PHASE EQUILIBRIA AND SOLUBILITY
MEASUREMENTS OF GASES IN WATER IN THE
HYDRATE FORMATION REGION
by
Jason Gaudette
Department of Chemical Engineering
McGill University
Montreal, Quebec, Canada
July, 2007
A thesis submitted to McGill University in partial fulfillment of the
requirements of the degree of Masters of Engineering
© Jason Gaudette, 2007
Abstract
Gas hydrates are a topic of intense investigation primarily due to the vast
amount of methane trapped in the form of gas hydrate on Earth and to the
possibility of reducing greenhouse gas emissions via the sequestration of carbon
dioxide in the form of gas hydrate. In the present study, phase equilibrium
relationships of pressure, temperature, and composition in the liquid, vapour, and
hydrate phases for the pure propane-water and CO2-CH4 mixed hydrate-water
systems have been investigated.
In the first part of the study, the concentration of propane dissolved in
water in the presence of propane gas hydrates has been measured at temperatures
from 274 K to 277 K and pressures ranging from 150 kPa to 350 kPa. Solubility
measurements in the absence of hydrate were found to be in agreement with
literature values, which predict an increase in solubility as temperature is
decreased. In the hydrate formation region, the solubility of propane decreased
with decreasing temperature. Therefore, hydrate formation reverses the gas-liquid
solubility trend. Results also show that pressure does not have a strong influence
on solubility in the presence of gas hydrate.
In the second part of the study, phase equilibrium relationships for a 50/50
CH4/CO2 mixed hydrate-water system have been investigated at temperatures
between 274 K and 282 K and at pressures of 2000 kPa and 2500 kPa. In the
absence of hydrate, solubility of each gas in the aqueous phase decreased with
increasing temperature. In the hydrate formation region, solubility of both CH4
and CO2 in water was found to decrease with decreasing temperature. Therefore,
ii
as previously concluded with single gas systems, hydrate formation reversed the
gas-liquid solubility trend for each gaseous component in the mixed hydrate
system. Results also showed that pressure did not have a strong influence on the
solubility of each component in the presence of mixed gas hydrate. Furthermore,
by mole balance, water-free mixed hydrate composition and formation selectivity
of CO2 hydrate over CH4 hydrate has been calculated to show that carbon dioxide
hydrates do indeed form selectively over methane hydrates in the presence of the
50/50 gas mixture.
iii
Resumé
L’étude des hydrates gazeux est un sujet de recherche très actif dû à la
vaste quantité de méthane présente sur Terre sous cette forme ainsi que la
possibilité de pouvoir réduire les émissions de gaz à effet de serre grâce à la
séquestration du dioxyde de carbone sous forme d’hydrate gazeux. Cette étude
présente les différentes relations d’équilibre de phases entre la pression, la
température et la composition des phases liquide, vapeur et d’hydrate pour deux
systèmes; un système propane-eau et un système CO2-CH4-eau.
La première partie de cette étude consistait à déterminer la concentration
de propane dissous dans l’eau en présence d’hydrates de propane à des
températures et des pressions variant respectivement entre 274 et 277 K et 150 à
350 kPa. Les solubilités mesurées en absence d’hydrates étaient en accordance
avec les données de littérature disponibles, prédisant une augmentation de la
solubilité avec une diminution de température. La solubilité du propane dans la
région de formation d’hydrate a une relation inverse par rapport à la solubilité
dans la région gaz-liquide. Conséquemment, la solubilité du propane en présence
d’hydrates diminue avec une diminution de la température. Les résultats obtenus
montrent également que la pression a une faible influence sur la solubilité en
présence d’hydrates gazeux.
La deuxième partie de cette étude consistait à étudier les relations
d’équilibre de phases pour un système d’hydrates mixte de CH4/CO2 –eau à des
températures variant entre 274 et 282 K et des pressions variant entre 2000 et
2500 kPa. En l’absence d’hydrates, la solubilité de chaque gaz dans la phase
iv
liquide décroissait avec une augmentation de la température. Dans la région de
formation d’hydrates gazeux, la solubilité du CH4 et du CO2 dans l’eau diminuait
avec une diminution de la température. Similairement à des systèmes avec un
seul gaz, la formation d’hydrate gazeux inverse la relation de solubilité gazliquide pour chaque gaz présent pour un système d’hydrate mixte. Les résultats
obtenus démontrent également que la pression n’avait pas une influence
significative sur la solubilité de chaque gaz en présence d’hydrates gazeux mixte.
De plus, la composition sèche en hydrate gazeux et la sélectivité des hydrates de
CO2 sur les hydrates de CH4 ont été calculées à l’aide d’un bilan de moles pour
démontrer que les hydrates de dioxyde de carbone sont formés préférablement aux
hydrates de méthane en présence d’un mélange 50/50 CH4/CO2.
v
Acknowledgements
I would first like to thank Professor Phillip Servio for his supervision
throughout my research project. His vast knowledge and innovative mind helped
me to overcome numerous difficulties throughout the course of my research.
Furthermore, his support and trust in allowing me to work freely and
independently is greatly appreciated. I must also thank Professor Arturo Macchi
for his guidance and advice in helping me to decide on a field of research that best
suited my interests.
Next, I would like to thank the members of Servio’s hydrate research team
(John, Lindsay, Naomi, Juan, Yeshai, Shadi, Hal, and Sébastien) that I have
worked with at McGill over the past two years. In particular, I would like to thank
John for his early guidance in the laboratory, André for his help in the
construction of the phase equilibrium apparatus and in the acquisition of supplies,
Sébastien for his programming skills, and Shadi for his assistance with several
phase equilibrium experiments. On a more personal note, I would also like to
thank Yeshai, André, and my officemate, Shadi, for their close friendship and
personal support.
Furthermore, I would like to thank the staff and the excellent graduate
student community at McGill University for their philosophical discussions and
for enhancing my understanding of chemical engineering.
Finally, I would like to thank my family and friends for their continued
love and support and in helping to make these past two years a truly remarkable
experience.
vi
Table of Contents
1
Introduction............................................................................................ 1
1.1
Gas Hydrates ........................................................................................... 1
1.2
Hydrate Structure .................................................................................... 5
1.3
Propane Hydrates .................................................................................... 7
1.4
Hydrates of Gas Mixtures ....................................................................... 8
1.5
Thermodynamics - Hydrate Formation and Equilibrium........................ 9
1.5.1
Hydrates of Methane and Carbon Dioxide ..................................... 9
1.5.2
Hydrates of Propane ..................................................................... 11
1.6
Gas Solubility in Water in the Hydrate Formation Region................... 12
1.6.1
Carbon Dioxide Solubility in the Hydrate formation region ........ 14
1.6.2
Methane Solubility in the Hydrate formation region .................... 15
1.6.3
Propane Solubility in the Hydrate formation region .................... 16
1.7
Hydrate Equilibrium for Systems Involving Gas Mixtures .................. 17
1.8
Thermodynamic Modeling.................................................................... 18
1.8.1
Chemical Potential........................................................................ 18
1.8.2
Fugacity of Liquids and Solids ..................................................... 20
1.8.3
Phase Equilibrium (Liquid water-Vapour-Solid hydrate) ............ 21
1.9
Research Objectives.............................................................................. 23
2
Materials and Methods........................................................................ 24
2.1
Reactor Design...................................................................................... 24
2.2
Equilibrium Apparatus.......................................................................... 25
2.3
Data Acquisition ................................................................................... 27
2.4
Additional Equipment ........................................................................... 28
2.5
Materials ............................................................................................... 29
2.6
Experimental Conditions ...................................................................... 30
2.7
Experimental Procedure........................................................................ 31
2.7.1
Three-Phase H-Lw-V Equilibrium................................................. 32
2.7.2
Solubility Experiments .................................................................. 32
2.7.3
Mole Balance ................................................................................ 34
3
Results and Discussion ........................................................................ 36
3.1
Propane Experiments ............................................................................ 36
3.2
50/50 Methane/Carbon Dioxide Experiments....................................... 38
3.2.1
Three-Phase H-Lw-V Equilibrium................................................. 38
3.2.2
Solubility Experiments .................................................................. 40
vii
3.2.3
4
Mole Balance ................................................................................ 43
Conclusions and Recommendations................................................... 44
4.1
4.2
Conclusions........................................................................................... 44
Recommendations................................................................................. 45
References.................................................................................................... 47
Appendix A: Detailed Reactor Schematics .................................................I
viii
List of Figures
Figure 1.1. Basic hydrate cavity (512) and illustration of........................................ 6
Figure 1.2. The two types of cavities unique to Structure H .................................. 6
Figure 1.3. Partial phase diagram for methane (Deaton and Frost 1946). ............ 10
Figure 1.4. Partial phase diagram for carbon dioxide. Upper Line indicates the
vapour pressure line for carbon dioxide and lower line indicates three-phase
H-Lw-V equilibrium values (Deaton and Frost 1946)................................... 11
Figure 1.5. Overview of the phase equilibria for the water-propane system where
Lw represents liquid water, LC3H8 liquid propane, V vapour, H hydrate and I
ice. Q1 and Q2 represent the two quadruple points of the system. ................ 12
Figure 1.6. Typical plot of moles consumed vs. time in a hydrate formation
experiment..................................................................................................... 13
Figure 1.7. Plot of equilibrium mole fraction as a function of pressure and ........ 15
Figure 1.8. Plot of equilibrium mole fraction as a function of pressure and ........ 16
Figure 2.1. Photograph of hydrate crystallizer...................................................... 25
Figure 2.2. Schematic diagram of the experimental solubility apparatus............. 27
Figure 2.3. Chandler digital gasometer................................................................. 29
Figure 2.4. Partial phase diagram for the propane-water system and experimental
conditions for the measurement of dissolved propane in water. The line
represents three-phase H-Lw-V equilibrium points (Deaton and Frost 1946).
Below the line, gaseous propane and liquid water coexist at equilibrium, and
above the line liquid water and propane hydrate may exist at equilibrium. . 31
Figure 3.1. Plot of equilibrium mole fraction of propane, x1, as a function of
temperature at 250 kPa, 300 kPa, and 350 kPa respectively (three phase HLw-V equilibrium temperatures are 275.2 K, 276.0 K and 276.7 K
respectively).................................................................................................. 37
Figure 3.2. Partial phase diagrams of the CH4-water (Deaton and Frost 1946),
CO2-water (Deaton and Frost 1946), and 50/50 CH4/CO2-water systems. The
solid points correspond to three-phase H-V-Lw points for the respective
system. .......................................................................................................... 39
ix
Figure 3.3. Comparison of the experimentally determined three-phase equilibrium
for the 50/50 CH4/CO2-liquid water system to the prediction of the van der
Waals and Platteuw model (van der Waals and Platteeuw 1959; Sloan 1998).
....................................................................................................................... 40
Figure 3.4. Plot of the equilibrium mole fraction of methane in water for the 50/50
CH4/CO2-liquid water system as a function of temperature at the indicated
pressures........................................................................................................ 42
Figure 3.5. Plot of the equilibrium mole fraction of carbon dioxide in water for the
50/50 CH4/CO2-liquid water system as a function of temperature at the
indicated pressures. ....................................................................................... 42
Figure 3.6. Comparison of experimental and literature (Sloan 1998) water-free
mole fractions of methane in the hydrate phase under three-phase H-Lw-V
equilibrium.................................................................................................... 43
x
List of Tables
Table 3.1. Mole fraction of propane in water, x1, at given temperatures and
pressures........................................................................................................ 36
Table 3.2. Comparison of the experimentally determined solubility in the twophase vapour-liquid water region to those calculated using the correlations of
Carroll and Mather and Chapoy (Carroll and Mather 1997; Chapoy,
Mokraoui et al. 2004).................................................................................... 37
Table 3.3. Mole fraction of CH4 and CO2 in water at given temperatures and
pressures a...................................................................................................... 41
xi
1
1.1
Introduction
Gas Hydrates
Gas Hydrates, or clathrate hydrates, are non-stoichiometric crystalline
compounds in which suitable guest molecules are enclosed in a network of
hydrogen-bonded water molecules. The water network is stabilized by weak van
der Waals forces between the host and the internal guest molecules. Currently,
more than 130 different compounds have been found as guests in water clathrates
(Sloan 1998). Clathrate hydrates occur naturally within and below the permafrost
zone and in sub-sea sediment where the existing pressures and temperatures allow
for thermodynamic stability of the hydrate (Sloan 1998).
Gas hydrates were discovered in 1810 by Sir Humphry Davy when he
observed that a solid compound formed while mixing chlorine with water at 9°C
(Davy 1811). This observation was later confirmed by Faraday who concluded
that the ratio of water molecules to chlorine molecules was about 10:1 in the solid
compound (Faraday 1823). Much of the early work pertaining to gas hydrates
involved identifying guest molecules capable of forming hydrates and the
pressure-temperature conditions at which hydrate formation occurs. Methane is
one such suitable guest molecule, and during the 1930’s, it was recognized that
the plugging of natural gas pipelines was often due to the formation of gas
hydrates (and not ice) in the natural gas pipeline, causing a major problem for the
rapidly growing gas and oil industry (Hammerschmidt 1934).
At this time,
intense industrial and academic research on gas hydrates commenced with
1
particular focus on phase equilibrium and inhibiting the formation of methane
hydrates in natural gas pipelines (Englezos 1993).
The next major advance in the field of gas hydrates occurred in the 1950’s
when Pauling and Marsh determined the crystal structure of methane hydrates
using X-ray diffraction. This initiated the development of a statistical
thermodynamic model to predict hydrate formation and equilibrium. First
presented by van der Waals and Platteeuw in 1959 (van der Waals and Platteeuw
1959), this model is still used today, though it has been revised numerous times
over the past 50 years.
Another milestone in the field of gas hydrates was the discovery of
hydrates of natural gas in large quantities in the earth’s crust under the ocean and
in permafrost regions of the world by Makogon and his coworkers, initiating
large-scale hydrate research efforts throughout the world. While the exact amount
of methane trapped in hydrates on Earth is uncertain, even conservative estimates
are substantial. These estimates indicate that approximately 1016 kg of carbon are
trapped in oceanic sediments in the form of hydrates, which far exceeds any
existing hydrocarbon reserve on the planet (Buffett 2000). The vast supply of
methane in hydrates has stimulated research into the extraction of this energy
source and has also raised questions about the role of hydrates in past and present
global climate change. There are concerns that if large stores of methane were to
become unstable and be released into the atmosphere, it would have a devastating
impact on the world’s climate as methane is known to be a strong greenhouse gas
with a global warming potential of 21 times that of carbon dioxide (Englezos
2
1993). Furthermore, it has been hypothesized that large submarine landslides
could occur as a result of the destabilization of large sub-sea methane hydrate
reserves with catastrophic results (Suess, Torres et al. 1999).
In addition to the ongoing research efforts to extract methane from hydrate
reserves and monitor the release of greenhouse gases from these reserves, many
studies have been carried out to explore other applications of gas hydrates. One
major benefit of hydrates is their ability to efficiently transport and store of
natural gas. Studies have shown that one cubic metre of methane hydrates
contains approximately 160 sm3 of natural gas at reasonable temperatures (-10oC
to 1oC) and pressures (1 to 10 atm) and it has been demonstrated in literature that
it is economically beneficial to transport and store methane in hydrate form rather
than to cryogenically cool or compress it (Khokhar, Gudmundsson et al. 1998),
which requires both very low temperatures and extreme pressures.
Carbon dioxide is another suitable guest molecule that can physically
combine with water under the proper thermodynamic conditions to form clathrate
hydrates (Englezos 1993). CO2 hydrates are of particular importance to
researchers for two reasons. First, the presence of CO2 and water in natural gas
streams and oil reservoirs complicates the extraction of natural gas, and second,
CO2 is known to be a harmful greenhouse gas that contributes to the depletion of
ozone, thus accelerating global warming. Scientists are currently exploring the
option of trapping and sequestering carbon dioxide from industrial flue gases in
hydrate form in deep ocean sediments to slow the depletion of the Earth’s ozone
3
layer (Ohmura and Mori 1999; Servio and Englezos 2001; Chatti, Delahaye et al.
2005).
Gas hydrates have also proven themselves to be a promising separation
technology. In the 1960’s, a process was developed to desalinate sea water via the
formation of gas hydrates (Knox, Hess et al. 1961). By forming hydrates from
seawater and decomposing them in a separate tank, the salt was removed from the
water. Also, it is known that hydrates can be used to remove gases from
hydrocarbon mixtures. For example, nitrogen and hydrogen sulfide can be
separated from methane using hydrate technology.
As mentioned earlier, one of the early reasons for studying gas hydrates
was the problems they posed to the gas and oil industry. Hydrate plugs are still a
persistent problem in industry today and the focus of many research efforts.
Natural gas hydrate propagation in pipelines tends to gradually form a plug that
separates the pipe into two pressure sections: a high pressure section between the
well and the plug and a second section at low pressure between the plug and the
recovery division. A blast can occur in the upstream section due to increased
pressures, or alternatively, the plug can also behave as a projectile that destroys
the pipe or pumping equipment as the pressure difference between the upstream
and
downstream
sections
increases
(Sloan
1998).
Various
kinetic,
thermodynamic, mechanical, and thermal inhibition processes have been proposed
for the prevention of hydrate formation in pipelines, but pipeline blockage by gas
hydrates remains a concern in the oil and gas industry.
4
1.2
Hydrate Structure
In the 1950’s, x-ray diffraction studies identified the crystal structure of
gas hydrates and allowed for the identification of various hydrate structures
(Englezos 1993). At this time, two primary naturally occurring hydrate structures
were recognized: structure I and structure II. When water networks are formed
via hydrogen bonding, the basic cavity created is a polyhedron with 12 pentagonal
faces. Structure I gas hydrates are formed when these cavities arrange themselves
such that a manner that they are connected at their vertices. Because the basic
cavity structure does not allow for precise packing in this manner, the resulting
structure is a polyhedron with 12 pentagonal and two hexagonal faces (51262)
consisting of 46 water molecules. A typical structure I hydrate guest molecule
has a diameter in the range of 410-580pm. Thus, only smaller molecules such as
methane, carbon dioxide, and ethane can form structure I hydrates (Englezos
1993). Structure II hydrates are formed when the cavities arrange themselves
such that they link together via face sharing.
The resulting structure is a
polyhedron with 12 pentagonal faces and 4 hexagonal faces (51264) consisting of
136 water molecules. Molecules that form structure II hydrates typically have
diameters less than 410pm or greater than 550pm (Englezos 1993). Examples of
suitable gust molecules for structure II hydrates are propane and O2.
5
Figure 1.1. Basic hydrate cavity (512) and illustration of
Structure I (51262) and Structure II (51264) hydrates
Cavaties (Tohidi 2001).
In the late 1980’s, a third naturally occurring hydrate structure was
proposed by Ripmeester et al, termed structure H (sH) (Ripmeester, Tse et al.
1987). A structure H hydrate has three different types of cavities. Small
molecules, such as methane or xenon, occupy the two smaller cavities and act as
‘helper’ gases while larger molecules, such as various neohexanes, occupy the
larger cavity. Structure H hydrates require less energy to nucleate and grow than
other hydrates, and are therefore the focus of much of today’s research efforts
(Servio 2003).
Figure 1.2. The two types of cavities unique to Structure H
methane hydrates (Tohidi 2001).
6
All three naturally occurring hydrate structures form unit cells consisting
of a set number of each of their cages. These unit cells combine to create a crystal.
Not every cage in the unit cell has to be occupied by a guest molecule in the
formation of a stable crystal. In fact, structures I and II can form stable crystals
with gases that are not small enough to occupy the small cage. This means that
stable structure I and II hydrates can still form without any of their small cages
being occupied, which is not the case with structure H. Structure H requires at
least two types of guest molecules to be stable. One guest must be large enough to
stabilize the largest cage and this guest is typically a volatile liquid such as
neohexane. The remaining guest molecules must be small enough to occupy the
remaining two types of cages. Methane and hydrogen sulphide are example of two
such guest molecules (Englezos 1993).
1.3
Propane Hydrates
It is important to study gas hydrates not only because of the large potential
they possess as a future energy source, but also because of the problems they pose
to the petroleum industry during the production, transportation and processing of
natural gas and oil. While most hydrate research focuses on methane, the primary
component of natural gas, propane is another component of natural gas that is
known to physically combine with water under correct temperature and pressure
conditions to form structure II hydrates. Although propane hydrates form at
relatively modest conditions of temperature and pressure when compared to other
hydrate formers, their formation has been often overlooked by scientists because
of the narrow temperature range between which the formation of propane hydrates
7
can occur. For storage and transportation of liquefied petroleum gases (LPG’s),
composed mainly of propane and butane, it is important to know and be able to
predict the conditions of hydrate formation in the presence of humidity or ice
(Giavarini, Maccioni et al. 2003).
1.4
Hydrates of Gas Mixtures
Recently, mixed hydrate systems are becoming a topic of increasing
interest to researchers for their ability to separate hydrocarbon mixtures and due
to the possibility of methane exploitation via supply of alternate hydrate formers
to a hydrate reserve. It is well known that a hydrocarbon mixture (gas or liquid)
can be separated by applying thermodynamic conditions that result in the desired
fractionization through the formation of hydrates (Ng 2000). For example, acid
gases such as hydrogen sulfide and carbon dioxide can be separated from methane
using hydrate technology. Also, as an example of the exploitation potential of
mixed hydrate systems, it is suggested that in-situ methane in a hydrate reserve
can be selectively replaced with carbon dioxide under the correct thermodynamic
conditions (Ohgaki, Takano et al. 1996). Furthermore, the formation of CO2
hydrates acts as a heat source as the enthalpy of CO2 hydration exceeds the energy
required to decompose a methane hydrate. Therefore, methane hydrate
dissociation could be further assisted by the heat supplied from the formation CO2
hydrates (Handa 1986). The net result of the process is the extraction of methane
in combination with the semi-permanent storage of carbon dioxide in hydrate
form.
8
1.5
Thermodynamics - Hydrate Formation and Equilibrium
Thermodynamics is essential to better understand hydrate formation and
growth conditions. Most studies in this field focus on finding the minimum
conditions (temperature and pressure) necessary for an infinitesimal amount of
hydrate in the system to be stable. These conditions are commonly referred to as
the incipient hydrate formation conditions (Englezos 1993). In the hydrate
formation region, the following phases may be present: solid hydrate, aqueous
liquid, non-aqueous liquid, gas and ice.
Incipient hydrate formation conditions are typically determined using the
isothermal pressure-search method (Deaton and Frost 1946). This experimental
procedure requires a hydrate forming system to be kept at a constant temperature
while the pressure of the system is slowly increased and monitored for hydrate
formation. The experimental pressure at which hydrates begin to form is the
equilibrium pressure of the system at the temperature of the system. This
procedure can be repeated over a range of temperatures to produce a partial phase
diagram in the hydrate formation region. The advantage of this method over a
method varying the temperature is that the thermal and mechanical equilibrium
can be reached faster following a change in pressure than with a change in the
temperature of the system.
1.5.1
Hydrates of Methane and Carbon Dioxide
The conditions of formation of methane and carbon dioxide hydrates in
water have been known to researchers for many years. Figures 1.3 and 1.4
illustrate partial phase diagrams for methane and carbon dioxide respectively.
9
Both carbon dioxide and methane combine with water to form structure-I hydrates
under correct thermodynamic conditions. In the figures below, H-Lw-V lines
indicate a series three-phase, solid hydrate-liquid water-vapour, equilibrium
points. Below this line, liquid water and gas are in equilibrium (Lw-V), and above
this line, hydrate and liquid water may be in equilibrium (H-Lw).
10000
9000
8000
H-Lw-V
Pressure (kPa)
7000
H-Lw
6000
5000
Lw-V
4000
3000
2000
1000
0
272
274
276
278
280
282
284
286
288
Temperature (Deg.K)
H-Lw-V for CH4
Figure 1.3. Partial phase diagram for methane (Deaton and Frost 1946).
10
6000
5000
LCO2-V
Pressure (kPa)
4000
H-Lw-V
3000
H-Lw
2000
Lw-V
1000
0
272
274
276
278
280
282
284
Temperature (Deg.K)
H-Lw-V for CO2
L-V for CO2
Figure 1.4. Partial phase diagram for carbon dioxide. Upper Line indicates the vapour
pressure line for carbon dioxide and lower line indicates three-phase H-Lw-V equilibrium
values (Deaton and Frost 1946).
1.5.2
Hydrates of Propane
Propane forms structure II hydrate when combined with water under
correct thermodynamic conditions. A partial phase diagram for propane is
illustrated in Figure 1.5. In the propane-water system, the location of the two
quadruple points occurs at relatively low pressures (PQ1 = 150 kPa and PQ2 = 600
kPa) with the upper quadruple point existing at a relatively low temperature (TQ2
= 279K) in comparison with other hydrate formers (den Heuvel, Peters et al.
2002). The nearly vertical H-Lw-LC3H8 equilibrium line restricts hydrate formation
to temperatures just above TQ2. Therefore, while propane hydrate occurs at
11
modest pressures and temperatures, the thin borders of the formation region
restrict hydrate formation potential (Giavarini, Maccioni et al. 2003).
Figure 1.5. Overview of the phase equilibria for the water-propane system where Lw
represents liquid water, LC3H8 liquid propane, V vapour, H hydrate and I ice. Q1 and Q2
represent the two quadruple points of the system.
1.6
Gas Solubility in Water in the Hydrate Formation Region
Solubility measurements in the hydrate formation region are of particular
importance to researchers because they help us to better understand hydrate
formation kinetics, which is essential to the successful design of hydrate relevant
processes. A typical hydrate formation curve is presented below in Figure 1.6.
The onset of hydrate formation occurs at some time, tb, known as the turbidity
time. For the purposes of kinetic modeling, the solubility or amount of gas
dissolved in the aqueous phase at the turbidity point, neq, is desired. The
12
difference between the total number of moles consumed at the turbidity time, ntb,
and neq is estimated to be the amount of gas consumed in the formation of the
hydrate nuclei (Parrish and Prausnitz 1972).
Figure 1.6. Typical plot of moles consumed vs. time in a hydrate formation experiment.
Several studies have been performed to determine pure component
solubility in the hydrate formation region, with particular focus on single
component systems involving methane and carbon dioxide. Due to simplicity and
lack of available models, a modified Henry’s Law was initially employed to
determine gas solubility under H-Lw-V and H-Lw equilibrium (Sloan 1998; Servio
and Englezos 2002). However, this approach displayed several fundamental
inadequacies in the H-Lw region, and recently, more rigorous solubility
experiments and more advanced models have been developed to improve the
accuracy of pure component solubility predictions in the hydrate formation region
(Hashemi, Macchi et al. 2006).
13
1.6.1
Carbon Dioxide Solubility in the Hydrate formation region
In the CO2-water system, under V-Lw equilibrium, the solubility of carbon
dioxide in water is known to decrease as system temperature is increased or
pressure is decreased. However, in the hydrate formation region, solubility does
not follow these same trends. Until recently, the limited experimental data on the
solubility of carbon dioxide in the hydrate formation region exhibited
contradicting results. Ohmura and Mori reviewed the literature pertaining to CO2
solubility and concluded that the solubility of carbon dioxide in the hydrate
formation region should decrease with decreasing temperature (Ohmura and Mori
1999). Servio and Englezos later confirmed this conclusion experimentally and
further added that gas solubility is not a strong function of pressure in the hydrate
formation region (Servio and Englezos 2001). Figure 1.7 shows experimental
results and model predictions for the solubility of carbon dioxide in and around
the hydrate formation region (Hashemi, Macchi et al. 2006). Inflection points in
the model represent the predicted three-phase H-Lw-V equilibrium points at the
indicated pressure. To the right of the inflection point, the system is under twophase V-Lw equilibrium, and to the left, two-phase H-Lw equilibrium.
14
Figure 1.7. Plot of equilibrium mole fraction as a function of pressure and
temperature for the CO2–water system in the hydrate formation region (Hashemi, Macchi et
al. 2006).
1.6.2
Methane Solubility in the Hydrate formation region
In 2002, Servio and Englezos showed that solubility measurements in the
methane-water system displayed similar trends as observed with the carbon
dioxide-water system in the hydrate formation region (Servio and Englezos 2002).
Figure 1.8 shows experimental results and model predictions for the solubility of
methane over a temperature range of 274-285K and at pressures ranging from 35
to 65 bar (Hashemi, Macchi et al. 2006). As with carbon dioxide, methane
solubility was found to decrease with decreasing temperature and was not a strong
function of pressure in the hydrate formation region.
15
Figure 1.8. Plot of equilibrium mole fraction as a function of pressure and
temperature for CH4-water system in the hydrate formation region (Hashemi, Macchi et al.
2006).
1.6.3
Propane Solubility in the Hydrate formation region
No previous literature exists on the subject of propane solubility in the
hydrate formation region. In the vapour-liquid water equilibrium region, Henry’s
Law and the correlations of Carroll and Mather and Chapoy for Henry’s constants
are typically used to determine equilibrium propane solubility in water (Carroll
and Mather 1997; Chapoy, Mokraoui et al. 2004). Henry’s law is shown in
equation 1.1 below followed by the correlation of Carroll and Mather and the
correlation of Chapoy for Henry’s constant for the propane-water system in
equations 1.2 and 1.3.
16
xiw =
Pi
H iw
(1.1)
ln( H iw,1 / kPa) = 552.65815 + 0.077514T − 21334.4 / T − 8584949 ln(T )
(1.2)
ln( H iw, 2 / kPa) = 552.64799 + 0.078453T − 21334.4 / T − 85.89736 ln(T )
(1.3)
In the above correlations, xiw is the mole fraction of propane in water, Pi is the
pressure of propane above the liquid in the system, T is liquid temperature, and
Hiw,1 and Hiw,2 refer to Henry’s constants obtained using the correlations of Carroll
and Mather and Chapoy respectively. These correlations are particularly
important in assessing the accuracy and reliability of the experimental procedures
proposed in this study.
1.7
Hydrate Equilibrium for Systems Involving Gas Mixtures
A better understanding of the kinetics and phase equilibria for mixed
hydrate systems is essential to further the study of the exploitation and separation
potential of hydrate formation in the presence of gas mixtures. As stated
previously, aqueous phase solubility experiments for pure methane and carbon
dioxide in water in and around the hydrate formation region have been completed
(Ohmura and Mori 1999; Servio and Englezos 2001; Servio and Englezos 2002)
and several solubility models have been published to predict pure component
solubility in water in the hydrate formation region (Hashemi, Macchi et al. 2006).
Also, Ohgaki et al. have studied the phase equilibria of gaseous mixtures of
methane and carbon dioxide in the presence of mixed gas hydrate as a function of
17
gas phase composition at a constant temperature of 280.3 K, and determined that
the average distribution coefficient of methane between the gas phase and the
hydrate phase is 2.5 at this temperature (Ohgaki, Takano et al. 1996).
Furthermore, Sloan et al. has developed a model to predict the phase equilibria
and mixed hydrate phase composition in the presence of gas mixtures (Sloan
1998). However, very little literature exists on the effect of temperature and
pressure on methane and carbon dioxide solubility in water in the presence of
mixed gas hydrate.
1.8
1.8.1
Thermodynamic Modeling
Chemical Potential
The following discussion of chemical potential is in accordance with the
multiphase equilibrium text written by JM Prausnitz et al (Prausnitz 1986). In
classical thermodynamics, open systems are those that can exchange matter and
energy with their surroundings. Therefore, the fundamental equations (for U, H,
A, G) of thermodynamics for closed systems, which can be found in any
thermodynamics text book, need to be modified to account for the ability of the
system to exchange matter. Taking internal energy, U, as an example, we can
expand the expression for a closed system to account for the dependency on the
amount of each component that is present. Therefore, we write
U = U(S, V, n1, n2, …, nc-1, nc)
(1.4)
18
where c is the number of components present. Taking the total derivative of the
above expression, we obtain
c
⎛ dU
⎛ dU ⎞
⎛ dU ⎞
dU = ⎜
⎟ dS + ⎜
⎟ dV + ∑ ⎜⎜
⎝ dS ⎠V ,ni
⎝ dV ⎠ S ,ni
i =1 ⎝ dni
⎞
⎟⎟
dni
⎠ S ,V ,n j
(1.5)
The new term,
⎛ dU ⎞
⎜⎜
⎟⎟
= μi
⎝ dni ⎠ S ,V ,n j
(1.6)
is the chemical potential of component i. By repeating the above procedure for
enthalpy (H), Helmholtz energy (A), and Gibb’s energy (G), we obtain the
following definition for the chemical potential of component i in a mixture,
⎛ dU ⎞
⎛ dH ⎞
⎛ dA ⎞
⎛ dG ⎞
⎟⎟
⎟⎟
⎟⎟
⎟⎟
= ⎜⎜
= ⎜⎜
= ⎜⎜
μ i = ⎜⎜
⎝ dni ⎠ S ,V ,n ⎝ dni ⎠ S , P ,n ⎝ dni ⎠ T ,V ,n ⎝ dni ⎠ T , P ,n
j
j
j
(1.7)
j
The chemical potential is an important variable in multiphase equilibrium
predictions.
19
1.8.2
Fugacity of Liquids and Solids
Fugacity is a variable that accounts for the difference between the
chemical potential of interest, µ(P,T), and the chemical potential of the pure
component at a reference pressure and temperature. Expressing the chemical
potential of a component in a mixture in terms of its fugacity, we can write
μ i = RT ln f i + Θ j
(1.8)
where Θj is a function of temperature. The fugacity of a component in a mixture
in either the gas or liquid phase can be written as:
RT ln
∞⎡
⎛ dP ⎞
fi
RT ⎤
⎥ dV − RT ln Z
⎟⎟
= ∫ ⎢⎜⎜
−
yi P
dn
V
⎢
⎥
i
⎠ T ,V ,n j
V ⎝
⎣
⎦
(1.9)
where Z is the compressibility factor. In order to obtain the fugacity using the
above expression, we need an appropriate equation of state written in a pressureexplicit form. Because of its simplicity and its relative success in predicting
liquid-vapour equilibrium for methane-water systems, the Trebble-Bishnoi
equation of state (Trebble and Bishnoi 1987) is used extensively in equilibrium
solubility predictions for gas hydrates.
The fugacity of a pure solid is related to the fugacity of a pure liquid by
the following
20
c
fi = fi
sat
⎛ P ν c dP ⎞
⎟
exp⎜ ∫ i
⎜ sat RT ⎟
⎝ Pi
⎠
(1.10)
where the subscript c denotes the condensed phase. We now have all the tools
necessary to solve a three phase equilibrium problem. In the next section, a typical
model for three phase, liquid-vapour-hydrate equilibrium is presented.
1.8.3
Phase Equilibrium (Liquid water-Vapour-Solid hydrate)
The classic model for determining hydrate equilibrium pressures and
temperatures was developed by van der Waals and Platteeuw (van der Waals and
Platteeuw 1959) and later adapted by Parrish and Prausnitz (Parrish and Prausnitz
1972) to account for multiple hydrate formers. According to van der Waals and
Patteeuw (vdWP), the basic conditions for three-phase equilibrium are that the
chemical potential of water in the hydrate phase is equal to that of water in all
other equilibrium phases.
Δ μwH (T , P, Θ) = μWβ − μWH = μWβ − μWπ = Δ μwπ (T , P)
(1.11)
where μ wβ (T , P) is the chemical potential of the empty hydrate, which is purely
hypothetical since a hydrate requires a guest molecule to form a stable phase, and
μ wπ (T , P) is the chemical potential of water in all other equilibrium phases. In
their approach, van der Waals and Platteeuw used statistical based on the
following four key assumptions:
1. Guest molecules do not distort the hydrate cavity.
21
2. At most, one guest can occupy a hydrate cavity, and a guest cannot diffuse
between hydrate cavities.
3. The interaction between guests in neighboring cavities is negligible.
4. Interactions beyond the surrounding water cavity are negligible.
Parrish and Prausnitz proposed the following vdWP type model for the
calculation of the chemical potential of water in the hydrate phase when one or
more hydrate formers are present:
μwH − μ wMT = Δμ wL = RT ∑ν m ln(1 + ∑ C mj f j ) − RT ln( x w )
m
(1.12)
j
where νm is the number of cavities of type m per water molecule in the lattice
(Sloan 1998), Cmj is the Langmuir constant and fj is the fugacity of component j.
Values for the Langmuir constants can be obtained using the correlation of Parrish
and Prausnitz. The RT ln( x w ) term is omitted if ice is the co-existing phase.
Liquid and vapour phase fugacities can be calculated using an equation of
state such as the Trebble-Bishnoi equation of state (Trebble and Bishnoi 1988).
Combined with the following expression, taken from the work of Parrish and
Prausnitz, it is then possible to determine the chemical potential of water in the
equilibrium liquid and vapour phases:
22
P
Δμ wπ (T , P) Δμ wπ (T0 , P0 ) T ΔH wπ
ΔVwπ
=
−∫
dT
+
2
∫ RT dP − ln(γ w x w )
RT
RT0
To RT
Po
(1.13)
where Δμ wπ (T0 , P0 ) is the reference chemical potential taken at the reference
temperature and pressure (T0,P0), usually taken to be the freezing point of water,
and ΔH wπ and ΔVwπ are difference in the empty hydrate lattice and the additional
water phase for enthalpy and volume (Parrish and Prausnitz 1972).
This vdWP type model is used extensively in gas hydrate research for
predicting phase equilibrium and modeling kinetic behavior of hydrate forming
systems. With an understanding of this model, we now have all the tools
necessary to study the phase equilibrium and solubility of pure and mixed gases in
water in the hydrate formation region.
1.9
Research Objectives
The main objective of this work was to study the phase equilibrium
relations for gases in water in the presence of gas hydrate. First, the propane-water
system was studied to generate accurate equilibrium solubility measurements of
propane in liquid water in the presence of propane hydrate. Next, a 50/50 mixture
of methane and carbon dioxide was used to study the phase equilibria of the
CH4/CO2-water system in the presence of mixed gas hydrate. Three phase vapourliquid
water-mixed
hydrate
equilibrium
points
were
determined
and
measurements of each gas dissolved in the aqueous phase were examined to study
the behavior of gas mixtures in the hydrate formation region. To complete the
primary objectives of this study, many minor accomplishments were necessary:
23
1. Design and construct a crystallizer capable of withstanding pressures
above 10,000 kPa.
2. Design and construct an apparatus to measure the phase equilibrium of
pure and mixed gases in water in the hydrate formation region.
3. Develop a method to determine dissolved gas concentrations for pure
and mixed gases in water in the hydrate formation region.
4. Perform experiments at the selected operating conditions using both
propane and a 50/50 CH4/CO2 gas mixture as the hydrate formers.
2
2.1
Materials and Methods
Reactor Design
At the heart of the hydrate equilibrium apparatus is a high-pressure
crystallizer constructed of 316-stainless steel and capable of handling pressures of
up to 20,000 kPa. The crystallizer body has a 3 inch internal diameter, 1.75 inch
wall thickness, and an internal volume of 550mL. The crystallizer lid is 1.88
inches thick and is secured to the reactor using six ½ inch rods extending from the
reactor body and accompanying ½ inch bolts, and a pressure-tight seal is created
using a 3-inch OD Buna o-ring. The front and back of the crystallizer contain
circular polycarbonate viewing windows that are sealed with 2-1/8 inch OD, ¼
inch thick Buna o-rings (Hercules Bulldog Sealing Products, Dorval, QC). The
crystallizer is equipped with a top mount Dyna/Mag magnetic mixer with rpm
control capable of agitation at speeds up to 2500 rpm (Pressure Product Industries,
24
Warminster, PA). The mixer is attached to the reactor via a 1.5 inch parallel
thread connection and is welded into place to minimize the potential for leaks.
The crystallizer contains a total of five 1/8 inch female NPT ports, each equipped
with Swagelok 1/8 inch male NPT to 1/8 inch male tube unions. Two of these
ports are occupied by Omega high accuracy RTD probes for temperature
measurement in the top and bottom of the crystallizer, and the remaining three
ports are connected to 1/8 inch stainless steel Swagelok seamless tubing for the
purposes of gas and liquid sampling, purging, and introducing liquid and gas into
the reactor. Detailed schematics of the crystallizer are shown in Appendix A and a
photograph of the crystallizer is shown below in Figure 2.1.
Figure 2.1. Photograph of hydrate crystallizer
2.2
Equilibrium Apparatus
The primary components of the hydrate equilibrium apparatus are
illustrated in Figure 2.2. A variable volume gas feeding reservoir and a Baumann
51000 series low flow control valve (Laurentide Control, Montreal, QC) are
25
connected to the crystallizer and are used to hold the crystallizer pressure constant
during experiments. Hydrate formation consumes gas, and therefore, the feeding
reservoir must be pressurized higher than the crystallizer pressure throughout
experiments so that gas will flow into the crystallizer and replace the gas
consumed in hydrate formation. The absolute pressure in the crystallizer and the
variable volume is measured using model 3051S Rosemount pressure transducers
(Laurentide Control, Montreal, QC), programmed for pressure measurements over
a range of 0-13,789 kPa with a reference accuracy of less that 0.065 % of the
span. In addition to the crystallizer and reservoir, two additional gas reservoirs
exist in the setup: the bias reservoir, and the bias reactor. The bias reservoir is
identical to the reservoir but is not connected to the reactor. The reservoir and bias
reservoir are pressurized together before experiments begin. Once the temperature
and pressure in the reservoir and bias reservoir have equilibrated, the bias
reservoir is isolated using a Swagelok 1/8 inch needle valve.
The pressure
difference between the bias reservoir (or initial reservoir pressure) and the
reservoir is monitored using a model 3051S pressure transducer programmed for
pressure measurements from 0 to 2000 kPa with reference accuracy of less than
0.065 % of the span. In order to improve the sensitivity of the Baumann control
valve, a model 3051S Rosemount pressure transducer, spanned from 0 to 2000
kPa, measures the pressure difference between the bias reactor and the reactor.
The bias reactor is a gas reservoir pressurized slightly higher than the crystallizer
pressure and isolated using a Swagelok needle valve prior to experimentation. By
using a bias reactor and transducer with a span of approximately 1/7 of that of the
26
crystallizer’s pressure transducer, the pressure controller is approximately 7 times
more sensitive to pressure changes within the crystallizer.
The crystallizer and reservoirs are all immersed in an insulated bath
consisting of a 20 % glycol-water mixture. The bath is kept at constant
temperature using a chiller that circulates glycol continuously through a 3/8 inch
copper coil installed in the bath. The temperature inside the top and bottom of the
crystallizer and in the variable volume reservoir is monitored using Omega RTD
probes accurate to ±0.3 ºC.
Figure 2.2. Schematic diagram of the experimental solubility apparatus.
1: Crystallizer; 2: Mixer; 3: Bias reactor; 4: Bias reservoir;
5: Variable volume feeding reservoir; 6: Propane tank;
7: Positive displacement pump;
8: Vacuum pump; 9: Sample cylinder.
2.3
Data Acquisition
In the phase equilibrium apparatus, all pressure transducers and RTD
measurements are recorded using a National Instrument data acquisition system
27
containing SCC modules (current and RTDs) for signal conditioning and a PCI
data acquisition card with 18 bit resolution. The data is recorded in Labview 7.1 at
a rate of 50 000 samples/sec and averaged to get one data point per second. The
data is then exported and saved in a Microsoft Excel file.
2.4
Additional Equipment
A motorized high pressure positive displacement (HPD) pump
(Schlumberger Canada Ltd, Edmonton, AB) is required to displace the gas
volume in the reactor at constant pressure in order to achieve two-phase mixed
hydrate-liquid water equilibrium. Using a piston-cylinder arrangement, the HPD
pump is capable of operating at pressures of up to 140 MPa and has a
displacement volume of 5 to 500 mL with a volume resolution as low as 0.005
mL.
A high-pressure filter assembly (Millipore, Bedford, MA) is used when
necessary to ensure that liquid sample being analyzed does not contain any
hydrates. The assembly is capable of withstanding a 20 MPa difference across the
filter and removes all particles greater than 10 nm in diameter.
A digital gasometer (Chandler Engineering, Tulsa, OK), shown in Figure
2.3 below, is used to measure the volume and temperature of gas expanded from
the liquid sample bomb. The gasometer consists of two pyrex chambers of 1000
mL and 2000 mL respectively that can be used separately or in series to give a
maximum volume of 3000 mL. A floating piston in each chamber is connected to
a rack and pinion that allows for the pistons to be positioned through the use of
28
control knobs. When a sample is expanded into the gasometer, the movement and
position of the pistons are monitored using dual digital volume meters calibrated
in cubic centimeters. The temperature inside each chamber is monitored using
omega thermocouples accurate to ±0.1 ºC. Volume measurements by the
gasometer are accurate to 0.2 % of the volume reading.
Figure 2.3. Chandler digital gasometer
When necessary, a Varian CP-3800 gas chromatograph (Varian Inc.,
Mississauga, ON) is used to analyze vapour samples from both the reactor and the
gasometer. The Varian CP-3800 is equipped with a thermal conductivity detector
(TCD) and sample separation is accomplished using a packed column consisting
of 80-100 mesh HayeSep® R packing, ideal for the separating mixtures of light
hydrocarbons, air, and trace amounts of water. The gas chromatograph is
connected to a PC and is operated via Varian’s Galaxie chromatography software.
2.5
Materials
For propane experiments, high purity propane gas (MEGS, Montreal, QC)
was used as the supply gas in the equilibrium apparatus. For gas mixture
experiments, a mixture of 50 % ultra-high purity methane and 50 % ultra-high
29
purity carbon dioxide by mole (MEGS Specialty Gases, Montreal, QC) was used
as the supply gas. For all experiments, distilled and deionized water was used as
the aqueous phase in the crystallizer.
2.6
Experimental Conditions
In both the propane and gas mixture studies, experiments were performed in
and around the hydrate formation region to observe the effect of hydrate
formation on the equilibrium behavior of the system. Therefore, in order to
determine appropriate experimental conditions, accurate phase diagrams must be
generated to determine incipient hydrate formation of the system being examined.
For the propane-water system, the experimental data of Deaton and Frost
was used to determine three phase hydrate-liquid water-vapour equilibrium
points. Experimental conditions relative to these points are illustrated in Figure
2.4 below. As explained earlier, the narrow borders of the propane hydrate
formation region restrict hydrate formation potential and limit experimental
conditions to within a temperature range of only 4 K.
30
400
P /kPa
350
300
250
200
150
273.0
274.0
275.0
276.0
277.0
278.0
T /K
Three Phase H-Lw-V
Experimental Conditions
Figure 2.4. Partial phase diagram for the propane-water system and experimental conditions
for the measurement of dissolved propane in water. The line represents three-phase H-Lw-V
equilibrium points (Deaton and Frost 1946). Below the line, gaseous propane and liquid
water coexist at equilibrium, and above the line liquid water and propane hydrate may exist
at equilibrium.
For the 50/50 methane/carbon dioxide gas mixture experiments, accurate
three-phase mixed hydrate-liquid water-vapour points were required over a
temperature range of 274 K to 282 K before appropriate experimental conditions
could be chosen. An experimentally determined partial phase diagram for the
50/50 CH4/CO2-water system is presented later along with the experimental
pressure conditions for solubility measurements over the above range of
temperatures.
2.7
Experimental Procedure
For both the propane and gas mixture experiments, the procedure to
determine dissolved gas concentrations in water was adapted from the work of
Servio and Englezos (Servio and Englezos 2001; Servio and Englezos 2002). For
31
gas mixture experiments, additional incipient phase equilibria experiments and
mole balance calculations were required to complete the study of the equilibrium
behavior of the 50/50 methane/carbon dioxide-water system.
2.7.1
Three-Phase H-Lw-V Equilibrium
For experiments performed using propane as the hydrate former, three
phase hydrate-liquid water-vapour points were obtained from the work of Deaton
and Frost (Deaton and Frost 1946). Three phase hydrate-liquid water-vapour
points for the 50/50 CH4/CO2 gas mixture were determined using the isothermal
pressure-search method over a range of temperatures from 274 to 282 K (Deaton
and Frost 1946).
2.7.2
Solubility Experiments
The hydrate crystallizer was filled with 250 mL of distilled and deionized
water. Once the water had reached the desired temperature, supply gas (either
pure propane or the methane/carbon dioxide gas mixture) was added to the
equilibrium apparatus until the desired pressure was obtained. Next, the variable
volume supply reservoir was pressurized to a level above that of the crystallizer to
allow gas addition to the reactor in order to maintain constant pressure throughout
the experiment. The procedure for the measurement of the concentration of
dissolved gas in the bulk aqueous phase was dependent on which region of the
phase diagram the experiment was conducted. If the experiment was to be carried
out below the three-phase line in the two-phase V-Lw equilibrium region, a liquid
sample was collected in an evacuated sample bomb that was removed from the
32
apparatus once it had reached equilibrium. If the experiment was to be carried
above the three-phase line in the H-Lw equilibrium region, the gas volume in the
reactor must be displaced with water in the reactor while maintaining constant
pressure in the presence of hydrates. After equilibrium had been obtained between
the liquid water and hydrate phases, a hydrate-free liquid sample was then
collected in the evacuated sample bomb for analysis.
An analytic flash technique was used to determine the concentrations of
supply gas dissolved in the liquid sample (Servio and Englezos 2001; Servio and
Englezos 2002). Using the gasometer, the contents of the sample bomb were
brought to room temperature and atmospheric pressure. The gasometer
accomplishes this by allowing the gas to evolve from the sample bomb into the
floating piston where the gas volume and temperature are measured and recorded.
The gas was then injected into the gas chromatograph for analysis. The number of
moles of gas in the vapour phase within the gasometer was then calculated by
niG = y i ,G ( P − PHV 2O )
V
Z i RT
(3.1)
where P, V, R, T, yi,G and Zi are the atmospheric pressure, volume of the vapour in
the gasometer, universal gas constant, gasometer temperature, mole fraction of
component i in the gasometer, and the compressibility factor for methane or
carbon dioxide respectively. Values for Zi were obtained from the TrebbleBishnoi equation of state (Trebble and Bishnoi 1987; Trebble and Bishnoi 1988).
PHV 2O is the vapour pressure of water at the vapour temperature. Since the liquid
sample volume and the solubility of supply gas in water at room temperature and
atmospheric pressure are known (Carroll and Mather 1997; Yaws 2003), we can
33
proceed to calculating the mole fraction of each component, xi,eq, dissolved in the
aqueous phase at the experimental conditions using the following mole balance
equation
xiR, g n H 2O
xi ,eq =
1 − xiR, g
xiR, g n H 2O
1 − xiR, g
+ niG
(3.2)
+ ∑ n + n H 2O
G
i
i
where xiR, g is the mole fraction of residual gas dissolved in water at the gasometer
temperature and atmospheric pressure (Wilhelm, Battino et al. 1977) and n H 2O is
the number of moles of water in the sample bomb. Since the volume of the sample
bomb was known, n H 2O could be calculated using steam tables (Perry and Green
1997) at the experimental temperature and pressure.
2.7.3
Mole Balance
In experiments involving gas mixtures, a simple mass balance was
completed to determine the water-free molar composition of the hydrate phase,
z CH 4 and z CO2 , respectively (Ohgaki, Takano et al. 1996) under three-phase H-LwV equilibrium. Since both methane and carbon dioxide are known to form
structure-I hydrate, it was assumed that hydrates formed from a mixture of
methane and carbon dioxide will also be of structure-I. Therefore, a hydration
number of q = 6.2 was assumed for the mass balance (Uchida, Hirano et al. 1999).
In its most complete form, the mole balance performed on the gas mixture-water
system is as follows:
nCO 2,t = nCO 2,G + nCO 2, L + z CO 2 * n H
(3.3)
34
nCH 4,t = nCH 4,G + nCH 4, L + (1 − z CO 2 ) * n H
(3.4)
n w ,t = n w , L + q * n H
(3.5)
y CO 2,G =
xCO 2, L =
nCO 2,G
nCH 4,G + nCH 4,G
(dry basis)
nCO 2, L
nCH 4, L + nCH 4, L + nw, L
(3.6)
(3.7)
where the subscripts t, G, L, H, and w refer to total, gas, liquid, hydrate and water
respectively. The above mole balance can be simplified by making two key
assumptions. First, it can be assumed that the number of moles of methane and
carbon dioxide dissolved in the liquid phase is negligible in comparison to the
number of moles of methane and carbon dioxide present in the vapour phase
above the liquid and in comparison to the number of moles of liquid water in the
aqueous phase. Second, it can be assumed that the number of moles of water in
the vapour phase is negligible in comparison to the number of moles of gaseous
methane and carbon dioxide and in comparison to the number of moles of liquid
water in the aqueous phase. The resulting approximation essentially relates any
shift in gas phase composition of the closed hydrate forming system directly to the
formation of carbon dioxide and methane hydrates.
35
3
3.1
Results and Discussion
Propane Experiments
Experiments were conducted over a range of 274 K to 277 K and 150 to 350
kPa in both the vapour-liquid water and hydrate-liquid water equilibrium regions.
A series of replicate experiments at each temperature and pressure condition were
performed with a maximum absolute average deviation from the mean of 4.6 %.
The mean results at each temperature and pressure condition are presented in
Table 1 and measurements at 250 kPa, 300 kPa, and 350 kPa respectively are
plotted in Figure 3.1 below.
Table 3.1. Mole fraction of propane in water, x1, at given temperatures and pressures
T/K
P/kPa
104 x1
Regiona
274.21
150
1.118
V-Lw
274.18
188
1.440
V-Lw
274.25
200
1.417
V-Lw
275.17
201
1.243
V-Lw
275.15
250
1.502
V-Lw
276.21
250
1.445
V-Lw
274.23
253
1.439
H-Lw
276.20
301
1.702
V-Lw
274.16
301
1.440
H-Lw
275.20
302
1.572
H-Lw
275.20
352
1.572
H-Lw
276.16
355
1.642
H-Lw
274.33
358
1.546
H-Lw
a
H, Lw, and V refer to solid hydrate, liquid water and
vapour respectively
36
2.0
1.8
10 4 x1
250 kPa (H-Lw)
1.6
250 kPa (V-Lw)
300 kPa (H-Lw)
1.4
300 kPa (V-Lw)
350 kPa (H-Lw)
1.2
1.0
274.0
274.5
275.0
275.5
276.0
276.5
T /K
Figure 3.1. Plot of equilibrium mole fraction of propane, x1, as a function of temperature at
250 kPa, 300 kPa, and 350 kPa respectively (three phase H-Lw-V equilibrium temperatures
are 275.2 K, 276.0 K and 276.7 K respectively).
In Table 2, the measurements taken in the vapour-liquid water region are
presented and compared to the correlation of Carroll and Mather and the
correlation of Chapoy (Carroll and Mather 1997; Chapoy, Mokraoui et al. 2004).
As expected, the solubility in the absence of hydrate increases with decreasing
temperature and the results obtained are close to literature values.
Table 3.2. Comparison of the experimentally determined solubility in the two-phase vapourliquid water region to those calculated using the correlations of Carroll and Mather and
Chapoy (Carroll and Mather 1997; Chapoy, Mokraoui et al. 2004).
104 x1(calc)a
104 x1(calc)b
100(x1a - x1)/x1a
T/K
P/kPa
104 x1
274.18
188
1.440
1.334
1.363
-8.0
274.21
150
1.118
1.063
1.086
-5.2
274.25
200
1.417
1.417
1.447
0.0
275.15
250
1.502
1.690
1.725
11.1
275.17
201
1.243
1.357
1.386
8.4
276.21
250
1.445
1.611
1.644
10.3
a
Using Carroll and Mather’s correlation for Henry's constants.
b
Using Chapoy's correlation for Henry's constants.
100(x1b - x1)/x1b
-5.7
-2.9
2.1
12.9
10.2
12.0
37
The results for the solubility of propane in the presence of propane hydrate
show that at a given pressure, the solubility of propane in water decreases as the
temperature decreases in the hydrate formation region. Therefore, the formation of
gas hydrate reverses the gas-liquid solubility trend. This is in agreement with the
conclusions of Ohmura and Mori (Ohmura and Mori 1999) and Servio and
Englezos (Servio and Englezos 2001; Servio and Englezos 2002). The reason for
the reversal in the gas-liquid solubility trend is a subject of much debate. Most
recently, it has been suggested that a blockage at the gas-liquid interface by the
hydrate and sharp changes in surface tension forces at the gas-liquid and hydrate
liquid interfaces upon hydrate formation are responsible for the observed reversal
in the gas-liquid solubility trend (Makogon 1997).
Furthermore, it can also be seen that solubility is not a strong function of
pressure in the hydrate-liquid water equilibrium region. This result is expected as
both the hydrate and liquid water phases are condensed phases and are considered
to be nearly incompressible.
3.2
3.2.1
50/50 Methane/Carbon Dioxide Experiments
Three-Phase H-Lw-V Equilibrium
Three-phase equilibrium experiments were carried out to determine threephase points for the 50/50 CH4/CO2 gas mixture- water system over a temperature
range of 274 to 282 K. These points are plotted in Figure 3.2 along with the threephase equilibrium points for CH4-water and CO2-water systems respectively.
38
6000
5000
Pressure (kPa)
4000
50-50 Methane-Carbon
Dioxide Experiments
Carbon Dioxide
3000
Methane
2000
1000
0
272
274
276
278
280
282
284
Temperature (K)
Figure 3.2. Partial phase diagrams of the CH4-water (Deaton and Frost 1946), CO2-water
(Deaton and Frost 1946), and 50/50 CH4/CO2-water systems. The solid points correspond to
three-phase H-V-Lw points for the respective system.
The plot in Figure 3.3 compares the experimentally determined threephase equilibrium points to the predicted three-phase equilibrium line obtained
using the van der Waals and Platteeuw type model combined with the SoaveRedlich-Kwong equation of state to describe the hydrocarbon fluid phases(Sloan
1998). The conventional van der Waals and Platteeuw model is shown to
overestimate three-phase equilibrium pressures for mixed-hydrate formation in
the presence of a 50/50 mixture of methane and carbon dioxide. One explanation
for this is the ability of carbon dioxide, the larger of the two hydrate formers, to
distort and the small cavity in the structure-I hydrate crystal. The result is an
increased amount of carbon dioxide in the hydrate phase, leading to a lower
pressure of incipient hydrate formation. Recently, several thermodynamic models
39
have incorporated corrections to improve the accuracy of the conventional van der
waals and Platteeuw model for gas mixtures (Seo and Lee 2001; Ballard and
Sloan 2002) with much success.
6000
5000
Pressure (kPa)
4000
50-50 Methane-Carbon
Dioxide Experiments
3000
Model Predictions
(Sloan, 1998)
2000
1000
0
272
274
276
278
280
282
284
Temperature (K)
Figure 3.3. Comparison of the experimentally determined three-phase equilibrium for the
50/50 CH4/CO2-liquid water system to the prediction of the van der Waals and Platteuw
model (van der Waals and Platteeuw 1959; Sloan 1998).
3.2.2
Solubility Experiments
Solubility experiments were conducted at the three-phase equilibrium for
the gas mixture and in the hydrate formation region. Experimental conditions
ranged from 274 to 282 K at pressures of 20 and 25 bar respectively. The results
of these experiments are summarized in Table 3.3 and in Figures 3.4 and 3.5
below.
40
Table 3.3. Mole fraction of CH4 and CO2 in water at given temperatures and pressures a
T (K)
P (bar)
xeq,CH4
xeq, CO2
Region
274.5
20
0.0002742
0.001836
H-Lw
275.3
20
0.0002993
0.002064
H-Lw
276.3
20
0.0002997
0.002156
H-Lw-V
278.2
20
0.0002292
0.002177
V-Lw
279.8
20
0.0001689
0.002148
V-Lw
274.2
25
0.0003091
0.001840
H-Lw
277.1
25
0.0003546
0.001973
H-Lw
279.0
25
0.0003677
0.002207
H-Lw-V
280.4
25
0.0002325
0.002214
V-Lw
a
H, Lw, V are solid hydrate, liquid water and vapour, respectively
As shown in Table 3.3, several solubility measurements were taken
outside of the hydrate formation region to illustrate the expected trend of
decreased solubility with increasing temperature for both methane and carbon
dioxide in the absence of hydrate. In the hydrate formation region, results indicate
that the solubility of each gas decreases with decreasing temperature. Therefore,
the gas-liquid solubility trend is reversed in the hydrate formation region for each
gas in the system. This conclusion is in agreement with experiments for pure
methane and carbon dioxide (Servio and Englezos 2001; Servio and Englezos
2002) and with the conclusions of Ohmura and Mori (Ohmura and Mori 1999).
Also, as with observations for pure component systems, solubility of methane and
carbon dioxide does not appear to be a strong function of pressure in the presence
of mixed gas hydrate.
41
0.00040
Methane Solubility (mol frac)
0.00035
0.00030
0.00025
20 bar
0.00020
25 bar
0.00015
0.00010
0.00005
0.00000
273
274
275
276
277
278
279
280
281
Tempeature (K)
Figure 3.4. Plot of the equilibrium mole fraction of methane in water for the 50/50 CH4/CO2liquid water system as a function of temperature at the indicated pressures.
0.0025
0.0024
CO 2 Solubility (mol frac)
0.0023
0.0022
0.0021
20 bar
0.0020
25 bar
0.0019
0.0018
0.0017
0.0016
0.0015
273
274
275
276
277
278
279
280
281
Tempeature (K)
Figure 3.5. Plot of the equilibrium mole fraction of carbon dioxide in water for the 50/50
CH4/CO2-liquid water system as a function of temperature at the indicated pressures.
42
3.2.3
Mole Balance
With the liquid and vapour phases fully characterized for the three-phase
H-Lw-V solubility experiments at 20 and 25 bar, a mole balance was completed to
determine the water-free composition of the hydrate phase, z CH 4 and z CO2 ,
respectively. The results of the mole balance are shown in Figure 3.6 and were
found to be close to theoretical predictions (Sloan 1998).
0.50
0.45
z CH4 (water-free mol fraction)
0.40
0.35
0.30
Experiments
0.25
Prediction of Sloan (1998)
0.20
0.15
0.10
0.05
0.00
276.2K, 20bar
279.0K, 25 bar
Figure 3.6. Comparison of experimental and literature (Sloan 1998) water-free mole
fractions of methane in the hydrate phase under three-phase H-Lw-V equilibrium.
By defining the distribution coefficient of methane in the vapour and
hydrate phases as
S=
yCH 4 * zCO2
yCO2 * zCH 4
(3.8)
where y CH 4 , y CO2 , z CH 4 , z CO2 are the moles fractions of methane and carbon
dioxide in the vapour and hydrate phases in the crystallizer, it was found that S =
43
2.0 and 1.7 for the 20 bar and 25 bar experiments respectively. Thus, in the
presence of the 50/50 gas mixture at the experimental conditions shown in Figure
3.6, methane is approximately two times more likely to distribute itself into the
gas phase than the hydrate phase, indicating that methane can indeed be
selectively replaced by carbon dioxide in the hydrate phase. This is in agreement
with the conclusions of Ohgaki et al (Ohgaki, Takano et al. 1996), who have also
concluded that an increase in the fraction methane in the gas phase will result in a
proportional increase in the distribution coefficient defined previously.
4
4.1
Conclusions and Recommendations
Conclusions
The solubility of propane in water in the hydrate formation region was
measured using an analytical flash technique for temperatures ranging from 274 K
to 277 K and pressures of 150 kPa to 350 kPa. Solubility results show that the
amount of propane dissolved in water decreases with decreasing temperatures in
the hydrate formation region. Furthermore, solubility was not found to be a strong
function of pressure in the hydrate formation region.
Also, phase equilibrium relationships of pressure, temperature, and
composition of the liquid, vapour, and hydrate phases for the CO2/CH4 mixed
hydrate system were investigated at temperatures between 274 K and 282 K and
at pressures of 2000 kPa and 2500 kPa. In the absence of hydrate, solubility of
each gas in the aqueous phase was shown to decrease with increasing temperature,
as expected. In the hydrate formation region, results were found to be in
44
agreement with existing literature on single component systems as the solubility
of both CH4 and CO2 in water were found to decrease with decreasing
temperature in the presence of mixed hydrates. Therefore, hydrate formation
reverses the gas-liquid solubility trend for each gaseous component in the mixed
hydrate system. Results also show that pressure does not have a strong influence
on the solubility of each component in the presence of mixed gas hydrate.
It is hypothesized that a blockage at the gas-liquid interface by the hydrate
and sharp changes in surface tension forces at the gas-liquid and hydrate-liquid
water interfaces upon hydrate formation are responsible for the observed reversal
in the gas-liquid solubility trend in the H-Lw equilibrium region. Also, it is
expected that solubility of gas in the liquid phase does not vary with pressure in
the H-Lw equilibrium region as both the hydrate and liquid water phases are
considered to be nearly incompressible.
Finally, using a mole balance, it was determined that the distribution
coefficient of methane between the gas and hydrate phase is approximately 2 for
the 50/50 gas mixture-liquid water-mixed hydrate system. Therefore, carbon
dioxide hydrates do indeed form selectively over methane hydrates in the
presence of the 50/50 gas mixture.
4.2
Recommendations
Experimentation on the CH4/CO2-water system should be continued. By
varying the composition of the supply gas to the system, the equilibrium behavior
of the gas mixture could be studied over a range of compositions to determine
phase equilibrium and solubility trends as a function of composition. Also,
45
analytical techniques such as Raman spectroscopy should be employed to directly
determine the composition of the hydrate phase as a comparison to the mole
balance approach used in this study. Furthermore, the apparatus and techniques
discussed should be employed to study other gas mixtures that are of particular
interest to researchers in the field of gas hydrates, such as nitrogen/carbondioxide, important in the continuing research effort towards the sequestration of
flue gases, methane/propane, important to hydrate promotion studies for the
purposes of transportation and storage of methane, and natural gas (methane,
ethane, propane, butane, nitrogen, hydrogen sulfide), important to the ongoing
efforts to extract and collect natural gas from existing hydrate reserves.
46
References
Ballard, A. L. and E. D. Sloan (2002). "The Next Generation of Hydrate
Prediction: An Overview." Journal of Supramolecular Chemistry 2(45): 385-392.
Buffett, B. A. (2000). "Clathrate Hydrates." Annu. Rev. Earth Planet Sci. 28:
477-507.
Carroll, J. J. and A. E. Mather (1997). "A model for the solubility of light
hydrocarbons in water and aqueous solutions of alkanolamines."
Chemical Engineering Science 52(4): 545-552.
Chapoy, A., S. Mokraoui, et al. (2004). "Solubility measurement and
modeling for the system propane-water from 277.62 to 368.16 K."
Fluid Phase Equilibria 226: 213-220.
Chatti, I., A. Delahaye, et al. (2005). "Benefits and drawbacks of clathrate
hydrates: a review of their areas of interest." Energy Conversion and
Management 46(9-10): 1333-1343.
Davy, H. (1811). "The Bakerian Lecture: On Some of the Combinations of
Oxymriatic Gas and Oxygene, and on the Chemical Relations of These
Principles to Inflammable Bodies." Philiosophical Transactions of the
Royal Society of London (1776-1886) 101: 1.
Deaton, W. M. and E. M. J. Frost (1946). "Gas Hydrates and Their Relation
to the Operation of Natural Gas Pipelines." Monograph for the US
Dept. of the Interior.
den Heuvel, M. M. M.-v., C. J. Peters, et al. (2002). "Gas hydrate phase
equilibria for propane in the presence of additive components." Fluid
Phase Equilibria 193(1-2): 245-259.
Englezos, P. (1993). "Clathrate Hydrates." Ind. Eng. Chem. Res. 32: 12511274.
Faraday, M., Davy, H. (1823). "On Fluid Chlorine." Philiosophical
Transactions of the Royal Society of London (1776-1886) 113: 160.
Giavarini, C., F. Maccioni, et al. (2003). "Formation Kinetics of Propane
Hydrates." Ind. Eng. Chem. Res. 42: 1517-1521.
Hammerschmidt, E. G. (1934). "Formation of Gas Hydrates in Natural Gas
Transmission Lines." Industrial Engineering and Chemistry 26: 851.
Handa, Y. P. (1986). "Calorimetric determinations of the compositions,
enthalpies of dissociation, and heat capacities in the range 85 to 270 K
for clathrate hydrates of xenon and krypton." The Journal of
Chemical Thermodynamics 18(9): 891-902.
Hashemi, S., A. Macchi, et al. (2006). "Prediction of methane and carbon
dioxide solubility in water in the presence of hydrate." Fluid Phase
Equilibria 246(1-2): 131-136.
Khokhar, A. A., J. S. Gudmundsson, et al. (1998). "Natural Gas Storage
Properties of Structure H Hydrate." Fluid Phase Equilibria 151: 383392.
Knox, W. G., M. Hess, et al. (1961). "Hydrate Process." Chemical
Engineering Progress 57: 71.
47
Makogon, Y. Y. (1997). Hydrates of Hydrocarbons. Tulsa, Okla, PennWell.
Ng, H.-J. (2000). Hydrate Phase Composition for Multicomponent Gas
Mixtures. Annals of the New York Academy of Sciences, New York
Academy of Sciences. 912: 1034-1039.
Ohgaki, K., H. Takano, et al. (1996). "Methane Hydrate Exploitation by
Carbon Dioxide from Gas Hydrate." Journal of Chemical
Engineering of Japan 29: 478-483.
Ohmura, R. and Y. H. Mori (1999). "Solubility of Liquid CO2 In Synthetic
Sea Water at Temperatures from 278 K to 293 K and Pressures from
6.44 MPa to 29.49 MPa, and Densities of the Corresponding Aqueous
Solutions." Journal of Chemical and Engineering Data 44: 1432-1433.
Parrish, W. R. and J. M. Prausnitz (1972). "Dissociation Pressures of Gas
Hydrates Formed by Gas Mixtures." Ind. Eng. Chem. Process Des.
Dev. 11: 26-35.
Perry, R. H. and D. W. Green (1997). Perry's Chemical Engineering
Handbook (7th edition), McGraw Hill.
Prausnitz, J. M. (1986). Molecular Thermodynamics of Fluid-Phase
Equilibria, 2nd Ed., Prentice-Hall.
Ripmeester, J. A., J. S. Tse, et al. (1987). "A New Clathrate Hydrate
Structure." Nature 325: 135.
Seo, Y.-T. and H. Lee (2001). "Multiple-Phase Hydrate Equilibria of the
Ternary Carbon Dioxide, Methane, and Water Mixtures." J. Phys.
Chem 105: 10084-10090.
Servio, P. (2003). Gas Hydrate Research in Energy Energy and
Environmental Sciences. Montreal, Quebec, McGill University.
Servio, P. and P. Englezos (2001). "Effect of temperature and pressure on the
solubility of carbon dioxide in water in the presence of gas hydrate."
Fluid Phase Equilibria 190(1-2): 127-134.
Servio, P. and P. Englezos (2002). "Measurement of Dissolved Methane in
Water in Equilibrium with Its Hydrate." Journal of Chemical and
Engineering Data 47: 87-90.
Sloan, E. D. J., Ed. (1998). Clathrate Hydrates of Natural Gases. New York.
Suess, E., M. E. Torres, et al. (1999). "Gas hydrate destabilization: enhanced
dewatering, benthic material turnover and large methane plumes at
the Cascadia convergent margin." Earth and Planetary Science
Letters 170(1-2): 1-15.
Tohidi, B. (2001). "Gas Hydrates."
Retrieved September, 2006, from
http://www.pet.hw.ac.uk/research/hydrate/.
Trebble, M. A. and P. R. Bishnoi (1987). "Development of a new fourparameter cubic equation of state." Fluid Phase Equilibria 35(1-3): 118.
Trebble, M. A. and P. R. Bishnoi (1988). "Extension of the Trebble-Bishnoi
equation of state to fluid mixtures." Fluid Phase Equilibria 40(1-2): 121.
48
Uchida, T., T. Hirano, et al. (1999). "Raman Spectroscopic Determination of
Hydration Number of Methane Hydrates." AIChE Journal 45(12):
2641-2645.
van der Waals, J. H. and J. C. Platteeuw (1959). "Clathrate Solutions." Adv.
Chem. Phys. 2: 1-57.
Wilhelm, E., R. Battino, et al. (1977). "Pressure Solubilities of Gases in liquid
Water." Chemical Reviews 77(2): 219-262.
Yaws, C. L. (2003). Henry's Law Constants for Compounds in Water
Yaw's Handbook of Thermodynamic and Physical Properties of Chemical
Compounds
knovel.
49
Appendix A: Detailed Reactor Schematics
I
II