58
56
54
53
10
131
130
130
129
129
128
127
127
126
125
124
124
123
122
121
121
120
119
118
117
116
115
115
114
113
112
111
110
109
108
107
106
104
103
102
101
100
99
98
96
95
94
93
92
90
89
88
86
85
84
82
20
140
140
139
139
139
138
138
137
137
137
136
136
135
135
134
134
133
133
132
131
131
130
130
129
128
128
127
126
126
125
124
124
123
122
121
120
120
119
118
117
116
115
114
113
113
112
111
110
109
108
106
30
145
145
145
145
145
144
144
144
144
143
143
143
143
142
142
142
141
141
141
140
140
140
139
139
139
138
138
137
137
136
136
136
135
135
134
134
133
133
132
131
131
130
130
129
128
128
127
126
126
125
124
40
148
148
148
148
148
147
147
147
147
147
147
147
147
146
146
146
146
146
146
145
145
145
145
145
144
144
144
144
144
143
143
143
143
142
142
142
141
141
141
140
140
140
139
139
139
138
138
137
137
136
136
50
149
149
149
149
149
149
149
149
149
149
149
149
149
149
148
148
148
148
148
148
148
148
148
148
148
147
147
147
147
147
147
147
147
146
146
146
146
146
146
145
145
145
145
145
144
144
144
144
144
143
143
60
150
150
150
150
150
150
150
150
150
150
150
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
148
148
148
148
148
148
148
148
148
148
148
148
147
147
147
147
147
147
70
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
149
80
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
90
z [m]
150
1000
150
980
150
960
150
940
150
920
150
900
150
880
150
860
150
840
150
820
150
800
150
780
150
760
150
740
150
720
150
700
150
680
150
660
150
640
150
620
150
600
150
580
150
560
150
540
150
520
150
500
150
480
150
460
150
440
150
420
150
400
150
380
150
360
150
340
150
320
150
300
150
280
150
260
150
240
150
220
150
200
150
180
150
160
150
140
150
120
150
100
150
80
150
60
150
40
150
20
150
0
100 x [m]
76
75
74
73
72
71
70
69
68
67
66
65
64
63
62
61
59
58
57
56
55
54
53
52
50
49
48
47
46
45
44
42
41
40
39
38
37
35
34
33
32
31
29
28
27
26
25
24
22
21
20
0
95
94
93
92
91
91
90
89
88
87
86
85
84
83
82
81
80
79
78
77
76
75
74
73
72
71
70
69
68
67
66
65
64
63
61
60
59
58
57
56
55
54
53
51
50
49
48
47
46
45
43
10
110
110
109
108
108
107
106
105
105
104
103
102
101
101
100
99
98
97
97
96
95
94
93
92
91
90
89
89
88
87
86
85
84
83
82
81
80
79
78
77
76
75
74
73
72
71
70
69
68
67
66
20
123
122
122
121
121
120
119
119
118
118
117
116
116
115
114
114
113
112
112
111
110
110
109
108
107
107
106
105
104
104
103
102
101
101
100
99
98
97
96
96
95
94
93
92
91
90
89
88
87
87
86
30
132
132
131
131
130
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40
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60
146
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70
148
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80
149
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90
149
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148
148
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148
148
148
148
148
148
148
148
148
148
148
148
148
148
147
147
147
147
147
147
100 x [m]
Figure 17. Temperature distribution in rock and water at three time instances.
From left, t = 1, 15 and 30 years.
The scale of Figure 17 does not give a complete picture of the temperature field at the
interface between rock and water. In Figure 18 the temperature distribution at t = 30 years is
shown at a different scale, x = 0-10 m into the rock. The color coding representing
temperature is the same as in Figure 17.
In Figure 18 we can see the effect of the boundary condition that states that the rock and
water has the same temperature at the interface x = 0 m. Since the water flow velocity is low,
in the base case 0.005 m/s, this assumption is realistic.
34
z [m]
1000
950
900
850
800
750
700
650
600
550
500
450
400
350
300
250
200
150
100
50
0
76
74
71
69
66
63
61
58
55
52
49
46
44
41
38
35
32
29
26
23
20
0
77
74
71
69
66
63
61
58
55
52
50
47
44
41
38
35
32
29
26
23
20
0,1
78
76
73
71
68
65
63
60
57
54
52
49
46
43
40
37
34
31
28
25
22
1
80
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75
73
70
67
65
62
59
57
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48
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42
39
37
34
31
28
25
2
82
80
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72
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67
64
62
59
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53
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48
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36
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30
27
3
84
82
79
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58
55
53
50
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29
4
86
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63
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5
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34
6
90
87
85
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67
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62
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36
7
91
89
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80
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75
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39
8
93
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66
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61
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53
50
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44
41
9
95
93
91
88
86
84
81
79
76
74
71
68
66
63
60
58
55
52
49
46
43
10 x [m]
Figure 18. Temperature distribution at rock water interface.
In Figure 19 the water temperate along the fracture in z-direction is shown at a specific point
in time, t = 30 years. We can see that at constant flow velocity the temperature rise of the
fluid is linear along the fracture in z-direction.
80
Water temperature [°C]
70
60
50
40
30
20
0
200
400
600
800
Height position in f racture [m]
1000
Figure 19. Water temperature along fracture height.
The most interesting output from the model is water outlet temperature over time. In Figure
20 we can see how the outlet temperature drops with time and ends at 76 °C after 30 years of
production. The outlet temperature is constant only for a short period of time. Thermal power
is proportional to the outlet temperature and could be described by the same curve but with
different y-axis unit. In the beginning at 150 °C the system produces 30 MW, at the end at 30
years the power has dropped to 13 MW according to Eq. 13.
35
160
Outlet temperature [°C]
140
120
100
80
60
40
20
0
0
5
10
15
Time [y ears]
20
25
30
Figure 20. Outlet temperature over time.
Heat conduction in the surrounding rock is the limiting factor for heat transfer to the flowing
water. In the beginning of the process cold water is in contact with rock of high temperature.
The temperature difference that drives heat conduction makes the heat transfer process fast.
With time when the temperature gradient decreases the heat transfer slows down.
From this first study we can conclude that changing the water flow velocity will change the
behavior of the system and the outlet temperature. A higher initial rock temperature will also
naturally yield higher thermal power. Changing the material properties of the rock, such as
the thermal conductivity will also have effect on the system. In the next three studies these
aspects will be investigated.
36
4.3
OUTLET TEMPERATURE AT DIFFERENT INITIAL
ROCK TEMPERATURE
The effect of different initial rock temperature was investigated. Four different rock
temperatures was studied: 100, 150, 200 and 250 °C. Assuming global average geothermal
gradient of 30 °C/km, these temperatures can be expected at the depth of 3300, 5000, 6700
and 8300 m. As stated earlier and seen in Figure 21 the outlet temperature drops with time
250
Tr0=250 °C
Tr0=200 °C
Tr0=150 °C
Outlet temperature [°C]
200
Tr0=100 °C
150
100
50
0
0
5
10
15
Time [y ears]
20
25
30
Figure 21. Outlet temperature at different initial rock temperature.
At constant flow rate the ratio between outlet temperature and initial rock temperature is the
equal for each case. This ratio is called thermal drawdown. It depends only on the flow rate
and effective heat transfer area. It scales directly with the area normalized water mass flow
rate ṁ/2A, where A is the total fracture area (1 000 000 m2) and 2A is the total effective heat
transfer surface area since the artificial fracture consist of two rock surfaces (Tester et al.
2011).
(20)
In these four cases the thermal drawdown is about 0.5 according to Eq. 20. From Eq. 13 and
15 thermal and electrical power is calculated. The integral of these functions Eq. 16 and 17
gives the produced energy. The results from these calculations are presented in Figure 22.
37
60
25
Tr0=250 °C
20
Electric power [MW]
Thermal power [MW]
50
40
30
20
Tr0=150 °C
15
Tr0=100 °C
10
5
10
0
0
0
5
10
15
20
Time [y ears]
25
30
0
5
10
15
20
Time [y ears]
25
30
0
5
10
15
20
Time [y ears]
25
30
4
Produced electric energy [TWh]
10
Produced thermal energy [TWh]
Tr0=200 °C
8
6
4
2
0
3
2
1
0
0
5
10
15
20
Time [y ears]
25
30
Figure 22. Power and energy at different initial rock temperature.
As seen in Figure 22 the magnitude of power and produced energy depends fully on the
temperature of the rock resource. High rock temperature means deeper depths, which means
higher access costs. It can be assumed that a certain depth exists related to an economical
optimum for a system with a certain geothermal gradient and a certain exponentially rising
drilling or excavation cost. In chapter 7 such an optimum will discussed further.
Table 3 shows the average power per fracture area of the four cases according to Eq. 18 and
19.
Table 3. Average power at different initial rock temperature.
Initial rock
temperature
[°C]
100
150
200
250
Flow
velocity
[m/s]
0.005
0.005
0.005
0.005
Mass
flow
[kg/s]
Final outlet
temperature
[°C]
55
55
55
55
Average
thermal power
[W/m2]
55
76
98
120
38
Average
electric power
[W/m2]
12
19
26
34
1.8
4.3
7.7
12
The average thermal power per fracture area varies in these four cases between 12 and 34
Wth/m2. Note that the average thermal power per heat transferring surfaces is half of that (1 m2
of fracture consist of 2 m2 of heat transferring surface). From this it is possible to conclude
that very large heat transferring surfaces are needed to maintain any substantial power
production. It is also possible to conclude than such heat transferring surfaces must be able to
be constructed fast and at a low cost to make a system with artificial fractures economically
viable.
4.4
OUTLET TEMPERATURE AT DIFFERENT FLOW
VELOCITY
The effect of different water flow velocity was investigated. Figure 23 shows the outlet
temperature over time at four different flow velocities, U = 0.04, 0.01, 0.005 and 0.001 m/s.
The initial rock temperature is 150 °C in all four cases.
160
U=0.040 m/s (440 kg/s)
140
U=0.010 m/s (110 kg/s)
U=0.005 m/s (55 kg/s)
Outlet temperature [°C]
120
U=0.001 m/s (11 kg/s)
100
80
60
40
20
0
0
5
10
15
Time [y ears]
20
25
30
Figure 23. Outlet temperature at different flow velocity.
Naturally it is possible to maintain a high outlet temperature over time with a low fluid flow
velocity as in the case U = 0.001 m/s. In our base case with fracture dimensions 2w = 0.011
m, H = 1000 m and L = 1000 m this velocity equals a mass flow of ṁ = 11 kg/s.
Increasing the flow velocity to U = 0.005 m/s gives a mass flow of ṁ = 55 kg/s, at this rate
the outlet temperature begins do drop with time and after 30 years it is 76 °C. Increasing the
39
flow velocity further enhances this effect, U = 0.01 m/s yields ṁ = 110 kg/s and Tout = 49 °C.
Finally U = 0.04 m/s yields ṁ = 440 kg/s and Tout = 27 °C after 30 years of production.
The increased velocity and mass flow has a substantial effect on power and energy
production. At 0.01 m/s (440 kg/s) the initial thermal power is almost 240 MW (out of the
chart scale in Figure 24) but decreases very fast due to the fast decrease in rock temperature,
after only 5 years the outlet temperature has dropped under 40 °C. It is apparent that an
optimal flow velocity exists for any specific set of fracture parameters and desired output
application.
100
10
80
8
Electric power [MW]
Thermal power [MW]
U=0.040 m/s
60
40
20
U=0.005 m/s
6
U=0.001 m/s
4
2
0
0
0
5
10
15
20
Time [y ears]
25
30
0
5
10
15
20
Time [y ears]
25
30
0
5
10
15
20
Time [y ears]
25
30
1.5
Produced electric energy [TWh]
8
Produced thermal energy [TWh]
U=0.010 m/s
6
4
2
0
1
0.5
0
0
5
10
15
20
Time [y ears]
25
30
Figure 24. Power and energy at different flow velocity.
High flow velocity yields higher amounts of produced thermal energy, but since the high flow
is at low temperature the energy is not as usable as in the case with higher temperatures and
lower flow velocities. This effect is seen in the amount of potential electric power. We can
see that electric power drops fast and even below the low fluid flow cases. The Carnot
efficiency, the ability to transfer heat to mechanical work, is dependent on temperature of the
working medium. The fast drop in temperature leads to lower potential electric power which
40
leads to lower amounts of produced electric energy. In the last plot in Figure 24 we can
clearly see than an optimal flow velocity for maximal production of electric energy exists. In
these four cases the third case at 0.005 m/s (55 kg/s) yields the highest production.
In chapter 4.6 optimal flow for thermal and electrical power will be investigated further. The
average power from the four simulations above is presented in Table 4.
Table 4. Average power at different flow velocity.
Initial rock
temperature
[°C]
150
150
150
150
4.5
Flow
velocity
[m/s]
0.001
0.005
0.010
0.040
Mass
flow
[kg/s]
Final outlet
temperature
[°C]
11
55
110
440
Average
thermal power
[W/m2]
149
76
49
27
6.0
19
23
26
Average
electric power
[W/m2]
1.8
4.4
3.8
1.8
OUTLET TEMPERATURE AT DIFFERENT ROCK
THERMAL CONDUCTIVITY
The effect of material and thermodynamic properties of different rock was investigated. In the
base case the rock is assumed to be granite with the following constant properties: specific
heat capacity 1050 J/kg K, density 2700 kg/m3 and thermal conductivity 2.9 W/mK. These
values are based on the values used by Tester et al. (2011). Since rock is a non-homogenous
material its properties varies according to composition and physical aspects.
Specific heat capacity and thermal conductivity are temperature dependent. Thermal
conductivity decreases with higher temperature while specific heat capacity increases with
higher temperature. Vosteen & Schellschmidt (2003) reports a difference of 3.5 to 1.0 W/mK
and Maqsood, Hussain Gul, & Anis-ur-Rehman (2004) 3.5 to 1.5 W/mK for different granite
samples.
Thermal conductivity also depends on porosity and water content; dry low porosity granite
has lower thermal conductivity while high porosity saturated granite has higher conductivity.
Cho, Kwon, & Choi (2009) find a range from 2.12 W/mK to 3.62 W/mK for different
samples.
41
Since there are many variables that effect material and thermodynamic properties of granite
rock we modeled a range of thermal conductivity of 2.0 to 4.0 W/mK. This interval will
include most of the variable aspects due to varying chemistry and porosity.
In Figure 25 outlet temperature during production period of 30 years is presented at four
different values of thermal conductivity of rock. Lower thermal conductivity yields as
expected lower outlet temperature and higher thermal drawdown ratio.
160
kr=4.0 W/mK
140
kr=3.5 W/mK
kr=2.9 W/mK
Outlet temperature [°C]
120
kr=2.0 W/mK
100
80
60
40
20
0
0
5
10
15
Time [y ears]
20
25
30
Figure 25. Outlet temperature at different thermal conductivity.
Earlier we stated that heat transfer is limited by the heat conduction in the rock and that
conduction decreases with lower temperature gradients in the system. As seen in Figure 25
higher thermal conductivity of rock mitigates this effect, but the heat conduction in the rock
mass is still the limiting factor for heat extraction.
42
Figure 26 shows power and produced energy at the four different values of thermal
conductivity. Average power is presented in Table 5.
35
10
kr=4.0 W/mK
8
Electric power [MW]
Thermal power [MW]
30
25
20
15
10
kr=2.9 W/mK
6
kr=2.0 W/mK
4
2
5
0
0
0
5
10
15
20
Time [y ears]
25
30
0
5
10
15
20
Time [y ears]
25
30
0
5
10
15
20
Time [y ears]
25
30
1.5
Produced electric energy [TWh]
6
Produced thermal energy [TWh]
kr=3.5 W/mK
5
4
3
2
1
0
1
0.5
0
0
5
10
15
20
Time [y ears]
25
30
Figure 26. Power and energy at different rock thermal conductivity.
If comparing the two cases 2.0 W/m K and 4.0 W/mK the amount of produced thermal energy
is 25 % higher in the latter case. This in turn has significant impact in the produced electrical
energy where the difference between the two cases above is 44 %.
Table 5. Average power different rock thermal conductivity.
Thermal
conductivity
[W/mK]
2.0
2.9
3.5
4.0
Initial rock
temperature
[°C]
150
150
150
150
Flow
velocity
[m/s]
0.005
0.005
0.005
0.005
Final outlet
temperature
[°C]
Average
thermal power
[W/m2]
68
76
81
85
43
17
19
20
21
Average
electric power
[W/m2]
3.6
4.4
4.8
5.1
4.6
OPTIMAL POWER AND ENERGY PRODUCTION
4.6.1
INTRODUCTION
In chapter 4.3 we concluded that the temperature of the rock resource is the most important
aspect of heat mining operations. We also concluded that an optimal depth exists if drilling or
excavation costs increase exponentially width depth. Since the rock temperature is related to
the local geothermal gradient and depth, and since depth is related to the cost of drilling or
excavating and the construction of the whole production system an optimization of these
conditions exceeds the scope of this report.
In chapter 4.4 we concluded that and optimal water flow exists for a certain fracture system
with a certain initial temperature and during a certain production period. In the follow
chapters this optimal flow will be investigated.
In chapter 4.5 we concluded that higher thermal conductivity yields higher power and energy
production. The material parameters will not be investigated further in the optimization
context.
4.6.2
OPTIMAL THERMAL ENERGY PRODUCTION
As concluded earlier an optimal water flow velocity exists for a particular fracture system and
output usage. If the system is to be used for district heating only, with no electricity
production, the limiting factor is the lowest acceptable outlet temperature from the system.
This lowest acceptable temperature can depend on the cost of heat exchangers or the technical
limitations of the district heating distribution system.
A lowest acceptable outlet temperature was set to 60 °C after 30 years of production. In
Figure 27 the outlet temperature after 30 years is presented as a function of water flow
velocity. If the rock resource has the initial temperature of 150 °C a water flow velocity of
0.0072 m/s (79 kg/s) is the optimal flow that yields a final temperature of 60 °C after 30
years.
44
250
Tr0=250 °C
Tr0=200 °C
Outlet temperature at 30 years [°C]
Tr0=150 °C
200
Tr0=100 °C
150
100
50
0
0
0.005
0.01
Flow v elocity [m/s]
0.015
0.02
Figure 27. Outlet temperature at 30 years at different flow velocity.
In Figure 28 the outlet temperature at the optimal flow rates found in Figure 27 is presented.
The outlet temperature drops faster at the higher flow velocities as seen earlier. After half the
production time the outlet temperature is almost the same for the four cases.
250
Tr0=250 °C, U=0.0130 m/s
Tr0=200 °C, U=0.0101 m/s
Tr0=150 °C, U=0.0072 m/s
Outlet temperature [°C]
200
Tr0=100 °C, U=0.0042 m/s
150
100
50
0
0
5
10
15
Time [y ears]
20
25
30
Figure 28. Outlet temperature at optimal flow for thermal energy production.
45
In Figure 29 power and energy for these four cases are presented. The cases with higher flow
velocity and mass flow yields higher power even though the temperature reaches the same
magnitude in the latter part of the production period.
150
60
Tr0=250 °C, U=0.0130 m/s
Electric power [MW]
Thermal power [MW]
50
100
50
Tr0=200 °C, U=0.0101 m/s
Tr0=150 °C, U=0.0072 m/s
40
Tr0=100 °C, U=0.0042 m/s
30
20
10
0
0
0
5
10
15
20
Time [y ears]
25
30
5
10
15
20
Time [y ears]
25
30
0
5
10
15
20
Time [y ears]
25
30
2.5
Produced electric energy [TWh]
Produced thermal energy [TWh]
12
0
10
8
6
4
2
0
2
1.5
1
0.5
0
0
5
10
15
20
Time [y ears]
25
30
Figure 29. Power and energy for optimal thermal energy production flow velocity.
As seen in Figure 29 and Table 6 high initial rock temperature enables higher mass flow
which leads to a higher power and energy production. In the case with initial rock temperature
of 250 °C a mass flow of 143 kg/s is possible while still fulfilling the condition of outlet
temperature of 60 °C after 30 years. This system has an average power per fracture area of 42
W/m2.
Table 6. Average power at flow for optimal thermal energy production.
Initial rock
temperature
[°C]
100
150
200
250
Flow
velocity
[m/s]
0.0042
0.0072
0.0101
0.0130
Mass
flow
[kg/s]
46.2
79.2
111
143
Final outlet
temperature
[°C]
Average
thermal power
[W/m2]
60
60
60
60
46
11
21
32
42
Average
electric power
[W/m2]
1.8
4.1
6.7
9.4
The condition of outlet temperature of 60 °C after 30 years is only an assumption to make it
possible to find an optimal flow. Limiting condition could be chosen in several ways. Water
with 60 °C temperature is still valuable and could be used for example together with heat
pumps to utilize more of the available heat (Henkel 2006).
4.6.3
OPTIMAL ELECTRIC ENE RGY PRODUCTION
The available power for electricity production, the exergy content in the fluid flow, depends
on the outlet temperature. The dependence is exponential due to temperature dependent
conversion efficiency. Higher temperatures yields higher Carnot efficiencies and a larger part
of the thermal energy can be converted into mechanical and electric energy. The efficiencies
for converting thermal power to electric power are low for the temperature intervals in
question for geothermal energy. At Tout = 150 °C the Carnot efficiency is ηc = 0.31, at Tout =
76 °C it is ηc = 0.16. Real world geothermal plant efficiencies are even lower, see Figure 3.
(DiPippo, 2007)
In Figure 30 the amount of produced electrical energy during 30 years is presented as a
function of the flow velocity. An optimal flow exists that yields an outlet temperature
function that yields maximum amount of produced electric energy. The optimal flow
velocities found is near the base case flow velocity value of 0.005 m/s. In Figure 31 and Table
7 the power and produced energy is presented at the optimal flow for each initial rock
temperature found in Figure 30.
47
3.5
Tr0=250 °C
Tr0=200 °C
3
Produced electric energy [TWh]
Tr0=150 °C
Tr0=100 °C
2.5
2
1.5
1
0.5
0
0
0.01
0.02
0.03
Flow v elocity [m/s]
0.04
0.05
60
30
50
25
Electric power [MW]
Thermal power [MW]
Figure 30. Optimal flow velocity for electricity production.
40
30
20
10
Tr0=200 °C, U=0.0048 m/s
Tr0=150 °C, U=0.0046 m/s
20
Tr0=100 °C, U=0.0044 m/s
15
10
5
0
0
0
5
10
15
20
Time [y ears]
25
30
0
5
10
15
20
Time [y ears]
25
30
0
5
10
15
20
Time [y ears]
25
30
4
Produced electric energy [TWh]
10
Produced thermal energy [TWh]
Tr0=250 °C, U=0.0051 m/s
8
6
4
2
0
3
2
1
0
0
5
10
15
20
Time [y ears]
25
30
Figure 31. Power and energy at optimal flow velocity for electricity production.
48
At optimal flow and with initial rock temperature of 250 °C it is possible to produce an
average electric power per fracture area of 12 W/m2. The outlet temperature is in this case still
high at 30 years, 125 °C, and still contains useful energy.
Table 7. Average power at flow for optimal electricity production.
Initial rock
temperature
[°C]
100
150
200
250
Flow
velocity
[m/s]
0.0044
0.0046
0.0048
0.0051
Mass
flow
[kg/s]
48.4
50.6
52.8
56.1
Final outlet
temperature
[°C]
Average
thermal power
[W/m2]
59
83
102
125
Average
electric power
[W/m2]
11
18
26
33
1.8
4.3
7.6
12
A combination of electricity production and district heating could be the most cost effective
way of utilizing the heat resource. This depends on the price of which it is possible to sell
district heating as well as the price of electricity. This optimization exceeds the scope of this
report and will be left uninvestigated but noted.
49
5
RESULTS FROM THE NUMERICAL MODEL
5.1
INTRODUCTION
A numerical model of a single fracture with surrounding rock was created in the simulation
software COMSOL Multiphysics. The model is described in detail by Källberg (2012). The
numerical single fracture COMSOL model describes the same geometry as the analytical
model and uses the same base case parameters values. The COMSOL model is more refined
and uses built-in coupled physical processes and parameters dependencies.
The same three major studies done with the analytical model was done in the numerical
COMSOL model.

Outlet temperature at different initial rock temperature

Outlet temperature at different flow velocity

Outlet temperature at different rock thermal conductivity
The results from these studies are presented by Källberg (2012). In chapter 5.3 the results
from the numerical COMSOL model is compared with the results from numerical model
presented earlier in this report.
An additional COMSOL model and study was created to investigate properties of multiple
fractures and the effects of distances between them. The result of this study is presented in
this report.
50
5.2
COMSOL MULTIPLE FRACTURE MODEL
A multiple fracture model was developed in COMSOL in order to study how heat extracting
fractures affect each other and at what distance. Geometry and mesh of the model is presented
in Figure 32 together with the regular single fracture model. The model describes three
fractures by using mid-plane symmetry. Five different fracture distances were modeled, D =
125, 100, 75, 50 and 25 m. To the far right (and far left according so symmetry) 200 m of
bulk rock surrounds the fracture system, on top and below 100 m of rock surrounds the
fracture. The outlet temperature in the middle fracture was measured.
Figure 32. Mesh and geometry of numerical COMSOL models:
single fracture model (left) and multiple fracture model (right).
The results were compared with the outlet temperature from the COMSOL single fracture
model using the same input parameter values. The study was based on the base case of
parameter values with fracture geometry 0.011 m width, 1000 m height and 1000 m depth,
51
constant water flow velocity of 0.005 m/s, initial rock temperature 150 °C and production
time of 30 years. Material properties of water and granite were also the same as in the base
case with the addition of definition of thermal conductivity of water kw = 0.6 W/mK (not used
in analytical model).
Figure 33. Temperature distribution at 30 years, from left D = 125, 100, 75, 50 and 25 m.
In Figure 33 temperature distribution in rock and fracture after 30 years is shown. At fracture
distance of 125 m (left) unaffected rock mass still exists between the two fractures. At 100 m
the cold wave around the middle fracture looks similar to the cold wave of the single fracture
at the same time.
At fracture distance 75, 50 and 25 m the rock mass surrounding the middle fracture has been
cooled significantly compared to the case of a single fracture.
In Figure 34 (left) the result from the single fracture model is presented. In the middle is the
multiple fracture results at D = 100 at the same time 30 years. To the right is a mirrored
picture of the multiple fracture model showing the three described fractures modeled by using
symmetry along the mid-plane in the middle fracture. We can see that multiple fractures at
distance about 100 m have similar temperature distribution as a single fracture.
52
Figure 34. Single fracture model and multiple fracture model with D = 100 m.
In Figure 35 the outlet temperature during 30 years is presented for fracture distance D = 100,
75, 50 and 25 m. The result from the single fracture model for the same parameters is also
presented in the graph for comparison.
53
160
Single f racture
140
D = 100 m
D = 75 m
Outlet temperature [°C]
120
D = 50 m
D = 25 m
100
80
60
40
20
0
0
5
10
15
Time [y ears]
20
25
30
Figure 35. Outlet temperature in central fracture at different fracture distances.
In this particular case and geometry a fracture distance of 100 m leads to a final outlet
temperature only 3.5 % lower than of a single fracture. At D ≥ 125 m the multiple fracture
model gives the same outlet temperature results as the single fracture model.
These findings correspond to the thermal penetration estimate presented by Armstead &
Tester (1987) which state that in a conductive controlled environment the thermal penetration
depth can estimated by
√
(21)
where
t
Time
s
αr
α = kr / ρr cp,r
Thermal diffustivity rock
m2/s
kr
2.9
Thermal conductivity rock
W/m K
ρr
2700
Density rock
kg/m3
cp,r
1050
Specific heat capacity rock
J/kg K
Figure 36 shows the thermal penetration according to Eq. 21. After 30 years the cooling at the
fracture surface has affected the initial rock temperature over 60 m into the rock mass.
54
Thermal penetration depth [m]
70
60
50
40
30
20
10
0
0
5
10
15
Time [y ears]
20
25
30
Figure 36. Theoretical estimation of thermal penetration depth.
From this it is possible to conclude that fractures at the distance of around 120 m or closer
will affect each other during the time studied. At this distance the effect is low which makes it
possible to place fractures at closer distances without having a significant loss in outlet
temperature. As seen in the COMSOL model a distance of 100 m does not reduce the outlet
temperature significantly.
The thermal penetration depth is of importance in construction design and economical
optimization of an artificial fracture heat exchanger system.
5.3
COMPARISON OF RESULTS FROM THE
ANALYTICAL AND THE NUMERICAL MODEL
The results from the analytical model implemented in MATLAB were compared with the
results from the numerical COMSOL model for the same set of input parameters.
The first study shows outlet temperature over a production time of 30 years at four different
initial rock temperatures at constant flow 0.005 m/s.
55
250
T r0=250 °C Analytical
T r0=200 °C Analytical
T r0=150 °C Analytical
T r0=100 °C Analytical
T r0=250 °C Numerical
T r0=200 °C Numerical
T r0=150 °C Numerical
T r0=100 °C Numerical
Outlet temperature [°C]
200
150
100
50
0
0
5
10
15
Time [y ears]
20
25
30
Figure 37. Comparison of model results: Outlet temperature at different initial rock temperature.
As seen in Figure 37 the temperature results from the COMSOL model are consistently
higher than the results from the analytical MATLAB model. At the start, before thermal
breakthrough, the outlet temperature is constant and therefore equal in the two models. When
thermal breakthrough occurs and the outlet temperature begins to drop the difference between
the two models start to increase. At the end of the production period the difference decreases
slightly.
In Table 8 the outlet temperate at 30 years and 15 years are shown. At 30 years the COMSOL
results are 2.4 to 3.5 % higher than the analytical model. At 15 years the difference in outlet
temperature is between 2.4 to 3.7 %.
Table 8. Comparison of results: Outlet temperature at different initial rock temperature.
30 years
15 years
Tr,0
100
150
200
250
°C
Numerical COMSOL
56.2
79.0
100.6
122.6
°C
Analytical MATLAB
54.7
76.3
98.0
119.7
°C
Difference
1.5
2.7
2.6
2.9
°C
Difference
2.7%
3.5%
2.7%
2.4%
Numerical COMSOL
68.9
99.2
128.3
157.6
°C
Analytical MATLAB
66.6
95.7
124.8
153.9
°C
Difference
2.3
3.5
3.5
3.7
°C
Difference
3.5%
3.7%
2.8%
2.4%
56
A probable cause for this difference between the two models is the heat conduction
dimensional setup. The analytical model is based on an energy balance that neglects
conduction in z-direction (height), heat conduction occurs only in one dimension, in xdirection. The COMSOL model calculates heat conduction in two dimensions, both in xdirection and z-direction. The COMSOL model also has two additional surrounding rock
masses on top and bottom to withdraw heat from. Tester et al. (2011) find similar differences
between the analytical model and the numerical TOUGH2 model and the same conclusion
was made.
The second study shows the outlet temperature at four different flow velocities at constant
initial rock temperature Tr,0 = 150 °C. The results are shown in Figure 38. The outlet
temperature from the analytical model and the numerical model differ in the same manner as
seen in the earlier study. The numerical COMSOL model yields consistent higher outlet
temperature.
160
U=0.001 m/s
U=0.005 m/s
U=0.010 m/s
U=0.040 m/s
U=0.001 m/s
U=0.005 m/s
U=0.010 m/s
U=0.040 m/s
140
Outlet temperature [°C]
120
Analytical
Analytical
Analytical
Analytical
Numerical
Numerical
Numerical
Numerical
100
80
60
40
20
0
0
5
10
15
Time [y ears]
20
25
30
Figure 38. Comparison of model results: Outlet temperature at different flow.
The third and final comparison study shows the outlet temperature at four different values of
rock thermal conductivity at constant initial rock temperature Tr,0 = 150 °C. The results are
shown in Figure 39. The outlet temperature from the analytical model and the numerical
model differ in the same manner as seen in above, the numerical COMSOL model yields
consistent higher outlet temperature.
57
160
140
Outlet temperature [°C]
120
100
80
60
kr=4.0 W/mK
kr=3.5 W/mK
kr=2.9 W/mK
kr=2.0 W/mK
kr=4.0 W/mK
kr=3.5 W/mK
kr=2.9 W/mK
kr=2.0 W/mK
40
20
Analytical
Analytical
Analytical
Analytical
Numerical
Numerical
Numerical
Numerical
0
0
5
10
15
Time [y ears]
20
25
30
Figure 39. Comparison of model results: Outlet temperature at different thermal conductivity.
58
6
CONSTRUCTION OF HEAT EXCHANGE
SURFACES
6.1
INTRODUCTION
The concept investigated in this report is based on the use of diamond wire cutting as
construction method for the heat transfer system. In this chapter the capabilities, limitations
and costs of diamond wire cutting are investigated.
Two cost models are presented, the first model represents a future automated or semiautomated implementation specially adjusted for the construction method. The model is used
with both selected parameter values and with Monte Carlo simulation of parameter values.
The second additional model represents diamond wire cutting performed today in stone
quarries. The ‘Quarry model’ takes additional time dependent parameters into account, most
significantly work costs.
Finally in chapter 6.7 the construction cost is compared with the power production of the
fracture system which enables an estimation of the economic viability of the system.
6.2
DIAMOND WIRE CUTTING
A diamond wire saw is basically a motor that rotate a flywheel that drive a loop of diamond
coated wire. The diamond wire is abrasive and grinds its ways through the rock. The wire is
tensioned by the machine moving slowly along a track. The wire rotates in its path grinding
the rock and creates a slit between two flat rock surfaces.
A typical electric powered diamond wire saw uses 75 kW to drive the wire through hard rock.
A 75 kW machine can handle about 200 m of wire. By using boreholes and wire pulleys
almost any kind of cut geometry is possible.
59
Figure 40. Diamond wire cutting in stone quarry (Pellegrini Meccanica 2012).
There are two main types of cutting methods and setups, the wire loop can be either pulled or
pushed. The most effective and straight forward way is cutting by pulling the wire. The wire
is passed through boreholes and by pulleys to create a closed loop around the cut area. The
wire machine is then tensioning the loop while at the same time rotating and driving the
diamond wire around in its path.
Cutting by pushing the wire is called ‘blind cut’, this method is used when it is possible to
access the cut area from one surface only. Large diameter boreholes are drilled in which rodmounted pulleys are lowered. The wire is led down the holes, around the pulleys, and back to
the surface. When the wire machine is tensioning the wire the wire is pushing forward at the
cut area between two neighboring boreholes.
60
Figure 41. Diamond wire cutting by pulling (Pellegrini Meccanica 2012) (Wachtmeister 2012).
Figure 42. Diamond wire cutting by pushing (blind cut). From upper left: 1. Large diameter drilling (250
mm core drill). 2. Diamond coated wire 11 mm diameter. 3. Blind cut set up. 4. Picture taken down the
access hole showing the rod-mounted pulley and a 11 mm finished “artificial fracture” to the left
(Wachtmeister 2012).
61
Figure 43. Setup (left) and finished blind cut (right) (Wachtmeister 2012).
Figure 44. Co-researcher Christoffer Källberg inspecting results of diamond wire cutting in quarries (left).
The result of 11 mm wire cut – an artificial fracture (right) (Wachtmeister 2012).
62
6.3
WIRE CUT COST PARAMETERS
To assess the cost of diamond wire cutting the wire life time and wire cutting speed is of
importance. These aspects can vary a lot depending on the rock composition, diamond wire
composition, rock stress, skill of the operator etc. The cost of the wire itself is naturally a
critical parameter. Also the power of the machine and the price of electricity (or diesel) to
drive it have impact on the total cut cost.
The cost related parameters and their value range presented in Table 9 were developed
together with Arne Hallin, Scandinavian representative of TYROLIT Schleifmittelwerke
Swarovski K.G., a leading manufacturer of diamond wire. Wire data in form of recorded wire
wear and cutting speeds from 35 different quarries was also examined.
The first cost model developed represent cutting cost for a future application of the above
described concept with construction of large underground heat transferring surfaces. This
entails the assumption of large scale implementation of the cutting process with full or semi
full automation. Operator work cost and capital cost for machines and equipment is not
included in this first model.
Table 9. Wire cut cost parameters.
Wire cost
Cut speed
Wire lifetime
Machine power
Electricity cost
WC
CS
WL
MP
EC
Normal
NC
550
10
15
75
1
Low
L
350
5
10
50
0.5
High
H
1000
15
20
100
2
Unit
SEK/m
m2/h
m2/m
kW
SEK/kWh
During discussion with Hallin the question of the possible future development of these cost
parameters was raised. Improved materials and experience has increased cutting performance
a lot since it was introduced 30 years ago. Under certain circumstances cutting speeds up to
45 m2/h has been achieved. This positive trend will probably continue, with improved wire
lifetime and cutting speeds. The cost of the wire is hard to foreseen, the methods of
manufacturing artificial diamonds are improving, but the manufacturing of the wire and
composition of the diamonds require skill and precision.
63
6.4
TOTAL CUT COST BY SELECTED PARAMETER
VALUES
A model was developed to assess the total diamond wire cutting cost per area (SEK/m2) by
modeling the different cases of the parameter values set up in Table 9. Based on the normal
cost case (NC) each parameter was changed to its lowest (L) and highest (H) value each at a
time. This generates a cloud of possible cut cost levels based on the selected parameter
values, see Figure 45.
100
90
80
Cut cost [SEK/m2]
70
60
50
40
30
20
10
0
NC
WC-L WC-H
CS-L
CS-H WL-L WL-H
Cut cost case
MP-L
MP-H
EC-L
EC-H
Figure 45. Cut cost cases with selected parameter values.
By picking the ‘best’ value for each parameter an additional optimal case was created with
total cut cost of 20 SEK/m2. Based on the discussion of future cost development an additional
optimistic case was created. This case is based on cut speed of 40 m2/h, wire life time 25
m2/m and wire cost of 200 SEK/m. The total cut cost for the future case is 8.9 SEK/m2.
Table 10. Three wire cut cost scenarios.
Wire cost
Cut speed
Wire lifetime
Machine power
Electricity cost
Total cut cost
WC
CS
WL
MP
EC
Normal
NC
550
10
15
75
1
Optimal
OPT
350
15
20
75
0.5
Future
FOPT
200
40
25
75
0.5
Unit
44
20
8.9
SEK/m2
64
SEK/m
m2/h
m2/m
kW
SEK/kWh
For further assessment these three cost scenarios were used: the normal cut cost of 44
SEK/m2, optimal cut cost of 20 SEK/m2 and optimistic future scenario of 8.9 SEK/m2.
6.5
TOTAL CUT COST BY MONTE CARLO
SIMULATION
As a complement to the three cost cases described above with selected parameter values
additional investigation of cutting cost was done by Monte Carlo simulation. There is no strict
definition of a Monte Carlo simulation but it is normally performed by repeated calculations
with randomly generated input. First, possible input parameter range is defined (the domain),
the probability distribution of the domain is likewise defined. Then repeated random sampling
of inputs and calculation of outputs begins. For each iteration a new set of randomly
generated inputs are used for deterministic output calculation. The output results are saved
and aggregates to probability distributions of possible outcomes. Monte Carlo simulation is
useful in cases with large uncertainties in input parameter values, it approximates possible
outcomes and how likely they are to occur. In the case of the cost estimate model of diamond
wire cutting a Monte Carlo simulation can give valuable additional information for cost
analysis by including the effect of addition of probability distributions of input parameter
values.
Two cost models where developed for Monte Carlo simulation. First a Monte Carlo
simulation was done based on the same set and interval of wire cut cost parameters as
described in Table 9. Two simulations were done with these parameters: one with all
parameters at uniform distribution (all values between the minimum and maximum are
equally likely to occur), and one simulation with all parameters at an estimated normal
distribution with an estimated mean value and standard deviation. The second cost model is
described in the next chapter.
The Monte Carlo simulations were executed with the spreadsheet-based application Oracle
Crystal Ball. The outcome of ‘Total cut cost’ in SEK/m2 from the two simulations is showed
in Figure 46 and Figure 47. Each simulation consisted of 1 000 000 iterations.
65
Figure 46. Outcome of Monte Carlo simulation of total cut cost in SEK/m2 with input parameters at
uniform distribution.
Figure 47. Outcome of Monte Carlo simulation of total cut cost in SEK/m2 with input parameters at normal
distribution.
The mean value of the first simulation at uniform distribution was 57 SEK/m2 with median 55
SEK/m2. The mean value of the second simulation at normal distribution parameters was 54
SEK/m2 with median 47 SEK/m2.
In Figure 48 results from a sensitivity analysis are presented. In this model the cost of wire
(both in form of wire cost per meter and in wire lifetime) dominates the total cut cost
outcome. In this model the only time related cost is power (electricity), this cost has a small
effect on the total outcome whereby the parameter cut speed has small impact. In the next
additional model the important time aspect and cut speed will be investigated and represented
further.
66
Figure 48. Sensitivity study of simulation with parameters at uniform distribution (left) and normal
distribution (right).
6.6
ADDITIONAL CUT COST MODEL ‘QUARRY
MODEL’
For a more accurate representation of wire cutting cost performed in quarries today a refined
second cost model was developed for comparison. In this model four additional parameters
were added: machine cost, machine lifetime, operators per machine and operator work cost.
The range of the five initial parameters was also altered slightly to better fit with wire data
obtained from stone quarries. Parameters and value range is presented in Table 11.
Table 11. Parameter range for 'Quarry model'.
Uniform distribution
Min
Max
Normal distribution
Mean
Std. dev.
Unit
Wire cost
Cut speed
Wire lifetime
Machine power
Electricity cost
350
3
8
50
0.5
1100
20
25
100
2
600
9
16
75
1
150
4
3
15
0.4
SEK/m
m2/h
m2/m
kW
SEK/kWh
Machine cost
Machine lifetime
Operator per machine
Operator work cost
200 000
5
0.25
250
500 000
10
1
500
350 000
7
uni. dist.
uni. dist.
75 000
2
uni. dist.
uni. dist.
SEK
Years
SEK/h
67
‘Total cut cost’ in SEK/m2 was evaluated by Monte Carlo simulation as described above. The
first simulation was done with parameters at uniform distribution and the second at normal
distribution. The results are presented in Figure 49 and Figure 50.
The first Monte Carlo simulation with parameter rage at uniform distribution yielded a for
‘Total cut cost’ a mean of 86 SEK/m2 and median 79 SEK/m2.
The second Monte Carlo simulation with parameter rage at normal distribution yielded a
mean of 86 SEK/m2 median of 75 SEK/m2
Figure 49. Total cut cost 'Quarry model' with input parameters values at uniform distribution.
Figure 50. Total cut cost 'Quarry model' with input parameter values at normal distribution.
68
Figure 51. Sensitivity study of simulation of ‘Quarry model’ with parameters at uniform distribution (left)
and normal distribution (right). Wire cut speed is the most important parameter.
In this additional ‘Quarry model’ the time cost aspect is better represented and the impact of
cutting speed is clearly observable. Wire cost (price per m wire and lifetime) has still a
significant effect on total cut cost but cutting speed and the related cost of operators is
dominating the total outcome. The capital cost of the machine and cost of power is almost
insignificant in comparison.
69
6.7
POWER PRODUCTION INSTALLATION COST
In the earlier chapters we calculated average thermal power per fracture area to 11-42 Wth/m2
depending on the fracture system properties. From the first wire cut cost model we estimated
total cut cost to 8.9-44 SEK/m2 by selected parameter value scenarios. By comparing the
power yield of an artificial fracture and the cost of constructing it, an estimation of the
production installation cost can be made. From this figure a first estimation of the economic
viability of the whole heat extraction system can be made.
Comparing average thermal power per fracture area (Wth/m2) and total cut cost per fracture
area (SEK/m2) gives an estimation of the installation cost in SEK/MWth. The results based on
the three cost scenarios presented in chapter 6.4 (8.9 SEK/m2, 20 SEK/m2 and 44 SEK/m2).
x 10
6
9
Normal cut cost
8
Optimal cut cost
Future optimal cut cost
Installation cost [SEK/MWth]
7
6
5
4
3
2
1
0
5
10
15
20
25
30
35
40
Fracture av erage power [Wth/m2]
45
50
Figure 52. Estimation of installation cost of artificial fracture.
A fracture system at initial rock temperature 200 °C yields on average about 32 Wth/m2
thermal power during 30 years (flow optimized according to the restriction Tout> 60 °C). At
this power the installation cost is around 1 300 000 SEK/MWth at normal cut cost, at optimal
cut cost it is 600 000 SEK/MWth and at the optimistic future cut cost is 275 000 SEK/MWth.
The same initial rock temperature of 200 °C yields an average of 7.6 Wel/m2 electric power
during 30 years (flow optimized according to maximum aggregated electricity production).
This yields an installation cost for electrical power at 5 800 000 SEK/MWel, 2 600 000
SEK/MWel and 1 200 000 SEK/MWel for the three costs scenarios.
70
As a comparison to the above we can use the cut cost from the mean value from the Monte
Carlo simulation of the second ‘Quarry model’. In this case the total cut cost was 86 SEK/m2.
Using the same fracture production case as above with thermal power of 32 Wth/m2 and
electric 7.6 Wel/m2 yields an installation cost of 2 700 000 SEK/MWth for thermal production
and 11 000 000 SEK/MWel for electric.
Another important aspect to investigate is the time of constructing such a system of artificial
fractures. In the calculation presented in Figure 53 the construction time per fracture thermal
power is estimated. In this calculation the assumption is made that 10 wire saw machines
operates simultaneously. The cut speed in the three cases is therefore multiplied by a factor
10.
90
Normal cut speed
80
Optimal cut speed
Future optimal cut speed
Construction time [days/MWth]
70
60
50
40
30
20
10
0
5
10
15
20
25
30
35
40
Fracture av erage power [Wth/m2]
45
50
Figure 53. Construction time of artificial fracture system.
If we look at the example with a fracture system with 32 Wth/m2 again we can see that such a
system, assuming the same size as earlier (1 000 000 m2) yielding 32 MWth total, will take
160 to 480 days to construct with 10 wire machines operating continuously.
71
7
DISCUSSION
The purpose of this thesis was to investigate and evaluate a method for mechanical
construction of heat transferring surfaces for deep geothermal energy extraction systems. The
potential energy production from a constructed fracture was investigated as well as the cost of
constructing such a fracture.
In the initial literature study it was observed that the continuous heat flow from the core is far
too low for any practical or economical implementation of status quo production. Any
substantial or profitable energy production will be achieved by some form of heat mining
process. The rock will lose temperature during extraction and when cooled to a certain point
the production will move on to new unaffected rock volumes. A specific heat extraction
system can in this way be regarded as coupled to a limited energy quantity. Optimal use of
this limited energy quantity is therefore important for the overall profitability of the
production concept. Depending on both economic and technical time related aspects certain
operational strategies will be more profitable than others. Also, due to the heat mining aspect,
the study of recovery times will be important for long-term system design.
The analytical heat transfer model developed showed that the energy production potential of
an artificial fracture is dependent on several variables. Three key parameters where identified
and investigated: rock temperature, fluid flow velocity and thermal conductivity. The
temperature of the rock, which in turn depends on depth, had as expected the largest impact
on the final result. Since it is reasonable to assume that the access cost (drilling or shaft
construction) will increase exponentially with depth it is possible to assume that an optimal
depth exists for a certain type of production system and access cost. Since access cost was not
investigated in this report this optimum was left unexamined. Instead four different initial
rock temperatures were investigated. In these four cases thermal power production increase
linearly with rock temperature while electrical power production increases exponentially due
to the temperature dependent conversion efficiency of heat to mechanical work. From this it is
possible to conclude that an optimal depth for the energy extraction system can be calculated
if the following parameters are known: exponential access cost, geothermal gradient,
conversion efficiency temperature dependency, revenue from produced heat and revenue from
produced electricity.
72
The fluid flow velocity (and hence the fluid mass flow) changes the characteristics of the
outlet temperature profile and the power production over time. Except for a very low flow
velocity the outlet temperature from any kind of system will gradually drop with time. The
flow velocity necessary for production at constant outlet temperature is too low to be of
economic interest. The analytical model developed is limited to scenarios with constant fluid
velocity. Four such scenarios with different constant flow velocities were examined. As seen
in these cases, high flow velocity yields high power production initially. However, since high
fluid mass flow decreases rock and outlet temperature, the high initial power production will
equally decrease at fast pace. It is apparent that an optimal flow velocity exists for every
specific set of fracture parameters and desired output application. For direct use of heat, e.g.
district heating, a flow velocity as high as possible that still fulfills the requirement of
producing outlet temperature higher than the lowest acceptable for the user system is the best
option. For electricity production, with temperature dependent conversion efficiencies, there
is an optimal flow which yields an optimal outlet temperature profile with corresponding
highest amount of produced electricity. This optimal flow was determined in chapter 4.6.3 for
different initial rock temperatures. The optimal flow velocity found in these cases was slightly
lower than the velocity used in the base case set of parameter values (U = 0.005 m/s).
Due to the limitations of the analytical model all scenarios modeled require constant fluid
velocity which, as seen, yields decreasing power production with time. With a time-varying
fluid velocity other power production profiles can be achieved. With an initially low and with
time increasing flow velocity constant power production can be achieved during a specific
production period. This was tested and confirmed with a numerical COMSOL model capable
of simulating variable fluid velocity but was left to be further investigated due to limitations
in the scope of his thesis.
The energy production potential also depends on the material properties of the rock. Since the
rock in Earth’s crust is a non-homogeneous material with shifting structure and physical
properties the effect of material composition on the energy production is difficult to decide
accurately. For the heat extraction process the thermal conductivity of the rock is of most
importance. Thermal conductivity depends on temperature, this dependency was disregarded.
Instead a specific study was performed to investigate the impact of different possible thermal
conductivity values on power production. In chapter 4.5 it was shown that the amount of
produced thermal energy during 30 years could differ by 25 % due to different possible values
of thermal conductivity. Thermal conductivity also affects thermal penetration, i.e. how far
into the rock heat is withdrawn, and is therefore of importance in designing systems of
multiple fractures and their interference with each other. The results from the numerical
COMSOL multiple fracture model showed that it is possible to place fractures next to each
73
other at distance of between 100 and 125 meter without any major thermal interference on a
timescale of 30 years.
The thermal recovery process after energy extraction was investigated and reported by
Källberg (2012). Tester et al. (2011) also study this aspect. According to Tester et al. (2011),
if extraction occurs during 30 years, recovery to 80 % of initial temperature will take about
180 years. Similar results were found by Källberg (2012) for a single fracture. However for a
system of several fractures placed next to each other, which together have the comparable
effect of a cooled cubic volume of large dimension, the thermal recovery process was
significantly longer. For optimal design of systems consisting of several fractures further
study of recovery time is important.
The results from the analytical heat transfer model presented in this report were in chapter 5.3
compared with the results from the numerical COMSOL model presented by Källberg (2012).
The comparison showed that the outlet temperature was consistently higher in the COMSOL
model, about 2.4-3.7 %. The analytical model does only take heat conduction in x-direction
into account. The COMSOL model solves heat conduction in two dimensions, x and z. This is
probably the cause of the consistent difference between the two models. Otherwise the results
were matching, showing the same trends in the different studies. This, together with the
validation of the models in chapter 3.5 makes us confident in the validity of our results. It is
reasonable to assume that the numerical COMSOL model, with conduction in two dimensions
yielding higher outlet temperatures, describes reality more accurate than the analytical model.
The cost of constructing artificial fractures with diamond wire technology was investigated.
Two different cost models were developed. The first model representing cost of a future
automated implementation of the construction method yielded total cut cost of 8.9-44 SEK/m2
with selected parameter values. The same model and parameter range yielded a mean value of
54-57 SEK/m2 with Monte Carlo simulation. In this model the dominating cost was the cost
of the wire, since this cost depends on both price per meter and lifetime both these two
parameters showed equally important.
The second model developed referred to as ‘Quarry model’ representing cutting costs in
quarries today yielded a mean of 86 SEK/m2 by Monte Carlo simulation. The second model
included time dependent costs, most important operator work cost which was the dominating
one. When dependent on operators the single most important parameter is cutting speed.
The modeling of wire cutting costs showed that the cost can vary significantly. Cutting speed,
wire lifetime and wire price per meter was the dominating cost parameters. Machine capital
cost and electricity for power had low impact on the final result. If achieving high cutting
74
speed, long wire lifetime and low wire price the total cut cost can be as low as 8.9 SEK/m2 in
the future. With technology and manual operation used today a total cut cost of 40-100
SEK/m2 is more reasonable to assume.
By combining fracture power production (W/m2) with the construction cost (SEK/m2) a basic
theoretical estimation of the installation cost of the system (SEK/MW) was done. The
analytical model yielded a range of 11-42 Wth/m2 of thermal power and 1.8-12 Wel/m2
electrical power from the fracture under the studied circumstances. Assuming cutting costs
according to the three scenarios construction cost was in the range of 8.9-44 SEK/m2.
Combining the full range of these parameter values yields an installation cost for thermal
power of 210 000 – 4 000 000 SEK/MWth and 740 000 – 24 000 000 SEK/MWel. This is
lower or equal to installation cost of most conventional power production systems.
Conventional electricity generation technologies deployed today has an installation cost in the
range of 15 000 000 – 40 000 000 SEK/MWel (U.S. Energy Information Administration,
2010). This calculation indicates that basic conditions for economic feasibility could exist for
the investigated heat extraction system.
Since the access cost is not included in this calculation, the results above show only that the
heat extracting system by itself may be economical in relation to its own construction cost.
The question whether the whole system is economically viable must be assessed by further
research. The results in this report can be used in further studies to investigate what other
system costs the heat extraction system needs to bear, with access cost – construction of a
main access shaft – being the crucial one.
An initial comparison with the similar GTKW shaft concept can be done as a preliminary
estimate of complete system feasibility. According to Hämmerle (2012) the GTKW heat
extracting boreholes are assumed to produce 150-250 Wth/m. In a project cost analysis the
GTKW borehole cost is defined as 1740 SEK/m. This yields a thermal power extraction
system installation cost of the GTKW of 7 000 000 – 12 000 000 SEK/MWth. According to
the Ehoch10 workgroup the GTKW system concept is economically feasible under these
circumstances, including shaft cost, tunnel cost etc. (Hämmerle 2012). Based on these
conditions it is possible to assume that the investigated system concept presented in this
report could likewise be economically feasible, with thermal power cost of 210 000 –
4 000 000 SEK/MWth.
In addition to the excluded and unknown access cost, the calculations are based on several
other disregarded and unknown aspects as well as on several ideal and simplifying
assumptions. The risk is high that the cost of these disregarded aspects will exceed any
positive result from the heat extraction system.
75
The installation cost for electricity production does not take equipment for energy conversion
into account (turbine, generator etc.). Also only the ideal Carnot efficiency has been used for
energy conversion. Real power plants and conversion processes have lower efficiencies. For
such comparison the results presented here could be multiplied with an efficiency factor, e.g.
0.58 according to DiPippo (2007).
According to the calculations the margin for potential profitability is higher for thermal
energy production than for electrical. Also, for a shaft based system to be profitable it needs
to be implemented in large scale to cover the initial access cost. For example, the GTKW
concept is designed for 10 000 MWth, this leads to the practical problem that very few
markets could absorb that amount of thermal energy without incurring the expenses of very
long pipelines, which will reduce any initial positive profit margin further. According to John
Garnish (personal communication, 2012), the economics of EGS systems must be based on
sales of electricity alone; any incidental sales of heat are simply a welcome bonus. Assuming
this view the prospect of economic feasibility of a shaft based concept is less likely.
The practical aspects of developing and operating remote controlled and large scale diamond
wire cutting machinery is a limiting factor as well as the extreme working conditions all
equipment need to be able to withstand. The geophysical aspect of the integrity of the
artificial fractures is also a crucial uncertain factor.
To summarize, even though ideal calculations indicate that basic conditions for economic
feasibility could exist, the cost of practical and today unknown issues might exceed any ideal
positive margin when looking at a complete system. Nevertheless, shaft based systems could
become reality in the future. Other and today unknown methods for creation of heat extracting
surfaces could develop as well as new cost effective and mechanized shaft construction
technologies. Meanwhile we will hopefully see an increased global use of geothermal energy
produced by EGS and conventional surface deep drilling, though not profitable today the
outlooks of these concepts are very promising.
However, an additional and less futuristic use of the construction method was found during
the research project. The combined drill and cut method could be used for construction of
Underground Thermal Energy Storages (UTES). This idea is further described in chapter 9.
As a final remark, there are some important aspects of energy systems that are difficult, if not
impossible, to quantify. There are some special features to remember and bear in mind when
evaluating the utility of geothermal energy systems and when comparing geothermal energy
with other energy sources. These features can be more easily identified by using a pair of
interdisciplinary spectacles of energy security. A common framework in energy security
76
analysis is the use of the four notions availability, accessibility, affordability and acceptability
(Chester 2010). Almost every energy source fails on at least one of these, geothermal energy
on the other hand has potential to fulfill all four.
Availability: The heat resource within Earth, which can be used for both heat and electricity
production, can be assumed infinite in regard to its overwhelming size and continuous
reproduction.
Accessibility: Geothermal energy is accessible all over the world. No strategic resources or
special infrastructure or know-how are necessary. The power produced is base load power
with almost 100 % capacity factor.
Affordability: Geothermal energy does not need any fuel. There is no economic uncertainty
connected to future fuel price developments, the installation is more or less a onetime cost.
Acceptability: Negligible CO2 emissions, limited environmental footprint with limited land
and water use.
Today geothermal energy fails on affordability. Energy from fossil fuels and other
conventional energy sources are still cheaper. But the affordability term is a term mankind
can alter, with new technology and innovation the cost of drilling and excavation is likely to
decrease to affordable levels making geothermal energy one of the few energy sources
capable of sustainable large scale implementation in the global energy system.
77
8
CONCLUSION
The purpose of this thesis was to investigate and evaluate a new method for mechanical
construction of heat transferring surfaces for deep geothermal energy production systems. The
research was focused around two key questions:

What is the energy production potential of a system constructed with the investigated
method?

What is the cost of constructing a system with the investigated method?
Based on the findings of this report, the following answers can be given:

The energy production potential is 11 – 42 Wth/m2 of thermal power and 1.8 – 12
Wel/m2 of electrical power per constructed fracture area.

The construction cost is 8.9 – 44 SEK/m2.
Combining the full range of the energy production potential and the construction cost yields a
basic
estimation
of
installation
cost
of
210 000
–
4 000 000
SEK/MWth
and
740 000 – 24 000 000 SEK/MWel for the energy extraction system. This cost is lower or equal
to installation costs of most conventional power production systems. This shows that basic
conditions for economic feasibility could exist.
However, the risk is high that the cost of disregarded, practical and today unknown issues will
exceed any ideal positive margin.
A less futuristic and more simple application of the investigated construction method was
identified: construction of Underground Thermal Energy Storages. This concept deserves
further study and is described briefly in the following chapter.
Finally, the many desirable properties of geothermal energy were recognized and further
support and funding for ambitious research projects like the Soultz project are therefore called
for. Geothermal energy is one of few energy sources capable of sustainable large-scale
implementation in the global energy system.
78
9
FURTHER RESEARCH: UNDERGROUND
THERMAL ENERGY STORAGE
During this research project a less futuristic and more practical use of the combined drill and
cut method was developed as an additional concept. The same idea and construction method
could be used for another purpose: construction of Underground Thermal Energy Storages
(UTES).
The most common and cost effective UTES technology today is Borehole Thermal Energy
Storage (BTES). A BTES system consists of several boreholes, typically 100-400 pcs, 100200 m in depth. During summer hot fluid from solar thermal, CHP-plants, housing or from
other waste heat sources is circulated in the borehole system transferring heat form the fluid
to the underground rock mass. During winter cold fluid is circulated in the system extracting
stored heat from the rock to the surface for residential heating or other usage.
The two main obstacles today for large scale use of BTES in energy systems are the
construction cost and the limited power charge and discharge capacity. High construction cost
depends on the large amounts of boreholes needed for any relevant storage capacity. The
limited power charge and discharge capacity depends on the limited heat transferring surface
between the borehole and the rock. Applying the concept with diamond wire cutting as a
method for constructing channels (artificial fractures) with large heat transferring surfaces has
the potential to overcome both barriers preventing major implementation of heat storages in
energy systems.
Channels for fluid circulation and heat transfer can be constructed from the surface with the
above described ‘blind cut’ method. A heat storage can be constructed in any shape and scale
by repeated blind cuts which connected forms a continuous flow path. Several channels can
be placed in parallel at suitable distance creating a large cubic shaped heat storage with
minimal seasonal heat loss.
A recent study by Svensk Fjärrvärme AB (2008) concludes that a heat storage in a CHP
system is economical if it can be constructed at a cost lower than 4 SEK per dischargeable
kWh of heat per seasonal storage cycle. It also concludes that only BTES is capable of such
costs today, but it also recognizes the limited charge and discharge rates. Our initial
calculations based on a derivative of our heat transfer and cut cost models show that a heat
storage constructed with the diamond wire method can be constructed at the cost of 0.5 - 2
SEK/kWh as well as being capable of high charge and discharge capacity. These findings
motivate further and detail study of the concept.
79
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