phase equilibria in co -brine system for co storage
TRANSCRIPT
The Pennsylvania State University
The Graduate School
John and Willie Leone Family Department of Energy and Mineral Engineering
PHASE EQUILIBRIA IN CO2-BRINE SYSTEM FOR CO2 STORAGE
A Dissertation in
Energy and Mineral Engineering
by
Haining Zhao
Β© 2014 Haining Zhao
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
December 2014
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The dissertation of Haining Zhao was reviewed and approved* by the following:
Serguei N. Lvov
Professor of Energy and Mineral Engineering
Professor of Material Science and Engineering
Director of Electrochemical Technologies Program
Dissertation Advisor
Chair of Committee
William D. Burgos
Professor of Civil & Environmental Engineering
Li Li
Assistant Professor of Petroleum and Natural Gas Engineering
John Yilin Wang
Assistant Professor of Petroleum and Natural Gas Engineering
Luis F. Ayala H.
Associate Professor of Petroleum and Natural Gas Engineering
Associate Department Head for Graduate Education
*Signatures are on file in the Graduate School
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ABSTRACT
The apparatus for measuring CO2 solubility at elevated temperatures and pressures were
developed in this study; new experimental CO2 solubility in the following brines were collected: (1).
Single-salt aqueous NaCl, CaCl2, Na2SO4, MgCl2, and KCl with ionic strength from 0.5 to 6 mol/kg; (2).
Synthetic mixed-salt (NaCl and CaCl2) brines with ionic strength 1.712 and 4.984 mol/kg; (3). Synthetic
mixed-salt (NaCl, CaCl2, Na2SO4, MgCl2, KCl, SrCl2, and NaBr) brines with ionic strength 1.712 and 4.984
mol/kg; (4). A natural Mt. Simon formation brine with ionic strength 1.815 mol/kg.
The experimental data are used to develop the proposed PSUCO2 model. The model is capable of
calculating mutual solubilities of CO2 and H2O for the system of CO2-salt-H2O containing NaCl, CaCl2,
Na2SO4, MgCl2, or KCl or a mixture of them. Comparisons against literature data reveal a clear
improvement of the proposed PSUCO2 model among the published models in predicting CO2 solubility in
the aforementioned brines.
A comparison of modeling results with experimental values on the P-x diagram (Figure 2. 14)
revealed a pressure-bounded "transition zone" in which the CO2 solubility decreases to a minimum and
then increases as the temperature increases. CO2 solubility is not a monotonic function of temperature in
the transition zone but outside of that transition zone, the CO2 solubility decreases or increases
monotonically in response to increased temperature. The similar phenomenon is also observed by plotting
CO2 solubility contours in P-T diagram (Figure 4. 9), where the path of the maximum gradient among the
CO2 solubility contours is defined to divide the P-T diagram into two regions: in Region I, the CO2
solubility in the aqueous phase decreases monotonically in response to increased temperature, but in region
II, the behavior of the CO2 solubility is the opposite of that in Region I as the temperature increases.
A web-based computation interface of the model PSUCO2 is developed by the author and can be
accessed via the link: http://www.carbonlab.org/psuco2/.
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TABLE OF CONTENTS
LIST OF FIGURES ........................................................................................................................................vi
LIST OF TABLES ...................................................................................................................................... viii
PREFACE ......................................................................................................................................................xi
ACKNOWLEDGMENTS ............................................................................................................................ xii
CHAPTER 1 INTRODUCTION ................................................................................................................... 1
CHAPTER 2 SOLUBILITY OF CO2 IN AQUEOUS NaCl SOLUTIONS................................................... 4
Abstract ....................................................................................................................................................... 5
2.1 Introduction ........................................................................................................................................... 6
2.2 Review of the experimental approaches................................................................................................ 8
2.3 Experimentation .................................................................................................................................. 10
2.3.1 Experimental P-T-x conditions .................................................................................................... 10
2.3.2 Chemicals .................................................................................................................................... 11
2.3.3 Apparatus ..................................................................................................................................... 11
2.3.4 Procedure ..................................................................................................................................... 12
2.3.5 Validation of the obtained data .................................................................................................... 14
2.3.6 Measured CO2 solubilities ........................................................................................................... 17
2.4. Thermodynamic model of the CO2-NaCl-H2O system ...................................................................... 21
2.4.1 Thermodynamic framework for vapor-liquid phase equilibrium ................................................. 21
2.4.2 Incorporating Pitzer's activity model ........................................................................................... 24
2.4.3. Improved mixing rule parameter for the CO2-rich phase ............................................................ 29
2.4.4 Results and discussion ................................................................................................................. 35
2.5 Conclusions ......................................................................................................................................... 52
CHAPTER 3 SOLUBILITY OF CO2 IN AQUEOUS SOLUTIONS OF CaCl2, MgCl2, Na2SO4 AND KCl
....................................................................................................................................................................... 53
Abstract ..................................................................................................................................................... 54
3.1 Introduction ......................................................................................................................................... 55
v
3.2 Experimentation .................................................................................................................................. 57
3.3 Theoretical essentials for PSUCO2 ..................................................................................................... 57
3.4 Results and discussion ........................................................................................................................ 64
3.4.1. Measured results ......................................................................................................................... 64
3.4.2. Modeling results ......................................................................................................................... 71
3.5 Conclusions ......................................................................................................................................... 86
CHAPTER 4 SOLUBILITY OF CO2 IN SYNTHETIC FORMATION BRINE ........................................ 87
Abstract ..................................................................................................................................................... 88
4.1 Introduction ......................................................................................................................................... 89
4.2 Materials and methods ........................................................................................................................ 91
4.2.1 Chemicals .................................................................................................................................... 91
4.2.2 Synthetic brine preparation. ......................................................................................................... 91
4.2.3 Apparatus and procedure ............................................................................................................. 93
4.3 Results and discussions ....................................................................................................................... 95
4.3.1 Experimental results .................................................................................................................... 95
4.3.2 Additivity rule of Setschenow Coefficients of the individual ions .............................................. 95
4.3.3 Comparison of model calculations against the experimental data ............................................... 99
CHAPTER 5 CONCLUISONS ................................................................................................................. 117
REFERENCES ............................................................................................................................................ 120
APPENDIXES ............................................................................................................................................ 134
Appendix A: Additional Model Equations.............................................................................................. 135
Appendix B: Pitzer Ion-Ion Interaction Model ....................................................................................... 138
Appendix C: Experimental Error Estimation .......................................................................................... 145
Appendix D: The PSUCO2 Web-Computational Interface .................................................................... 150
Appendix E. Original Experimental Data Records ................................................................................. 152
vi
LIST OF FIGURES
Figure 1. 1 CO2-brine system and energy production. .............................................................................. 2
Figure 2. 1 Approaches for CO2 solubility measurement. ........................................................................ 9
Figure 2. 2 Selected experimental pressure and temperature conditions. ............................................... 10
Figure 2. 3 Schematic of Experimental apparatus .................................................................................. 12
Figure 2. 4 Comparison of experimental CO2 solubility to literature data.............................................. 19
Figure 2. 5 Comparison of experimental CO2 solubility with model calculations .................................. 20
Figure 2. 6 Henry's law constant ............................................................................................................. 23
Figure 2. 7 Computational flow chart of the proposed PSUCO2 model................................................. 26
Figure 2. 8 The data fitting procedure .................................................................................................... 27
Figure 2. 9 Phase diagram for the CO2-H2O system up to 573 K and 2000 bar .................................... 35
Figure 2. 10 Phase diagram for the CO2-NaCl-H2O system up to 573 K and 2000 bar ............................ 36
Figure 2. 11 Phase diagram for the CO2-H2O system from 288-373 K, up to 300 bar. ........................... 40
Figure 2. 12 Phase diagram for the CO2-H2O system at temperatures 373.15-473.15 K and pressures 1-
100 bar for the CO2-rich phase. ............................................................................................ 41
Figure 2. 13 Comparison between the SP2010 model and this model at 523-573 K ................................ 41
Figure 2. 14 CO2 solubility transition zone .............................................................................................. 43
Figure 2. 15 Comparison of this model and the MZLL2013 model. ........................................................ 47
Figure 3. 1 Comparison of the experimental CO2 solubilities in various aqueous salt solutions at 298.15
K and 1.013 bar based on different concentration scales. .................................................... 68
Figure 3. 2 Comparison of the experimental CO2 solubilities in different aqueous salt solutions based
on different concentration scales at 323.15 K and 150 bar. .................................................. 69
Figure 3. 3 The average absolute deviation (AAD %) of the calculated CO2 solubility values in aqueous
CaCl2, Na2SO4, MgCl2 and KCl solutions by different models ............................................ 71
Figure 3. 4 Comparison of model calculated values against the experimental data ............................... 73
Figure 3. 5 Comparison of model calculations against the experimental CO2 solubility in aqueous
CaCl2 solutions ..................................................................................................................... 78
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Figure 3. 6 Comparison of the model calculations against the experimental CO2 solubility in aqueous
Na2SO4 solutions .................................................................................................................. 79
Figure 3. 7 Comparison of the model calculations against the experimental CO2 solubility in aqueous
MgCl2 solutions. ................................................................................................................... 80
Figure 3. 8 Comparison of the model calculations against the experimental CO2 solubility in aqueous
KCl solutions ........................................................................................................................ 82
Figure 3. 9 Comparison of model calculation of H2O solubility in the CO2-rich phase ......................... 84
Figure 4. 1 The schematic of the additivity rule of the Setschenow coefficients.................................... 97
Figure 4. 2 Comparison of model calculations with experimental data. ............................................... 101
Figure 4. 3 Comparisons of the modeling results against the experimental CO2 solubility data in both
synthetic reservoir brines and NaCl+CaCl2 brines ............................................................. 102
Figure 4. 4 Comparison of model calculations against the experimental data reported by Yasunishi et al.
(1979) at 1 atm and 298 K .................................................................................................. 104
Figure 4. 5 Comparisons of the model calculations (PSUCO2, SP2010 and OLI) against the
experimental CO2 solubility data in the Weyburn Formation brine .................................... 105
Figure 4. 6 Comparison of the model calculations against the experimental........................................ 108
Figure 4. 7 Comparison of PSUCO2 with published models up to 2000 bar at 523K. ......................... 110
Figure 4. 8 The average absolute deviation (AAD %) of the calculated CO2 solubility in aqueous
mixed-salt solutions among different models compared to the experimental data ............. 110
Figure 4. 9 The CO2 solubility contours in pure water and synthetic Mt. Simon formation ............. brine
generated by the PSUCO2 model ....................................................................................... 116
Figure D. 1 User-interface of CO2-brine phase equilibria model. Part I: CO2 solubility in pure H2O and
in single-salt brine; Part II: CO2 solubility in mixed-salt brine. ......................................... 150
Figure D. 2 User-interface of pure CO2 EoS. ........................................................................................ 151
Figure D. 3 User-interface of brine density model. ............................................................................... 151
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LIST OF TABLES
Table 2. 1 Comparison of measured CO2 solubility in the binary CO2-H2O system at 323.15 K and 100
bar with literature data and model calculations. ................................................................... 15
Table 2. 2 Experimental results of CO2 solubility in NaCl(aq) compared with literature data (collected
at the same P-T-x conditions) and model calculations. ........................................................ 16
Table 2. 3 Experimental CO2 solubility measurements in NaCl(aq) at 150 bar and temperatures from
323.15 to 423.15 K. The experimental data are compared with model calculations in terms
of the average absolute deviation (AAD %) between calculated and experimental results. . 18
Table 2. 4 The results vCO2 (cm3 mol-1) determined by this model. ....................................................... 22
Table 2. 5 Parameters of Henry's constant Eq. (2.3). ............................................................................ 22
Table 2. 6 Parameters of Eq. (2.13). ...................................................................................................... 27
Table 2. 7 Pitzer triple-ion interaction parameter .................................................................................. 28
Table 2. 8 The mixing rule binary interaction parameter ...................................................................... 28
Table 2. 9 The components, key parameters, approaches and limitations of the CO2 solubility model
presented in this study. ......................................................................................................... 32
Table 2. 10 The average absolute deviation (AAD %) of CO2 solubility in the aqueous phase between
model calculations and the selected reliable experimental data over a wide P-T-x range (25-
2000 bar, 288.15-573.15 K, and 0-6 mol kg-1 NaCl) ............................................................ 38
Table 2. 11 The average absolute deviation (AAD %) of the H2O solubility in the CO2-rich phase
between model calculations and the selected reliable experimental data at 1-2000 bar and
278.15-573.15 K .................................................................................................................. 39
Table 2. 12 The average absolute deviation (AAD %) of calculated CO2 solubility (mol kg-1) in aqueous
phase from experimental data for the CO2-H2O system at temperatures of 273.15-573.15 K
and pressures of 1-2000 bar: Comparison between this model and the MZLL2013 model. 49
Table 2. 13 The average absolute deviation (AAD %) of the calculated CO2 solubility (molality) in the
aqueous phase from experimental data for the CO2-NaCl-H2O system at 273.15-573.15 K,
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1-1400 bar and 0-6 mol kg-1 NaCl: Comparison between this model and the MZLL2013
model. ................................................................................................................................... 51
Table 3. 1 Coefficients of Eqs. (3.15) and (3.16). ................................................................................. 62
Table 3. 2 The results of concentration-dependent of the Pitzer triple-ion interaction parameter ........ 63
Table 3. 3 Experimental results for the CO2 solubility in aqueous CaCl2, Na2SO4, MgCl2 and KCl
solutions at 323.15-423.15 K and 150 bar. ........................................................................... 64
Table 3. 4 Comparison of the model calculations with experimental data. ........................................... 74
Table 4. 1 Chemical composition of the natural Mt. Simon brine. ........................................................ 92
Table 4. 2 Chemical compositions of the synthetic Mt.Simon brine and Antrim Shale formation brines
and the corresponding synthetic NaCl+CaCl2 proxy brines. ................................................ 92
Table 4. 3 Experimental CO2 solubility results in the synthetic formation and NaCl+CaCl2 brines. .... 94
Table 4. 4 Brine density (g cm-3) correlation (Eq. (4.7)) at 298K and 1 bar. ......................................... 98
Table 4. 5 The parameters of Eq. (4.8) .................................................................................................. 99
Table 4. 6 The average absolute deviation of the PSUCO2 model calculated CO2 solubility in
NaCl+CaCl2 and NaCl brines from the experimental CO2 solubility data in synthetic Mt.
Simon and Antrim Shale formation brines. ....................................................................... 100
Table 4. 7 The absolute average deviations (AAD %) of model calculations from the experimental
data. .................................................................................................................................... 111
Table 4. 8 The components, key parameters, and the limitations of PSUCO2. ................................... 112
Table 5. 1 P-T-x matrix of CO2 solubility study for single-salt system. .............................................. 119
Table 5. 2 P-T-x matrix of CO2 solubility study for mixed-salt system. ............................................. 119
Table A 1 Parameters for Eqs. (A.10-A.11). ....................................................................................... 137
Table B 1 Constants of Eqs. (B.1) β (B.4) .......................................................................................... 141
Table B 2 Constants in Eqs. (B.5) β (B.6). ......................................................................................... 142
Table B 3 Constants of Eqs. (B.7) β (B.10). ....................................................................................... 143
Table B 4 Constants of Eq. (B.12) ...................................................................................................... 144
Table E 1 Original Experimental CO2 solubility data record for the CO2-H2O system. ..................... 153
Table E 2 Original Experimental CO2 solubility data record for the CO2-NaCl-H2O system. ........... 154
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Table E 3 Original Experimental CO2 solubility data record for the CO2-CaCl2-H2O system. .......... 157
Table E 4 Original Experimental CO2 solubility data record for the CO2-Na2SO4-H2O system. ....... 159
Table E 5 Original Experimental CO2 solubility data record for the CO2-MgCl2-H2O system. ......... 162
Table E 6 Original Experimental CO2 solubility data record for the CO2-KCl-H2O system. ............. 164
Table E 7 Original Experimental CO2 solubility data record for the CO2-synthetic formation brine
system ................................................................................................................................ 165
Table E 8 Original Experimental CO2 solubility data record for the CO2-synthetic NaCl+CaCl2 brine
system ................................................................................................................................. 167
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PREFACE
This dissertation consists of the three peer-reviewed research papers either published or submitted.
Haining Zhao is the first author on all three papers presented herein. All the experimental CO2 solubility
data reported in this dissertation except the data listed in Table 4. 3 Method 2 (4 data points) were collected
by the author, Haining Zhao. The experimental CO2 solubility data listed in Table 4.3 Method 2 were the
contribution made by Robert Dilmore, Douglas E. Allen, Sheila W. Hedges, and Yee Soong. The author
(Haining Zhao) developed the proposed PSUCO2 model by improving the previous published models of
Spycher et al. (2003), Spycher and Pruess (2005, 2010) and Akinfiev and Diamond (2010). All the figures
in this dissertation are original art work made by the author.
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ACKNOWLEDGMENTS
There are so many people I would like to thank for their contribution to this work. First of all, I
would like to express my deepest gratitude to my advisor, Dr. Serguei N. Lvov, for supporting and
providing me with the resources to pursue this meaningful research over the past four years, and for helping
and guiding me throughout the entire research process: experiment design, data analysis, model
development, and publications. I cannot list all the details here, but a few cases deserve this page.
In the year 2011, I had struggled for about half a year to get the experimental apparatus to work,
and after that I almost wasted 3 months and got incorrect measurements. I knew something was wrong but I
couldnβt figure it out at that moment. I told you (Dr. Lvov) that the time and money were wasted and the
obtained data were useless. Your generosity and encouragement helped me to overcome the frustrating
feelings and find a correct solution; in the year 2012, I was experiencing a hard time to making progress for
the model development, so you asked Dr. Nikolay N. Akinfiev for his computer code in order to help me
get out of trouble. Without your help and guidance, the development of the PSUCO2 model wouldnβt have
been accomplished. In the year 2013, you encouraged me to publish our research work to a prestigious
journal and we finally got there.
We experienced many difficulties and unexpected situations at each step towards making reliable
measurements and high quality modeling. At the moment Iβm going to leave your research group, to leave
my forever home EME at Penn State as well, when I look back over the past four years, I realize what huge
help and support you have provided for me and for my family. Without your dedication and constructive
instruction/guidance, as well as the support from the EME department, I would not have the opportunity to
do quality research work here. Additionally, without encouragement and financial support from you, the
on-line computation tool of the proposed PSUCO2 model would not have been possible.
Secondly, I would like express my sincere gratitude to the rest of my dissertation committee
members:
Dr. William D. Burgos (Professor in Charge of Graduate Programs, Professor of Civil &
Environmental Engineering, Penn State),
Dr. Li Li (Assistant Professor of Petroleum and Natural Gas Engineering, Penn State)
xiii
Dr. John Yilin Wang (Assistant Professor of Petroleum and Natural Gas Engineering, Penn
State)
Dr. Luis F. Ayala H. (Associate Department Head for Graduate Education, Associate
Professor of Petroleum and Natural Gas Engineering)
for their friendly guidance and thought-provoking suggestions that each of them offered to me
over the years.
This work was jointly-supported by the U.S. Department of Energy, National Energy Technology
Laboratory, the EMS Energy Institute, and the John and Willie Leone Family Department of Energy and
Mineral Engineering at the Pennsylvania State University. With the help of my advisor, Dr. Serguei N.
Lvov, several well-known experts reviewed parts of this dissertation (Chapters 2 to 4) and provided many
constructive suggestions/recommendations, which significantly improved the overall quality of my work.
Thirdly, I would like to express my sincere gratitude to the following experts:
Dr. Robert Dilmore (Research Engineer, Geosciences Division, National Energy
Technology Laboratory, U.S Department of Energy), for his time and patience to read through
the manuscript of Chapters 2 to 4 carefully and provide useful discussions, many constructive
suggestions, and detailed scientific and editorial corrections;
Dr. Alfonso Mucci (Professor, Department of Earth and Planetary Sciences, McGill
University), for his time and patience to read through the manuscript of Chapter 2 carefully,
and provided detailed scientific and editorial corrections/recommendations and comments;
Dr. Nikolay N. Akinfiev (Professor, Russian Academy of Sciences), for his time and patience
to read through the manuscript of Chapter 2 carefully and provide many constructive
suggestions; for his insight to theoretically pointed out a few weakness of Chapter 2; I
particularly thank him for sharing the source code of the AD2010 (Akinfiev and Diamond,
2010) model, which gives me a great help during the development of the PSUCO2 model;
Dr. Nicolas Spycher (Geological Scientist, Lawrence Berkeley National Laboratory), for his
time and patience to read through the manuscript of Chapter 2 carefully and provided many
constructive suggestions. I particularly thank him for allowing me use his computer code (the
SP2010 model) for the model comparison throughout the dissertation;
xiv
Dr. Larryn W. Diamond (Professor for Geochemistry and Petrology, University of Bern),
for his time and patience to read through the manuscript of Chapter 2 carefully, and for his
suggestion to compare the PSUCO2 model with a recent published model MZLL2013 (Mao
et al., 2013);
One anonymous reviewer, for his time and patience to read through the manuscript of Chapter
2 carefully and provided many constructive suggestions;
Dr. Sheila W. Hedges (National Energy Technology Laboratory, U.S Department of
Energy), Dr. Yee Soong (Research Group Leader, National Energy Technology Laboratory,
U.S Department of Energy), and Douglas E. Allen (Professor, Department of Geological
Sciences, Salem State University), for their time and efforts to read through the manuscript of
Chapter 4 carefully, and provided detailed scientific and editorial corrections and comments;
Dr. Andre Anderko (Managing Director and Chief Technology Officer, OLI System Inc.)
and OLI System Inc., for provided the powerful OLI Studio 9.0.6 software package to EMS
Energy Institute. I also thank Dr. Andre Anderko for his time and patience to read through the
manuscript of Chapter 2 and provided many useful suggestions;
Mr. Derek Hall (PhD Candidate, Penn State), for useful discussions and proof-reading the
part of Chapter 2.
In addition, I am sincerely grateful to:
Dr. Luis F. Ayala H
Dr. Turgay Ertekin (Head, John and Willie Leone Family Department of Energy and
Mineral Engineering Professor of Petroleum and Natural Gas Engineering, Penn State)
Dr. Zulima Karpyn (Associate Professor of Petroleum and Natural Gas Engineering, Penn
State)
Antonio Nieto (Associate Professor of Mining Engineering)
Dr. Zi-Kui Liu (Director, Center for Computational Materials Design, Professor of Materials
Science and Engineering, Penn State)
Dr. Serguei N. Lvov (Director, EMS Electrochemical Technologies Program, Professor of
Energy and Mineral Engineering and Materials Science and Engineering)
xv
Mr. Pichit Vardcharragosad (EME Teaching Asisstant, Ph.D. Candidate)
for the highest quality classes I have ever attended. From these wonderful teachers I have learned
valuable knowledge in the classes of reservoir simulation, hydrocarbon thermodynamics, gas reservoir
engineering, theory of flow through porous media, materials thermodynamics, geostatistics methods,
electrochemical energy conversion and theory of corrosion. All of this knowledge brought me to a broad
view of energy and mineral engineering, and have prepared me continue to explore in the area of petroleum
engineering or other energy-related areas with confidence. Thanks again to all the great professors in the
Department of Energy and Mineral Engineering.
I would also like to thank Dr. Mark Fedkin (Research Associate, Penn State), Dr. Justin Beck
(Postdoctoral Fellow, Penn State), and Derek Hall for their help in designing experimental apparatus and
constructing the experimental system.
Thanks to all my friends for the share of memorable occasions during my stay at Penn State!
Finally, I wish to express my deepest gratitude to my wife, my lovely son, and my parents, for
their love, supports and encouragements throughout my life.
1
CHAPTER 1
INTRODUCTION
2
CO2-brine system are the most naturally encountered fluid system in geological formations. CO2
and brine are considered immiscible fluids but they are mutually soluble. The dissolution of CO2 in
formation brine can cause the changes of brine density (usually increase), wettability, saturation, and pH.
The brine pH change due to the dissolution of CO2 will influence the reaction rate occurred at the brine-
rock interface. In addition, the solubility of H2O in the supercritical CO2-rich phase could be large at the
formation temperatures higher than 373 K. The formation dry-out (Pruess and MΓΌller, 2009) and solids
precipitation from CO2 injection into subsurface reservoir, which changes the formation porosity and
permeability, could occur when a large amount CO2 is injected into a high temperature and high salinity
formation. Therefore, the mass transfer between the CO2-rich and the aqueous phases will change the fluid
and rock properties for the involved formation. Knowledge of the mass transfer between the two fluid
phases (mutual solubilities) at geological temperatures and pressures is essential for us to model the various
geochemical and industrial processes for energy recovery (Figure 1. 1).
Oil & Gas Reservoir
Saline Aquifier
Natural CO2 Reservoir
Oil & Gas
Production
Rig
CO2-
Enhanced
Geothermal
Energy
ProductionWater & CO2
injection
CO2
injection
Figure 1. 1 CO2-brine system existed in several of engineered-natural systems, including oil and gas
reservoir, saline aquifer, geothermal reservoir and natural CO2 reservoir.
3
This study experimental measured CO2 solubility in NaCl, CaCl2, Na2SO4, MgCl2, KCl and
mixed-salt brines at 100-200 bar, 323-423 K and ionic strength up to 6 mol kg-1. The experimental data, as
well as the data collected from literature, are used for model development. The proposed PSUCO2 model is
able to overcome the deficiencies of the previously published models for their limitations in P-T-x range,
accuracy, and salt species.
While the studies of the CO2 solubility in aqueous NaCl solutions are abundant, in Chapter 2, this
study added new experimental data for the CO2-NaCl-H2O system at 150 bar, 323-423 K and 0-6 mol/kg
NaCl. By using all available experimental data in both the aqueous and the CO2-rich phases for the CO2-
NaCl-H2O, a π β πΎ type thermodynamic model is developed to accurately compute the mutual solubilities
for the CO2-NaCl-H2O system at 1-2000 bar, 273-573 K, and NaCl concentration up to saturation condition.
The detail experimental methods and theoretical framework for the proposed thermodynamic model can be
found in Chapter 2.
In Chapter 3, the experimental CO2 solubility data in aqueous CaCl2, Na2SO4, MgCl2, KCl
solutions are given at 150 bar, 323.15-423.15 K, and total ionic strength up to 6 mol/kg. Using the newly
obtained experimental data, the thermodynamic model developed in Chapter 2 for the CO2-NaCl2-H2O
system are then extended to include the influence of different salt species on dissolved CO2 in the aqueous
phase, but the model still not be able to calculate CO2 solubility in mixed-salt solution or natural formation
brine.
In Chapter 4, based on the experiences and results gained from Chapters 2 and 3, in order to make
the model computable for CO2 solubility in natural formation brines, the additivity rule of the Setschenow
coefficients of the individual ions (Na+, Ca2+, Mg2+, K+, Cl-, and SO42-) is successfully used to calculate
CO2 solubility in natural formation brine at elevated temperatures and pressures. The modeling results are
validated by newly obtained experimental CO2 solubility data in natural and synthetic formation brines, and
in synthetic NaCl+CaCl2 brines.
Chapter 5 summarizes the principle findings as a conclusion of this dissertation.
4
CHAPTER 2
SOLUBILITY OF CO2 IN AQUEOUS NaCl SOLUTIONS1
1 The text for this chapter was originally prepared for the publication as "Haining Zhao, Mark V. Fedkin,
Robert M. Dilmore, and Serguei N. Lvov (2014) Carbon dioxide solubility in aqueous solutions of sodium
chloride at geological conditions: Experimental results at 323.15, 373.15, and 423.15 K and 150 bar and
modeling up to 573.15 K and 2000 bar, Geochimica et Cosmochimica Acta,
doi:10.1016/j.gca.2014.11.004".
5
Abstract
A new experimental system was designed to measure the solubility of CO2 at pressures and
temperatures (150 bar, 323.15-423.15 K) relevant to geologic CO2 sequestration. At 150 bar, new CO2
solubility data in the aqueous phase were obtained at 323.15, 373.15, and 423.15 K from 0 to 6 mol kg-1
NaCl(aq) for the CO2-NaCl-H2O system. A Ξ³ β Ο (activity coefficient β fugacity coefficient) type
thermodynamic model is presented for the calculation of both the solubility of CO2 in the aqueous phase
and the solubility of H2O in the CO2-rich phase for the CO2-NaCl-H2O system. Validation of the model
calculations against literature data and other models (MZLL2013, AD2010, SP2010, DS2006, and OLI)
show that the proposed model is capable of predicting the solubility of CO2 in the aqueous phase for the
CO2-H2O and CO2-NaCl-H2O systems with a high degree of accuracy (AAD < 3.9%) at temperatures from
273.15 to 573.15 K and pressures up to 2000 bar. A comparison of modeling results with experimental
values revealed a pressure-bounded "transition zone" in which the CO2 solubility decreases to a minimum
then increases as the temperature increases. CO2 solubility is not a monotonic function of temperature in
the transition zone but outside of that transition zone, the CO2 solubility is decrease or increase
monotonically in response to increased temperature. A web-based CO2 solubility computational tool can be
accessed via the link: www.carbonlab.org/psuco2/.
6
2.1 Introduction
The CO2-H2O and the CO2-NaCl-H2O fluid systems play an important role in various earth system
and engineered geologic processes (Schmidt and Bodnar, 2000; Dubacq et al., 2013). They represent the
most commonly encountered fluids in geological environments (Hu et al., 2007). In many technical
applications, such as CO2 storage and sequestration, CO2-enhanced oil recovery, and CO2-enhanced
geothermal systems (Spycher and Pruess, 2010), dissolution, precipitation, and ion-exchange processes
associated with these fluid systems can potentially impact the behavior of geologic media. Therefore, our
knowledge of the phase equilibria and properties of these two systems over a wide pressure-temperature-
composition (P-T-x) range is essential in the development of models for various geochemical and industrial
processes.
Numerous studies have contributed to phase equilibrium data for CO2-bearing binary and ternary
systems. The main goal of many of those works has been to measure the CO2 solubility in the aqueous
phase and the water solubility in the CO2-rich phase (e.g. TΓΆdheide and Franck, 1963). In this study,
research was oriented to CO2 solubility experiments in support of geological CO2 storage applications. The
solubility of CO2 in formation brines is a critical parameter to estimate the CO2 storage capacity, the
mechanism of trapping over site life, and the potential reactivity of the fluid-rock interface, as well as to
understand the fate of the dissolved CO2 in subsurface formations. Previous data (reported in this work)
from experimental CO2 solubility measurements in aqueous electrolyte solutions, along with reliable phase
equilibrium models can serve as the foundation for modeling a variety of CO2 storage and utilization
processes.
Hu et al. (2007) have pointed out that many cubic equations of state (EoS) and virial EoS
truncated at the second or third virial coefficient are adequate to predict the phase equilibria properties for
the CO2-H2O and CO2-NaCl-H2O systems at low to medium pressures (up to 500 bar), but the deviations of
these models from experimental values at high pressures were found to be unacceptable (Hu et al., 2007;
Spycher et al., 2003). Spycher and Pruess (2010) model allows computation of both the CO2 solubility in
the aqueous phase and the H2O solubility in the CO2-rich phase with high accuracy, but their model is
limited to pressures up to 600 bar. Akinfiev and Diamond (2010) developed a highly accurate CO2
7
solubility model for the CO2-H2O and CO2-NaCl-H2O systems, but the applicable temperatures and
pressures of their model are limited to 251.15-373.15 K and 1-1000 bar. In addition, Akinfiev and Diamond
(2010) model only provides a rough estimate of water solubility in the CO2-rich phase. The model
developed by Duan et al. (2006) allows the CO2 solubility in NaCl(aq) to be calculated up to 533.15 K,
2000 bar, and 4.5 mol kg-1 of NaCl(aq), but their model is generally less accurate than the Akinfiev and
Diamond (2010) and Spycher and Pruess (2010) models (see section 2.4.4, Table 2. 10). Moreover, Duan et
al.'s (2006) model does not allow calculation of the H2O solubility in the CO2-rich phase. The commercial
software OLI studio 9.0.6 (Springer et al., 2012) performs well at predicting the H2O solubility in the CO2-
rich phase at low to moderate pressures, but its estimates of the CO2 solubility in the aqueous phase are less
accurate than those of other models mentioned above - Akinfiev and Diamond (2010), Spycher and Pruess
(2010) and Duan et al. (2006) (see section 2.4.4, Table 2. 10 and Table 2. 11). Additionally, Mao et al.
(2013) developed a CO2 solubility model for the CO2-NaCl-H2O system in the temperature range of
273.15-723.15 K, pressures from 1-1500 bar and NaCl molality from 0-4.5 mol kg-1. Mao et al.'s (2013)
model is in excellent agreement with experimental CO2 solubility in the aqueous phase (see section 4.4,
Table 2. 10, Table 2. 12 and Table 2. 13), but this model does not allow calculation of H2O solubility in the
CO2-rich phase. Note also that these models cannot be used for reliable phase equilibrium calculations in
systems containing K+, SO42β (e.g. CO2-KCl-H2O and CO2-Na2SO4-H2O) at elevated temperatures and
pressures. Detailed comparisons between the model developed in this study and previously published
models are provided in section 2.4.4.
In this Chapter, an improved πΎ β π (activity coefficient - fugacity coefficient) type phase
equilibrium model is presented for the CO2-NaCl-H2O system. There are three major improvements in the
model relative to the previous models of Spycher et al. (2003) and Spycher and Pruess (2010). First, the
binary interaction parameter (kCO2βH2O) of the mixing rule was considered to be dependent on temperature
and pressure. The parameter kCO2βH2O in the mixing rule was carefully tuned against the experimental H2O
solubility in the CO2-rich phase (TΓΆdheide and Franck, 1963) at temperatures of 273.15-573.15 K and
pressures up to 2000 bar. This adjustment significantly improved the calculated water solubility in the CO2-
rich phase, as well as estimates of the CO2 solubility in the aqueous phase at high temperatures and
pressures. Second, in Eq. (2.1), the partial molar volume of CO2 at infinite dilution in water (vΜ CO2) was
8
treated as an adjustable parameter to fit the experimental CO2 solubility in the aqueous phase by TΓΆdheide
and Franck (1963). Third, the Pitzer activity model was used to calculate the activity coefficient of the
dissolved CO2 and osmotic coefficient of water. The triple-ion interaction parameter (ΞΎnca, see section 2.4.2
Eq. (2.10)) in the Pitzer model was considered to be dependent on temperature and NaCl concentration.
ΞΎnca values were determined using new experimental CO2 solubility data presented herein, assuming that
the pressure effect on this parameter can be neglected. These improvements allow the model to return more
accurate estimates of the activity of dissolved CO2 and the water osmotic coefficients for concentrated
NaCl(aq) as compared to the previous models of Spycher and Pruess (2010) and Duan et al. (2006).
The improved CO2 solubility model can reproduce literature data for the CO2-NaCl-H2O and CO2-
H2O systems with an overall average absolute deviation (AAD) of less than 3.9% over temperatures from
273.15 to 573.15 K and pressures up to 2000 bar. In Section 4.4, we compare our model with the models of
Mao et al. (2013), Akinfiev and Diamond (2010), Spycher and Pruess (2010), Duan et al. (2006) and OLI
Studio 9.0. This comparison shows that the model developed here provides reliable estimates of both the
solubility of CO2 in the aqueous phase and the solubility of H2O in the CO2-rich phase.
2.2 Review of the experimental approaches
In this and many previous studies, a high pressure/temperature-controlled stainless steel autoclave
with agitation was used to investigate the gas-liquid phase equilibria. The typical apparatus for such
measurements is described in Prutton and Savage (1945), Takenouchi and Kennedy (1964), Malinin and
Savelyeva (1972). The experimental systems used by Wiebe and Gaddy (1939), Nighswander et al. (1989),
and Stewart and Munjal (1970) are more complicated, but, in general, operate in a similar manner. For a
phase equilibrium experimental study, the autoclave is loaded with a CO2-brine mixture and the solution is
stirred for 6 to 24 hours until equilibrium is reached. The autoclave temperature is measured by a
thermocouple, while the pressure is measured using a pressure gauge or transducer. Generally, the aqueous
phase sample is taken from the autoclave to perform the CO2 solubility measurement. During the sampling
process, the pressure in the system should remain constant. Alternatively, static view-cell 'synthetic'
9
methods without sampling are employed to determine the CO2 solubility (Rumpf and Maurer, 1993; PΓ©rez-
Salado Kamps et al., 2007) and the dew-point of H2O in the CO2-rich phase (Mather and Franck, 1992).
There are two common methods to measure the CO2 solubility in a liquid sample. In the first
method, dissolved CO2 in a sample cell is expanded into a temperature-controlled pressure vessel, and the
mass of CO2 is determined volumetrically (Wiebe and Gaddy, 1939; Prutton and Savage, 1945;
Nighswander et al., 1989; Liu et al., 2011). In the second method, dissolved CO2 in a sample cell is released
from the aqueous phase and absorbed in a trap with NaOH(aq) or Ba(OH)2(aq) (Takenouchi and Kennedy,
1964, 1965; Stewart and Munjal, 1970; Malinin and Savelyeva, 1972; Rochelle and Moore, 2002). In
Method (1), the amount of CO2 is determined from the PVT changes in the pressure vessel before and after
the gas expansion. This method was used by Kim et al. (2008) to measure the mass of the injected CO2 into
the autoclave. Liu et al., (2011) also demonstrated the effectiveness of this method. The method can
precisely sense the mass change within a pressure cell through the variation in pressure and temperature.
Therefore, this method was selected for sample analysis in this study. In Method (2), the dissolved CO2 is
converted to CO32- in an alkaline absorbent. As long as the base is present in excess, the CO3
2- is stable
(Rochelle and Moore, 2002). The amount of trapped CO2 can be determined by a standard HCl titration of
the excess base absorbent.
Stainless
Steel
autoclave
Sampling
No
sampling
CO2 expansion
CO2 absorbed by
base absorbent
Gas phase and
aqueous phase
circulation
CO2 expands at
constant pressure
CO2 expands at
constant volume
Standard HCl titration
Gas chromatography
Ultra-low temperature water trap
1. Optical cell is needed to observe the phase boundary
2. The exact amount of H2O and CO2 loaded into system
should be known
3. The exact volume of CO2 phase is needed for the CO2
solubility calculations
Experimental system for CO2-
brine phase equilibria
Sample analysis for determining the CO2
solubility in aqueous phase
Figure 2. 1 Main approaches used to measure the CO2 solubility in an aqueous phase. The shaded boxes
represent the method implemented in this study.
10
The main approaches to sample and measure the CO2 solubility in the aqueous phases are
summarized in Figure 2. 1. Other methods such as the solid absorbent system (Ellis and Golding, 1963) and
heat flow calorimetry (Koschel et al., 2006) are not widely used to measure the CO2 solubility in the
aqueous phase due to the complexity of the systems and insufficient accuracy of the measurements.
2.3 Experimentation
2.3.1 Experimental P-T-x conditions
In this work, data from all available literature for the CO2-NaCl-H2O system at temperatures from
273.15 to 573.15 K and pressures up to 1500 bar were reviewed in order to identify possible gaps in the
experimental P-T-x matrix. A large amount of CO2 solubility data compiled by Scharlin (1996) was also
included in our data screening. New CO2 solubility measurements were performed in P-T-x space where
little or no data are available.
273.15
T / K
0
50
150
100
200
P /
ba
r
34.85
~Depth 1.0 km
~Depth 1.8 km
Critical point
Supercritical
region
CO2-rich phase
Aqueous
phase
Supercritical boundary
Basins Selected experimental points Critical point
Supercritical boundary Depth indication
323.15 373.15 423.15
Figure 2. 2 The common envelope of CO2 phase behavior in sedimentary basins along with selected
experimental pressure and temperature conditions (150 bar, 323.15, 373.15 and 423.15 K) in this study
(shown by solid circles).
11
A simplified approach proposed by Bachu (2003) was employed in this study to estimate a range
of temperatures and pressures of interest (Figure 2. 2). With respect to the salt concentration range, the
USGS-produced water database2 served to select the concentration of NaCl solutions. In addition, we took
into account the McIntosh et al. (2004) study where eighty five formation brine samples from the Michigan
Basin were collected and analyzed. The total ionic strength (Eq. (A9)) of formation brines in the Michigan
Basin was shown to range from zero to around 8 mol kg-1, with chloride, sodium, and calcium accounting
for more than 95 % of the ions in these brines (McIntosh et al. 2004); the composition of the reservoir
brines is dominated by NaCl. Based on the above discussion, the ionic strength of the NaCl(aq) solutions
for our CO2 solubility experiments was set to range from 0 to 6 mol kg-1.
2.3.2 Chemicals
The carbon dioxide used in all experiments was Coleman Instrument grade with a minimum purity
of 99.99 %. The water was purified by a Milli-Q system and degassed by boiling before loading into the
autoclave. The NaCl(aq) solutions were prepared using Milli-Q water (with conductivity below 610-6 S m-
1) and ACS reagent grade Sodium Chloride (J.T. Baker, 3624-01).
2.3.3 Apparatus
A schematic of the experimental apparatus is shown in Figure 2. 3. The setup includes a high
pressure liquid-CO2 pump (SFT-10), a vacuum pump (LEYBOLD TRIVAC D2A), a 600-ml stainless steel
Parr Instrument Co. autoclave with a Teflon liner, and a 40-ml stainless steel liquid sample cell attached to
the autoclave. The autoclave was enclosed in a heating mantle, and the contained solution was stirred by a
four-blade aluminum impeller with a Parr magnetic drive. Temperature and the impeller rotation speed
2 http://energy.cr.usgs.gov/prov/prodwat/
12
were controlled by the Parr 4842 controller. The autoclave was equipped with ports for both supercritical
CO2 and aqueous phase sampling from the top of the vessel.
An Omega PX602 pressure transducer with an accuracy of 0.45 % ranging from 0 to 345 bar was
used to monitor the system pressure. A J-type thermocouple was introduced from the top of the autoclave
into the aqueous phase to measure the temperature of the solution. Calibration of the thermocouple was
performed in both boiling DI water and an ice-water mixture prior to use. The uncertainty of the
temperature measurements was less than Β±1.0 K over the temperature range of interest (323.15 to 423.15
K).
V1 V2
V3 V4
V5
V6
V7
V8
8
2
9
10121315
7
6
4
5
3
1
11
14
Figure 2. 3 Schematic diagram of the experimental apparatus: (1) 0 to 345 bar pressure transducer, (2)
CO2-rich phase sample cell, (3) sample line for the CO2-rich phase, (4) rupture disc, (5) CO2-rich phase, (6)
thermocouple, (7) aqueous solution, (8) liquid phase sample cell, (9) liquid CO2 pump, (10) liquid CO2
cylinder, (11) liquid CO2 inlet, (12) sample line for the aqueous phase, (13) impeller, (14) heat mantle, (15)
Teflon liner.
2.3.4 Procedure
Degassed Milli-Q water was used in all experiments. Sodium chloride was placed into the
autoclave before loading the water. The autoclave was thoroughly evacuated using a vacuum pump and
water was loaded into the autoclave under vacuum. The autoclave was then heated to the desired
13
temperature. Once the experimental temperature was achieved, the liquid CO2 was pumped into the
autoclave to the desired pressure. Subsequently, the contents of the autoclave were agitated by the impeller
at a speed of about 60 RPM (revolutions per minute). Initial equilibrium was assumed to be reached when
no cell pressure variation was observed over a 12-hour period. Before taking the first sample, a small
amount of liquid sample was drawn and discarded to purge the sample line.
Whereas either a water-rich or a CO2-rich sample can be taken using the developed system, this
study focused on the aqueous phase. The sample cell was first evacuated to a vacuum pressure of about
0.02 bar. At high pressures, withdrawing fluid from the autoclave can result in a significant reduction of the
total pressure of the system. Hence, the pressure drop during the sampling process was compensated for by
pumping additional liquid CO2 into the CO2-rich phase at a flow rate of about 20 ml min-1. Pressure
fluctuations inside the autoclave were kept to within Β±2 bar of the set experimental pressure, and the
pumped liquid CO2 is assumed not to have disrupted the aqueous phase equilibrium due to the following
reasons. First, the liquid CO2 was injected in the upper layer of the CO2-rich phase, whereas the aqueous
sample was taken from the bottom of the autoclave (Figure 2. 3), so the pumped CO2 does not directly
contact the aqueous sample in the bottom of the autoclave. Second, the sampling time was very short (less
than 60 seconds) so there was no, or negligible, disturbance on the aqueous phase equilibrium.
After sample withdrawal was complete, the sample cell was disconnected and weighed on an
electronic balance (Veritas L403i) with an accuracy of Β±0.001g. The mass of the sample was defined by
weighing the sample cell before and after sampling. The sample cell was then connected to a 300-ml
pressure cell, which was used to determine the amount of dissolved CO2. The pressure cell volume was
calibrated by filling the cell with distilled water and measuring the mass when it was full and empty at a
well-defined temperature. The water density was calculated using IAPWS-95 EoS (Wagner and PruΓ,
2002).
The pressure cell was first evacuated by a vacuum pump and the dissolved CO2 was slowly
released into the pressure cell from the sample cell. The mass of the dissolved CO2 was determined by the
pressure and temperature change before and after CO2 expansion. Three consecutive expansions were
sufficient to determine the total amount of CO2 dissolved in the sample cell. The remaining CO2 in the
sample cell after three expansions was estimated by Henry's law (see section 2.4.1, Eq. (2.3)) and was less
14
than 0.0007 mol kg-1, which is negligible compared to the experimental error. The EoS for pure CO2
developed by Span and Wagner (1996) was used to calculate the mass of CO2 in the pressure cell after each
expansion. Finally, the CO2 solubility in the aqueous phase was obtained by relating the mass of the total
released CO2 to the total mass of the aqueous sample.
A small amount of water vapor might be transferred to the pressure cell during the CO2 expansion,
which could introduce a small error (approximately 0.0009 mol kg-1 CO2) in the CO2 solubility
measurement. To eliminate the error caused by water vapor during the sample analysis, the partial pressure
of water vapor in the CO2-H2O gas mixture was estimated by the model of Spycher et al. (2003) and
subtracted from the total pressure of the pressure cell. The error analysis based on the error propagation
theory showed that the instrumental error of the measurement of CO2 solubility was around 0.7 % and the
random error was from 0.5 to 4.5 %. The detailed error analysis procedure is described in Appendix C.
2.3.5 Validation of the obtained data
A temperature and pressure of 323.15 K and 100 bar were selected for the CO2-H2O system, and
several P-T-x conditions for the CO2-NaCl-H2O system, to validate the reliability of our apparatus and
procedures. In Table 2. 1 and Table 2. 2, the comparisons show that the experimental CO2 solubility at
these P-T-x conditions was in close agreement with the experimental solubility values found in the
literature, and was also consistent with CO2 solubility models (Mao et al., 2013; Akinfiev and Diamond,
2010; Spycher and Pruess, 2010; Duan et al., 2006; OLI Studio 9.0). Subsequently, the names of the
models are abbreviated as MZLL2013 for Mao et al. (2013), AD2010 for Akinfiev and Diamond (2010),
SP2010 for Spycher and Pruess, (2010), DS2006 for Duan et al. (2006) model, and OLI for the model
adopted in OLI Studio 9.0 software.
From Table 2. 1 and Table 2. 2, one can see that the measured CO2 solubilities are in good
agreement with both published experimental and model data. Thus, the reliability of the experimental
technique was confirmed before further measurements were performed at the target P-T-x conditions in the
CO2-NaCl-H2O system.
15
Table 2. 1 Comparison of measured CO2 solubility in the binary CO2-H2O system at 323.15 K and 100 bar
with literature data and model calculations.
T / K P / bar References mCO2 / mol kg-1
Experimental measurements
323.15 100 Bando et al. (2003) 1.116 Β± 0.033
323.15 101 Liu et al. (2011) 1.133(a)
323.15 101 Dohrn et al. (1993) 1.176(a)
323.15 101.3 Briones et al. (1987) 1.180(a)
323.15 100.9 Bamberger et al. (2000) 1.162 Β± 0.017
323.15 101.3 DβSouza et al. (1988) 1.121(a)
323.15 101.3 Wiebe and Gaddy (1939) 1.151(a)
323.15 100 This study 1.151 Β± 0.028
Modeling(b)
323.15 100 DS2006 1.148
323.15 100 AD2010 1.156
323.15 100 SP2010 1.136
323.15 100 OLI Studio 9.0 1.146(c)
323.15 100 MZLL2013 1.147
323.15 100 This model 1.151 (a)The experimental data without 'Β±' mean that the error was not given in the references. (b)DS2006, AD2010, SP2010 and MZLL2013, respectively, stand for the model developed by Duan et al.
(2006), Akinfiev and Diamond (2010), Spycher and Pruess (2010) and Mao et al. (2013) (b)Calculations made by OLI are under the following conditions: (1) enable the second liquid phase, (2) use
MSE model, (3) stream inflows contains 55.5082 mol water and 5 mol CO2.
16
Table 2. 2 Experimental results of CO2 solubility in NaCl(aq) compared with literature data (collected at the same P-T-x conditions) and model calculations.
T / K P /
bar
π¦ππππ₯ /
mol kg-1
This study
π¦πππ /
mol kg-1
Literature
π¦πππ /
mol kg-1
References
Model calculations(a), π¦πππ / mol kg-1
This
study
OLI(b) AD201
0
SP2010 DS200
6
MZLL2
013
323.15 150 0.529 1.114Β±0.017 1.102 Bando et al. (2003) 1.108 1.150 1.117 1.108 1.095 1.123
373.15 48 0.998 0.361Β±0.006 0.361 Malinin and Kurovskaya (1975) 0.377 0.358 0.368 0.369 0.370 0.376
413.15 92.01 5.999 0.278Β±0.014 0.288 Rumpf et al. (1994) 0.276 0.259 0.280 0.292 - -
Average absolute deviation (AAD %) of model calculations from the experimental CO2
solubility data
1.88 3.63 1.03 2.59 2.05 2.48
(a)OLI: OLI Studio 9.0, which is a simulation software for electrolyte chemistry developed by OLI Systems Inc. (Springer et al., 2012); AD2010: Akinfiev and
Diamond (2010); SP2010: Spycher and Pruess (2010); DS2006: Duan et al. (2006). (b)Calculations made by OLI are under the following conditions: (1) enable the second liquid phase, (2) use MSE model, (3) stream inflows contains 55.5082 mol
water and 5 mol CO2
17
2.3.6 Measured CO2 solubilities
The measured CO2 solubilities (πCO2) at 150 bar and 323.15-423.15 K for the CO2-NaCl-H2O
system at NaCl(aq) concentrations between 0 and 6 mol kg-1 are listed in Table 2. 3. Figure 2. 4 shows that
the measured CO2 solubility data fall closely in line with the data from Koschel et al. (2006), with the
model calculations of SP2010, and the model developed herein. In Figure 2. 5, the models AD2010,
SP2010, DS2006 and OLI were verified against new experimental data reported herein. The experimental
CO2 solubility data obtained in this study are in excellent agreement with both the MZLL2013 and AD2010
models at 150 bar and temperatures from 323.15 to 423.15 K. Given that the accuracy of the AD2010
model is claimed to be 1.6 % at temperatures from 251.15 to 373.15 K and pressures up to 1000 bar, it is
striking that deviations of the AD2010 model from experimental data at 423.15 K are still within its
computation error. The SP2010 model results also agree well with the measured CO2 solubility data
obtained in this study. The deviation of the DS2006 model results from our experimental data increases
with increasing NaCl molality because the model is limited to a NaCl concentration of 4.5 mol kg-1. The
OLI studio 9.0 model also performs well in predicting CO2 solubility in aqueous NaCl solutions. In general,
the models developed thus far agree well with the experimental CO2 solubility obtained in this work. The
average absolute deviations of the calculated values from our CO2 solubility data (given in Table 2. 3)
confirm this conclusion.
18
Table 2. 3 Experimental CO2 solubility measurements in NaCl(aq) at 150 bar and temperatures from 323.15 to 423.15 K. The experimental data are compared
with model calculations in terms of the average absolute deviation (AAD %) between calculated and experimental results.
Experimental CO2 solubility at 150 bar
(This study)
Calculated CO2 solubility: mCO2 / mol kg-1
T / K πππππ₯ /
mol kg-1
ππππ /
mol kg-1
π ππ«ππ§ππ¨π¦ /
mol kg-1(a)
This study OLI(b) AD2010 SP2010 DS2006 MZLL2013
323.15 0 1.245 0.006 1.244 1.271 1.256 1.233 1.223 1.253
323.15 1 1.016 0.010 1.016 1.055 1.017 1.012 0.995 1.024
323.15 2 0.859 0.007 0.853 0.889 0.849 0.845 0.822 0.853
323.15 3 0.734 0.015 0.727 0.761 0.724 0.716 0.690 0.723
323.15 4 0.623 0.006 0.629 0.661 0.629 0.618 0.587 0.625
323.15 5 0.551 0.005 0.552 0.582 0.553 0.541 - -
323.15 6 0.498 0.004 0.492 0.520 0.493 0.481 - -
AAD (%) at 323.15 K 0.59 4.17 0.80 1.66 3.96 0.79
373.15 0 1.020 0.006 1.012 1.020 1.010 1.001 0.984 1.032
373.15 1 0.836 0.008 0.842 0.839 0.827 0.819 0.808 0.843
373.15 2 0.706 0.007 0.714 0.704 0.699 0.686 0.675 0.704
373.15 3 0.618 0.006 0.614 0.600 0.603 0.588 0.575 0.601
373.15 4 0.527 0.005 0.536 0.520 0.529 0.515 0.499 0.526
373.15 5 0.469 0.005 0.474 0.458 0.471 0.463 - -
373.15 6 0.427 0.009 0.426 0.408 0.425 0.425 - -
AAD (%) at 373.15 K 0.90 1.67 0.98 2.26 4.75 1.03
423.15 0 1.001 0.007 0.994 0.975 0.969 1.028 0.961 0.992
423.15 1 0.800 0.017 0.794 0.794 0.793 0.824 0.780 0.798
423.15 2 0.647 0.018 0.660 0.659 0.670 0.679 0.647 0.659
423.15 3 0.566 0.025 0.565 0.558 0.578 0.577 0.549 0.560
423.15 4 0.498 0.010 0.494 0.480 0.507 0.503 0.476 0.488
423.15 5 0.440 0.004 0.438 0.419 0.451 0.450 - -
423.15 6 0.390 0.007 0.391 0.370 0.407 0.414 - -
AAD (%) at 423.15 K 0.74 2.87 2.62 3.12 2.81 1.26
Overall AAD (%) 0.74 2.91 1.47 2.35 3.84 1.03 (a)Ξ΄mrandom is the random error estimated on molality scale. The instrumental error was determined to be about 0.7 % of the measured values by application of
error propagation theory, with the procedure description detailed in the supplemental information; the Ξ΄mrandom was determined by repeated measurements at
each given P-T-x condition. (b)Calculations made by OLI are under the following conditions: (1) enable the second liquid phase, (2) use MSE model, (3) stream
inflows contains 55.5082 mol water and 5 mol CO2
19
P / bar
25 50 75 100 125 150 175 200 225
mC
O2 / m
ol kg
-1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
SP2010
This model
This study
323.15 K, 1 mol/kg NaCl
323.15 K, 3 mol/kg NaCl
373.15 K, 1 mol/kg NaCl
373.15 K, 3 mol/kg NaCl
323.15 K, 1 m NaCl
323.15 K, 3 m NaCl
373.15 K, 1 m NaCl
373.15 K, 3 m NaCl
Koschel et al., 2006
Figure 2. 4 Comparison of experimental CO2 solubility in aqueous NaCl solutions (1 and 3 mol kg-1 NaCl)
at 323.15 and 373.15 K obtained in this study and values obtained by Koschel et al. (2006). ππππ is the
CO2 molality in the aqueous phase; the solid symbols stand for the experimental data of Koschel et al.
(2006), whereas the open symbols represent the experimental data obtained in this work at 150 bar. The
dash-dot lines are the results from the SP2010 model; the solid lines represent the results of the model
developed in this work.
mNaCl
/ mol kg-1
0 1 2 3 4 5 6
mC
O2 / m
ol kg
-1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
This model
This study
Malinin and Savelyeva,1972
OLI
This model and AD2010 are overlapped here
DS2006
SP2010
323.15 K
150 bar
48 bar
AD2010
OLI
(a) 323.15 K
20
mNaCl
/ mol kg-1
0 1 2 3 4 5 6
mC
O2 / m
ol kg
-1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
This model
This study
Malinin and Kurovskaya, 1975
373.15 K
DS2006
OLI
SP2010
AD2010
This model
OLI
150 bar
48 bar
(b) 373.15 K
mNaCl / mol kg-1
0 1 2 3 4 5 6
mC
O2 / m
ol kg
-1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
This model
This study
Malinin and Kurovskaya, 1975
423.15 K
150 bar
48 bar
SP2010
DS2006
This model
SP2010
DS2006
OLIThis model
AD2010
(c) 423.15 K
Figure 2. 5(a-c) Comparison of measured CO2 solubility with model calculations at (a) 323.15 K, (b)
373.15 K, and (c) 423.15 K at 150 bar and concentrations of NaCl(aq) up to 6 mol kg-1. AD2010: Akinfiev
and Diamond (2010); SP2010: Spycher and Pruess (2010); DS2010: Duan et al. (2006); OLI: OLI Studio
9.0.6. The MZLL2013 model is almost same with this model, so it was not shown in figure for the purpose
of clarity. Use of AD2010 at T > 373.15 K, as done in Figure 2.5(c), is outside the nominal validity of the
model stated by Akinfiev and Diamond (2010).
21
2.4. Thermodynamic model of the CO2-NaCl-H2O system
2.4.1 Thermodynamic framework for vapor-liquid phase equilibrium
The thermodynamic equilibrium for the CO2-NaCl-H2O system can be described in terms of the
extended Henry's law for CO2 dissolved in aqeuous solutions with NaCl(aq) (Rumpf and Maurer., 1993) or
KCl(aq) (PΓ©rez-Salado Kamps et al., 2007):
ππΆπ2π¦πΆπ2π = ππ»,πΆπ2π exp[
οΏ½Μ οΏ½πΆπ2(πβππ€π )
π π]ππΆπ2 (2.1)
and by the extended Raoult's law for water:
ππ»2ππ¦π»2ππ = ππ€π ππ€
π exp[οΏ½Μ οΏ½π€(πβππ€
π )
π π]ππ»2π (2.2)
where yCO2andyH2O are, respectively, the mole fraction of CO2 and H2O in the CO2-rich phase. In Eqs. (2.1)
and (2.2), the reference state for the chemical potential of water is chosen to be the pure liquid at the system
temperature and pressure, whereas the chemical potential of dissolved CO2 (or other ionic species) is a
hypothetical, ideal Henryan (infinitely diluted) 1 mol kg-1 solution of the solute in pure water at the
temperature and pressure of the system (PΓ©rez-Salado Kamps et al., 2007). The pure water vapor pressure
(ππ€π ) and the fugacity coefficient of pure vapor water (ππ€
π ) were calculated using the IAPWS-95 equation of
state (EoS) given by Wagner and PruΓ (2002). The parameter οΏ½Μ οΏ½πΆπ2 in Eq. (2.1) was determined by fitting
model calculated results to reliable experimental data. The values of οΏ½Μ οΏ½πΆπ2 are presented in Table 2. 4. The
partial molar volume of water οΏ½Μ οΏ½π€, was approximated by the molar volume of saturated liquid water, π£π€π ,
which was also calculated using the IAPWS-95 EoS. In Eq. (2.1), ππ»,πΆπ2π is Henry's constant (molality scale)
of carbon dioxide in pure water determined from the experimental CO2 solubility data in pure water at
temperatures up to 573.15 K. In order to achieve the best possible results over a wide range of pressures
(from 1 to 2000 bar) and temperatures (from 273.15 to 573.15 K), Henry's constant was fitted separately for
22
two distinct regions (Figure 2. 6, and Table 2. 5): (1) below 2 bar and temperatures between 273.16 and
363.15 K, and (2) the remaining region of temperatures up to 573.15 K and pressures up to 2000 bar. The
expression for ππ»,πΆπ2π is as follows:
ln(ππ»,πΆπ2π ) = π + π (
π
ππ) + π (
ππ
π) + πln(π/ππ) (2.3)
where Tc = 647.096 K is the critical temperature of water; a, b, c, and d are empirical parameters given in
Table 2. 5.
Table 2. 4 The results of οΏ½Μ οΏ½πͺπΆπ (cm3 mol-1) determined by this model.
T / K P / bar
200 300 400 500 1000 1500 2000
278.15 32.90 32.35* 31.81* 31.26 29.30 30.26 30.26
323.15 32.90 32.35* 31.81* 31.26 29.30 30.26 30.30
373.15 35.42 33.80* 32.19* 29.60 29.67 30.30 30.55
423.15 36.20 34.35* 32.05* 30.65 33.18 32.95 32.87
473.15 37.00 35.08* 33.15* 31.23 33.57 33.11 33.25
523.15 27.80 26.27* 24.73* 23.2 24.66 27.15 28.90
533.15 33.80 16.50* 22.00* 20.75 24.20 24.44 25.44
538.15 43.86 16.50* 22.00* 20.75 22.72 22.08 17.97
540.15 46.71 16.50* 22.00* 20.75 20.29 18.60
541.15 47.75 16.50 22.00 20.75 18.68
543.15 49.23 14.40 20.10 18.50 17.49
548.15 51.40 16.50 17.34 17.36 9.05
573.15 77.50 15.60 13.40 11.85 *Indicates the data are interpolated by the method described in Table 2. 9. Other data in the table are
obtained by using the experimental CO2 solubility reported by TΓΆdheide and Franck (1963).
Table 2. 5 Parameters of Henry's constant Eq. (2.3).
P / bar T / K a b c d
1-2 273.15-363.15 2.77716Γ102 -3.62801Γ102 5.77716Γ101 3.00135Γ102
2-2000 273.15-573.15 7.25021 1.15385Γ101 -1.51174Γ101 -3.05448Γ101
23
Reduced temperature Tr = Tk / Tcr(H2O)
0.4 0.5 0.6 0.7 0.8 0.9
ln(k
o
H,C
O2)
2.5
3.0
3.5
4.0
4.5
This model (P>=2 bar)
Harvey (1996)
Rumpf and Maurer (1993)
Fernandez-Prini et al. (2003)
This model (P<2 bar)
Figure 2. 6 Comparison of Henry's constant (ππ―,πͺπΆππ / bar mol-1 Kg) obtained in this study (Eq. (2.3)) with
literature values. The Henry's constant correlation reported by Harvey (1996) and FernΓ‘ndez-Prini et al.
(2003) was converted from mole fraction scale to molality scale for comparison.
The fugacity coefficients of CO2 and H2O in the gas mixture were computed by a modified
Redlich-Kwong EoS given by Spycher et al. (2003). The activity coefficient of CO2(aq) and ionic species
on the molal concentration scale were calculated using Pitzer equations for aqueous electrolyte solutions
(Pitzer, 1991). By rearranging Eqs. (2.1) and (2.2), the mole fractions of CO2 and H2O in the CO2-rich
phase can be presented as:
yCO2 = AaCO2(aq) (2.4)
yH2O = BaH2O(l) (2.5)
where π΄ = ππ»,πΆπ2π exp [
οΏ½Μ οΏ½πΆπ2(πβππ€π )
π π] /(ππΆπ2π), π΅ = ππ€
π ππ€π exp [
οΏ½Μ οΏ½π€(πβππ€π )
π π] /(ππ»2ππ). A and B are constants
at a specific system temperature and pressure. Since yH2O +yCO2 = 1 , Eqs. (2.4) and (2.5) can be
combined as:
24
π΄ππΆπ2(ππ) + π΅ππ»2π(π) β 1 = 0 (2.6)
At a given salt molality, the Newton-Raphson method was used to solve Eq. (2.6) with respect to
mCO2 .
2.4.2 Incorporating Pitzer's activity model
The activity of dissolved CO2 and the activity of water in the aqueous phase can be calculated as
follows:
ππΆπ2 = πΎπΆπ2ππΆπ2 (2.7)
ππππ»2π = βππππ»2π
1000(2ππππΆπ +ππΆπ2) (2.8)
The derivatives of Eqs. (2.7) and (2.8) with respect to mCO2 are,
πππΆπ2
πππΆπ2= πΎπΆπ2 + πΎπΆπ2ππΆπ2(2πππ + 6ππΆπ2ππππ + 6ππππΆππΆπΆπ2βπΆπ2βπππΆπ) (2.9)
πππ»2π
πππΆπ2= β
ππ»2πππ»2π
1000[1 + 2(ππΆπ2πππ + 3ππΆπ2
2 ππππ +ππππΆππ΅πΆπ2βπππΆπ + 6ππΆπ2ππππΆππΆπΆπ2βπΆπ2βπππΆπ +
ππππΆπ2 ππππ)] (2.10)
The Pitzer's expressions for the activity coefficient of CO2 and the osmotic coefficient of H2O are
given in Appendix A by Eqs. (A6) and (A7), respectively. By substituting Eq. (A6) into Eq. (2.7), the
partial derivative of ππΆπ2 with respect to mCO2 can be obtained resulting in Eq. (2.9). The partial derivative
25
of ππ»2π with respect to ππΆπ2 resulting in Eq. (2.10) is obtained in the same manner by substituting Eq. (A7)
into Eq. (2.8). Thus, the mCO2 can be computed by substituting Eqs. (2.7)-(2.10) into Eq. (2.6). The overall
flow chart for calculating CO2 solubility, including the solution to Eq. (2.6), is shown in Figure 2. 7. In this
calculation, the initial guess of water content in the CO2-rich phase was made by using the ideal water
content, i.e., π¦π»2π = ππ€π /π. One of the main differences between our model and the SP2010 model is the
computation of the water activity. In this study, we used the Pitzer model with an iterative Newton-
Raphson procedure, whereas Spycher and Pruess (2010) assumed that the water activity equals the mole
fraction of water in the aqueous phase, which is a rough assumption for highly concentrated aqueous
solutions but allowed a non-iterative solution for Eq. (2.6).
The Pitzer equations for the activity coefficient of CO2 and the osmotic coefficient of water are
listed in Appendix A (Pitzer, 1991). In order to simplify the notation of Eq. (A6) and Eq. (A7), we defined
two parameters, π΅πΆπ2βπππΆπ and πΆπΆπ2βπΆπ2βπππΆπ according to Akinfiev and Diamond (2010) as follows:
π΅πΆπ2βπππΆπ = πππ + πππ (2.11)
πΆπΆπ2βπΆπ2βπππΆπ = ππππ + ππππ (2.12)
These two parameters are taken from Akinfiev and Diamond (2010). The neutral component
interaction parameters πππ and ππππ of the Pitzer's model in Eqs. (2.9) and (2.10) were determined using
experimental CO2 solubility data for the CO2-H2O system (data sources are listed in Table 2. 13). The
quadratic form of parameters πππ and ππππ suggested by Akinfiev and Diamond (2010) was used during
the data fitting process, and the results were expressed using Eq. (2.13). The detailed data fitting procedure
to obtain πππ and ππππ are illustrated in Figure 2. 8.
πππ(ππππππ) = a1 + a2T + a3 T2 (2.13)
26
Initial IPAWS-95 Water EoS
parametersInitial guess for yH2O
Mixing rule, Eq. (2.14)
Solve v-cubic form of the
modified RK-EoS
Calculate the fugacity
coefficients, ΟH2O and ΟCO2,
Eq. (A5)
Thermodynamic equilibrium
framework, Eqs. (2.1-2.2)
Solve Eq. (2.6), Newton
Raphson approach
If (mCO2(new)
/mCO2(old)
-1) < Ξ΅
Obtain mCO2 and aCO2 , aH2O
simultaneously
Obtain mCO2 and aCO2 simultaneously
Deviation = abs(yH2O(new)
/yH2O(old)
-1)
If Deviation < Ξ΅
Output
mCO2 and yCO2
IAPWS-95 Water EoS
Fugacity coefficient of pure water
Vapor pressure
Saturation molar volume
Input P-T-x condition
kCO2-H2O
Table 2.7
1. Henryβs constant, Eq. (2.3)
2. vCO2, Table 2.4
Pitzerβs activity model
Eqs. (2.7-2.10), (A6) and (A7)
Pitzer pure
component
parameter, Table
2.6, Eq.(2.13)
Pitzer triple-ion
interaction
parameter,
Table 2.7 Y
N
Y
N
Use Eq. (2.5) to update yH2O
Figure 2. 7 The flow chart used to calculate the mutual solubilities of CO2 and H2O in the CO2-NaCl-H2O
system. The inner loop solves the CO2 solubility in aqueous phase; the outer loop solves the H2O solubility
in the CO2-rich phase. The convergence criteria is set to π=10-5 during the calculations.
27
The parameters in Eq. (2.13) are given in Table 2. 6. The Pitzer binary ionβion interaction
parameters π½ππ(0)
, π½ππ(1)
and πΆππ for the CO2-NaCl system were taken from Pitzer et al. (1984).
Initial Henryβs law constant (koH,CO2)
FernΓ‘ndez-Prini (2003)
Activity of dissolved CO2 (aCO2)
6Activity of coefficient of
dissolved CO2
Ξ³CO2=aCO2/mCO2
Experimental CO2 solubility data (mCO2)
Least square fitting Eq. (A6) for binary CO2-H2O system using experimental data to
determine Ξ»nn and ΞΌnnn
Use Eq. (A6) to calculate a new activity
of dissolved CO2
Obtain a new Henryβs constant (koH,CO2)
5
1
4
2
3
Figure 2. 8 The data fitting procedure for determining the neutral component parameters πππ, ππππ (Eq.
(2.13)) and the Henryβs constant ππ―,πͺπΆππ (Eq. (2.3)): (1) Use Henryβs constant (FernΓ‘ndez-Prini et al., 2003)
as an initial value, the activity of dissolved CO2 can be calculated via Eq. (2.1); (2) Use experimental CO2
solubility data and the obtained activity of dissolved CO2, the activity coefficient of dissolved CO2 can be
calculated by a simple relation πΈπͺπΆπ = ππͺπΆπ/ππͺπΆπ; (3) Neutral component parameters πππ and ππππ are
obtained by least-square fitting of Eq. (A6) using experimental CO2 solubility data for the CO2-H2O system;
(4) Activity of dissolved CO2 is re-calculated using the newly obtained πππ and ππππ via Eq. (A6) as well
as the experimental CO2 solubility data; 5) Obtain a new Henryβs constant from Eq. (2.1). Iterations of the
steps (2)-(3)-(4)-(5)-(6)-(2) are needed to get a good consistency between the new- and old-Henryβs
constant. This procedure allows us to obtainππ―,πͺπΆππ , πππ and ππππ simultaneously after a few iterations.
The experimental data used during the fitting procedure are listed in Table 2. 12 (No. 1, 2, 3, 5, 9, 10, 13,
15, 16, 18, 19, 21, 22, 26, 28, 30, 41).
Table 2. 6 Parameters of Eq. (2.13).
Parameters a1 a2 a3
πππ -1.6662Γ10-01 4.9482Γ10-04 -5.1643Γ10-07
ππππ 8.9196Γ10-02 -2.8829Γ10-04 2.3197Γ10-07
The units of parameters a1, a2, a3 for Ξ»nn are kg mol-1, kg mol-1 K-1, kg mol-1 K-2, respectively and for ΞΌnnn
are kg2 mol-2, kg2 mol-2 K-1, kg2 mol-2 K-2, respectively
The Pitzer triple-ion interaction parameter ππππ in Eqs. (2.10), (A6) and (A7) was determined by
using the bisection search algorithm to find the exact values of ππππ against the experimental CO2 solubility
data collected in this study over a concentration range of 0-6 mol kg-1 NaCl and temperatures of 323.15-
28
423.15 K. In this study, the parameter ππππ was found to be insensitive to the pressure, but it is a function
of temperature and NaCl molal concentration. Using ππππ given in Table 2. 7, the cubic spline interpolation
was used to characterize the relationship between ππππ and NaCl molal concentration, the linear
interpolation for the temperature was used to determine values of ππππ at any temperatures between 273.15
and 573.15 K.
Table 2. 7 The Pitzer triple-ion interaction parameter (ππππ / kg2 mol-2) for the CO2-NaCl-H2O system at
temperatures from 323.15 to 423.15 K and molal NaCl(aq) concentrations from 1 to 6 mol kg-1.
T / K NaCl molality (mol kg-1)
1 2 3 4 5 6
298.15 0.01617* 0.00250* -0.00111* -0.00289* -0.00390* -0.00450*
323.15 0.01213 0.00218 -0.00079 -0.00238 -0.00334 -0.00395
373.15 0.00420 0.00161 -0.00012 -0.00133 -0.00221 -0.00285
423.15 0.04899 0.02003 0.00950 0.00466 0.00208 0.00062
473.15 0.09379* 0.03845* 0.01921* 0.01065* 0.00638* 0.00409*
523.15 0.13858* 0.05687* 0.02888* 0.01664* 0.01067* 0.00755*
573.15 0.18337* 0.07529* 0.03854* 0.02263* 0.01496* 0.01102* *Indicates the data interpolated at 150 bar and the corresponding temperatures (T / K) by the method
described in Table 2. 9.
Table 2. 8(a, b) The mixing rule binary interaction parameter, ππͺπΆπβπ―ππΆ (dimensionless), determined from
experimental H2O solubility in the CO2-rich phase.
(a) T < 473.15 K
T / K 273.15 288.15 298.15 304.19 313.15 323.15 348.15 373.15 423.15 473.15
kCO2βH2O -25 -20.5 -17 -14.3 -11.5 -9 -5.6 2.1 1.9 0.32
(b) T β₯ 473.15 K
T / K 473.15 523.15 533.15 538.15 540.15 541.15 543.15 548.15 573.15
P / bar kCO2βH2O
200 0.436 -0.065 -0.235 -0.247 -0.255 -0.273 -0.291 -0.312 -0.272
300 0.548* 0.025* -0.050* -0.070* -0.070* -0.078 -0.085 -0.095 -0.226
400 0.646* 0.098* 0.037* -0.012* -0.009* -0.008 -0.019 -0.045 -0.215
500 0.698 0.136 0.056 0.003 0.001 -0.013 -0.032 -0.081 -0.324
600 0.697* 0.118* 0.036* -0.020* -0.031* -0.058 -0.092 -0.160
700 0.692* 0.089* -0.002* -0.070* -0.090* -0.124 -0.164 -0.252
800 0.685* 0.060* -0.051* -0.125* -0.158* -0.192 -0.242 -0.366
900 0.674* 0.034* -0.098* -0.172* -0.218* -0.251 -0.308 -0.492
1000 0.660 0.015 -0.138 -0.211 -0.265 -0.307 -0.375 -0.679
1100 0.644* 0.003* -0.174* -0.248* -0.307* -0.359 -0.450
1200 0.627* -0.004* -0.207* -0.284* -0.349* -0.413 -0.537
1300 0.608* -0.010* -0.235* -0.320* -0.392* -0.473 -0.674
1400 0.595* -0.014* -0.259* -0.357* -0.438* -0.536
1500 0.590 -0.019 -0.278 -0.396 -0.491 -0.627
2000 0.643 -0.042 -0.314 -0.609
29
*Indicates the data interpolated by the method described in Table 2. 9. At T < 473.15 K, the values of
ππΆπ2βπ»2π were evaluated using experimental data of Weibe and Gaddy (1941), Malinin (1959), TΓΆdheide
and Franck (1963), MΓΌller et al. (1988), King et al. (1992). At T > 473.15 K, the values of ππΆπ2βπ»2π were
evaluated using experimental data of TΓΆdheide and Franck (1963).
2.4.3. Improved mixing rule parameter (ππͺπΆπβπ―ππΆ) for the CO2-rich phase
The Spycher and Pruess (2010) modified Redlich-Kwong equation of state (RK EoS) (see
Appendix A) was used in this study to calculate the fugacities of H2O and CO2 for the CO2-rich phase. A
combined rule for polar systems (e.g. CO2-H2O) proposed by Panagiotopoulos and Reid (1986) has been
proven successful when describing the gas mixture in the CO2-H2O system (Panagiotopoulos and Reid,
1986; Spycher and Pruess, 2010). In this approach, the binary interaction parameter, πππ , takes the
following form:
πππ = βππππ(1 β πππ + (πππ β πππ)π¦π) (2.14)
where π¦π is the mole fraction of component i in the gas mixture, and πππ and πππ are the binary interaction
parameters (in this study, i and j denote CO2 and H2O, respectively). The binary interaction parameters play
a critical role in describing the CO2-rich phase diagram. The parameters ππ»2πβπΆπ2 and ππΆπ2βπ»2π evaluated
by Spycher and Pruess (2010) were found to work fine at low to moderate pressures, but with these
parameters unchanged, the model cannot accurately predict the mutual solubilities of CO2 and H2O at
pressures above 800 bar. Therefore, a modification of the parameters should be made to allow the model to
apply over a wider pressure range. It was decided to modify one of the parameters, and ππΆπ2βπ»2π was
chosen because this parameter has the most pronounced influence on calculating the H2O solubility in the
CO2-rich phase. In such an approach, ππ»2πβπΆπ2 was treated in the same manner as Spycher and Pruess
(2010) did. The fitting results of the parameter ππΆπ2βπ»2π are shown in Table 2. 8.
Determination of the binary interaction parameter ππΆπ2βπ»2π was made using the experimental H2O
solubility data collected in the CO2-rich phases. The approach selected to obtain the ππΆπ2βπ»2π was purely
30
empirical. At a given temperature and pressure, the experimental H2O solubility data in the CO2-rich phase
was entered into the model, and the parameter ππΆπ2βπ»2π was then manually adjusted until consistency was
reached between calculated and experimental values. At temperatures below 473.15 K, the experimental
data used to determine the ππΆπ2βπ»2π parameter were taken from Wiebe and Gaddy (1941), TΓΆdheide and
Franck (1963), MΓΌller et al. (1988), and King et al. (1992). By fitting the experimental H2O solubility data
in the CO2-rich phase, we found that assuming a temperature dependence and pressure independence of
kCO2βH2O is suitable when the temperature is below 473.15 K.
The pressure influence on ππΆπ2βπ»2π , however, becomes more important as the temperature
increases, especially above 473.15 K. Reliable experimental data are desirable to evaluate the parameter
kCO2βH2O at high P-T conditions. Both Takenouchi and Kennedy (1964) and TΓΆdheide and Franck (1963)
reported experimental data for the CO2-H2O system at high temperatures and pressures using the sampling
method for both the CO2-rich and the aqueous phases (Mather and Franck, 1992). While the aqueous phase
compositions obtained by Takenouchi and Kennedy (1964) and TΓΆdheide and Franck (1963) are in fairly
good agreement, the compositions of the CO2-rich phase are significantly different. In order to resolve this
discrepancy, Mather and Franck (1992) used the so-called 'synthetic' experimental method to study the
phase equilibria of the CO2-H2O system. Initially, known amounts of CO2 and H2O are loaded into an
autoclave (with a sapphire window). By heating the components in the autoclave at constant volume,
homogeneous single-phase conditions can be observed through the window. By this means, Mather and
Franck (1992) measured the dew points (at 498.15-546.15 K and 1100-2640 bar) of H2O in the CO2-rich
phase to support the experimental data reported by TΓΆdheide and Franck (1963). The experimental data of
TΓΆdheide and Franck (1963) are also validated by the theoretical calculations of Gallagher et al. (1993) and
Shyu et al. (1997). Based on the above reasons, the data from TΓΆdheide and Franck (1963) were selected
for the determination of the binary interaction parameter ππΆπ2βπ»2π at temperatures above 473.15 K.
In order to correlate TΓΆdheide and Franckβs (1963) data, ππΆπ2βπ»2π were considered as a function
of both temperature and pressure. However, introducing a pressure-dependent binary interaction parameter
in the mixing rule will disrupt the cubic form of the original RK EoS, thus the expressions for the fugacity
coefficients of CO2 and H2O in Eq. (A5) may not hold true at temperatures higher than 473.15 K. In
addition, although ππΆπ2βπ»2π was considered a function of pressure and temperature, the analytical
31
relationships between ππΆπ2βπ»2π and (P, T) are still unknown; thus, it is impossible to derive a new fugacity
coefficient expression. By using the original fugacity coefficient expressions (Eq. (A5)), we compared our
calculated ππ»2π and ππΆπ2 for the CO2-rich phase with the SP2010 model at elevated temperatures; the
AAD(%) of calculated ππΆπ2 and ππ»2π from 473.15 to 573.15 K and up to 600 bar between the two models
are approximately 4.8% and 6.0%, respectively. Thus, the tuning of the parameter ππΆπ2βπ»2π caused a small
change in the fugacity coefficient calculations, but these changes were shown to improve the overall
performance of the model for the calculation of the mutual solubilities in the CO2-H2O system at elevated
temperatures and pressures (Figure 2. 9). The detailed descriptions of this new CO2 solubility model can be
found in Table 2. 9.
32
Table 2. 9 The components, key parameters, approaches and limitations of the CO2 solubility model presented in this study.
No. Model
Components
Description Sources of
Components
Applicable
P-T range
Ref.
1 RK EoS A modified RK EoS was selected to calculate fugacities of CO2 and H2O in the CO2-
rich phase in the CO2 solubility model.
Spycher et al
(2003)
Panagiotopou
los and Reid
(1986)
273.15-573.15K
1-2000 bar
Eqs. (A1),
(A5)
2 Mixing rule The two-parameter mixing rule for polar molecules was used. 273.15-573.15K
1-2000 bar
Eqs. (14),
(A3), A4
3 ππ»2πβπΆπ2 Mixing rule binary interaction parameter kH2OβCO2 for the CO2-H2O system was
given by Spycher et al. (2003).
273.15-573.15K
1-2000 bar
-
4 ππ»2π, ππΆπ2 Fugacity coefficients of H2O and CO2 for the CO2-rich phase were calculated using
equations provided by Spycher et al. (2003) and Panagiotopoulos and Reid (1986).
273.15-573.15K
1-2000 bar
Eq. (A5)
5 ππΆπ2βπ»2π Approach to obtain the ππΆπ2βπ»2π was purely empirical. At T>473.15 K, the kCO2-H2O
was determined using experimental data of TΓΆdheide and Franck (1963) for the
CO2-rich phase. At 273.15<T<473.15 K, ππΆπ2βπ»2πwas evaluated using experimental
data of Wiebe and Gaddy (1941), MΓΌller et al. (1988), and King et al. (1992).
Fitted in this
study
273.15-573.15K
1-2000 bar
Table 2. 8
6 Interpolation
methods used
to calculate
ππΆπ2βπ»2π
at any
targeted P-T
(1). At 273.15 K<T<473.15 K, ππΆπ2βπ»2π was considered as only temperature-
dependent. A cubic spline interpolation with a step of 1 K was used to get the
relationship between ππΆπ2βπ»2π and temperature (T). (2). At T>473.15 K, ππΆπ2βπ»2π
was treated as a function of both temperature (T) and pressure (P). A cubic spline
interpolation with a step of 1 bar was used to get the relationship between ππΆπ2βπ»2π
and P at a constant T, then the linear interpolation was applied to calculate ππΆπ2βπ»2π
at any targeted P-T point.
Fitted in this
study
273.15-573.15K
1-2000 bar
Table 2. 8
7 Henry's law
constant
We have fitted Henry's law constant separately for two distinct regions: (1). P<2 bar
and temperatures of 273.16-363.15 K; (2). the remaining P-T region. By fitting the
Henrys constant specific for low P conditions, the model calculated error at low
pressures (e.g. 1.013 bar) can be reduced dramatically from ~5% to ~1%. Thus, it is
worthwhile to include two distinct Henryβs constant for two P regions in the model.
The detailed data fitting procedure is provided in Figure 2. 8.
Fitted in this
study
273.15-573.15K
1-2000 bar
Eq. (2.3)
Figure 2. 8
Figure 2. 6.
8 ππ€π , Ps ,
π£π ,ππ, ππ»2π
The fugacity coefficient, vapor pressure, molar volume, and density of pure water
were computed using IAPWS-95 EoS. The relative permittivity was calculated by
equation given by FernΓ‘ndez et al. (1997) in order to compute the Debye-HΓΌckel
slope in the Pitzerβs activity model.
Wagner and
PruΓ (2002)
FernΓ‘ndez et
al.(1997)
238.15-873.15 K,
0.1-12000 bar for
ππ, the others
251.15-1273.15 K
0.1-10000 bar
Eqs. (2.1-2.2)
9 οΏ½Μ οΏ½πΆπ2 Our approach to obtain οΏ½Μ οΏ½πΆπ2 was purely empirical. The experimental CO2 solubility
data given by TΓΆdheide and Franck (1963) were used to determine the values of
Fitted in this
study
273.15-573.15K
1-2000 bar
Table 2. 4
33
No. Model
Components
Description Sources of
Components
Applicable
P-T range
Ref.
οΏ½Μ οΏ½πΆπ2 . The calculated CO2 solubility is not sensitive to οΏ½Μ οΏ½πΆπ2 at low pressures (e.g.
P<300 bar), but it has a significant influence in predicting CO2 solubility in the
aqueous phase at high pressures (e.g. P>1000 bar).
10 Interpolation
methods used
to get vΜ CO2at
targeted P-T
At a given P-T point, the οΏ½Μ οΏ½πΆπ2 can be obtained by: (1) using the cubic spline
interpolation to get the relationship between οΏ½Μ οΏ½πΆπ2 and P at a constant T; (2) and then
applying the linear interpolation of T to get the οΏ½Μ οΏ½πΆπ2 at any targeted P-T point.
Fitted in this
study
273.15-573.15K
1-2000 bar
Table 2. 4
11(a) Pitzer activity
model
The Pitzer activity model was incorporated into the CO2 solubility model. The
benefits of incorporating the Pitzer activity model are: (1). Calculate phase equilibria
of the CO2-H2O and CO2-NaCl-H2O system in a larger P-T region than previously
developed models (Spycher and Pruess, 2010; Akinfiev and Diamond, 2010, Duan
et al., 2006); (2). Provide a higher accuracy than some of previously developed
models (Spycher and Pruess, 2010; Duan et al., 2006); 3. The model can be
extended to other aqueous systems such as CaCl2(aq), MgCl2(aq), Na2SO4(aq) and
KCl(aq).
Fitted in this
study
273.15-573.15K
1-2000 bar
Eqs. (A6)-
(A7)
Eqs.
(2.7)-(2.10)
12 πππ, ππππ The Pitzer pure neutral components interaction parameters were determined in this
study by using the CO2 solubility data in pure water at elevated Ts and Ps. The
detailed data fitting procedure and experimental data references are provide in
Figure 2. 8.
Fitted in this
study
273.15-573.15K
Not sensitive to
pressure
Eq. (2.13)
Table 2. 6
Figure 2. 8
13* π½ππ(0)
, π½ππ(1)
,
πΆππ
The Pitzer binary ion-ion interaction model were taken from Pitzer et al. (1984). Pitzer et al.
(1984)
273.15-573.15K
1-1000 bar
0-6 mol kg-1 NaCl
-
14(b) π΅πΆπ2βπππΆπ
πΆπΆπ2βπΆπ2βπππΆπ
The combined Pitzer interaction parameters depend on T and NaCl concentration.
They were taken from Akinfiev and Diamond (2010)
Akinfiev and
Diamond
(2010)
273.15-373.15K
Not sensitive to
pressure
Eqs. (A10)-
(A11)
Table A1
15 ΞΎnca Pitzer's triple-ion interaction parameter ππππ was purely determined from our
experimental data at 323.15, 373.15, 423.15 K, and can be extrapolated to any
temperature from 273.15 to 573.15 K. No other experimental data listed in Table 2.
13 for the CO2-NaCl-H2O system were used to fit this parameter. A cubic spline
interpolation with a step of 0.001 mol kg-1 NaCl was used to get the relationship
between ππππ and NaCl molal concentration at a constant T, then the linear
interpolation was applied to calculate ππππ at any targeted P-T-x point. The model
can accurately reproduce experimental data which are not used in the data fitting
procedure.
Fitted in this
study
273.15-373.15K
Not sensitive to
pressure
Table 2. 7
34
No. Model
Components
Description Sources of
Components
Applicable
P-T range
Ref.
16 Phase
equilibria
calculations
The phase equilibria equations were solved by using the Netwon-Raphson method.
There are two iteration loops: the inner loop solves the CO2 solubility in aqueous
phase (mCO2); the outer loop solves the H2O solubility in the CO2-rich phase (yH2O)
based on the inner loop results of mCO2 .
Calculated in
this study
273.15-573.15K
1-2000 bar
Eqs. (2.1-
2.10)
Figure 2. 7
(a)The Pitzer model for the CO2-H2O system was confirmed at pressures up to 2000 bar and temperatures up to 573.15 K using the experimental data of TΓΆdheide
and Franck (1963) (b)BCO2βNaCl and CCO2βCO2βNaCl were determined by Akinfiev and Diamond (2010) at the temperatures from 273.15 to 373.15 K, these parameters were used in
Eq. (A6) to calculate the activity coefficient of the dissolved CO2 in the aqueous phase. In this study, any uncertainties caused by these parameters at the
temperature above 373.15 K is absorbed by triple-ion interaction parameter ΞΎnca during the data fitting process.
35
2.4.4 Results and discussion
The calculated phase diagrams of the CO2-H2O and CO2-NaCl-H2O systems for both the aqueous
and CO2-rich phases are shown in Figure 2. 9 and Figure 2. 10, respectively. In Figure 2. 9 and Figure 2.
10, at temperatures higher than 538.15 K, the modeling results begin to deviate from the experimental
values at pressures near the critical region, and finally the calculation does not converge when the pressure
increases further. The model is incapable of predicting the CO2 solubility around critical points, most likely
because the πΎ β π approach uses different models for the CO2-rich and aqueous phases (e.g. RK EoS for
the CO2-rich phase, Pitzer activity model for the aqueous phase).
xCO2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P / b
ar
0
250
500
750
1000
1250
1500
1750
2000
573.15 K
548.15 K
543.15 K
541.15 K
540.15 K 533.1
5 K
523.1
5 K
473.1
5 K
423.1
5 K
Critic
al l
ine
Supercritical
CO2-rich phase
Aqueous phase
538.1
5 K
533.1
5 K
523.1
5 K
473.1
5 K
423.1
5 K
538.1
5 K
540.1
5 K
541.1
5 K
543.1
5 K
573.15 K
548.
15 K
Figure 2. 9 Pressure-composition phase diagram for the CO2-H2O system at temperatures from 423.15 to
573.15 K and pressures up to 2000 bar for both the aqueous and the CO2-rich phases. The solid lines
represent the calculated results from our model and the lines on the left-hand of the dashed critical line
stand for the bubble-point curves of CO2-saturated H2O(l) whereas the curves on the right-hand of the
critical line represent the dew-point curves of H2O-saturated supercritical CO2. The open circles and
triangles represent the experimental data from TΓΆdheide and Frank (1963), the solid circles and inverted
solid triangles show Malininβs (1959) data, the solid triangles correspond to the results of MΓΌller et al.
(1988). The model has AAD of 1.51% for the aqueous phase and 4.11% for the CO2-rich phase when
compared with the experimental data reported by TΓΆdheide and Frank (1963).
36
x'CO2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P / b
ar
0
250
500
750
1000
1250
1500
1750
2000
573.15 K
548.15 K
543.15 K
541.15 K
540.15 K
533.1
5 K
523.1
5 K
473.1
5 K
433.1
5 K
Critic
al l
ine
Supercritical CO2-rich phase
Aqueous phase
538.15 K
533.1
5 K
523.1
5 K
433.1
5 K
538.1
5 K
540.15 K
541.15 K
543.15 K
573.15 K
548.15 K
4 mol kg-1
NaCl
Figure 2. 10 The model-calculated pressure-composition phase diagram of the CO2-NaCl-H2O system for 4
mol kg-1 NaCl at temperatures from 433.15 to 573.15 K, and pressures from 1 to 2000 bar for both the
aqueous phase and CO2-rich phase. ππͺπΆπβ² stand for salt-free mole fraction of CO2, and it is calculated as
ππͺπΆπβ² = ππͺπΆπ/(ππͺπΆπ + ππππ/π΄ππ―ππΆ), where 1000 is the amount of water in gram. Open circles are the
experimental data for the CO2-H2O binary system from TΓΆdheide and Frank (1963), served as the
benchmark for the comparisons of the phase behavior when NaCl is introduced into the system.
As shown in Figure 2. 9 and Figure 2. 10, convergence problems in the vicinity of critical region
are also due to relatively high temperatures and pressures where the cubic EoS has a single root (Veeranna
and Rihani, 1984), and the VLE calculation in the presence of H2O could be more complex around the
critical point due to the strong non-ideality of the polar molecules. Gallagher et al. (1993) used a Helmholtz
free energy model to calculate thermodynamic properties of the CO2-H2O binary system up to 623.15 K
and observed a numerical instability near the critical region. Shyu et al. (1997) presented a calculated CO2-
H2O phase diagram at 623.15 K by using an EoS and the Wong-Sandler mixing rule. Their phase diagram
has a smooth transition through the no-convergence regions encountered by Gallagher et al. (1993) (as well
as by us), but no details on the calculation procedure are provided by Shyu et al. (1997).
The CO2 solubility model developed in this study for the CO2-NaCl-H2O system can be used to
predict CO2 solubility in the aqueous phase, as well as H2O solubility in the CO2-rich The CO2 solubility
model developed in this study for the CO2-NaCl-H2O system can be used to predict CO2 solubility in the
aqueous phase, as well as H2O solubility in the CO2-rich phase, at a P-T-x range of 1-2000 bar, 273.15-
37
573.15 K and 0-6 mol kg-1 NaCl. In Table 2. 10, the calculated CO2 solubilities in the aqueous phase are
compared with selected reliable experimental data (Wiebe and Gaddy, 1939; Malinin and Savelyeva, 1972;
Malinin and Kurovskaya, 1975; Rumpf et al. 1994; Yasunishi and Yoshida, 1979a; TΓΆdheide and Franck,
1963) and the published CO2 solubility models (MZLL2013, AD2010, SP2010, DS2006, and OLI). The
average absolute deviation (AAD = 100
Npβ |
mCO2,icalc βmCO2,i
exp
mCO2,iexp |
NPi=1 %) of the CO2 solubility in the aqueous phase
between the model calculations and the experimental data shows that our model provides the most reliable
performance among the aforementioned models (Table 2. 10).
The model also predicts the H2O solubility in the CO2-rich phase over a wide P-T range (1-2000
bar, 273.15-573.15 K) with a very good degree of accuracy (Table 2. 11, Figure 2. 9, Figure 2. 11 and
Figure 2. 13). A comparison of the literature models reveals that the AD2010 model only provides a rough
estimate of the H2O solubility in the CO2-rich phase and the DS2006 and MZLL2013 models do not
provide the H2O solubility in the CO2-rich phase. Therefore, thus far, the most reliable models to estimate
the H2O solubility in the CO2-rich phase are the SP2010 model and the commercial software package OLI
Studio 9.0. Table 2. 11 shows a comparison between the calculated results of three models (SP2010, OLI,
and our model) and the reliable experimental H2O solubility data in the CO2-rich phase (Wiebe and Gaddy,
1941; TΓΆdheide and Franck, 1963; MΓΌller et al., 1988; Valtz et al., 2004). One can see that these three
models (our model, OLI, SP2010) predict very similar H2O solubility in the CO2-rich phase in low to
moderate P-T regions, but the model developed herein covers the largest P-T range (Table 2. 11).
38
Table 2. 10 The average absolute deviation (AAD %) of CO2 solubility in the aqueous phase between model calculations and the selected reliable experimental
data over a wide P-T-x range (25-2000 bar, 288.15-573.15 K, and 0-6 mol kg-1 NaCl). The values in parentheses represent the number of experimental data points
evaluated by each model.
Ref.
No.#(a)
Np(b) P / bar T / K πππππ₯
/ mol kg-1
Model deviation from experimental data, AAD %
This study OLI(c) AD2010 SP2010 DS2006 MZLL2013
1 21 150 323.15-423.15 0-6 0.74(21) 2.91(21) 1.47(15) 2.35(21) 3.84(15) 0.91(21)
2 29 25-709 323.15-373.15 0 1.90(29) 3.05(29) 1.82(29) 1.70(25) 1.66(29) 2.55(29)
3 32 48 298.15-423.15 0-5.91 1.86(32) 4.64(32) 1.48(28) 1.95(32) 1.74(28) 2.04(28)
4 63 1-100 313.15-433.15 4-6 1.62(63) 4.63(63) 1.46(38) 5.53(63) 3.37(35) 2.09(35)
5 27 1.013 288.15-308.15 0.45-5.73 1.83(27) 3.97(27) 2.65(27) 2.59(27) 2.82(23) 2.09(24)
6 78 200-2000 323.15-573.15 0 1.51(78) 9.98(56) 1.07(6) 3.94(35) 6.27(30) 7.03(69)
Overall AAD % (No.1-No.5) 1.59(172) 3.84(172) 1.78(137) 2.82(168) 2.67(130) 1.94(137)
Overall AAD % (No.1-No.6) 1.58(250) 4.86(228) 1.66(143) 3.01(203) 3.28(160) 2.79(206)
Total data coverage rate by each model (N/Np) 100% 91% 57% 81% 64% 82% (a)1. This study; 2. Wiebe and Gaddy (1939); 3. Malinin and Savelyeva (1972), Malinin and Kurovskaya (1975); 4. Rumpf et al. (1994); 5. Yasunishi and
Yoshida (1979); 6. TΓΆdheide and Franck (1963). (b)Np is the total number of experimental data located in the targeted P-T range (P: 1-2000 bar, T: 298.15-573.15 K). (c)Calculations made by OLI are under the following conditions: (1) enable the second liquid phase, (2) use MSE model, (3) stream inflows contains 55.5082 mol
water and 15 mol CO2.
39
Table 2. 11 The average absolute deviation (AAD %) of the H2O solubility in the CO2-rich phase between model calculations and the selected reliable
experimental data at 1-2000 bar and 278.15-573.15 K. The numbers in the round brackets are stand for the amount of experimental data points evaluated by the
model.
Ref. Np(a) P / bar T / K Model deviations from experimental data, AAD %(b)
This study OLI(c) SP2010
Valtz et al. (2004) 30 4-80 278.15-318.15 11.88(30) 11.92(30) 12.06(27)
MΓΌller et al. (1988) 49 3-80 373.15-473.15 6.88(49) 5.66(49) 4.85(49)
Wiebe and Gaddy (1941) 39 1-709 298.15-348.15 7.88(16)(b) 4.42(16)(b) 5.67(16)(b)
TΓΆdheide and Franck (1963) 78 200-2000 323.15-573.15 4.11(78) 7.02(3)(b) 6.18(31)(b)
Overall AAD % 7.69 (173) 7.26(98) 7.79(123)
Total data coverage rate by each model (N/Np) 88.3% 50% 62.8% (a)Np is the total number of experimental data located in the targeted P-T range (1-2000 bar and 273.15-573.15 K). (b)For the H2O solubility in the CO2-rich phase, the data points which AAD is larger than 20 % were not included in the comparison. (c)Calculations made by OLI are under the following conditions: (1) enable the second liquid phase, (2) use MSE model, (3) stream inflows contains 55.5082 mol
water and 15 mol CO2
40
xCO2
0.000 0.010 0.020 0.030 0.990 0.995 1.000
P / b
ar
50
100
150
200
250
300From the right to the left288.15 K293.15 K298.15 K304.19 K(No exp. data)323.15 K348.15 K373.15 K
From the right to the left 288.15 K293.15 K298.15 K304.19 K308.15 K313.15 K323.15 K
348.15 K
H2O(l)+CO2(l)+CO2(g) three phase lines
Figure 2. 11 Pressure-composition phase diagram for the CO2-H2O system from 288.15 to 373.15 K, and
pressures up to 300 bar for both the aqueous phase and CO2-rich phase. The circles stand for the
experimental values for the aqueous phase, and the triangles represent the experimental values for the CO2-
rich phase. For the aqueous phase, the solid circles are the experimental data from Wiebe and Gaddy (1939)
at 323.15, 348.15 and 373.15 K. The gray circles are the experimental data from King et al. (1992) at
288.15, 293.15 and 298.15 K. The white circles are the experimental data taken from and Tong et al. (2013).
For the CO2-rich phase, the solid triangles are from Wiebe and Gaddy (1941) at 298.15, 304.19, 323.15 and
348.15 K. The gray triangles are the data from King et al. (1992) at 288.15, 293.15, 298.15, 308.15, and
313.15 K; the white triangle are the data from Valtz et al. (2004) at 288.15, 298.15, 308.15 K. The solid
lines are the results of model calculations from this study. The calculations show the well-known three-
phase [H2O(l)+CO2(l)+CO2(g)] coexistence lines where the system pressure lies below the CO2 critical
point (73.77 bar, 304.19 K).
Figure 2. 11 shows the phase diagram of the CO2-H2O system at low temperatures (less than
373.15 K). The model accurately predicts the phase behavior of both the CO2-rich and aqueous phases. In
addition, the three-phase (H2O(l)+CO2(g)+CO2(l)) coexistence pressure at temperatures below the CO2
critical temperature (304.19 K) can be obtained by the model (Figure 2. 11). For example, the calculated
three-phase coexistence pressure at 298.15 K is 65.89 bar, and this result is supported by the experimental
result (64.08 bar) of Wendland et al. (1999) at 298.15 K.
41
xCO2
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
P / b
ar
0
10
20
30
40
50
60
70
80
90
MΓΌller et al., 1988
This model
473.
15 K
453.
15 K
433.1
5 K
413.1
5 K
393.1
5 K
373.
15 K
Figure 2. 12 Phase diagram of the CO2-H2O system at temperatures 373.15-473.15 K and pressures 1-100
bar for the CO2-rich phase. The solid lines are our model calculations and points are from experimental
work of MΓΌller et al. (1988).
573.15 K
xCO2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
P / bar
0
100
200
300
400
500
600
523.1
5 K
548.1
5 K
573.
15 K
523.1
5 K
548.1
5 K
Figure 2. 13 Comparison between calculations using SP2010 and the model of this study at temperatures
from 523.15-573.15 K, and pressures up to 600 bar for the CO2-H2O system. Solid lines are our calculation
results for both the aqueous phase and CO2-rich phases, dash-dot lines are the calculation results from
Spycher and Pruess (2010). The circles are experimental data taken from TΓΆdheide and Frank (1963). The
solid circles denote the CO2 solubility in the aqueous phase, whereas the open circles stand for the water
solubility in the CO2-rich phase. The triangles stand for the calculated CO2 solubility in the aqueous phase
at 523.15 K by DS2006.
42
Figure 2. 12 shows the comparison of the model calculation with the experimental H2O solubility
in the CO2-rich phase (MΓΌller et al., 1988) at the moderate temperatures of 373.15-473.15 K. There is very
good agreement between experimental and calculated values at the highest and lowest temperatures in this
interval, but deviations appear at temperatures between 433.15 and 453.15 K.
Figure 2. 13 shows a comparison of three models (this model, SP2010, and DS2006) with the
experimental data of TΓΆdheide and Franck (1963) for both phases at temperatures of 523.15-573.15 K. Our
model and SP2010 capture the phase behavior of the CO2-H2O system very well at pressures up to 500 bar
at 523.15 K, whereas our model provides more accurate results of H2O solubility in the CO2-rich phase
than the SP2010 model at higher temperatures (e.g. 548.15 and 573.15 K).
Figure 2. 14(a, b) shows a comparison between the calculated values of this model and the
experimental CO2 solubility data from various sources (including 4 data points of this study) at 323.15,
373.15, 423.15 K and 1-1000 bar for the CO2-H2O system. Our measured CO2 solubility data in water fall
closely in line with the data from the literature, and the model developed in this study describes the phase
behavior of the CO2-H2O system with good accuracy. In Region I (P < PA, Figure 2. 14a), the CO2
solubility in the aqueous phase decreases as the temperature increases, until at point A (at pressure PA
=163.1 bar, calculated by this model), the CO2 solubility in the aqueous phase at two different temperatures
(373.15 and 423.15 K) reached the same value (mCO2|A=1.051 mol/kg). As pressure increases to PB =256.9
bar (Region II, PA < P < PC), although no experimental data are available to validate this observation, the
CO2 solubility in the aqueous phase at two different temperatures (323.15 and 423.15 K) is the same
(mCO2|B=1.370 mol/kg) as shown by the calculated results of this model (Figure 2. 14b). A similar
observation can be found at the pressure PC = 466.2 bar, where the CO2 solubility again is identical at
323.15 and 373.15 K (mCO2|C=1.569 mol/kg). When the pressure is larger than PC, the solubility of CO2
increases, as shown by the ascending trend in Figure 2.14a (Region III, P > PC), as the temperature
increases. The behavior of the CO2 solubility in response to temperature increase in Region III is the
opposite of that in Region I (Figure 2. 14a).
43
P / bar
1 10 100 1000
mC
O2 / m
ol kg
-1
0.0
0.5
1.0
1.5
2.0
2.5323.15 K
373.15 K
423.15 K
This study
This model
P
mCO2
A
B
C
PA
PC
m1
CO2
m2
CO2
PB
(a)
P / bar
150 200 250 300 350 400 450 500 550
mC
O2 / m
ol kg
-1
1.0
1.1
1.2
1.3
1.4
1.5
1.6
323.15 K
373.15 K
423.15 K
This study
This modelA
B
C
423.
15 K
323.15
373.15 K
Region
PA=163.1 bar P
B=256.9 bar P
C=466.2 bar
(b)
Figure 2. 14 The phase diagram of the CO2-H2O binary system at 323.15-423.15 K and 1-1000 bar. Solid
lines are bubble-point curves of CO2-saturated H2O(l) at different temperatures corresponding to the
experimental CO2 solubility data. Two vertical lines (i.e. ππ and ππ) create three distinct regions (I, II and
III) in the diagram. In region I (P<PA), the solubility of CO2 decreases as the temperature increases; In
region II (PA<P<PC), the CO2 solubility decrease to a minimum then start to increase as the temperature
increases; In region III (P>PC), the CO2 solubility in aqueous phase is increasing as the temperature
increases. Region II is a transition zone in which at certain pressure (e.g. PB), the bubble-point curves of
CO2-saturated water with different temperatures may have intersections. Point A, B and C in the region II
44
are the intersections between those bubble-point curves at temperatures 323.15, 373.15 and 423.15 K at
pressures PA, PB and PC, respectively. The experimental data at 323.15, 373.15 and 423.15 K were taken
from the references (No. 1, 2, 5, 6, 7, 9, 10, 11, 13, 15, 16, 18, 21, 22, 26, 28, 32, 33, 35, 36, 37, 38, 39, 40,
and 41) listed in Table 2. 12. Figure 2.14b is an enlarged view of the region II, the values of PA, PB and PC
can be determined via model calculations as shown in Figure 2.14b.
While in region I (or III) the CO2 solubility in the aqueous phase is decrease (or increase)
monotonically in response to increased temperature, at a given pressure in region II, the CO2 solubility is
not a monotonic function of temperature. In fact, region II serves as a transition zone for the temperature-
dependent behavior of CO2 solubility in the aqueous phase between regions I and III. Therefore, we define
the pressure-bounded region II in the P-x phase diagram as the CO2 solubility βtransition zoneβ at given
temperatures. The lower- and upper-boundary pressures of the CO2 solubility transition zone (i.e., Region
II) can be founded by the intersection points of the CO2 solubility curves at given temperatures in the P-x
phase diagram (Figure 2. 14b). For example, there are three temperature pairs (a) 373.15 and 423.15 K, (b)
323.15 and 423.15 K, and (c) 323.15 and 373.15 K corresponding to the intersection points A, B and C as
shown in Figure 2.14b. It is implied that the CO2 solubility curves (bubble point curves of the CO2-
saturated water) with the highest temperature combination (e.g. pair (a)) tend to intersect at the lower
pressure boundary (PA) of the transition zone; whereas the CO2 solubility curves with the lowest
temperature combination (e.g. pair (c)) tend to intersect at the upper pressure boundary (PC) of the
transition zone.
Figure 2. 15(a-f) shows a comparison between this model and the MZLL2013 model. The
calculated results of those two models are compared with the reliable literature data (In Table 2. 12: Ref.
No. 3, 5, 6, and 7 for Figure 2. 15a; In Table 2.13: Ref. No. 2, 3, 5, 7, 10, 12 for Figure 2. 15b, Ref. No. 15
for Figure 2. 15c and Figure 2. 15d, Ref. No. 8, 9 for Figure 2. 15e, and Ref. No. 19 for Figure 2. 15f). Both
models are in excellent agreement with the experimental data. Figure 2. 15 also illustrates that the
performance between the two models are close to each other in the 1-1500 bar, 298.15-573.15 K and 0-4.5
mol/kg NaCl region, but the model developed in this study has a wider pressure and salt concentration
coverage, whereas the MZLL2013 model covers a wider temperature range. In addition to Figure 2. 15, we
presented the detailed comparison results between the two models in Table 2. 12 and Table 2. 13 for the
systems of CO2-H2O and CO2-NaCl-H2O, respectively.
45
P / bar
300 600 900 1200 1500
mC
O2 / m
ol kg
-1
0
2
4
6
8
10
12
14Takenouchi and Kennedy, 1964
Takenouchi and Kennedy, 1965
TΓΆdheide and Frank, 1963
Malinin, 1959
MZLL2013
This model
573.15 K
Takenouchi and Kennedy, 1964
473.15 K
423.15 K
573.15 KOther data
(a)
mNaCl / mol kg-1
0 1 2 3 4 5 6
mC
O2 / m
ol kg
-1
0.010
0.015
0.020
0.025
0.030
0.035
0.040
Markham and Kobe, 1941
Harned and Davis, 1943
Yeh and Peterson, 1964
Onda, et al., 1970
Yasunishi and Yoshida, 1979
Burmakina et al., 1982
This model
MZLL2013
1.013 bar298.15 K
(b)
46
P / bar
0 20 40 60 80 100 120
mC
O2 / m
ol kg
-1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7This model
MZLL2013
313.15 K
333.15 K
353.15 K
393.15 K
413.15 K
433.15 K
4 mol/kg NaClRumpf et al., 1994
(c)
P / bar
0 20 40 60 80 100
mC
O2 / m
ol kg
-1
0.0
0.1
0.2
0.3
0.4
0.5This model
313.15 K
333.15 K
353.15 K
393.15 K
413.15 K
433.15 K
6 mol/kg NaClRumpf et al., 1994
(d)
47
mNaCl / mol kg-1
0 1 2 3 4 5 6
mC
O2 / m
ol kg
-1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4This model
MZLL2013
298.15 K
323.15 K
348.15 K
373.15 K
423.15 K
48 barMalinin and Savelyeva, 1972Malinin and Kurovskaya, 1975
(e)
P / bar
80 100 120 140 160 180 200 220
mC
O2 / m
ol kg
-1
0.8
0.9
1.0
1.1
1.2
1.3
1.4
303.15 K
313.15 K
323.15 K
333.15 K
This model
MZLL2013
0.529 mol/kg NaClBando et al., 2003
(f)
Figure 2. 15(a-f) Vapor-liquid equilibrium of the CO2-H2O and CO2-NaCl-H2O systems. Comparison of
this model and MZLL2013 (Mao et al., 2013) to experimental CO2 solubility data in aqueous phase.
Results are shown in (a) for the CO2-H2O system at 423.15-573.15 K, 1-1500 bar; (b) for the CO2-NaCl-
H2O system at ambient conditions, (c) for the CO2-NaCl-H2O system at 313.15-433.15 K, 1-120 bar and 4
mol kg-1 NaCl, (d) for the CO2-NaCl-H2O system at 313.15-433.15 K, 1-120 bar and 6 mol kg-1 NaCl (the
MZLL2013 model is not applicable in this case due to the high NaCl molality), (e) for the CO2-NaCl-H2O
system at 298.15-423.15 K, 48 bar, and 0-6 mol kg-1 NaCl, and (f) for the CO2-NaCl-H2O system at
303.15-333.15 K, 80-220 bar, at 0.529 mol kg-1 NaCl.
48
In Table 2. 12 and Table 2. 13, the calculated results of the two models (This model and
MZLL2013) are compared with available experimental CO2 solubility data for the CO2-H2O and CO2-
NaCl-H2O systems at elevated temperatures and pressures. The average absolute deviation (AAD%) of the
calculated CO2 solubility values of this model from the experimental data is 3.82 % and 3.83% for the CO2-
H2O (Table 2. 12) and CO2-NaCl-H2O (Table 2. 13) systems, whereas the results from the MZLL2013
model (AAD%) are 4.18% and 4.11%, respectively. Therefore, the model developed in this work provides
reliable estimates of the CO2 solubility in NaCl(aq) solutions as well as the H2O solubility in the CO2-rich
phase of the CO2-NaCl-H2O system over a wide P-T-x range (273.15-573.15 K, 1-2000 bar, 0-6 mol/kg
NaCl(aq)).
49
Table 2. 12 The average absolute deviation (AAD %) of calculated CO2 solubility (mol kg-1) in aqueous phase from experimental data for the CO2-H2O system
at temperatures of 273.15-573.15 K and pressures of 1-2000 bar: Comparison between this model and the MZLL2013 model.
No. References P / bar T / K N AAD %
(This model)
AAD %(e)
(MZLL2013)
1 Wiebe and Gaddy (1939) 25-709 323.15-373.15 29 1.82 2.72
2 Prutton and Savage (1945) 23-654 373.15-393.15 26 5.27 6.96(f)
3 Malinin (1959) 98-490 473.15-573.15 16(a) 5.30 2.28
4 Ellis and Golding (1963) 25-200 450.15-538.15 10 9.16 3.50
5 TΓΆdheide and Franck (1963) 200-2000 323.15-573.15 78 1.51 7.03(4.51)(b)
6 Takenouchi and Kennedy (1964) 100-1500 383.15-573.15 96 7.06 5.28(f)
7 Takenouchi and Kennedy (1965) 100-1400 423.15-573.15 35 4.90 5.18
8 Stewart and Munjal (1970) 10.1-45.6 273.15-298.15 12 11.06 10.85
9 Malinin and Savelyeva (1972) 48 298.15-348.15 3(a) 1.51 1.53(f)
10 Malinin and Kurovskaya (1975) 48 298.15-423.15 3(a) 1.60 3.24(f)
11 Drummond (1981) 40-180 303.15-573.15 50 5.00 9.01(f)
12 Cramer (1982)(c) 8-58 306.15-486.25 7 3.89 7.28(c)
13 Briones et al. (1987) 68-177 323.15 7 3.12 2.30
14 Nakayama et al. (1987) 36.3-109.9 298.25 6 4.06 4.11
15 D'Souza et al. 1988 101-152 323.15-348.15 4 4.73 5.07
16 MΓΌller et al. (1988)(d) 3-81 373.15-473.15 49 3.11 3.27
17 Nighswander et al. (1989) 23-102 353.15-473.15 33 5.40 6.16
18 Sako et al. (1991) 100-200 348.15-423.15 7 6.79 7.31
19 King et al. (1992) 60-243 288.15-298.15 27 1.87 1.40
20 Mather and Franck (1992) 1614-1692 500.15-533.15 6 5.45 -
21 Dohrn et al. (1993) 101-301 323.15 3 1.87 1.16
22 Rumpf et al. (1994) 11-58 323.15 7 0.65 1.64(f)
23 Teng et al. (1997) 64.4-294.9 278.05-293.05 24 4.29 3.85
24 Gu (1998) 17.1-58.3 304.19-313.15 10 2.78 3.20
25 Dhima et al. (1999) 100-1000 344.15 7 5.37 5.03
26 Bamberger et al. (2000) 40-140 323.15-353.15 29 1.61 1.45
27 Teng and Yamasaki (2002) 75-300 298.05 6 0.44 0.89
28 Bando et al. (2003) 100-200 303.15-333.15 12 2.31 2.76
29 Chapoy et al. (2004) 1.9-93.3 273.85-351.35 27 2.76 3.02
30 Valtz et al. (2004) 5-80 278.15-318.15 47 4.19 4.65
31 Li et al. (2004) 33.4-198.9 332.15 6 3.09 7.24
32 Koschel et al. (2006) 20.6-194.7 323.15-373.15 8 2.97 3.72
50
No. References P / bar T / K N AAD %
(This model)
AAD %(e)
(MZLL2013)
33 Qin et al. (2008) 106-499 323.65-375.75 7 3.07 3.77
34 Ferrentino et al. (2010) 75-150 313.05 4 2.41 0.87
35 Han et al. (2011) 3.8-20.2 313.05-333.05 15 5.71 5.69(f)
36 Liu et al. (2011) 20-160 308.15-328.15 31 1.70 1.67
37 Yan et al. (2011) 50-400 323.15-413.15 18 2.33 3.39(f)
38 Hou et al. (2013) 25-175 283.15-448.15 42 7.74 7.49(f)
39 Tong et al. (2013) 72-273 374.15 5 2.08 5.06(f)
40 Serpa et al. (2013) 1.3-4.1 298.15-323.15 9 6.04 5.32(f)
41 This work 100-150 323.15-423.15 4 0.39 0.76(f)
Overall 825 3.81 4.18(4.11)
N is the number of data points evaluated by this model. (a)The repeated measurements were counted as 1 datum. (b)AAD=4.51% is calculated by Mao et al. (2013) using 39 experimental data points given by TΓΆdheide and Franck (1963). We report the calculate AAD=7.03
for the MZLL2013 model by using 69 experimental data points from TΓΆdheide and Franck (1963) within the P-T range of 1-1500 bar and 273.15-573.15 K. (c)Cramer's (1982) data are compared with our model calculated values using a modified Henry's law constant defined by π = ππΆπ2ππΆπ2/π₯πΆπ2 . (d)The experimental data were taken from a large data compilation given by Scharlin (1996). (e)Taken from Mao et al. (2013). (f)Calculated using the MZLL2013 model.
51
Table 2. 13 The average absolute deviation (AAD %) of the calculated CO2 solubility (molality) in the aqueous phase from experimental data for the CO2-NaCl-
H2O system at 273.15-573.15 K, 1-1400 bar and 0-6 mol kg-1 NaCl: Comparison between this model and the MZLL2013 model.
No. References P / bar T / K π¦ππππ₯/ mol kg-1 N AAD %
(This model)
AAD %
(MZLL2013)
1(a) Setchenow (1892) 1.013 288.35 0.225-6.088 9 3.47 2.09(e)
2 Markham and Kobe (1941) 1.013 273.35-313.15 0.1-4 15 3.71 3.66(f)
3 Harned and Davis (1943) 1.013 273.15-323.15 0.2-3 55 2.65 3.14(f)
4 Ellis and Golding (1963) 54-210.1 449.15-603.15 0.5-2 29 4.19 4.48(f)
5 Yeh and Peterson (1964) 1.013 298.15-318.15 0.15 4 1.69 5.83(f)
6 Takenouchi and Kennedy (1965)(b) 100-1400 423.15-673.15 1.09-4.28 55 13.81(b) 5.18(f)
7 Onda, et al. (1970) 1.013 298.15 0.51-3.21 8 1.72 2.90(f)
8 Malinin and Savelyeva (1972)(c) 48 298.15-348.15 0.36-4.46 13 1.57 1.19(e)(4.62)(f)
9 Malinin and Kurovskaya (1975)(c) 48 298.15-423.15 1-5.91 13 2.18 2.20(e)(7.18)(f)
10 Yasunishi and Yoshida (1979)(c) 1.013 288.15-308.15 0.45-5.73 27 1.82 2.09(e)(6.63)(f)
11 Drummond (1981) 34-387.6 292.85-673.15 1-6.3 339 5.73 6.62(f)
12(a) Burmakina, et al. (1982) 1 298.15 0.001-0.2 8 1.34 1.67(g)
13 Cramer (1982)(d) 8-62 296.75-511.75 0.5-1.95 13 9.55 12.74(c)
14 Nighswander et al. (1989) 21-100 353.15-473.65 0.173 34 5.56 6.28(f)
15 Rumpf et al. (1994) 4.67-96.37 313.15-433.15 4-6 63 1.62 2.09(f)
16(a) VΓ‘zquez et al. (1994) 1.013 298.15-308.15 0.69-2.9 20 1.52 2.78(f)
17 Gu (1998) 17.7-59.0 303.15-323.15 0.5-2.0 60 6.55 5.66(f)(4.05)(f)
18 Kiepe et al. (2002) 1-100.61 313.15-353.15 0.52-4.34 64 5.15 5.78(f)
19 Bando et al. (2003) 100-200 303.15-333.15 0.17-0.53 36 1.02 2.30(f)
20 Koschel et al. (2006) 51-202.4 323.15-373.15 1-3 14 5.19 4.50(f)
21 Kim et al. (2008) 101-201 278.9-280.4 1 6 4.87 7.09(e)
22 Ferrentino et al. (2010) 100-150 313 0.17 2 2.57 2.89(f)
23 Liu et al. (2011) 21-158.3 318.15 1.9 8 3.62 4.84(f)
24 Yan et al. (2011) 50-400 323.15-413.15 1-5 36 3.80 3.73(f)
25 This study 150 323.15-423.15 1-6 18 0.78(d) 1.06(e)
Overall 949 3.83 4.11(4.62)
N is the number of evaluated data points for each experimental work. (a)Experimental data taken from a large data compilation given by Scharlin (1996); (b)The
experimental data reported by Takenouchi and Kennedy (1965) has a large uncertainty when compared with our model; (c)Cramer's (1982) experimental CO2
solubility is expressed in terms of a modified Herny's constant therefore the value computed from Mao et al.'s (2013) model could not be used for a direct
comparison to the experimental data given by Cramer (1982). We have converted Cramer's data to molality using our model and then make comparison with the
calculated results of Mao et al.'s (2013) results; (d)The number differs from Table 2. 3 due to the removal of the computed results for the CO2-H2O system; (e)Calculated by using the MZLL2013 model; (f)Taken from Mao et al. (2013).
52
2.5 Conclusions
A new PVT apparatus to measure the CO2 solubility in aqueous solutions at temperatures and
pressures corresponding to CO2 storage conditions has been constructed and shown to provide accurate and
reproducible CO2 solubility measurements at temperatures up to 423.15 K and pressures up to 150 bar. At
150 bar, new CO2 solubility data in the aqueous phase were obtained for the CO2-NaCl-H2O system at
temperatures of 323.15, 373.15, and 423.15 K and from 0 to 6 mol kg-1 NaCl(aq). Error analysis showed
that the instrumental error of the observed CO2 solubility is around 0.7 % and the random error is from 0.5
to 4.5 % based on the molal concentration scale.
In Chapter 2, we improved upon the previously published model of Spycher and Pruess (2010) by
including Pitzer's model to calculate the activity coefficient of the dissolved CO2 and the osmotic
coefficient of water in the CO2-NaCl-H2O system. The new model can accurately predict the CO2 solubility
in the aqueous phase for both the CO2-H2O and CO2-NaCl-H2O systems with an overall accuracy better
than 3.9 % at temperatures from 273.15 to 573.15 K and pressures up to 2000 bar. A comparison between
our model and four widely accepted models (AD2010, SP2010, DS2006, and OLI), as well as a recent
published model MZLL2013, showed that our model provides accurate predictions of CO2-H2O mutual
solubilities for the CO2-H2O and CO2-NaCl-H2O systems.
A comparison of our model results at three different temperatures (323.15, 373.15 and 423.15 K)
with a large number of experimental data reveals a CO2 solubility transition zone, which is bounded by a
low and a high pressure boundary (Plow and PHigh, respectively). In the transition zone (Plow < P < PHigh), the
CO2 solubility decreases to a minimum before increasing as the temperature increases. The CO2 solubility
is not a monotonic function of temperature in the transition zone. Conversely, outside of that transition
zone, the CO2 solubility decreases (P < Plow) or increases (P > PHigh) in response to increased temperature.
This phenomenon is clearly observed and validated by both experimental data and modeling results for the
CO2-H2O systems.
53
CHAPTER 3
SOLUBILITY OF CO2 IN AQUEOUS SOLUTIONS OF CaCl2, MgCl2, Na2SO4
AND KCl3
3 The text for this chapter was originally prepared for the publication as βHaining Zhao, Robert Dilmore,
and Serguei N. Lvov, Experimental studies and modeling of CO2 solubility in high temperature aqueous
CaCl2, MgCl2, Na2SO4, and KCl solutions, Geochimica et Cosmochimica Acta, in reviewβ
54
Abstract
New experimental CO2 solubility data in aqueous CaCl2, MgCl2, Na2SO4 and KCl solutions were
collected at temperatures 323.15, 373.15, and 423.15 K, pressure of 150 bar, and ionic strengths from 0 to 6
mol kg-1 of dissolved salt species. This study experimentally demonstrates that CO2 solubility in aqueous
solutions with different salt species are significantly different, whether the solutions have the same percent
of salt by weight or have the same ionic strength. The experimental results also show that in the aqueous
phase a cation with a higher charge density will have more significant salting-out effect on dissolved CO2
than other ions. In addition, the measured CO2 solubility data are used to extend the capability of a
previously developed CO2 solubility model (for the CO2-NaCl-H2O system) to account for aqueous
solutions containing salt species other than NaCl. Comparisons against literature data reveal a clear
improvement of the proposed PSUCO2 model among the published models in predicting CO2 solubility in
aqueous CaCl2, MgCl2, Na2SO4 and KCl solutions. Also, the modeling results show a positive correlation
between the H2O solubility in the CO2-rich phase and the activity of H2O in the aqueous phase, the
influence of salts species on solubility of H2O in the CO2-rich phase is clearly observed. A web-based CO2
solubility computational tool can be accessed via the link: www.carbonlab.org/psuco2/.
55
3.1 Introduction
CO2 capture and sequestration (CCS) in deep geological formations has emerged as an important
option for reducing CO2 emissions from industrial sectors (Benson and Cole, 2008). Important mechanisms
for CO2 trapping in geologic sequestration systems include: structure/stratigraphic and capillary (pore-scale)
trapping of dense-phase CO2, solubility trapping, and mineral trapping. These physical and chemical
processes due to the phase transition of the CO2-brine system at geological temperatures and pressures have
significant influences on formation fluid and rock properties because of 1) solubility trapping and its
influences on mineral deposition; 2) variations of the buoyancy of the CO2-rich phase and the density in the
aqueous phase due to the dissolution of CO2 in brine (Benson and Cole, 2008; Haugan and Drange, 1992;
Duan et al., 2008); 3) the swelling and shrinking effects of reservoir brine as a function of CO2 saturation
(Bachu and Adams, 2003; Steele-MacInnis et al., 2013); 4) the wettability alteration of the brine due to the
dissolution of CO2 (Yang et al., 2005); and 5) the formation dry-out effect due to H2O evaporates into the
CO2-rich phase (Pruess and MΓΌller, 2009). Therefore, the CO2 and H2O mutual solubilities are the critical
parameters for understanding these trapping mechanisms. Developing a robust characterization of CO2
solubility in formation brine can help to improve evaluations of storage potential of a reservoir and to
identify the risks associated with long term storage by performing reservoir simulation studies (Pruess et al.,
2001; Kumar et al., 2005; Bickle et al., 2007).
The solubility of CO2 in NaCl(aq) solutions at elevated pressures has been widely studied from 1-
1400 bar and 273.15-673.15 K (Springer et al., 2012; Zhao et al., 2014a). However, CO2 solubility in other
salt solutions, such as CaCl2(aq), Na2SO4(aq), MgCl2(aq), and KCl(aq), has not been fully understood,
especially for the CO2-Na2SO4-H2O and CO2-MgCl2-H2O systems. High quality experimental data are still
necessary in order to develop a reliable CO2 solubility model for these CO2-salt-H2O systems.
Three available models capable of calculating CO2 solubility in CO2-salt-H2O systems containing
salt species other than NaCl were considered: (1) OLI: OLI Studio 9.0.6 (a commercial software developed
by OLI Systems Inc.) with its mixed-solvent electrolyte (MSE) thermodynamic framework (Springer et al.,
2012); (2) SP2010: the model developed by Spycher et al.(2003) and modified by Spycher and Pruess
(2010), and (3) DS2006: the model developed by Duan and Sun (2003) and improved by Duan et al. (2006).
56
Each of these models has its own advantages and disadvantages in calculating CO2 solubility in
aqueous salt solutions other than NaCl. OLI Studio 9.0.6 exhibits an excellent performance in predicting
H2O solubility in the CO2-rich phase (Zhao et al., 2014a), and also performs well in predicting CO2
solubility in NaCl(aq) and KCl(aq) brines. However, OLI Studio 9.0.6 shows a relatively larger error in
predicting CO2 solubility in CaCl2(aq) and MgCl2(aq) than other models (SP2010; DS2006) based on
comparison to previously published data (See section 3.4.2, Table 3. 4). The model DS2006 provides a very
good result in calculating CO2 solubility in NaCl(aq), CaCl2(aq), and MgCl2(aq) at temperatures from
273.15-533.15 K, pressures up to 2000 bar, and salt molality up to 4.5 mol kg-1, but it does not provide the
calculation of H2O solubility in the CO2-rich phase. Moreover, the CO2 solubility values calculated using
the DS2006 model in aqueous Na2SO4 and KCl solutions, as shown herein, significantly deviate from new
experimental values.
The SP2010 model has an excellent performance on predicting H2O solubility in the CO2-rich
phase. As for CO2 solubility in aqueous phase, the performance between the models SP2010 and DS2006 is
similar. However, the applicable pressure range of the model SP2010 is limited to 600 bar and, similar to
the model DS2010, it is also incapable of accurately computing CO2 solubility in aqueous solutions of
Na2SO4 and KCl (See section 3.4.2, Table 3. 4). Therefore, there is a need for a new model to accurately
estimate mutual solubilities of H2O and CO2 for various CO2-salt-H2O systems in geological CO2 storage
conditions.
Our previously developed model (Zhao et al., 2014a) for the CO2-NaCl-H2O system is based on
the thermodynamic framework given by Spycher et al. (2003), Spycher and Pruess (2010) and Akinfiev and
Diamond (2010). Akinfiev and Diamond's (2010) approach to estimate Pitzer parameters (π΅πΆπ2βπ πππ‘ and
πΆπΆπ2βπΆπ2βπ πππ‘) is proven successful for the CO2-NaCl-H2O system. Therefore, this work was motivated by
Akinfiev and Diamond's (2010) approach and set out to extend the model (Zhao et al., 2014a) to other CO2-
salt-H2O systems. By doing so, the combined Pitzer interaction parameters π΅πΆπ2βπ πππ‘ and πΆπΆπ2βπΆπ2βπ πππ‘
were determined using experimental CO2 solubility for each CO2-salt-H2O system. In addition, the new
experimental CO2 solubility values were used to evaluate the triple-ion interaction parameters (ππππ) for
each CO2-salt-H2O system. As a result, the previously developed CO2 solubility model for the CO2-NaCl-
57
H2O system was successfully extended to the aqueous salt solutions of CaCl2, Na2SO4, MgCl2 and KCl.
The updated model is named as PSUCO2.
3.2 Experimentation
The experimental approaches and procedures used herein for measuring CO2 solubility in aqueous
solutions at elevated temperatures and pressures were described and validated in Chapter 2 (Table 2. 1 and
Table 2. 2). The carbon dioxide used in all experiments was Coleman Instrument grade with a purity of
99.99 %. Water was purified by a Milli-Q system and was degassed before being loading into the autoclave.
The purified water conductivity was below 610-6 S m-1. All aqueous salt solutions were prepared using
this Milli-Q water and ACS Grade reagents: calcium chloride (CaCl2β2H2O, Alfa Aesar, 99%), sodium
sulfate (Na2SO4, Amresco, 99%), magnesium chloride (MgCl2, Alfa Aesar, 99%), and potassium chloride
(Alfa Aesar, 99%). The experimental system consisted of a 600-ml stainless steel autoclave (Parr
Instrument Co.), a 40-ml stainless steel sample cell, a liquid CO2 pump and a 300-ml stainless steel
pressure cell for sample analysis. Details on the CO2 solubility measuring technique and the error analysis
approach can be found in Section 2.3, Chapter 2.
3.3 Theoretical essentials for PSUCO2
The thermodynamic framework for vapor-liquid-phase equilibrium (VLE) calculation was
described in Chapter 2 and the previous publications (Spycher et al., 2003; Spycher and Pruess; 2010). In
Chapter 3, the previously developed model for the CO2-NaCl-H2O system given by Chapter 2 has been
extended to aqueous systems containing other salt species: CaCl2, Na2SO4, MgCl2, or KCl. The Pitzer
equations for the activity coefficient of CO2 and the osmotic coefficient of water are shown below as Eqs.
(3.1) and (3.2), respectively (Pitzer, 1991).
πππΎπΆπ2
= 2ππΆπ2πππ + 3ππΆπ22 ππππ + 2πππππ + 2πππππ +ππππππππ + 6ππΆπ2ππππππ + 6ππΆπ2ππππππ (3.1)
58
π β 1 =2
ππ+ππ+ππΆπ2{βπ΄π
πΌ1.5
πΌ+ππΌ0.5+ππππ[π½ππ
(0)+ π½ππ
(1)ππ₯π(βπΌ1πΌ
0.5) + (ππ|π§π| + ππ|π§π|)πΆππ] +
1
2ππΆπ22 πππ +ππΆπ2
3 ππππ +ππΆπ2πππππ + 3ππΆπ22 ππππππ +ππΆπ2πππππ + 3ππΆπ2
2 ππππππ +
ππΆπ2ππππππππ} (3.2)
In these equations, ππΆπ2 is the molality of CO2; ππand ππ are, respectively, the molality of
anions and cations in the aqueous phase. In Eq. (3.2), πΆππ = 0.5πΆπππ/|π§ππ§π|
0.5, π΄π is the Debye-HΓΌckel
slope for the osmotic coefficient, and π = 1.2 kg1/2 mol-1/2, πΌ1 = 2.0 kg1/2 mol-1/2. I is the ionic strength
based on the molality scale. The empirical equations for calculating the Pitzer binary ionβion interaction
parameters (π½ππ(0)
, π½ππ(1)
and πΆππ) were taken from literature and summarized in Appendix B. The Pitzer pure
CO2 interaction parameters (πππ and ππππ) in the temperature range 273.15-573.15 K can be found in Eq.
(2.13) and Table 2. 6.
According to Akinfiev and Diamond (2010), the combined Pitzer interaction parameters
(π΅πΆπ2βπ πππ‘ and πΆπΆπ2βπΆπ2βπ πππ‘) can be written for any salt species as:
π΅πΆπ2βπ πππ‘ = π+πππ + π
βπππ (3.3)
πΆπΆπ2βπΆπ2βπ πππ‘ = π+ΞΌπππ + π
βππππ (3.4)
Subsequently, the Eq. (3.1) can be simplified as
πππΎπΆπ2
= 2ππΆπ2πππ + 3ππΆπ22 ππππ + 2π΅πΆπ2βπ πππ‘ππ πππ‘ + π
+πβππ πππ‘2 ππππ + 6ππΆπ2ππ πππ‘πΆπΆπ2βπΆπ2βπ πππ‘ (3.5)
The combined Pitzer interaction parameters π΅πΆπ2βπ πππ‘ and πΆπΆπ2βπΆπ2βπ πππ‘ in Eq. (3.5) were
determined using experimental CO2 solubility data for the CO2-H2O and CO2-salt-H2O systems. In order to
59
evaluate those two parameters, we have made an assumption that the chemical potentials of CO2 between
the CO2-H2O and CO2-salt-H2O systems are the same at a given P-T condition based on the similar
approach used by Akinfiev and Diamond (2010). At equilibrium, the chemical potential of CO2 in the CO2-
rich phase is equal to that in the aqueous phase, given by ππΆπ2(π)
= ππΆπ2(ππ)
for the CO2-H2O system and ππΆπ2(π)β²
=
ππΆπ2(ππ)β²
for the CO2-salt-H2O system. In fact, the chemical potentials of CO2 between salt-bearing and salt-
free systems are different, due to a small variation of water solubility in the CO2-rich phase between the
two systems. However, assuming that ππΆπ2(π)
= ππΆπ2(π)β²
corresponds to a mean error of about 0.3 % of
calculated CO2 solubility in the aqueous phase (Akinfiev and Diamond, 2010), so this assumption is not
significantly impactful to the overall model results. Thus, from ππΆπ2(π)
= ππΆπ2(π)β²
, the equality of CO2 activity
between the CO2-H2O and CO2-salt-H2O systems can be described as follows:
ππ(ππΆπ2πΎπΆπ2) = ππ(ππΆπ2π πΎπΆπ2
π ) (3.6)
ππ (ππΆπ2π
ππΆπ2) = πππΎπΆπ2 β πππΎπΆπ2
π (3.7)
In Eqs. (3.6) and (3.7), ππΆπ2 and πΎπΆπ2 are the solubility of CO2 (mole CO2 per kilogram of H2O)
and the activity coefficient of CO2 in aqueous salts solutions, respectively; whereas ππΆπ2π and πΎπΆπ2
π are
those in pure water. Eq. (3.5) can be reduced to Eq. (3.8) by setting the parameters π΅πΆπ2βπ πππ‘ , ππππ and
πΆπΆπ2βπΆπ2βπ πππ‘ equal to zero for the CO2-H2O binary system as below,
πππΎπΆπ2π = 2ππΆπ2
π πππ + 3(ππΆπ2π )2ππππ (3.8)
Substituting Eqs. (3.5) and (3.8) into Eq. (3.7), we obtain:
ππ (ππΆπ2π
ππΆπ2) β πΆ = 2ππ πππ‘πΉ (3.9)
60
where C and F in Eq.(3.9) are given by Eqs. (3.10) and (3.11), respectively.
πΆ = 2πππ(ππΆπ2 βππΆπ2π ) + 3ππππ(ππΆπ2
2 β (ππΆπ2π )2) (3.10)
πΉ = π΅πΆπ2βπ πππ‘ +π£+π£β
2ππ πππ‘ππππ + 3ππΆπ2πΆπΆπ2βπΆπ2βπ πππ‘ (3.11)
And, from Eq. (3.9)
πΉ = (ππ (ππΆπ2π
ππΆπ2) β πΆ) /(2ππ πππ‘) (3.12)
By equating Eqs. (3.11) and (3.12), we obtain
πΉ = π΅πΆπ2βπ πππ‘ +π£+π£β
2ππ πππ‘ππππ + 3ππΆπ2πΆπΆπ2βπΆπ2βπ πππ‘ =
(ππ(ππΆπ2π
ππΆπ2)βπΆ)
(2ππ πππ‘) (3.13)
The parameter C was calculated by Eq. (3.10) using experimental CO2 solubilities data in both the
CO2-H2O and CO2-salt-H2O systems. In order to determine the combined Pitzer interaction parameters
π΅πΆπ2βπ πππ‘ and πΆπΆπ2βπΆπ2βπ πππ‘ in Eq. (3.13), a function for F suggested by Akinfiev and Diamond (2010) was
chosen for the data fitting process as shown in Eq. (3.14).
πΉ = π1 + π2100
πβπ+ π3
π
1000+ π4
π£+π£β
2ππ πππ‘ + π53ππΆπ2 + π6π(π₯) (3.14)
Comparing Eqs. (3.13) and (3.14), we obtain
π΅πΆπ2βπ πππ‘ = π1 + π2100
πβπ+ π3
π
1000+ π6π(π₯) (3.15)
πΆπΆπ2βπΆπ2βπ πππ‘ = π5 (3.16)
61
where π=228 K, π(π₯) =2
π₯2(1 β (1 + π₯)πβπ₯) , π₯ = πΌ1πΌ
0.5, and πΌ1 = 2.0 kg0.5 mol-0.5. The parameters
π΅πΆπ2βπ πππ‘ and πΆπΆπ2βπΆπ2βπ πππ‘ were determined from experimental CO2 solubility data for each CO2-salt-H2O
system, the data source are listed in Section 3.4.2, Table 3. 4. Suppose there are n sets of experimental CO2
solubility data available at different P-T-x points, the Eq. (3.14) can then be written in matrix form as:
π΄π₯ = π (3.17)
where
π΄ =
(
1(1)100
π(1)βπ
π(1)
1000
1(2)100
π(2)βπ
π(2)
1000. . .
π£+π£β
2ππ πππ‘(1)
3ππΆπ2(1)
π(1)(π₯)
π£+π£β
2ππ πππ‘(2)
3ππΆπ2(2)
π(2)(π₯). . .
. . .
. . .
1(π)100
π(π)βπ
π(π)
1000
. . .
. . .π£+π£β
2ππ πππ‘(π)
3ππΆπ2(π)
π(π)(π₯))
πΓ6
;
π₯ =
(
π1π2π3π4π5π6)
6Γ1
; π =
(
πΉ(1)
πΉ(2)
..
.πΉ(π))
πΓ1
The least-squares solution (οΏ½ΜοΏ½) (Schay, 2012) for Eq. (3.17) is
[π΄ππ΄]6Γ6[οΏ½ΜοΏ½]6Γ1 = [π΄ππ]6Γ1 (3.18)
where π΄π is the transpose of matrix A. The parameters (π1~π6)for each CO2-salt-H2O system are obtained
by solving the linear Eqs. (3.18), the results are shown in Table 3. 1. Thus, the parameters π΅πΆπ2βπ πππ‘ and
πΆπΆπ2βπΆπ2βπ πππ‘ can be calculated by Eqs. (3.15) and (3.16).
62
Table 3. 1 Coefficients of Eqs. (3.15) and (3.16) for calculating π©πͺπΆπβππππ and πͺπͺπΆπβπͺπΆπβππππ as a function of temperature.
Salt species* a1 a2 a3 a4 a5 a6
CaCl2(a) -2.3219 10-1 1.3069 10-1 8.0693 10-1 -5.6456 10-3 7.0156 10-3 4.9642 10-2
Na2SO4 (b) 1.2396 10-1 1.1765 10-1 2.0199 10-1 -2.3589 10-2 -1.7424 10-3 1.4198 10-3
MgCl2 (c) -5.0410 10-2 2.2742 10-2 2.3521 10-1 -7.9747 10-4 -2.8093 10-4 1.1069 10-1
KCl(c) -1.8409 10-1 6.2729 10-2 5.0722 10-1 -4.4679 10-3 -2.6025 10-3 8.7653 10-2 (a)For the CO2-CaCl2-H2O sytem, the parameters π1 to π6 were determined from the experimental data given by: Setchenow (1892), Prutton and Savage (1945),
Onda et al. (1970), Malinin and Savelyeva (1972), Malinin and Kurovskaya (1975), Yasunishi and Yoshida (1979a), Liu et al. (2011), and this work. (b)For the CO2-Na2SO4-H2O system, the parameters π1 to π6 were determined from the experimental data given by Yasunishi and Yoshida (1979a), Corti et al.
(1990), Rumpf and Maurer (1993), Bermejo et al. (2005), and this work. (c)For the CO2-MgCl2-H2O system, the parameters π1 to π6 were determined from the experimental data reported by Yasunishi and Yoshida (1979a) and this
work. (d)For the CO2-KCl-H2O system, the parameters a1 to a6 were determined from the experimental data given by Setchenow (1892), Geffcken (1904), Findley and
Shen (1912), Markham and Kobe (1941), Gerecke (1969), Yasunishi and Yoshida (1979a), Burmakina et al. (1982), Kiepe et al. (2002), PΓ©rez-Salado Kamps et
al. (2007); Liu et al. (2011) and this work.
63
The Pitzer triple-ion interaction parameter ππππ in Eqs. (3.1) and (3.2) were then calculated by
performing a binary search for ππͺπΆπ until consistency between calculated and experimental values was
obtained. The results of ππππ determined in that manner are listed in Table 3. 2. The parameter ππππ is
shown to have a strong dependence on temperature and salt concentration, especially at high temperatures
and low salt concentrations, but is insensitive to system pressure. Finally, by using the calculated results of
π·ππ(π)
, π·ππ(π)
, and πͺπππ
(See Appendix B) along with the parameters π©πͺπΆπβππππ , πͺπͺπΆπβπͺπΆπβππππ and ππππ, the
CO2 solubility model is effectively extended to the aqueous CaCl2, Na2SO4, MgCl2, KCl solutions.
Table 3. 2 The results of concentration-dependent of the Pitzer triple-ion interaction parameter (ππππ).
T / K CaCl2 ionic strength (mol kg-1)
1 2 3 4 5 6
323.15 0.77073 0.39436 0.26277 0.19510 0.15454 0.12769
373.15 0.92645 0.46400 0.30811 0.22918 0.18232 0.15141
423.15 1.103936 0.55441 0.36504 0.26831 0.21085 0.17319
T / K Na2SO4 ionic strength (mol kg-1)
1 2 3 4 5 6
323.15 -0.05670 -0.03783 -0.03180 -0.02852 -0.02644 -0.02508
373.15 -0.10374 -0.05646 -0.04081 -0.03287 -0.02802 -0.02489
423.15 -0.06269 -0.04135 -0.03205 -0.02657 -0.02293 -0.02038
T / K MgCl2 ionic strength (mol kg-1)
1 2 3 4 5 6
323.15 0.63298 0.32062 0.21067 0.15474 0.12163 0.09991
373.15 0.64031 0.32867 0.21797 0.16100 0.12696 0.10452
423.15 0.86806 0.40224 0.25688 0.18685 0.14620 0.11964
T / K KCl ionic strength (mol kg-1)
0.5 1 2 3 4 4.5
323.15 0.59800 0.32006 0.16333 0.10802 0.07958 0.07004
373.15 0.71435 0.36749 0.18537 0.12400 0.09210 0.08128
423.15 0.95168 0.45440 0.21731 0.14267 0.10498 0.09233
64
3.4 Results and discussion
3.4.1. Measured results
Table 3. 3(a-d) Experimental results for the CO2 solubility in aqueous CaCl2, Na2SO4, MgCl2 and KCl
solutions at 323.15-423.15 K and 150 bar.
(a) The CO2-CaCl2-H2O system
T / K ππͺππͺππ
/ mol kg-1
ππͺπΆπ
/ mol kg-1
πΉπππππ ππ
/ mol kg-1
323.15 0.333 1.094 0.021
323.15 0.667 0.965 0.020
323.15 1.000 0.853 0.011
323.15 1.333 0.746 0.002
323.15 1.667 0.663 0.002
323.15 2.000 0.618 0.009
373.15 0.333 0.898 0.015
373.15 0.667 0.777 0.008
373.15 1.000 0.683 0.011
373.15 1.333 0.614 0.007
373.15 1.667 0.544 0.008
373.15 2.000 0.491 0.006
423.15 0.333 0.866 0.025
423.15 0.667 0.723 0.006
423.15 1.000 0.632 0.003
423.15 1.333 0.550 0.006
423.15 1.667 0.490 0.009
423.15 2.000 0.442 0.004
(b) The CO2-Na2SO4-H2O system
T / K ππ΅πππΊπΆπ
/ mol kg-1
ππͺπΆπ
/ mol kg-1
πΉπππππ ππ
/ mol kg-1
323.15 0.333 1.029 0.015
323.15 0.667 0.866 0.022
323.15 1.000 0.716 0.015
323.15 1.333 0.584 0.016
323.15 1.667 0.502 0.017
323.15 2.000 0.442 0.015
373.15 0.333 0.855 0.012
373.15 0.667 0.729 0.010
373.15 1.000 0.617 0.010
373.15 1.333 0.534 0.013
373.15 1.667 0.452 0.007
373.15 2.000 0.395 0.012
423.15 0.333 0.831 0.025
423.15 0.667 0.710 0.026
423.15 1.000 0.611 0.016
423.15 1.333 0.524 0.019
423.15 1.667 0.444 0.008
423.15 2.000 0.389 0.009
65
(c) The CO2-MgCl2-H2O system
T / K ππ΄ππͺππ
/ mol kg-1
ππͺπΆπ
/ mol kg-1
πΉπππππ ππ
/ mol kg-1
323.15 0.333 1.071 0.007
323.15 0.667 0.961 0.012
323.15 1.000 0.834 0.020
323.15 1.333 0.743 0.006
323.15 1.667 0.671 0.022
323.15 2.000 0.609 0.010
373.15 0.333 0.875 0.009
373.15 0.667 0.767 0.005
373.15 1.000 0.664 0.001
373.15 1.333 0.594 0.012
373.15 1.667 0.533 0.016
373.15 2.000 0.483 0.002
423.15 0.333 0.815 0.012
423.15 0.667 0.699 0.008
423.15 1.000 0.618 0.023
423.15 1.333 0.536 0.020
423.15 1.667 0.468 0.012
423.15 2.000 0.430 0.002
(d) The CO2-KCl-H2O system
T / K ππ²πͺπ
/ mol kg-1
ππͺπΆπ
/ mol kg-1
πΉπππππ ππ
/ mol kg-1
323.15 0.500 1.174 0.018
323.15 1.000 1.112 0.007
323.15 2.000 1.005 0.014
323.15 3.000 0.929 0.003
323.15 4.000 0.880 0.014
323.15 4.500 0.855 0.017
373.15 0.500 0.941 0.011
373.15 1.000 0.895 0.002
373.15 2.000 0.805 0.015
373.15 3.000 0.740 0.030
373.15 4.000 0.683 0.017
373.15 4.500 0.657 0.005
423.15 0.500 0.881 0.008
423.15 1.000 0.816 0.012
423.15 2.000 0.724 0.020
423.15 3.000 0.651 0.004
423.15 4.000 0.593 0.014
423.15 4.500 0.565 0.006
Note: The instrument error πΏππππ tπ was not listed in the table and it was estimated approximately 0.7% of
the measured results (detailed error estimation please see Zhao et al., 2014). The range of random errors are:
1) CO2-CaCl2-H2O system, 0.31-2.90%, the average is 1.31%; 2) CO2-Na2SO4-H2O system, 0.74-3.58%,
the average is 2.39%; 3) CO2-MgCl2-H2O system, 0.17-3.76%, the average is 1.71%; 4) CO2-KCl-H2O
system, 0.29-4.01%, the average is 1.49%. ππΆπ2 is the molality of CO2 in aqueous phase, mol kg-1; and
πΏπππππππ denotes random error caused by repeated measurements.
66
New experimental CO2 solubility data at 150 bar and 323.15-423.15 K for the systems of CO2-
CaCl2-H2O, CO2-Na2SO4-H2O, CO2-MgCl2-H2O and CO2-KCl-H2O at the ionic strength of the solutions up
to 6 mol kg-1 are reported in Table 3. 3.
At atmospheric pressure, Li and Tsui (1971) measured CO2 solubility in aqueous NaCl solution
(0.6413 mol kg-1 NaCl) and acidified seawater (with 10, 20, and 29β° Chlorinity) at the temperature range
from 273.85 to 303.15 K. Based on their experimental results, Li and Tsui (1971) concluded that the
Buchβs assumption (Buch et al., 1932)βthe effect of a given weight of sea salts on solubility of CO2 is the
same as that of an identical weight of NaClβis proved to be valid. However, in this study we have
experimentally demonstrated that CO2 solubilites in aqueous solutions with different salt species are
significantly different at 150 bar, whether the solutions have the same percent of salt by weight or have the
same ionic strength. This observation is also substantiated by experimental CO2 solubility data given by
Yasunishi and Yoshida (1979a) and Onda et al. (1979) at ambient conditions (Figure 3. 1). Therefore, the
Buchβs assumption and the conclusion made by Li and Tsui (1971) are unable to extend to a more general
case: the effect of a given weight of any salt (or mixed-salt) on solubility of CO2 is the same as that of an
identical weight of NaCl. Figure 3. 1b and Figure 3. 2b show that, based on the same ionic strength, the
magnitude of CO2 solubility in aqueous salt solutions follows a decreasing sequence of ππΆπ2πΎπΆπ> ππΆπ2
πΆππΆπ2 >
ππΆπ2πππΆπ2 > ππΆπ2
πππΆπ > ππΆπ2ππ2ππ4 .
Figure 3. 1 and Figure 3. 2 clearly show the trend of reduction of CO2 solubility in the aqueous
phase as salt concentration increases, this 'salting-out' effect on CO2 solubility is the results of the various
interactions occurring in the aqueous phase, mainly due to the hydration of ions, and the interactions
between the hydrated ions and the dissolved CO2(aq). In addition to the 'salting-out' effect, these ion-water
molecule interactions dominate the CO2 solubility behavior in different aqueous salt solutions. For example,
on the basis of the number of ions produced when an electrolyte molecule dissociates in solution, MgCl2
and CaCl2 are the same type electrolytes (1-2 type), and the measured solubility of CO2 in CaCl2(aq) and in
MgCl2(aq) are quite close at a wide P-T-x range (Figure 3. 1 and Figure 3. 2). Moreover, the measured CO2
solubility in CaCl2(aq) is slightly greater than that in MgCl2(aq). Whereas, in spite of the same type (1-1
type) of electrolyte between NaCl and KCl, the effects of these two salts on the CO2 solubility in aqueous
67
solution are significantly different: The solubility of CO2 in aqueous NaCl solution is much smaller than
that in aqueous KCl solution (Figure 3. 1 and Figure 3. 2).
The studies of ion hydration and ionβwater molecule interactions (Samoilov, 1957; Collins, 1997)
demonstrated that small ions of high charge density bind water molecules strongly, whereas large ions of
low charge density bind water molecules weakly. In addition, Collins (1997) pointed out that ion effects on
water structure could be explained by a competition between charge density dominated ionβwater
interactions and hydrogen bonding dominated waterβwater interactions. For example, the 1-2 type
electrolytes MgCl2 and CaCl2 share the same type of anion (Cl-). By assuming that the contributions of Cl-
to the salting-out effect between the salts MgCl2 and CaCl2 are the same, the small differences of the
salting-out effects between these two salts are mainly caused by the cations Mg2+ and Ca2+. The alkali
(MΓ€hler and Persson, 2011) and alkaline earth metal ions tend to attract surrounding water molecules in the
aqueous phase to form a hydration shellβMn+(H2O)m (M = Na, K, Ca, or Mg; n = 1 for alkali metals, n = 2
for alkaline earth metals; m is cluster number for H2O molecules) (Bush et al., 2009). The effective number
of water molecules in a hydration shell depends on the charge density of the involved cation. Mg2+ and Ca2+
have the same charge number, but the ionic radius of Mg2+ (0.07Β±0.004 nm) is smaller than that of Ca2+
(0.103Β±0.005) (Marcus, 1988). As such, the charge density of Mg2+ is slightly greater than that of Ca2+,
thus Mg2+ tends to attract slightly more water molecules in its hydration shell than does Ca2+. Therefore, the
amount of free water moleculesβnot involved in the formation of the hydration shell and therefore
available to trap dissolved CO2 (aq) by forming hydrogen bonds4 between CO2(aq) and H2O molecules
(Moin et al., 2011) in aqueous MgCl2 solutionβis smaller than those in aqueous CaCl2 solution based on
the same ionic strength. As a result, at the same ionic strength, the solubility of CO2 in aqueous MgCl2
solution is smaller than that in aqueous CaCl2 solution. This explanation is corroborated by the
experimental CO2 solubility obtained in this study (Table 3. 3, Figure 3. 1b and Figure 3. 2b).
4 According to Moin et al.'s (2010) study, the average lifetime of hydrogen bonding between oxygen atoms
of CO2 and atoms of water molecules is higher than the hydrogen bonding lifetime of pure water. Their
simulation results are supported by experimental infra-red (IR) spectrum of a saturated aqueous CO2
solution.
68
298.15 K, 1.013 bar
Percent of salt by weight / %
0 10 20 30 40
mC
O2 / m
ol kg
-1
0.00
0.01
0.02
0.03
0.04
NaCl
CaCl2
Na2SO4
MgCl2
KCl
PSUCO2
Na2SO4
MgCl2CaCl2
NaCl
KCl
(a)
(a)
298.15 K, 1.013 bar
Ionic strength / mol kg-1
0 2 4 6 8 10 12 14 16 18
mC
O2 / m
ol kg
-1
0.00
0.01
0.02
0.03
0.04
NaCl
CaCl2
Na2SO4
MgCl2
KCl
PSUCO2
KCl
CaCl2
MgCl2
Na2SO4
NaCl
(b)
Figure 3. 1 Comparison of the experimental CO2 solubilities in various aqueous salt solutions at 298.15 K
and 1.013 bar based on different concentration scales: (a) Percent of salt by weight; (b) Ionic strength. The
experimental data are taken from Setschenow (1892), Geffcken (1904), Findley and Shen (1912), Kobe and
Williams (1935), Onda et al. (1970), Yasunishi and Yoshida, (1979a), Burmakina et al. (1982), and the
large CO2 solubility data compilation given by Scharlin (1996). Solid lines represent the calculated values
from the PSUCO2 model.
69
323.15 K, 150 bar
Percent of salt by weight / %
0 5 10 15 20 25
mC
O2 / m
ol kg
-1
0.2
0.4
0.6
0.8
1.0
1.2
1.4
NaCl
CaCl2
Na2SO4
MgCl2
KCl
PSUCO2
MgCl2
Na2SO4
KCl
NaCl
CaCl2
(a)
323.15 K, 150 bar
Ionic strength / mol kg-1
0 1 2 3 4 5 6
mC
O2 / m
ol kg
-1
0.2
0.4
0.6
0.8
1.0
1.2
1.4
NaCl
CaCl2
Na2SO4
MgCl2
KCl
PSUCO2
KCl
CaCl2
MgCl2
NaClNa2SO4
(b)
Figure 3. 2 Comparison of the experimental CO2 solubilities (this study) in different aqueous salt solutions
based on different concentration scales at 323.15 K and 150 bar (the comparison at 373.15 K and 423.15 K
were not shown due to the similar pattern, but the curves at the higher temperatures (i.e., 373.15 and 423.15
K) become more closer to each other): (a) Percent of salt by weight (%); (b) Ionic strength. Experimental
CO2 solubility in aqueous NaCl solution is given by Zhao et al. (2014a). Solid lines represent the calculated
values from the PSUCO2 model.
70
In spite of the same type of electrolyte with the identical anion, CO2 solubility in aqueous
electrolyte solutions could be significantly different. The measured solubility of CO2 in aqueous NaCl
solution was found to be considerably different from that in aqueous KCl solution (Figure 3. 1b and Figure
3. 2b). The calculated ion radius for K+ and Na+ are 0.141Β±0.008 and 0.097Β±0.006 nm (Marcus, 1988),
respectively. Na+ has a significantly greater charge density than K+ and the hydration number of a hydrated
Na+ will be larger than that of a hydrated K+. Therefore, the number of free water molecules in aqueous
KCl solution is greater than those in aqueous NaCl solution, which allowing more CO2(aq) to be trapped by
aqueous KCl solution, and therefore the solubility of CO2 in aqueous KCl solution is larger than that in
aqueous NaCl solution, especially at high KCl molality (Figure 3. 1 and Figure 3. 2).
Assuming that the volume occupied by an ion can be approximated by the volume of a sphere, the
charge density ratios for the ions of K+, Na+, Ca2+, and Mg2+ are estimated to be 1:3:5:16. The charge
densities, as well as the corresponding attraction forces between an ion and H2O molecules, of K+ and Na+
are smaller relative to that of Ca2+ and Mg2+. Thus, the hydration shell surrounding these low charge
density ions (K+ or Na+) are loosely packed and have potential to hold more water molecules than does the
hydration shell of the high charge density ions (Ca2+ or Mg2+). Therefore, the increase of charge density
from K+ to Na+ will result in a significant increase in the number of H2O molecules in the hydration shell,
meanwhile cause a remarkable decrease in the number of free H2O molecules in bulk solution, and
consequently lead to a sharp reduction of the CO2 solubility in aqueous NaCl solutions compared to that in
aqueous KCl solutions at the same ionic strength. This explanation elucidates why the CO2 solubility in
aqueous NaCl solution is much smaller than that in aqueous KCl solution at the same ionic strength.
However, the cations Ca2+ and Mg2+ exert a larger attraction force on surrounding water molecules
due to the charge density of these ions are larger relative to that of K+ and Na+. As a result, the hydration
shells around these ions are tightly packed and therefore have no (or much less) place to hold additional
water molecules (i.e., the hydration shell is saturated). As a result, the increase in charge density for these
high charge density ions (e.g., change from Ca2+ to Mg2+) effects no significant change on the number of
H2O molecules in its hydration shell, and the change of the amount of free H2O molecules in the bulk
solution is correspondingly small. This provides explanation for the small difference between the CO2
solubilities in aqueous CaCl2 and MgCl2 solutions.
71
3.4.2. Modeling results
The calculated CO2 solubilities in the aqueous phase from various models (PSUCO2, SP2010,
DS2006 and OLI) were compared to the experimental data listed in Table 3. 4 by average absolute
deviation (AAD %), which is defined as below:
π΄π΄π·(%) =100
ππβ |
ππΆπ2,πππππ βππΆπ2,π
ππ₯π
ππΆπ2,πππ₯π |π
π=1 % (3.19)
where ππΆπ2,πππππ represents the calculated CO2 solubility values from the CO2 solubility models (PSUCO2,
SP2010, DS2006, and OLI); ππΆπ2,πππ₯π
denotes the experimental CO2 solubility taken from literature; and N
means the total number of experimental data of each work. In Table 3. 4, one can see that the model
PSUCO2 predicts the CO2 solubility in aqueous CaCl2, Na2SO4, MgCl2 and KCl solutions with a high
degree of accuracy over a wide P-T-x range (273.15-573.15 K, 1-2000 bar and ionic strength up to 6 mol
kg-1). Moreover, Figure 3. 3 clearly indicates that the proposed PSUCO2 model provides the best
performance in calculating the CO2 solubility in all CO2-salt-H2O systems considered herein compared
with the remaining models (SP2010, DS2006, and OLI).
AAD (%)
0 2 4 6 8 10 12 14
PSUCO2
OLI Studio 9.0
Spycher and Pruess (2010)
Duan et al. (2006)
3.6
%
7.5
%
9.3
%
12.2
%
Figure 3. 3 The average absolute deviation (AAD %) of the calculated CO2 solubility values in aqueous
CaCl2, Na2SO4, MgCl2 and KCl solutions by different models compared to the experimental data (See
section 3.4.2, all available experimental data listed in Table 3. 4).
72
150 bar, CaCl2(aq)
mCaCl2 / mol kg-1
0.0 0.5 1.0 1.5 2.0
mC
O2 / m
ol kg
-1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
323.15 K
373.15 K
423.15 K
SP2010
DS2006
OLI Studio 9.0
PSUCO2
(a)
150 bar, Na2SO4(aq)
mNa2SO4 / mol kg-1
0.0 0.5 1.0 1.5 2.0
mC
O2 / m
ol kg
-1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
323.15 K
373.15 K
423.15 K
SP2010
DS2006
OLI Studio 9.0
PSUCO2
(b)
73
mMgCl2 / mol kg-1
0.0 0.5 1.0 1.5 2.0
mC
O2 / m
ol kg
-1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
323.15 K
373.15 K
423.15 K
SP2010
DS2006
OLI Studio 9.0
PSUCO2
150 bar, MgCl2(aq)
(c)
150 bar, KCl(aq)
mKCl / mol kg-1
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
mC
O2 / m
ol kg
-1
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
323.15 K
373.15 K
423.15 K
SP2010
DS2006
OLI Studio 9.0
PSUCO2
(d)
Figure 3. 4 Comparison of model calculated values against the experimental data (this study): (a) CO2-
CaCl2-H2O system; (b) CO2-Na2SO4-H2O system (c) CO2-MgCl2-H2O system (d) CO2-KCl-H2O system.
.
74
Table 3. 4 Comparison of the model calculations with experimental data. The results are shown by average absolute deviation (AAD %, Eq. (3.19)). The
numbers in parentheses stand for the number of experimental data evaluated by each model.
No. References Systems P /
bar
T / K msalt /
mol kg-1
π΅ Model calculations, AAD %
PSUCO2 OLI(d) SP2010 DS2006
1(a) Setschenow (1892) CO2-CaCl2-H2O
1.01 288.35 0.1-5.0 11 4.11(11) 5.58(9)(b) 4.34(9)(b) 7.08(10)(c)
CO2-KCl-H2O 1-4.3 3 1.92(3) 4.60(3) 21.47(3) 15.98(3)
2(a) Geffcken (1904) CO2-KCl-H2O 1.01 288.15-298.15 0.4-1.1 8 0.70(8) 2.29(8) 10.30(8) 6.37(8)
3 Findley and Shen
(1912) CO2-KCl-H2O 1.01 298.15 0.2-1 4 0.56(4) 3.40(4) 8.25(4) 6.18(4)
4 Kobe and Williams
(1935)
CO2-Na2SO4-H2O 1.01 298.15 1.76 2 1.30(2) 26.82(2) N/A(0) N/A(0)
CO2-MgCl2-H2O 1.01 298.15 4.5 1 5.50(1) N/A(1)(b) N/A(0)(b) N/A(0)(c)
5 Markham and
Kobe (1941)
CO2-Na2SO4-H2O 1.01
298.15-313.15 0.2-1.5 8 0.61(8) 7.85(8) 7.03(4) 25.89(8)
CO2-KCl-H2O 273.35-313.15 0.1-4 16 0.84(16) 4.59(16) 15.65(10) 10.62(16)
6 Prutton and Savage
(1945) CO2-CaCl2-H2O 15-712 348.15-394.15 1-3.9 116 5.58(116) 3.86(116) 9.06(104) 9.22(116)
7(a) Gerecke (1969) CO2-KCl-H2O 15-60 274.16 0.5-3.4 40 3.69(40) 7.19(40) 16.73(40) 13.01(40)
8 Onda et al. (1970) CO2-CaCl2-H2O 1.013 298.15 0.2-2.3 8 0.49(8) 5.94(8) 4.16(8) 1.00(8)
CO2-Na2SO4-H2O 1.013 298.15 0.5-1.5 3 1.77(3) 10.60(3) 26.49(3) 30.33(3)
9
Malinin and
Savelyeva (1972)
Malinin and
Kurovskaya (1975)
CO2-CaCl2-H2O 48 298.15-423.15 0.2-6.9 25 4.32(25) 5.74(25) 1.64(25) 3.17(21)(c)
10 Yasunishi and
Yoshida (1979a)
CO2-CaCl2-H2O
1.013
298.15-308.15 0.2-5.3 16 3.46(16) 6.14(16) 5.76(14)(b) 3.16(15)(c)
CO2-Na2SO4-H2O 288.15-308.15 0.2-2.4 26 3.46(26) 11.95(26) 5.35(7) 28.49(25)
CO2-MgCl2-H2O 288.15-308.15 0.1-4.4 29 3.66(29) 9.72(29) 7.47(25) 2.63(29)
CO2-KCl-H2O 298.15-308.15 0.4-4.8 16 0.95(16) 8.01(16) 22.39(16) 17.05(14)(c)
11 Burmakina et al.
(1982) CO2-KCl-H2O 1 298.15 0.001-0.2 8 1.15(8) 4.48(8) 5.90(8) 3.93(8)
12 Corti et al. (1990) CO2-Na2SO4-H2O 16-200 323.15-348.15 1-3.3 24 13.91(24) 20.50(15)(b) N/A(0) 38.87(8)
13 Rumpf and Maurer,
(1993) CO2-Na2SO4-H2O 4-97 313.15-433.15 1-2 102 2.73(102) 6.91(102) N/A(0) 27.57(102)
14 Kiepe et al. (2002) CO2-KCl-H2O 1-105 313.15-353.15 0.5-4 88 10.16(88) 9.42(88) 13.58(87) 13.07(88)
15 Bermejo et al.
(2005) CO2-Na2SO4-H2O 20-131 287.15-369.15 0.25-1 113 6.70(113) 12.77(113) 12.73(24) 22.72(113)
16 PΓ©rez-Salado
Kamps et al. CO2-KCl-H2O 4-94 313.15-433.15 2-4 98 1.65(98) 2.67(98) 18.35(98) 18.34(98)
75
No. References Systems P /
bar
T / K msalt /
mol kg-1
π΅ Model calculations, AAD %
PSUCO2 OLI(d) SP2010 DS2006
(2007)
17 Liu et al. (2011) CO2-CaCl2-H2O 20-160 318.15 1 8 8.43(8) 11.26(8) 9.63(8) 11.76(8)
CO2-KCl-H2O 20-160 318.15 1.5 8 2.93(8) 3.32(8) 13.78(8) 15.39(8)
18 Tong et al. (2013) CO2-CaCl2-H2O 15-380 308.15-424.15 1-5 36 7.36(36) 6.73(24)(b) 4.85(24)(b) 4.69(24)(c)
CO2-MgCl2-H2O 12-350 308.15-424.15 1-5 39 5.14(39) 6.14(26)(b) 5.67(26)(b) 5.83(26)(c)
19 This study
CO2-CaCl2-H2O 150 323.15-423.15 0.33-2 18 0.88(18) 2.13(18) 3.12(18) 3.61(18)
CO2-Na2SO4-H2O 150 323.15-423.15 0.33-2 18 0.75(18) 8.04(18) 7.50(3) 15.90(18)
CO2-MgCl2-H2O 150 323.15-423.15 0.33-2 18 0.83(18) 2.30(18) 3.49(18) 3.20(18)
CO2-KCl-H2O 150 323.15-423.15 0.5-4.5 18 0.33(18) 4.21(18) 14.91(18) 16.71(18)
Overall AAD % for the
system of
(Including this study)
CO2-CaCl2-H2O 4.3(238) 5.9(224) 5.3(210) 5.5(220)
CO2-Na2SO4-H2O 3.9(296) 13.2(287) 11.8(41) 27.1(277)
CO2-MgCl2-H2O 3.8(87) 6.1(73) 5.5(69) 3.9(73)
CO2-KCl-H2O 2.3(307) 4.9(307) 14.7(300) 12.4(305)
Overall AAD % CO2-salt-H2O 3.6 7.5 9.3 12.2
Experimental data P-T-x
coverage rate CO2-Salts-H2O 100% 96% 67% 94%
'N/A' in the table denotes the P-T-x region of the experimental data beyond the capacity of the corresponding model. (a)Indicates the experimental data are taken from large data compilation by Scharlin (1996). (b)The experimental P-T-x points at mCaCl2 > 3 mol kg-1 were removed from the comparison for both the OLI and SP2010 model due to the poorly results for these
model at high CaCl2 concentration. (c)The experimental P-T-x points at mCaCl2 > 4.5 mol kg-1 were removed due to the DS2006 model is limited to 4.5 mol kg-1 salt molality. (d)Calculations made by OLI are under the following conditions: (1) enable the second liquid phase, (2) use MSE model, (3) stream inflows contains 55.5082 mol
water and 5 mol CO2
76
Figure 3. 4 and Table 3. 4(row 19) show that SP2010 and DS2006 models predict the new
experimental data obtained herein quite well for the CO2-CaCl2-H2O and CO2-MgCl2-H2O systems,
however, these same models predict the measured CO2 solubility poorly in aqueous Na2SO4 and KCl
solutions. The similar performance between the models SP2010 and DS2006 is mostly due to the fact that
both models use the same type of simplified Pitzer equation, which is proposed by Duan and Sun (2003), to
calculate activity coefficient of dissolved CO2. Note that the simplified Pitzer equation used in the SP2010
model is re-parameterized so it can be used up to 573.15 K (Spycher and Pruess, 2010). OLI Studio 9.0.6
performs very good in calculating CO2 solubility in the aqueous phase for the systems of CO2-KCl-H2O,
CO2-CaCl2-H2O, and CO2-MgCl2-H2O, but the results for the CO2-Na2SO4-H2O system are significantly
deviated from the experimental CO2 solubility data (Table 3. 4, also Figure 3. 4b). In addition, some of the
experimental data (e.g., Corti et al., 1990 and Kiepe et al., 2002), are seriously deviate from calculated
results of all available models (Table 3. 4), additional experimental work should be pursued in the future to
explore this discrepancy.
mCaCl2 / mol Kg-1
0 1 2 3 4 5 6
mC
O2 / m
ol kg
-1
0.00
0.01
0.02
0.03
0.04
0.05
288.35 K, Setchenow, 1892
308.15 K, Yasunishi and Yoshida, 1979
298.15 K, Onda et al., 1970
298.15 K, Yasunishi and Yoshida, 1979
PSUCO2
1.013 bar, CaCl2(aq)
(a)
77
mCaCl2 / mol kg-1
0 1 2 3 4 5 6 7
mC
O2 / m
ol kg
-1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
PSUCO2
298.15 K, Malinin and Savelyeva, 1972
323.15 K, Malinin and Savelyeva, 1972
348.15 K, Malinin and Savelyeva, 1972
373.15 K, Malinin and Kurovskaya, 1975
423.15 K, Malinin and Kurovskaya, 1975
48 bar, CaCl2(aq)
(b)
P / bar
0 100 200 300 400 500 600 700
mC
O2 / m
ol kg
-1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
PSUCO2
1.012 mol/kg CaCl2
2.281 mol/kg CaCl2
3.899 mol/kg CaCl2
394.15 K, CaCl2(aq)
Prutton and Savage, 1945
(c)
78
P / bar
0 100 200 300 400
mC
O2 / m
ol kg
-1
0.0
0.2
0.4
0.6
0.8
1.0
PSUCO2
1 mol/kg CaCl2
3 mol/kg CaCl2
5 mol/kg CaCl2
424.35 K, CaCl2(aq)
Tong et al., 2013
(d)
Figure 3. 5(a-d) Comparison of model calculations against the experimental CO2 solubility in aqueous
CaCl2 solutions: (a) 1.013 bar, 288.15-308.15 K, and 0.14-5.31 mol kg-1 CaCl2 (Setschenow, 1892; Onda et
al., 1970; Yasunishi and Yoshida, 1979a); (b) 48 bar, 298.15-423.15 K, and 0.16-6.95 mol kg-1 CaCl2
(Malinin and Savelyeva, 1972; Malinin and Kurovskaya, 1975); (c) 21-712 bar, 394.15 K, and 1.01-3.90
mol kg-1 CaCl2 (Prutton and Savage, 1945); (d) 44-380 bar, 424.35 K, and 1-5 mol kg-1 CaCl2 (Tong et al.,
2013).
The comparisons of the calculated results of PSUCO2 with literature data are also shown in Figure
3. 5 to Figure 3. 8. Figure 3. 5(a-d) shows an excellent agreement of our modeling results with the reliable
experimental CO2 solubility data in the aqueous CaCl2 solutions at 1-712 bar, 288.15-424.35 K, and CaCl2
molality from 0.1 to 7.0 mol kg-1. With the similar performance to the CO2-CaCl2-H2O system, the
proposed PSUCO2 model is capable of accurately calculating CO2 solubility in aqueous Na2SO4, MgCl2,
and KCl solutions at elevated temperatures and pressures, the examples are shown in Figure 3. 6(a, b),
Figure 3. 7(a, b), and Figure 3. 8(a-c) for the systems of CO2-Na2SO4-H2O, CO2-MgCl2-H2O, and CO2-
KCl-H2O, respectively.
79
P / bar
0 20 40 60 80 100
mC
O2 / m
ol kg
-1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
313.15 K
323.15 K
333.15 K
353.15 K
393.15 K
413.15 K
433.15 K
PSUCO2
1.011-1.013 mol kg-1
Na2SO4(aq)
Rumpf and Maurer, 1993
(a)
P / bar
0 20 40 60 80 100
mC
O2 / m
ol kg
-1
0.0
0.1
0.2
0.3
0.4
0.5
313.15 K
333.15 K
353.15 K
393.15 K
413.15 K
433.15 K
PSUCO2
2.002-2.01 mol Kg-1
Na2SO
4(aq)
Rumpf and Maurer, 1993
(b)
Figure 3. 6(a, b) Comparison of the model calculations against the experimental CO2 solubility in aqueous
Na2SO4 solutions: (a) 4-97 bar, 313.15-433.15 K, and ~1 mol kg-1 Na2SO4; (b) 7-92 bar, 313.15-433.15 K,
and ~2 mol kg-1 Na2SO4. The experimental data are reported by Rumpf and Maurer (1993).
80
mMgCl2 / mol kg-1
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
mC
O2 / m
ol kg
-1
0.005
0.015
0.025
0.035
0.045
PSUCO2
288.15 K
298.15 K
303.15 K
1.013 bar, MgCl2(aq) Yasunishi and Yoshida (1979)
(a)
P / bar
0 50 100 150 200 250 300 350 400
mC
O2 / m
ol kg
-1
0.0
0.1
0.2
0.3
0.4
PSUCO2
309.6 K
344.68 K
374.6 K
424.4 K
5 mol/kg MgCl2(aq)
Tong et al., 2013
(b)
Figure 3. 7(a, b) Comparison of the model calculations against the experimental CO2 solubility in aqueous
MgCl2 solutions: (a) 1.013 bar, 288.15-303.15 K, and 0.15-4.45 mol kg-1 MgCl2 (Yasunishi and Yoshida,
1979); (b) 35-312 bar, 309.6-424.4 K, and 5 mol kg-1 MgCl2 (Tong et al., 2013).
81
mKCl / mol kg-1
0 1 2 3 4 5
mC
O2 / m
ol kg
-1
0.01
0.02
0.03
0.04
0.05
PSUCO2
288.15, 288.35 K
298.15 K
308.15 K
313.15 K
1.013 bar, KCl(aq)
(a)
P / bar
0 20 40 60 80 100
mC
O2 / m
ol kg
-1
0.0
0.2
0.4
0.6
0.8
1.0
313 K
333 K
353 K
373 K
393 K
413 K
433 K
PSUCO2
3.995-4.05 mol kg-1
KCl(aq)
PΓ©rez-Salado Kamps et al., 2007
(b)
82
P / bar
0 20 40 60 80 100
mC
O2 / m
ol kg
-1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
PSUCO2, 313.15 K
PSUCO2, 353.15 K
313.15 K, 0.5 m KCl
313.15 K, 1.0 m KCl
313.15 K, 2.5 m KCl
313.15 K, 4.0 m KCl
353.15 K, 0.5 m KCl
353.15 K, 1.0 m KCl
353.15 K, 2.5 m KCl
353.15 K, 4.0 m KCl
KCl(aq)Kiepe et al. (2002)
(c)
Figure 3. 8(a-c) Comparison of the model calculations against the experimental CO2 solubility in aqueous
KCl solutions: (a) 1.013 bar, 288.15-313.15 K, and 0-4.75 mol kg-1 KCl (Setchenow, 1892; Geffcken, 1904;
Findley, 1912; Markham and Kobe, 1941; Yasunishi and Yoshida, 1979a; Burmakina et al., 1982); (b) 6-94
bar, 313.15-433.03 K, and ~4 mol kg-1 KCl (PΓ©rez-Salado Kamps et al., 2007); (c) 1-105 bar, 313.15-
353.15 K, and 0.5-4 mol kg-1 KCl (Kiepe et al., 2002).
The comparison of the calculated results of the PSUCO2 model with the experimental data for the
CO2-KCl-H2O system at ambient conditions also shows a remarkable agreement (Figure 3. 8(a,b)), whereas
at elevated pressures and temperatures, a large discrepancy of experimental results for the CO2-KCl-H2O
system between PΓ©rez-Salado Kamps et al. (2007) (Figure 3. 8b) and Kiepe et al. (2002) (Figure 3. 8c) was
observed, the calculated results from the PSUCO2 model support the experimental CO2 solubility given by
PΓ©rez-Salado Kamps et al. (2007).
In Figure 3. 9a, the comparisons of calculated H2O solubility in the CO2-rich phase among the
different models (PSUCO2, OLI, and SP2010) were made at 298.15 and 423.15 K, and up to 500 bar. At
298.15 K, the differences among the three models are rather small (Figure 3. 9a). All three models are
capable of predicting the phase change (Figure 3. 9a, enlarged view) from gaseous to liquid CO2-rich phase
(Spycher et al., 2003) at 298.15 K as compared with the experimental data from Wiebe and Gaddy (1941).
At 423.15 K, both PSUCO2 and SP2010 models are shown agree well with the experimental data given by
TΓΆdheide and Franck (1963), but the OLI shows a gradually deviation in predicting H2O solubility in the
83
CO2-rich at 423.15 K as pressure increases, i.e. from 150 to 500 bar (Figure 3. 9a). Also, the calculated
results from OLI show a sharp phase change around 435-445 bar at 423.15 K, this change deviates from
both the experimental data (TΓΆdheide and Franck, 1963) and the results calculated by the other two models
(SP2010 and PSUCO2).
P / bar
0 100 200 300 400 500 600
yH
2O %
0
5
10
15
20
25
TΓΆdheide and Franck, 1963
Weibe and Gaddy, 1941
SP2010
OLI Studio 9.0
PSUCO2
P / bar
0 20 40 60 80 100 120
yH
2O %
0.1
0.2
0.3
0.4
0.5
0.6
298.15 K
423.15 K
Phase change
enlarged view at
298.15 K (0-120 bar)
CO2-H
2O binary system at 298.15 and 423.15 K
(a)
P / bar
100 200 300 400 500
yH
2O %
5.1
5.3
5.5
5.7
5.9
6.1
PSUCO2
SP2010
MgCl2(aq)
CaCl2(aq)
Na2SO4(aq)
NaCl(aq)
KCl(aq)
NaCl(aq) and KCl(aq)
CaCl2(aq), MgCl2(aq)and Na2SO4(aq) are overlapped here
Salt molality:
2.0 mol kg-1
H2O
CO2-salt-H
2O system at 423.15 K
(b)
84
P / bar
100 200 300 400 500
Activity o
f H
2O
(a
H2O)
0.84
0.86
0.88
0.90
0.92
0.94
Na2SO4(aq)
NaCl(aq)
KCl(aq)CaCl2(aq)
MgCl2(aq)Salt molality
2.0 mol kg-1
H2O
CO2-salt-H2O system at 423.15 K
(c)
Figure 3. 9(a-c) Comparison of model calculation of H2O solubility in the CO2-rich phase: (a) model
calculations (SP2010, OLI, and PSUCO2) for the binary CO2-H2O system, experimental data at 298.15 and
423.15 K are taken from Wiebe and Gaddy (1941) and TΓΆdheide and Franck (1963), respectively; (b)
comparison of calculated H2O solubility in the CO2-rich phase at 423.15 K in the CO2-salt-H2O systems
between SP2010 and PSUCO2, the results from OLI deviates from these two models and therefore not
shown in the figure (b); (c) the PSUCO2 model calculated activity of H2O in the aqueous phase for the
various CO2-salt-H2O system at 423.15 K. Calculations made by OLI Studio 9.0.6 are under the following
conditions: (1) enable the second liquid phase, (2) use MSE model, (3) stream inflows contains 55.5082
mol water and 5 mol CO2.
In Figure 3. 9b, the computed H2O solubilities in the CO2-rich phase for various CO2-salt-H2O
systems demonstrate that the different salt species presented in the aqueous phase will influence the H2O
solubility in the CO2-rich phase. Given the same salt molality (e.g. 2 mol kg-1 in Figure 3. 9b), the
differences of H2O solubility in various single-salt aqueous solutions are quite large, whereas the SP2010
model reflects a relatively smaller variation of H2O contents in the CO2-rich phase caused by the presence
of different salt species than does PSUCO2. Additionally, the results from the SP2010 model show that the
H2O solubilities in the CO2-rich phase are overlapped for certain systems (Figure 3. 9b). This is because the
activity model used by the SP2010 model differentiates cations only based on their charge number, and
therefore all monovalent cations (e.g. K+ and Na+) are the same kind of cation (and all divalent cations (e.g.
Ca2+ and Mg2+) are also the same during the CO2 solubility calculations. Thus, for the SP2010 model, the
computed CO2 solubilities in aqueous NaCl and KCl solutions with same salt molality are the same,
85
consequently, the calculated H2O solubilities in the CO2-rich phase for the systems of CO2-NaCl-H2O and
CO2-KCl-H2O are also identical. The same situations occur for the CO2-CaCl2-H2O and CO2-MgCl-H2O
systems by using the SP2010 model. Because the similar activity equation is used in both DS2006 and
SP2010 models, at the same salt concentration, the CO2 solubilities in aqueous NaCl and KCl solutions,
likewise in aqueous CaCl2 and MgCl2 solutions, are also indistinguishable by using DS2006 model. Unlike
the SP2010 and DS2006 models, the proposed PSUCO2 model is able to predict the mutual solubilities of
CO2 and H2O in a CO2-salt-H2O system by taking into account the effects caused by different salt species,
e.g., a strong dependence of H2O solubility in the CO2-rich phase on salt species are observed from the
PSUCO2 model (Figure 3. 9b).
Figure 3. 9c provides an explanation of the observed differences of H2O solubility in the CO2-rich
phase among the various CO2-salt-H2O systems (Figure 3. 9b). The H2O solubility in the CO2-rich phase
are dominated by the activity of H2O in the aqueous phase. Even at the same P-T-x condition, the H2O
solubility in the CO2-rich phase is different for the various CO2-salt-H2O system due to each salt species
has distinctive influence on the activity of H2O (aH2O) in the aqueous phase. The modeling results shows
that a positive correlation between the H2O solubility in the CO2-rich phase and the activity of H2O in the
aqueous phase for the various CO2-salt-H2O system (Figure 3. 9c). In this case (100-500 bar, 423.15 K, and
2 mol kg-1 salt), the activity of H2O in aqueous Na2SO4 solution takes the greatest value among the others
(Figure 3. 9c), so that there is the corresponding largest H2O solubility in the CO2-rich phase (yH2O) for the
CO2-Na2SO4-H2O system at the same P-T-x condition. For other salt species (NaCl, CaCl2, MgCl2 and
KCl), the magnitude of H2O solubility in the CO2-rich phase is also preserved corresponding to the
variation of H2O activity in the aqueous phase in response to changed salt species (Figure 3. 9b and Figure
3. 9c). The observation of higher activity of H2O yields higher solubility of H2O in the CO2-phase is based
on the comparison among different CO2-salt-H2O systems, note that for the same salt species the increase
of the H2O activity does not guarantee the increased H2O solubility in the CO2-rich phase.
86
3.5 Conclusions
At 150 bar, new CO2 solubility data in the aqueous phase were obtained for the CO2-CaCl2-H2O,
CO2-Na2SO4-H2O, CO2-MgCl2-H2O and CO2-KCl-H2O systems at temperatures 323.15, 373.15, and
423.15 K and ionic strengths from 0 to 6 mol kg-1 of dissolved salt species. Error analysis showed that the
instrumental error of the observed CO2 solubility is around 0.7% and the random error is from 0.1 to 3.0 %
based on the molal concentration scale.
The comparisons of experimental results based on the same concentration scale (ionic strength or
salt percent by weight) showed that (1) the solubilities of CO2 in aqueous solutions in the presence of
different salt species are quite different; (2) the solubilities of CO2 in CaCl2(aq) and MgCl2(aq) solutions
are close to each other; and (3) in the aqueous phase a cation with a higher charge density (a smaller radii
and a larger charge number) will have more significant salting-out effect on dissolved CO2 than other ions.
By using new experimental CO2 solubility data collected in different aqueous salt solutions, we
extended the previously developed CO2 solubility model for the CO2-NaCl-H2O system (see Chapter 2) to
include the salt species of CaCl2, Na2SO4, MgCl2 and KCl into the proposed PSUCO2 model. Comparisons
against literature data reveal a clear improvement of the proposed PSUCO2 model among the published
models in predicting CO2 solubility in aqueous CaCl2, MgCl2, Na2SO4 and KCl solutions at temperatures
from 273.15-573.15 K and pressures up to 2000. Also, the modeling results show a positive correlation
between the H2O solubility in the CO2-rich phase and the activity of H2O in the aqueous phase, the
influence of salts species on solubility of H2O in the CO2-rich phase is clearly observed.
87
CHAPTER 4
SOLUBILITY OF CO2 IN SYNTHETIC FORMATION BRINE5
5 The text for this chapter was originally prepared for the publication as βHaining Zhao, Robert Dilmore,
Douglas E. Allen, Sheila W. Hedges, Yee Soong and Serguei N. Lvov, Measurement and modeling of CO2
solubility in natural and synthetic formation brines, Environmental Science & Technology, in reviewβ.
88
Abstract
CO2 solubility data in the natural formation brine, synthetic formation brine, and synthetic
NaCl+CaCl2 brine were collected at the pressures from 100 to 200 bar, temperatures from 323-423 K.
Experimental results demonstrate that the CO2 solubility in the synthetic formation brines can be reliably
represented by that in the synthetic NaCl+CaCl2 brines. We extended our previously developed model
(PSUCO2) to calculate CO2 solubility in aqueous mixed-salt solution by using the additivity rule of the
Setschenow coefficients of the individual ions (Na+, Ca2+, Mg2+, K+, Cl-, and SO42-). Comparisons with
previously published models against the experimental data reveal a clear improvement of the proposed
PSUCO2 model. Additionally, the path of the maximum gradient on the CO2 solubility contour map is
defined to divide the P-T diagram into two regions: in Region I, the CO2 solubility in the aqueous phase
decreases monotonically in response to increased temperature, but in region II, the behavior of the CO2
solubility is the opposite of that in Region I as the temperature increases. A web-based CO2 solubility
computational tool can be accessed via the link: www.carbonlab.org/psuco2/.
89
4.1 Introduction
Knowledge of the properties of the CO2-brine system is essential not only for the CO2 related
industrial applications but also for understanding its behavior in geochemical systems. Since the start of the
first CO2 enhanced oil recovery (CO2-EOR) project in the Kelly-Snyder Oil Field in West Texas began in
1971, CO2 has been injected into geological formations to economically improve recovery of incremental
hydrocarbon from mature oil-bearing reservoirs.6 Further, the world's first industrial-scale CO2 capture and
sequestration (CCS) project was initialed at the Sleiper Field in the North Sea since 1996.7 As a part of a
portfolio of low-carbon technologies, 20 large-scale integrated CCS projects are currently operating or have
secured financial backing to proceed to construction (Global CCS Institute).8 In addition to the CO2-EOR
and CCS, CO2 enhanced geothermal system (CO2-EGS) has been proposed β utilizing supercritical CO2 as
the heat transmission fluid to extract heat energy from geothermal reservoirs as a means to produce
renewable geothermal energy, and to concomitantly geologically store CO2 through potential fluid losses at
depth (Brown, 2000; Spycher and Pruess, 2010; Tester et al., 2006). The CO2-brine system containing ions
of Na+, Ca2+, Mg2+, K+, Cl-, and SO42-, will be the most commonly encountered fluid system in all of above
mentioned engineered natural systems; a good understanding of the thermodynamic properties of the CO2-
brine system is, therefore, critical for evaluating, designing and modeling these industrial processes
(Spycher and Pruess, 2010; Pruess et al., 2001; Kumar et al., 2005; Bickle et al., 2007).
In geosciences, there are various sources from which the CO2-brine system could be naturally
generated and presented in the sallow crust of the earth (Kaszuba et al., 2006), e.g., the CO2-brine fluid
generated from a hydrocarbon reservoir at intermediate levels of thermal maturity of organic matter (Cappa
and Rice, 1995), or generated by degassing of CO2 in magma-hydrothermal system (Lowenstern, 2001).
Under high temperatures and pressures, the evidence that the CO2-brine systems transform the subsurface
rock matrix are abundant, such as the formation of ore deposits (Gize and Macdonald, 1993; Phillips and
Evans, 2004), the CO2-rich fluid inclusions in minerals (Lamb et al., 1987), and the participation of rock-
forming processes (Sisson et al, 1981). Therefore, over geologic time, the CO2-brine system can also be
6 Texas State Historical Association Website:https://www.tshaonline.org/handbook/online/articles/doksu 7 British Geological Survey Website: http://www.bgs.ac.uk/science/CO2/home.html 8 CCS Applications, Global CCS Institute:
http://www.globalccsinstitute.com/sites/default/files/pages/92241/projects-action-rgb-low-res.pdf
90
expected to have great influence on the rock and fluid properties in various geologic environments,
understanding the thermodynamic properties of this fluid system is of significant importance for
geosciences.
In spite of the fact that CO2 solubility in pure water (Spycher et al., 2003; Springer et al., 2012)
and in single-salt aqueous systems (Akinfiev and Diamond, 2010; Spycher et al., 2003; Springer et al.,
2012; Zhao et al., 2014a, Zhao et al., 2014b) has been widely studied, investigation of CO2 solubility in
mixed-salt solutions at elevated temperatures and pressures remains few and therefore the complexity of
ion-ion and ion-neutral interactions for the CO2-mixed-salt-H2O system is largely unknown. Correlating
and predicting CO2 solubility in such mixed-salt aqueous systems at elevated temperatures and pressures
has remained a difficult task (Yasunishi et al., 1979b; Rumpf et al., 1994). While some recent studies report
experimental CO2 solubility in aqueous mixed-salt solutions, they are unable or just using a simple
correlative equation to provide corresponding theoretical solubility calculations for the CO2-mixed-salt-
H2O system (Liu et al., 2011; Tong et al., 2013).
Nevertheless, three previously published models are capable of computing CO2 solubility in the
mixed-salt aqueous systems: the DS2006 model (Duan and Sun, 2003; Duan et al., 2006) the SP2010
model (Spycher et al., 2003; Spycher and Pruess, 2005, 2010) and the OLI Studio 9.0.6 β a commercial
software package developed by OLI Systems Inc (Springer et al., 2012). All three models show excellent
performance in calculating CO2 solubility in pure water and single-salt systems of CO2-NaCl-H2O, CO2-
CaCl2-H2O, and CO2-MgCl2-H2O (See Chapters 2 and 3) but their capacity for predicting CO2 solubility in
real brines remains to be validated, since: (1) the experimental data of CO2 solubility in mixed-salt brine at
elevated temperatures and pressures are too scarce to substantiate their performance, (2) for brine with a
relatively high concentrations of SO42- and K+ ions, the DS2006 and SP2010 models cannot be fitted well
to the experimental data (See Chapter 3). Therefore, a more accurate model is needed to predict the
solubility of CO2 in aqueous mixed-salt solutions.
Inspired by the studies of GΓΆrgΓ©nyi et al. (2006) and Gordon and Thorne (1967) on salting-out
effects on non-electrolytes, we have demonstrated that the additivity rule of Setschenow Coefficients
(Setchenow, 1889) of individual ions can be used to accurately calculate the solubility of CO2 in mixed-salt
solutions at elevated temperatures and pressures. Without previous experimental and modeling efforts on
91
CO2 solubility in pure water and in five single-salt aqueous systems (Chapters 2 and 3), the goal of
accurately predicting CO2 solubility in mixed-salt solutions cannot be easily achieved. Throughout Chapter
4, PSUCO2 denotes our updated CO2 solubility model for aqueous mixed-salt solution.
4.2 Materials and methods
4.2.1 Chemicals
The carbon dioxide used in all experiments was Coleman Instrument grade with a purity of
99.99 %. Water was purified by Milli-Q system and was degassed before loading it into the autoclave. The
purified water conductivity was below 610-6 S m-1. All aqueous salt solutions were prepared using this
Milli-Q water and ACS Grade reagents: sodium chloride (NaCl, J.T. Baker, 99%), calcium Chloride
(CaCl2β§2H2O, Alfa Aesar, 99%), sodium sulfate (Na2SO4, Amresco, 99%), magnesium chloride (MgCl2,
Alfa Aesar, 99%), potassium chloride (KCl, Alfa Aesar, 99%), Strontium chloride (SrCl2, anhydrous, Alfa
Aesar, 99%) and Sodium bromide (NaBr, Alfa Aesar, 99%).
4.2.2 Synthetic brine preparation.
The ionic strength based on molality was used herein as a measure of the concentration of mixed-
salt aqueous solutions, it is defined as πΌ = 0.5β πππ§π2
π , where ππ and π§π respectively represent the molality
and charge number of the i-th ion. The brines used for the CO2 solubility measurements include:
1) a natural Mt. Simon brine with IS = 1.815 mol kg-1;
2) a synthetic Mt. Simon formation brine with IS = 1.712 mol kg-1;
3) a synthetic NaCl+CaCl2 brine with IS = 1.712 mol kg-1;
4) a synthetic Antrim Shale formation brine35 with IS = 4.984 mol kg-1;
5) a synthetic NaCl+CaCl2 brine with IS = 4.984 mol kg-1.
92
The chemical compositions of the brines used for experimental studies are listed in Table 4. 1 and
Table 4. 2.
Table 4. 1 Chemical composition of the natural Mt. Simon brine.
Species Chemical composition of the natural Mt. Simon brine
mg/L mol/kg H2O IS mol/kg H2O
Ba2+ 1.1000 10-1 8.2655 10-7 1.6531 10-6
B 1.3300 10+1 1.2696 10-3 6.3479 10-4
Ca2+ 6.8770 10+3 1.7706 10-1 3.5413 10-1
Fe2+/3+ 4.2000 10+1 7.7607 10-4 1.5521 10-3
Mg2+ 1.2670 10+3 5.3792 10-2 1.0758 10-1
Mn2+ 4.9000 9.2036 10-5 1.8407 10-4
K+ 7.1700 10+2 1.8923 10-2 9.4616 10-3
Si 9.0000 3.3068 10-4 1.6534 10-4
Na+ 2.3317 10+4 1.0466 5.2329 10-1
Sr2+ 1.6500 10+2 1.9423 10-3 3.8864 10-3
S2- 5.6800 10+2 1.8278 10-2 3.6557 10-2
Br- 2.4600 10+2 3.1769 10-3 1.5884 10-3
Cl- 5.1068 10+4 1.4864 7.4319 10-1
I- 2.3100 1.8783 10-5 9.3916 10-6
SO42- 1.5110 10+3 1.6230 10-2 3.2459 10-2
Total ionic strength (IS / mol kg-1) 1.815
Note: Metals were determined by inductively coupled plasma optical emission spectrometry, anions were
determined by ion chromatography. The element boron (B) and silicon (Si) usually presented in the
aqueous phase as B(OH)4-(aq) and H3SiO4
-(aq), so the ionic strengths of (B) and (Si) were treated as the
same as that of. B(OH)4- and H3SiO4
-.The density of the Mt. Simon brine at 298 K and 1.013 bar is 1.0549
g/cm3, which was calculated by the empirical correlation (Eq.(4.7)).
Table 4. 2 Chemical compositions of the synthetic Mt.Simon brine and Antrim Shale formation brines and
the corresponding synthetic NaCl+CaCl2 proxy brines.
Salt species Synthetic Mt. Simon formation brine
/ mol kg-1 H2O
Synthetic Antrim Shale formation brine
/mol kg-1 H2O
Proxy brine I(a) Proxy brine II(b) Proxy brine I(a) Proxy brine II(b)
NaCl 1.0601 1.0601 2.9856 2.9856
CaCl2 0.1365 0.2172 0.3937 0.6661
Na2SO4 0.0165 - 0.0001 -
MgCl2 0.0544 - 0.2535 -
KCl 0.0188 - 0.0222 -
SrCl2 0.0021 - 0.0083 -
NaBr 0.0042 - 0.0090 -
IS 1.712 4.984 (a)The synthetic formation brines and the corresponding synthetic NaCl+CaCl2 brines are have the same
ionic strength. During the PSUCO2 model calculation, the synthetic formation brine composed of seven
salt species were simplified to five salt species because the PSUCO2 model is not able to take SrCl2 and
NaBr into consideration. The amount of SrCl2 and NaBr in synthetic formation brines are converted to the
equivalent amount of NaCl based on the ionic strength, while the concentration of the other salt species
remains the same.
93
(b)The proxy NaCl+CaCl2 brine has the same amount of NaCl as the corresponding synthetic formation
brine, while the concentrations of the other salt species are converted to the equivalent amount of CaCl2
based on the ionic strength.
4.2.3 Apparatus and procedure
Because the experimental CO2 solubility data reported herein were collected at two different
laboratories (PSU Energy Institute and National Energy Technology Laboratory (NETL)) independently,
there are two different methods employed to measure the solubility of CO2 in the synthetic brines and in the
natural Mt. Simon brine. Method 1 (used by PSU Energy Institute): the experimental system consisted of a
600-ml stainless steel autoclave (Parr Instrument Co.), a 40-ml stainless steel sample cell, a liquid CO2
pump and a 300-ml stainless steel pressure cell for sample analysis. After sampling, the dissolved CO2 in a
40-ml sample cell was slowly released to a 300-ml pressure cell. The mass of the dissolved CO2 was
determined by the pressure and temperature change before and after CO2 expansion. Details on the CO2
solubility measuring technique of the Method 1 and the error analysis approach can be found in a previous
publication (See Section 2.3, Chapter 2). Method 2 (used by NETL): the experimental system contains a
flexible gold cell hydrothermal rocking autoclave reactor for gas-liquid equilibration. Fluid samples were
withdrawn directly into glass, gas-tight syringes containing a small quantity of 45% (w/w) KOH, which
prevents the loss of CO2 during sampling and analysis. After sampling, KOH-stabilized samples were
injected into the acidification module of a UIC coulometric carbon analyzer, titrated using a perchloric acid
solution, and the evolved CO2 was transferred via inert gas stream into a coupled coulometric CO2 titration
cell. The UIC coulometric carbon analyzer is capable of detecting carbon in the range of 0.01 πg to 100 mg,
the detailed experimental procedure can be found in Dilmore et al. (2008).
94
Table 4. 3 Experimental CO2 solubility results in the synthetic formation and NaCl+CaCl2 brines.
T
/ K
P
/ bar
Method 1
IS=1.712 mol kg-1 IS=4.984 mol kg-1
Synthetic Mt. Simon
formation brine Synthetic NaCl+CaCl2 brine
Synthetic Antrim Shale
formation brine Synthetic NaCl+CaCl2 brine
mCO2 /
mol kg-1
err /
mol kg-1
mCO2 /
mol kg-1
err /
mol kg-1
mCO2 /
mol kg-1
err /
mol kg-1
mCO2 /
mol kg-1
err /
mol kg-1
323 100 0.843 0.013 0.850 0.015 0.535 0.015 0.539 0.028
323 125 0.902 0.014 0.898 0.021 0.573 0.014 0.578 0.010
323 150 0.931 0.012 0.925 0.017 0.604 0.014 0.600 0.012
323 175 0.956 0.012 0.951 0.022 0.605 0.008 0.608 0.009
373 100 0.595 0.007 0.590 0.012 0.376 0.011 0.386 0.006
373 125 0.696 0.009 0.691 0.012 0.433 0.004 0.438 0.008
373 150 0.756 0.010 0.759 0.014 0.483 0.010 0.490 0.015
373 175 0.812 0.013 0.818 0.008 0.506 0.010 0.521 0.011
423 100 0.506 0.010 0.505 0.007 0.326 0.013 0.328 0.008
423 125 0.616 0.013 0.608 0.016 0.394 0.026 0.397 0.011
423 150 0.697 0.012 0.703 0.014 0.446 0.004 0.444 0.019
423 175 0.777 0.023 0.780 0.028 0.484 0.010 0.489 0.019
T
/ K
P
/ bar
Method 2
IS=1.815 mol kg-1
Natural Mt. Simon formation
brine
mCO2 /
mol kg-1
err /
mol kg-1
328 50.5 0.488 0.030
328 99.8 0.785 0.036
328 150.4 0.849 0.026
328 200.7 0.927 0.011
Note: The instrumental error of Method 1 is about 0.7%. The chemical compositions of synthetic formation brines and NaCl+CaCl2 brines are listed in Table 4. 2.
The chemical compositions of the natural Mt. Simon brine are listed in Table 4. 1.
95
4.3 Results and discussions
4.3.1 Experimental results
Experimental CO2 solubility data in synthetic formation brine, synthetic binary NaCl+CaCl2 brine,
and the natural Mt. Simon brine of this study are listed in Table 4. 3.
4.3.2 Additivity rule of Setschenow Coefficients of the individual ions
The salting-out effects of a salt mixture with two or more salt species on a non-electrolyte have
been shown to be accurately additive at ambient conditions (Gordon and Thorne, 1967):
πππ πΆπΆπ2 = πππ πΆπΆπ2π β β ππ
ππΎπ ππ
π=1 πΆπ‘ (4.1)
where πΆπΆπ2 and πΆπΆπ2π are, respectively, the CO2 molarity (mole per liter of solution) in a mixed-salt solution
and in pure water at the same temperature and pressure. ππ is the fraction of the i-th salt species defined by
ππ = πΆπ π/πΆπ‘, with πΆπ‘ = β πΆπ
πππ=1 , where πΆπ
π and πΆπ‘ are the molarity of the i-th salt species and the total molar
concentration of all dissolved salts, respectively. πΎπ π in Eq. (4.1) is the Setschenow coefficient for the CO2
solubility in a single-salt aqueous solution. πΎπ π can be evaluated by the classical Setschenow equation34 as
below:
πΎπ π =
1
πΆπ πππ
πΆπΆπ2π
πΆπΆπ2π (4.2)
where πΆπΆπ2π is the CO2 molarity in pure water, and πΆπΆπ2
π is the CO2 molarity in the single-salt aqueous
solution with i-th salt species. The Setschenow coefficient of a given salt species may be separated by the
contribution of individual ions as below (GΓΆrgΓ©nyi et al., 2006):
96
πΎπ π = π+πΎπ ,πππ
π,π + πβπΎπ ,ππππ,π
(4.3)
where πΎπ ,ππππ,π
and πΎπ ,ππππ,π
are the separated Setschenow coefficients for cation and anion of the i-th salt
species; and π+ and πβ are the stoichiometric coefficients of the corresponding cation and anion,
respectively. In PSUCO2, an aqueous mixed-salt solution is treated as the mixture of the six types of ions
(Na+, Ca2+, Mg2+, K+, Cl- and SO42-) and H2O molecules. Other ions in a natural brine, such as Ba2+, Sr2+,
Fe3+ and Br-, were neglected during the calculation due to their typically low concentrations in natural
solutions. Therefore, for a brine with a salt mixture of NaCl, CaCl2, Na2SO4, MgCl2 and KCl, Eq. (4.3) can
be rewritten as below:
πΎπ πππΆπ = πΎπ ,πππ
ππ+ + πΎπ ,ππππΆπβ
πΎπ πΆππΆπ2 = πΎπ ,πππ
πΆπ2+ + 2πΎπ ,ππππΆπβ
πΎπ ππ2ππ4 = 2πΎπ ,πππ
ππ+ + πΎπ ,πππππ42β
πΎπ πππΆπ2 = πΎπ ,πππ
ππ2++ 2πΎπ ,πππ
πΆπβ
πΎπ πΎπΆπ = πΎπ ,πππ
πΎ+ + πΎπ ,ππππΆπβ
πΎπ ,ππππΆπβ = 0 (4.4)
In Eq. (4.4), the Cl- was chosen as a reference ion by assigning πΎπ Cπβ equals zero. Given that
Setschenow coefficient (πΎπ π) for CO2 solubility of each single-salt solution is known by Eq. (4.2), the
Setschenow coefficients for the individual ions (πΎπ ππ+, πΎπ
πΆπ2+ , πΎπ ππ2+
, πΎπ πΎ+, and πΎπ
ππ42β
) can be computed
by solving the set of linear equations (Eq. (4.4)). The Setschenow coefficient (πΎπ πππ₯) on CO2 solubility due
to the addition of mixed salts in aqueous solutions can be calculated using the additivity rule for individual
ions as below:
πΎπ πππ₯ = β ππ ,πππ
π πΎπ ,πππππ
π=1 (4.5)
97
where πΎπ πππ₯ is the Setschenow coefficient of a salt mixture; ππ ,πππ
π is the fraction of the i-th ion defined by
ππ ,ππππ = πΆπ ,πππ
π /πΆπ‘,πππ and πΆπ‘,πππ = β πΆπ ,πππππ
π=1 , where πΆπ ,ππππ is the molar concentration of the i-th ion, and
πΆπ‘,πππ is the sum of the molar concentration of all ions dissolved in the solution. Once πΎπ πππ₯ is obtained, the
CO2 molarity in a real brine can be calculated by Eq. (4.6) as below (Gordon and Thorne, 1967)
πππ πΆπΆπ2 = ππg πΆπΆπ2π β πΎπ
πππ₯πΆπ‘,πππ (4.6)
For a given brine composed of the five most frequently encountered salt species (NaCl, CaCl2,
Na2SO4, MgCl2, and KCl), the calculated results from Eq. (4.6) and Eq. (4.1) are the same. However, the
concentration of a natural brine is usually reported by ion molarity (mol L-1), thus Eq. (4.6) provides a more
convenient way for users to input a brine composition. The schematic of the additivity rule of the
Setschenow coefficients is illustrated in Figure 4. 1.
P, T and Brine
composition
NaCl(aq)
CaCl2(aq)
Na2SO4(aq)
MgCl2(aq)
KCl(aq)
Brine density
n
i
i
s
i
sCOCO CKCC1
0
22 loglog
CO2 solubility in
formation brine
Ks1
Ks2
Ks3
Ks4
Ks5
mCO
21
mCO22
mCO23
mCO2
4
mCO2 5
Figure 4. 1 The schematic of the additivity rule of the Setschenow coefficients. At a given P-T-x condition,
firstly, the PSUCO2 model calculate the CO2 solubility (mCO2: mol kg-1) in each single salt aqueous
solution; secondly, the Setschenow coefficients (Ksi) for each single salt species on CO2 solubility can be
calculated by using Eq. (4.3); finally the additivity rule of the single salt (or single ion) Setschenow
coefficients is used to compute the CO2 solubility in mixed-salt solutions.
98
The calculated CO2 molarity (πΆπΆπ2) can be converted to CO2 molality (ππΆπ2) by using the density
correlations of the different types of brine. The density of brine at 298K and 1.013 bar can be calculated by
Eq. (4.7).
ππππππ(πππβ3) = ππ₯2 + ππ₯ + π (4.7)
where coefficients a, b and c are constants (Listed in Table 4. 4) dependent on the specific brine, and they
were determined by fitting the literature experimental density of different brines (McIntosh et al., 2004;
Pitzer et al., 1984; Gates and Wood, 1985; Ghafri et al., 2012; and Dresel and Rose, 2010).
Table 4. 4 Brine density (g cm-3) correlation (Eq. (4.7)) at 298K and 1 bar.
Brine x(a) a b c
NaCl m, mol kg-1 -1.08 10-3 3.9376 10-2 9.9777 10-1
CaCl2 m, mol kg-1 -3.371 10-3 8.4788 10-2 1.0049
Na2SO4 m, mol kg-1 -8.2 10-3 1.2301 10-1 9.9775 10-1
MgCl2 m, mol kg-1 -3.967 10-3 7.8024 10-2 9.9673 10-1
KCl m, mol kg-1 -1.574 10-3 4.4934 10-2 9.9791 10-1
Mixed-salt TDS, g L-1 0 6.5251 10-4 1.00097 (a)m: salt molality, mol kg-1; TDS: total dissolved solids, g L-1.
In addition, at the pressures larger than 100 bar, an error correction term was used in the PSUCO2
model to compensate for the calculation error at pressures greater than 100 bar (Eq. (4.7)). The correction
term πΏππΆπ2 is about 0-5% when compared to the calculated CO2 solubility (ππΆπ2: mole CO2 per kilogram
of H2O) in the aqueous phase.
πΏππΆπ2 = 0(π β€ 100πππ)
πΏππΆπ2 = π1 +π2
πβπ©+ π3πΌ
0.5 + 10β3π4π + π5ππΆπ2β² (π > 100πππ) (4.8)
The form of Eq. (4.8) is the same as the expression of Setchenow coefficients proposed by
Akinfiev and Diamond (2010). In Eq. (4.7), I is the total ionic strength (mol kg-1) of the brine, π© is a
constant, equal to 228 according to Akinfiev and Diamond (2010). T is temperature in K, and ππΆπ2β² is the
99
computed CO2 molality without any correction. The parameters a1 to a5 (given in Table 4. 5) were
determined by the least-squares fitting of the errors between the experimental CO2 solubility data (this
study; Li et al., 2004; Liu et al., 2011; Tong et al., 2013) and the PSUCO2 model calculated values.
Table 4. 5 The parameters of Eq. (4.8)
Parameter(a) value
a1 -0.6610
a2 17.4446
a3 1.0699
a4 0.0614
a5 0.0712 (a)The parameter are determined only using the experimental data (Yasunishi et al., 1979; Li et al., 2004;
Liu et al., 2011; Tong et al., 2013)
As a result, the CO2 solubility (ππΆπ2) in the mixed-salt solutions can be obtained by adding the
correction term as below,
ππΆπ2 = ππΆπ2β² + πΏππΆπ2 (4.9)
4.3.3 Comparison of model calculations against the experimental data
The reliability of the experimental technique of Method 1 is confirmed in Chapters 2 and 3. Figure
4. 2 shows that the experimental data collected using Method 2 are in good agreement with the previously
published models (DS2006, SP2010, and OLI Studio 9.0.6). In Figure 4. 2, the experimental data collected
by Method 2 were slightly lower than the predicted values of the PSUCO2 model. There can be many
reasons for the small difference between the experimental CO2 solubility in natural Mt. Simon formation
brine and the modeling results. Firstly, the natural Mt. Simon formation brine contains some ions (e.g. Ba2+,
Fe2+/3+, Sr2+, Br-, etc.) that is neglected in the PSUCO2 model and therefore the salting-out effect of these
ions on CO2 solubility are not accounted during the model calculations. Secondly, the influence of the
initial pH on the CO2 solubility in the aqueous phase is not considered during the model calculations. The
pH and composition of the natural Mt. Simon brine maybe changed after initial analysis, this variation in
100
natural brine can also leads to slightly different experimental results. Thirdly, a small difference between
experimental and modeling results can also result from both the experimental uncertainty and the
inaccuracy of the model calculations. Considering the two sets of experimental data were collected at
different temperatures (323 and 328K), brine concentrations, and even using different approaches (Method
1 and Method 2), based on the comparison between the experimental and modeling results (Figure 4. 2), the
Method 2 considered to be reliable for measuring CO2 solubility in brine at the P-T-x conditions pertinent
to geologic CO2 storage. Figure 4. 2b shows the proposed PSUCO2 model is capable of predicting the
experimental results both in synthetic Mt. Simon brine (Method 1) and the natural Mt. Simon brine
(Method 2).
Sodium chloride (NaCl) is the dominant component of most reservoir brines and therefore the
single-salt aqueous NaCl solution is widely used as a proxy for natural formation brine for CO2 solubility
studies. In this study, the experimental results corroborates that NaCl+CaCl2 brine can be used as a proxy
for studying CO2 solubility in synthetic (or natural) formation brines (Figure 4. 3(a,b)), provided that the
same NaCl molality and the total ionic strength for both brines. As for NaCl+CaCl2 and NaCl-only brines,
in order to identify a more realistic surrogate for studying CO2 solubility in natural formation brines, a
comparison of the experimental CO2 solubilities between the two brines (NaCl+CaCl2 and NaCl-only) with
the same ionic strength is needed.
Table 4. 6 The average absolute deviation of the PSUCO2 model calculated CO2 solubility in NaCl+CaCl2
and NaCl brines from the experimental CO2 solubility data in synthetic Mt. Simon and Antrim Shale
formation brines.
Experimental CO2
solubility in synthetic
formation brine
T / K
AAD % (Compared to the experimental CO2 solubility
data in synthetic formation brine)
PSUCO2
(NaCl+CaCl2+MgCl2
+Na2SO4+KCl)
PSUCO2(a)
(NaClβonly)
Experimental
data(b)
(NaCl+CaCl2)
Synthetic Mt. Simon
formation brine, IS=1.712
mol/kg
323 0.57 3.34 0.61
373 2.34 1.29 0.67
423 0.59 0.98 0.69
Synthetic Antrim Shale
formation brine, IS=4.984
mol/kg
323 1.41 6.43 0.69
373 2.58 0.65 2.05
423 1.38 1.14 0.71
Overall AAD % 1.48 2.31 0.91 (a)The PSUCO2 generated CO2 solubility data in aqueous NaCl solution provides comparable accuracy with
the corresponding experimental data.20 (b)The AAD in column 5 is calculated between the experimental CO2 solubility in NaCl+CaCl2 and
synthetic formation brines
101
P / bar
40 60 80 100 120 140 160 180 200 220
mC
O2 / m
ol kg
-1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
PSUCO2
DS2006
SP2010
OLI Studio 9.0
This study, Method 2
328 K, IS=1.815 mol/kgNatural Mt. Simon Brine
(a)
P / bar
40 60 80 100 120 140 160 180 200 220
mC
O2 / m
ol kg
-1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
323 K, 1.712 mol/kg, PSUCO2
328 K, 1.815 mol/kg, PSUCO2
323 K, 1.712 mol/kg, Method 1
328 K, 1.815 mol/kg, Method 2
Natural Mt. Simon brine at 328K and IS=1.815 mol/kg
Synthetic Mt. Simon brine at 323K and IS=1.712 mol/kg
(b)
Figure 4. 2(a, b) Comparison of model calculations with experimental data. Figure. 4.2a: Comparison of
model calculations (PSUCO2, DS2006, SP2010 and OLI Studio 9.0.6) with experimental CO2 solubility
measured by Method 2. For the experimental data collected by Method 2, the synthetic brine recipe used
for model calculations is: 1.0547 mol/kg NaCl, 0.1771 mol/kg CaCl2, 0.0162 mol/kg Na2SO4, 0.0538
mol/kg MgCl2, 0.0189 mol/kg KCl (IS=1.815). Figure 4.2b: Comparison of the PSUCO2 modeling results
with our experimental CO2 solubility data in natural Mt. Simon brine (IS=1.712 mol kg-1) at 323 K and in
102
synthetic Mt. Simon brine (IS=1.815 mol kg-1) at 328 K. For the experimental data collected by Method 1,
the synthetic brine recipe used for PSUCO2 calculation is listed in Table 4. 2(IS=1.712 mol kg-1).
P / bar
60 80 100 120 140 160 180 200
mC
O2 / m
ol kg
-1
0.25
0.45
0.65
0.85
1.05
PSUCO2
SP2010
DS2006
OLI Studio 9.0
Syn. Mt. Simon brine
Syn. NaCl+CaCl2 brine
Syn. Mt. Simon and NaCl+CaCl2 brinesIS=1.712 mol/kg
323 K
373 K
423 K
(a)
P / bar
60 80 100 120 140 160 180 200
mC
O2 / m
ol kg
-1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
PSUCO2
SP2010
DS2006
OLI Studio 9.0
Syn. Michigan Basin brine
Syn. NaCl+CaCl2 brine
Syn. Michigan Basin and NaCl+CaCl2 brinesIS=4.984 mol/kg
323 K
373 K
423 K
(b)
Figure 4. 3(a, b) Comparisons of the modeling results against the experimental CO2 solubility data in both
synthetic reservoir brines and NaCl+CaCl2 brines collected using the Method 1. (a) IS=1.712 mol kg-1; (b)
IS=4.984 mol kg-1.
103
TDS / g L-1
0 50 100 150 200 250 300 350
mC
O2 / m
ol kg
-1
0.010
0.015
0.020
0.025
0.030
0.035
PSUCO2
SP2010
DS2006
OLI Studio 9.0
CaCl2+KCl (1:3)
CaCl2+KCl (1:1)
CaCl2+KCl (3:1)
298.15 K and 1.013 barSyn. CaCl2+KCl brineYasunishi et al. (1979)
(a)
TDS / g L-1
0 50 100 150 200 250
mC
O2 / m
ol kg
-1
0.012
0.016
0.020
0.024
0.028
0.032
0.036OLI Studio 9.0
PSUCO2
SP2010
DS2006
NaCl+Na2SO4 (1:3)
NaCl+Na2SO4 (1:1)
NaCl+Na2SO4 (3:1)
298.15 K and 1.013 barSyn. NaCl+Na2SO4 brineYasunishi et al. (1979)
(b)
104
TDS / g L-1
25 75 125 175 225 275
mC
O2 / m
ol kg
-1
0.012
0.016
0.020
0.024
0.028
0.032
0.036PSUCO2
SP2010
DS2006
OLI Studio 9.0
NaCl+KCl (1:3)
NaCl+KCl (1:1)
NaCl+KCl (3:1)
298.15 K and 1.013 barSyn. NaCl+KCl brineYasunishi et al. (1979)
(c)
TDS / g L-1
10 30 50 70 90 110
mC
O2 / m
ol kg
-1
0.016
0.020
0.024
0.028
0.032PSUCO2
SP2010
DS2006
OLI Studio 9.0
NaCl+CaCl2+KCl (2:1:1)
298.15 K and 1.013 barSyn. NaCl+CaCl2+KCl brineYasunishi et al. (1979)
(d)
Figure 4. 4(a-d) Comparison of model calculations against the experimental data reported by Yasunishi et
al. (1979) at 1 atm and 298 K (a) synthetic CaCl2+KCl brine; (b) synthetic NaCl+Na2SO4 brine; (c)
synthetic NaCl+KCl brine; (d) synthetic NaCl+CaCl2+KCl brine. The ratios of the salt concentration in the
figure are based on the molarity (mole per liter of solutions).
105
P / bar
0 50 100 150 200 250
mC
O2 / m
ol kg
-1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
PSUCO2
SP2010
OLI Studio 9.0
DS2006
Li et al. (2004)
332 K, Weyburn Formation brine
Figure 4. 5 Comparisons of the model calculations (PSUCO2, SP2010 and OLI) against the experimental
CO2 solubility data7 in the Weyburn Formation brine. The chemical composition of the Weyburn Formation
brine is: 1.3022 mol kg-1 Na+, 0.0505 mol kg-1 Ca2+, 0.0239 mol kg-1 Mg2+, 0.0119 mol kg-1 K+, 1.5255 mol
kg-1 Cl- and 0.0406 mol kg-1 SO42-.
However, in this study, we use the modeling results in place of the experimental CO2 solubility in
aqueous NaCl-only solutions to save effort and time from additional experimental work for the CO2-NaCl-
H2O system, because (1) the CO2 solubility in aqueous NaCl solution is well-understood at the P-T-x
conditions of interest (See Chapter 2) it can be accurately calculated by either previously published models
(DS2006, AD2010 (Akinfiev and Diamond, 2010), SP2010, and OLI Studio 9.0.6) or the PSUCO2 model,
and (2) we believe that the PSUCO2 calculated CO2 solubility in single salt aqueous NaCl solutions
(Column 4, Table 4. 6) provides comparable accuracy (average absolute deviation (AAD)<1%) to the
corresponding experimental data in aqueous NaCl solutions at 323-423 K, 100-175 bar and 0-6 mol kg-1
NaCl (See Chapter 2).
The overall AAD of the experimental CO2 solubility in NaCl+CaCl2 brine (Column 5, Table 4. 6)
and the PSUCO2 modeling results in NaClβonly brine (Column 4, Table 4. 6) from the experimental CO2
solubility data in the synthetic formation brines are 0.91% and 2.31%, respectively. This comparison
demonstrates that the NaCl+CaCl2 brine performs better than NaClβonly brine as a surrogate for studying
CO2 solubility in synthetic (or natural) formation brines. Therefore, for geological carbon storage and CO2-
106
EGS applications, the synthetic NaCl+CaCl2 brine offers an accurate, accessible and inexpensive
alternative to researchers who may experience difficulty securing and preserving natural brine samples.
While each of the previously published CO2 solubility model is able to predict the CO2 solubility
in synthetic formation brines with a very good accuracy (AAD<3%) at the experimental P-T-x region
(Figure 4. 3), Figure 4. 4 demonstrates that the SP2010 and DS2006 models does not match the data from
Yasunishi et al. (1979), especially for the case of CaCl2+KCl (Figure 4. 4a) and NaCl+Na2SO4 (Figure 4.
4b). This difference arises from the fact that the brines used by Yasunishi et al. (1979) have a high
concentration of K+, SO42-. It is difficult for the DS2006 and SP2010 model to perform well for mixed-salt
aqueous solutions with relatively high concentrations of Na2SO4 or KCl, or both of them (See Chapter 3)
The commercial software OLI Studio 9.0.6 performs much better than the DS2006 and SP2010 models in
predicting the CO2 solubility in aqueous solutions with high concentration of K+ and SO42- ions (See
Chapter 3). However, naturally encountered brine is usually dominated by NaCl, CaCl2, and MgCl2, plus a
small amount of K+ and SO42- ions (McIntosh et al., 2004) the influences of K+ and SO4
2- ions on the CO2
solubility in commonly found natural brines are small. Therefore, although there is a lack of capacity to
deal with K+ and SO42- ions, the SP2010 and DS2006 models can still predict the experimental CO2
solubility data (Li et al., 2004) in typical formation brine with quite good accuracy as shown in Figure 4. 2a
and Figure 4. 5.
In Figure 4. 6a, with the same percent of salts by weight, among the systems of NaCl+KCl,
NaCl+CaCl2 and CaCl2+KCl, the experimental CO2 solubility in CaCl2+KCl aqueous solution has the
greatest value, whereas the CO2 solubility in the NaCl+CaCl2 solution has the smallest values (Liu et al.,
2011) The particular pattern on the magnitude of the CO2 solubility in these three mixed-salt solutions was
also shown in the calculated results of PSUCO2, but was not preserved in the results of the other models
(DS2006, SP2010 and OLI Studio 9.0.6). Figure 4. 6(b-d) shows that the DS2006 and SP2010 models tend
to systematically underpredict the experimental CO2 solubility given by Liu et al. (2011) more than does
PSUCO2. Additionally, at the pressures below 100 bar, the calculation results between the OLI Studio
9.0.6 and PSUCO2 are close to each other, at the higher pressures (P>100 bar), although the OLI Studio
9.0.6 tend to underpredict the experimental data at 308 K, it still performs better than the DS2006 and
SP2010 models for aqueous mixed-salt solutions.
107
P / bar
20 40 60 80 100 120 140 160 180
mC
O2 / m
ol kg
-1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
PSUCO2
SP2010
DS2006
OLI Studio 9.0
NaCl+KCl
NaCl+CaCl2
CaCl2+KCl
PSUCO2
CaCl2+KCl
NaCl+KCl
NaCl+CaCl2
Liu et al. (2011)318.15 K
DS2006
NaCl+KCl
CaCl2+KCl
NaCl+CaCl2
SP2010
NaCl+KCl
CaCl2+KCl
NaCl+CaCl2
OLI Studio 9.0
NaCl+KCl
CaCl2+KCl
NaCl+CaCl2
(a)
P / bar
0 50 100 150 200
mC
O2 / m
ol kg
-1
0.1
0.3
0.5
0.7
0.9
1.1
PSUCO2
SP2010
DS2006
OLI Studio 9.0
308.15 K
318.15 K
328.15 K
Liu et al. (2011)14.3 wt% syn. NaCl+CaCl2+KCl brine
0.9518 mol/kg NaCl0.5012 mol/kg CaCl20.2408 mol/kg KCl
(b)
108
P / bar
0 50 100 150 200
mC
O2 / m
ol kg
-1
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
PSUCO2
SP2010
DS2006
OLI Studio 9.0
308.15 K
318.15 K
328.15 K
Liu et al. (2011) 5 wt% syn. NaCl+CaCl2+KCl brine
0.3002 mol/kg NaCl0.1581 mol/kg CaCl20.2353 mol/kg KCl
(c)
P / bar
0 50 100 150 200
mC
O2 / m
ol kg
-1
0.1
0.3
0.5
0.7
0.9
1.1
1.3
PSUCO2
SP2010
DS2006
OLI Studio 9.0
308.15 K
318.15 K
328.15 K
Liu et al. (2011)10 wt% syn. NaCl+CaCl2+KCl brine
0.6338 mol/kg NaCl0.3337 mol/kg CaCl20.4968 mol/kg KCl
(d)
Figure 4. 6(a-d) Comparison of the model calculations against the experimental data given by Liu et al.
(2011) for the synthetic brines at elevated temperatures and pressures. (a) results for the NaCl+KCl,
NaCl+CaCl2 and CaCl2+KCl brines; (b) results for 14.3 wt% NaCl+CaCl2+KCl brine; (c) results for 5wt%
NaCl+CaCl2+KCl brine; (d) results for 10wt% NaCl+CaCl2+KCl brine.
109
In addition, the calculated CO2 solubility of all available models (PSUCO2, DS2006, SP2010 and
OLI Studio 9.0.6) were compared at 1-600 bar and at 523 K in Figure 4. 7(a, b). The comparison showed
that over the P-T-x range of 1-600 bar, 523 K, and 0-5 mol/kg ionic strength, all models provide roughly
comparable results. Among these four models, only the PSUCO2 and DS2006 models can work at the
pressure range of 600-2000 bar, but the differences between the two models become quite large at higher
pressures for the formation brines. To the best of our knowledge, there is no experimental data available for
mixed-salt solutions to make a direct comparison between the experimental data and model calculations.
The experimental CO2 solubility in formation brines at high temperatures and pressures (e.g. 523 K, 1800
bar) is needed to resolve this discrepancy. However, the performance of the PSUCO2 and DS2006 models
for the CO2-H2O system at high temperatures and pressures were validated by the corresponding
experimental data (TΓΆdheide and Franck, 1963; Takenouchi and Kennedy, 1965; Malinin, 1959).
P / bar
0 500 1000 1500 2000
mC
O2 / m
ol kg
-1
0
2
4
6
8
10
12OLI Studio 9.0
PSUCO2
DS2006
SP2010
Takenouchi and Kennedy (1965)
TΓΆdheide and Franck (1963)
Malinin (1959)
523.15 K
Pure w
ater
Mt. Simon brine IS
= 1.712
Michigan Basin brine IS = 4.984
600 bar
(a)
110
P / bar
100 200 300 400 500 600
mC
O2 / m
ol kg
-1
0
1
2
3
4
5OLI Studio 9.0
PSUCO2
DS2006
SP2010
Takenouchi and Kennedy (1965)
TΓΆdheide and Franck (1963)
Malinin (1959)
523.15 K
Pure water
Mt. Simon brine IS = 1.712
Michigan Basin brine IS = 4.984
(b)
Figure 4. 7(a, b) Comparison of PSUCO2 with the DS2006 and SP2010 models up to 2000 bar at 523K:
The experimental CO2 solubility in pure water are taken from literature (TΓΆdheide and Franck, 1963;
Takenouchi and Kennedy, 1965; Malinin, 1959).
AAD %
0 2 4 6 8
PSUCO2
OLI Studio 9.0
SP2010
DS2006
4.3%
5.0%
6.3%
6.4%
Figure 4. 8 The average absolute deviation (AAD %) of the calculated CO2 solubility in aqueous mixed-
salt solutions among different models compared to the experimental data (Table 4. 7).
111
Table 4. 7 The absolute average deviations (AAD %) of model calculations from the experimental data.
References
No.
Systems P/
bar
T /
K
IS /
mol kg-1
N(a) Model calculation(b), AAD %
PSUCO2 SP2010 DS2006 OLI Studio
22 (c) Seawater 1-45.6 273-298 0.73 37 8.52 (37) 12.46 (24) 13.09 (31) 9.48(37)
23
KCl+CaCl2
NaCl+Na2SO4
NaCl+KCl
KCl+NaCl+CaCl2
1.013 298 0.4-9.1 54 2.05(54) 8.66 (47) 8.26 (51) 3.84(54)
24 (d) Utsira porewater 80-120 291-353 0.57 37 13.45 (37) 14.22 (37) 13.66 (37) 15.30(37)
25 Weyburn formation brine 17.6-208.7 332 1.58 6 7.39 (6) 7.74 (6) 7.75 (6) 7.45(6)
26
NaCl+CaCl2
CaCl2+KCl
KCl+NaCl
NaCl+CaCl2+KCl
13-160 308-328 1.0-3.2 99 5.52 (99) 8.98 (99) 10.87 (99) 5.40(99)
27 NaCl+KCl 10.7-171.6 309-425 1.05 14 4.50 (14) 5.91 (14) 5.53 (14) 5.05(14)
This study
NaCl+CaCl2
NaCl+CaCl2+Na2SO4+MgCl2
+KCl
100-175 323-423 1.71-4.98 48 1.72 (48) 2.82 (48) 2.94 (48) 1.93(48)
This study Natural Mt. Simon formation
brine 50-200 328 1.815 4 4.74 (4) 3.84 (4) 3.15 (4) 6.13(4)
Overall AAD* 4.3(225) 6.3(218) 6.4(222) 5.0(225) (a)N is the total number of experimental data reported in the literature. (b)Model calculation results were shown as average absolute deviation (AAD), the number in the parentheses represents the actual number of experimental data
evaluated by each model. The average absolute deviation (AAD) is defined as:π΄π΄π·(%) =100
πpβ |
ππΆπ2,πππππ βππΆπ2,π
ππ₯π
ππΆπ2,πππ₯π |
πππ=1
%, where ππΆπ2,πππππ is the model calculated
results; ππΆπ2,πππ₯π
is the experimental CO2 solubility taken from literature; and Np represents the total number of experimental data evaluated for each work. (c)The data from Stewart and Munjal22 were excluded from the overall AAD due to all the models are significant deviate from the experimental data (d)The data from Rochelle and Moore24 were excluded from the overall AAD due to: 1) the random error of the repeated measurements at the same P-T-x
condition ranging from 2 to 20% so there is a large uncertainty of the experimental work; 2) all the models are significant deviate from the experimental data.
112
Table 4. 8 The components, key parameters, and the limitations of PSUCO2 (Modified from Table 2. 9).
No. Model
Components
Description Applicable
P-T range
Ref.
1 Modified RK EoS Spycher et al. (2003) modified RK EoS 273-573K
1-2000 bar Spycher et al. (2003)
2 Mixing rule A two-parameter mixing rule for polar molecules 273-573K
1-2000 bar
Panagiotopoulos and Reid
(1986)
Spycher et al. (2003)
3 kH2O-CO2 Mixing rule parameter for the CO2-H2O system 273-573K
1-2000 bar Spycher et al. (2003)
4 kCO2-H2O
Empirical determined mixing rule parameter.
1. T<473 K, kCO2-H2O was considered as only temperature-
dependent.
2. T>473 K, kCO2-H2O is the function of both temperature and
pressure.
273-573K
1-2000 bar Table 2. 8
5 ππ»2π, ππΆπ2 Fugacity coefficients of H2O and CO2 for the CO2-rich
phase
273-573K
1-2000 bar
Spycher et al. (2003)
Panagiotopoulos and Reid
(1986)
6 Henry's law constant The Henry's law constant of CO2 in H2O is used for phase
equilibrium calculations
273-573K
1-2000 bar
FernΓ‘ndez-Prini et al.(2003)
Eq. (2.3), Table 2. 5
7 ππ€π , Ps , π£π ,ππ, ππ»2π
The fugacity coefficient, vapor pressure, molar volume,
relative permittivity and density of pure water
238-873K, 0-1.2 104 bar
for ππ, the others
251-1273K
up to 104 bar
IAPWS-95 EoS for pure water
(Wagner and PruΓ, 2002)
FernΓ‘ndez et al. (1997)
8 οΏ½Μ οΏ½πΆπ2
TΓΆdheide and Franck's (1963) data were used to determine
the values of οΏ½Μ οΏ½πΆπ2 at temperatures from 323-573K and
pressures from 200-2000 bar
273-573K
1-2000 bar Table 2. 4
9 Pitzer activity model
Calculating the activity coefficient of dissolved CO2 and
salts, and osmotic coefficient of water, at elevated
temperatures and pressures.
273-573K
1-2000 bar
Akinfiev and Diamond (2010)
Section 2.4.2 and Section 3.3
10 πππ, ππππ Pitzer pure neutral components interaction parameters 273-573K Table 2. 6
113
No. Model
Components
Description Applicable
P-T range
Ref.
11 π½ππ(0)
, π½ππ(1)
, πΆππ
The Pitzer binary ion-ion parameters for the binaryH2O-salt
systems at elevated temperatures and pressure were taken
from literature.
273-573K
1-1000 bar
0-6 mol kg-1 of NaCl,
CaCl2, and MgCl2
0-2 mol kg-1 of Na2SO4
0-4.7 mol kg-1 of KCl
Holmes et al. (1994)
Rogers and Pitzer (1981)
Rumpf and Maurer (1993)
Wang and Pitzer (1998)
Holmes and Mesmer (1983)
12 π΅πΆπ2βπ πππ‘
πΆπΆπ2βπΆπ2βπ πππ‘
The combined Pitzer interaction parameters for the CO2-
salt-H2O system 273-573K
Akinfiev and Diamond (2010)
Table 3. 1
13 ππππ
Pitzer's triple-ion interaction parameter determined by the
experimental data given by Zhao et al. (2014a) and Zhao et
al. (2014b).
Determined 323, 373,
423K
Extrapolated
273-573K
Table 2. 7
Table 3. 2
14 πΎπ ,ππππ , πΎπ ,πππ
π , πΎπ πππ₯
Setschenow coefficients for individual ions, mixed-salts of
CO2 solubility in brines at elevated temperatures and
pressures
273-573K
1-2000 bar Chapter 4
15 πΏππΆπ2
The error correction term for CO2 solubility in mixed-salt
solutions when P > 100 bar. This term is generally around
5% of the calculated CO2 molality at high P-T-x reigons.
P>100 bar
Determined at 323-423K Chapter 4
16 The additivity rule of
Setschenow coefficients Computing πΎπ
πππ₯ from πΎπ ,ππππ and πΎπ ,πππ
π 273-573K
1-2000 bar This study, Eqs. (4.1) and (4.6)
17 Solving phase
equilibria equations
The phase equilibria equations were solved by the Netwon-
Raphson approach with iterations.
273-573K
1-2000 bar Figure 2. 7
114
In sum, by using additivity rule of Setschenow Coefficients of the individual ions, the PSUCO2
model demonstrates an improvement (Table 4. 7 and Figure 4. 8) relative to the previously published
models (DS2006, SP2010, and OLI Studio 9.0.6) in predicting CO2 solubility in formation brines at the P-
T-x region pertinent to CCS and CO2-EGS. The components, key parameters, and limitations of the
PSUCO2 model are also summarized in Table 4. 8.
As an application of the proposed PSUCO2 model, the model calculated CO2 solubility contours
on the P-T diagram at 100-1500 bar and 298.15-523.15 K are shown in Figure 4. 9. A clear evidence of the
strong salting-out effect on CO2 solubility in the Mt. Simon formation brine (Figure 4. 9b) can be observed
when compared to the CO2 solubility contours in pure water (Figure 4. 9a). The point A on each contour
map indicates a fixed P-T condition of 900 bar and 373.15 K. The contour for 1.8 mol kg-1 CO2 is located
on the left side of the point A for the CO2-H2O system (Figure 4. 9a), when the aqueous phase is changed
from pure H2O to the Mt. Simon formation brine, the same contour (1.8 mol kg-1 CO2) is moved to the right
side of the point A (Figure 4. 9b).
In addition to the salting-out effect, each contour map can be divided into two regions (Region I
and Region II) based on the temperature-dependent behavior of CO2 solubility in the aqueous phase. The
boundary between Region I and Region II is defined as the maximum gradient path between the adjacent
CO2 solubility contours. In Figure 4. 9, the path of maximum gradient is roughly shown as the straight lines
between the neighbored contours. In Region I, the CO2 solubility in the aqueous phase decreases
monotonically in response to increased temperature, but at a given pressure in region II, the behavior of the
CO2 solubility in response to temperature increase is the opposite of that in Region I. For instance,
following the isobaric paths a-b-c (Region I) and d-e-f (Region II) on the P-T diagram (Figure 4. 9a), as
temperature increases, CO2 solubility decreases along the path a-b-c, but increases along the path d-e-f. In
addition, at the points b and e, CO2 solubility at two different temperatures reached the same value
(ππΆπ2|π=ππΆπ2|π=1.8 mol kg-1). Along the isobaric path a-b-c-d-e-f, CO2 solubility decreases to a minimum
then increases in response to increased temperature.
We have discussed this temperature-dependent behavior of CO2 solubility by defining a βtransition
zoneβ on the P-x diagram (Chapter 2, Figure 2. 14(a,b)), but the contours on the P-T diagram provide a
different perspective on this phenomenon. On the P-T diagram, the P-T region (100-400 bar, 298-373 K)
115
(Spycher and Pruess, 2010) for typical CCS project is located mainly in Region I, whereas the P-T window
(200-600 bar, 373-573 K) (Spycher and Pruess, 2010) for the CO2-EGS concept is located mainly in
Region II, as shown in Figure 4. 9b. Understanding the different temperature-dependent behavior of CO2
solubility in these two distinct regions may shed light on future work for evaluating and modeling the CCS
and CO2-EGS processes.
9.0
7.0
5.5
5.5
4.5
4.5
3.8
3.8
3.0
3.0
3.0
2.5
2.5
2.5
2.2
2.2
2.2
2.2
2.2
2.0
2.0
2.0
2.0
1.8
1.8
1.8
1.6
1.6
1.6
1.4
1.4
1.4
1.2
1.2
1.2
0.8
0.8
0.8
P / bar
100 300 500 700 900 1100 1300 1500
T / K
298.15
323.15
348.15
373.15
398.15
423.15
448.15
473.15
498.15
523.15
XA. .
. . .
.
.Region I
Region II.
...
.
.
abcd
e
f
(a)
116
5.04.5
4.0
4.0
3.5
3.5
3.0
3.0
2.5
2.5
2.2
2.2
2.2
1.8
1.8
1.8
1.8
1.8
1.6
1.6
1.6
1.6
1.4
1.4
1.4
1.2
1.2
1.21.0
1.0
1.0
P / bar
100 300 500 700 900 1100 1300 1500
T / K
298.15
323.15
348.15
373.15
398.15
423.15
448.15
473.15
498.15
523.15
XA.
. . . .
. Region II
Region I
CO2-EGS
CCS
(b)
Figure 4. 9(a, b) The CO2 solubility contours in pure water and synthetic Mt. Simon formation brine
generated by the PSUCO2 model. Numbers on the contour indicate the CO2 solubility value by molality
(mol kg-1): (a) pure water, IS = 0 mol kg-1; (b) synthetic Mt. Simon brine, IS = 1.712 mol kg-1.
117
CHAPTER 5
CONCLUISONS
118
A reliable PVT apparatus to measure the CO2 solubility in aqueous solutions at elevated temperatures
and pressures has been constructed and shown to provide accurate and reproducible CO2 solubility
measurements.
At 150 bar, new CO2 solubility data in the aqueous phase were collected at 144 P-T-x conditions
(Table 5. 1 and Table 5. 2). The instrumental error is around 0.7 % and the random error is from 0.3 to
4.5 % of the measured CO2 solubility values.
Experimental data demonstrates that CO2 solubility in aqueous solutions with different salt species are
significantly different, whether the solutions have the same percent of salt by weight or have the same
ionic strength. The experimental results also show that in the aqueous phase a cation with a higher
charge density will have more significant salting-out effect on dissolved CO2 than other ions.
A πΎ β π (activity coefficient - fugacity coefficient) type thermodynamic model (PSUCO2) is
developed and improved based on the measured CO2 solubility data. The model development starts
from the CO2-H2O and CO2-NaCl-H2O systems, then its capacity is extended to account for salt
species other than NaCl. Finally, the PSUCO2 model is capable of calculating CO2 solubility in natural
formation brine (or mixed-salt aqueous solution).
Based on both experimental and modeling results, a CO2 solubility βtransition zoneβ is found in the P-x
phase diagram for the CO2-H2O system. The CO2 solubility is not a monotonic function of temperature
in the transition zone. However, outside of that transition zone, the CO2 solubility decreases or
increases in response to increased temperature.
The path of the maximum gradient of the CO2 solubility contours is defined to divide the P-T diagram
into two regions: in Region I, the CO2 solubility in the aqueous phase decreases monotonically in
response to increased temperature; in region II, the behavior of the CO2 solubility is the opposite of
that in Region I as the temperature increases. The P-T region for typical CCS project is located mainly
in Region I, whereas for the CO2-EGS concept it is located mainly in Region II.
The modeling results show a positive correlation between the H2O solubility in the CO2-rich phase and
the activity of H2O in the aqueous phase, the influence of salts species on solubility of H2O in the CO2-
rich phase is clearly observed.
119
The comparison of the PSUCO2 model to the widely-accepted models and commercial software
reveals an improvement of the proposed model. A web-based CO2 solubility computational tool is also
developed for readerβs convenience and it can be accessed via the link www.carbonlab.org/psuCO2/
Table 5. 1 P-T-x matrix of CO2 solubility study for single-salt system (96 P-T-x points were measured,
random error up to 5%).
System* P / bar T / K Salt Molality / mol kg-1
H2O
150
323.15
373.15
423.15
0
NaCl 1 2 3 4 5 6
CaCl2 1/3 2/3 1 4/3 5/3 2
Na2SO4 1/3 2/3 1 4/3 5/3 2
MgCl2 1/3 2/3 1 4/3 5/3 2
KCl 0.5 1 2 3 4 4.5
*The CO2 and H2O presented in the experimental system are not shown in the table.
Table 5. 2 P-T-x matrix of CO2 solubility study for mixed-salt system (48 P-T-x points were measured,
random error up to 3%).
Experimental System* P / bar T / K Ionic strength / mol kg-1
NaCl+CaCl2+Na2SO4+MgCl2+KCl+SrCl2+NaBr 100
125
150
175
323.15
373.15
423.15
1.712
4.984 NaCl+CaCl2
*The CO2 and H2O presented in the experimental system are not shown in the table.
120
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APPENDIXES
135
Appendix A: Additional Model Equations
The fugacity coefficients for both CO2 and H2O in the CO2-rich phase were calculated using the
Redlich-Kwong equation of state (RK EoS) (Redlich and Kwong, 1949):
π = (π π
π£βπ) β (
π
π0.5π£(π£+π)) (A.1)
where π£ is the molar volume (cm3/mol) and parameters a and b account for the attraction and repulsion
interactions between molecules. By tuning the EoS against the pure CO2 properties, Spycher and Pruess
(2010) set the pure component parameter a as a function of temperature:
a = ko + k1T (A.2)
The parameters ππ, π1, and b for pure components (CO2 and H2O) can be found in Spycher and
Pruess (2010). The standard mixing rules were applied for the CO2-H2O gas mixture as
ππππ₯ = β β π¦ππ¦πππ
ππ πππ (A.3)
ππππ₯ = β π¦πππππ (A.4)
The cross parameters πππ (see Eq. (2.14)) in Eq. (A.3) are a measure of the strength of attraction
between the molecules of the components i and j. The fugacity coefficient of the k-th component in the
CO2-H2O gas mixture can be obtained using the equations given in Panagiotopoulos and Reid (1986) and
Spycher and Pruess (2010):
ππππ =ππ
ππππ₯(ππ£
π πβ 1) β ππ (π
(π£βππππ₯)
π π) +
(β π¦πππ=1 (πππ+πππ)ββ β π¦π
2π¦π(πππβπππ)βππππ+π₯π β π₯π(πππβπππ)βππππππ=1
ππ=1
ππ=1
ππππ₯β
ππ
ππππ₯) Γ(
ππππ₯
ππππ₯π π1.5) ππ (
π£
π£+ππππ₯) (A.5)
136
The Pitzer equations for calculating the activity coefficient of dissolved CO2, πΎπΆπ2 ,and the
osmotic coefficient of H2O,π, are given in Pitzer (1991):
πππΎπΆπ2 = 2ππΆπ2πππ + 3ππΆπ22 ππππ + 2ππππΆπ(πππ + πππ) + 6ππΆπ2ππππΆl(ππππ + ππππ) + ππππΆπ
2 ππππ (A.6)
π β 1 =2
2ππππΆπ+ππΆπ2{βπ΄π
πΌ1.5
πΌ+ππΌ0.5+ππππΆπ
2 [π½ππ(0)+ π½ππ
(1)ππ₯π(βπΌ1πΌ
0.5) + 2ππππΆππΆππ] + 1
2ππΆπ22 πππ +
ππΆπ23 ππππ +ππΆπ2ππππΆπ(πππ + πππ) + 3ππΆπ2
2 ππππΆπ(ππππ + ππππ) + ππΆπ2ππππΆπ2 ππππ} (A.7)
In Eqs. (A.6) and (A.7), the Pitzer ion-ion interaction parameters π½ππ(0)
,π½ππ(1)
and πΆπππ
for NaCl-H2O
system are taken from Pitzer et al. (1984). The molality of CO2 and NaCl in the aqueous phase are ππΆπ2
and ππππΆπ , respectively; π΄π is the Debye-HΓΌckel slope for the osmotic coefficient, π = 1.2 kg1/2 mol-1/2,
and πΌ1 = 2.0 kg1/2 mol-1/2; and I is the ionic strength based on the molality scale. The Debye-HΓΌckel slope
and the ionic strength are defined as follows:
π΄π =1
3(2πππ΄ππ»2π)
1/2(
π2
4π π πππ)3/2
(A.8)
πΌ =1
2β πππ§π
2π (A.9)
where ππ»2π is the density of water (g/L) calculated by the IAPWS-95 formulation (Wagner and PruΓ, 2002);
νπ is the relative permittivity of pure water calculated from the equation of FernΓ‘ndez et al. (1997), which is
adopted as the IAPWS standard for νπ; νπ = 8.8541910-12 (F/m) is the vacuum permittivity; e = 1.60218 10-
19 (C) is the elementary charge; k = 1.38065 10-23 (J K-1) is the Boltzmann constant; and T is temperature in
K.
The combined Pitzer interaction parameters π΅πΆπ2βπππΆπ and πΆπΆπ2βπΆπ2βπππΆπ are adopted from
Akinfiev and Diamond (2010),
137
π΅πΆπ2βπππΆπ = π1 + π2100
πβπ+π3
2πΌ[1 β (1 + 2βπΌ)ππ₯π(β2βπΌ)] (A.10)
πΆπΆπ2βπΆπ2βπππΆπ = π4 (A.11)
whereπ = 228πΎ and a constant, I is molality based ionic strength defined by Eq. (A.9). The parameters in
Eqs. (A.10) and (A.11) are given in Table A 1 (Akinfiev and Diamond, 2010).
Table A 1 Parameters for Eqs. (A.10-A.11).
Eqs. a1 a2 a3 a4
A10 5.7123 10-2 2.6994 10-02 4.5635 10-02 -
A11 - - - -5.76 10-04
138
Appendix B: Pitzer Ion-Ion Interaction Model
The empirical function f(T,P) to calculate Pitzer ion-ion interaction parameters (π½ππ(0)
, π½ππ(1)
and πΆπππ
)
at the desired temperatures and pressures for the system of CaCl2-H2O, Na2SO4-H2O, MgCl2-H2O and KCl-
H2O are summarized as below:
1. CaCl2-H2O system (Holmes et al. 1994)
π(π, π) = πΉ0 + πΉ1(π) + πΉ2(π)2 (B.1)
where P is the system pressure in bar. Fo, F1 and F2 are functions of temperature only and given by Eqs.
(B.2) to (B.4),
πΉ0 = π1 +1
2π2π +
1
6π3π
2 +1
12π4π
3 +1
6π5π
2 {πππ β5
6} + π6 {
π
2+3π22
2π+π2ππ₯
πππππ₯} + π7 {2
ππ¦
π+ 1} ππππ¦ (B.2)
πΉ1 = π8 + π91
π+ π10π + π11π
2 + ππ₯β1π12 + ππ¦
β1π13 (B.3)
πΉ2 = π14 + π151
π+ π16π + π17π
2 (B.4)
where T1 = 647 K, T2 = 227 K, Tx = (T-T2), and Ty = (T1-T). The constants q1~q17 were listed in Table B 1.
2. Na2SO4-H2O system (Rogers and Pitzer, 1981; Rumpf and Maurer, 1993)
π(π) = π1 + π2(π2 β ππ
2) + π3(π β ππ ) + π4 ππ (π
ππ ) + π5 (
1
πβπ1β
1
ππ βπ1) + π6π2 (
1
π(πβπ2)β
1
ππ (ππ βπ2)) +
π΄ (1
πβ
1
ππ ) (B.5)
139
π΄ = π7 + π8ππ + π9ππ 2 + π10ππ
3 + 2π1π11 (1
ππ βπ1+
π1
2(ππ βπ1)2) + 2π2π12 (
π2
2(ππ βπ2)2 β
1
π2βππ ) (B.6)
where ππ is the reference temperature which is conveniently set at 298.15 K. π1 is 263 K, and π2 is 263 or
680 K depending on which ion-interaction parameter is to be calculated (Table B 2).
3. MgCl2-H2O system (Wang and Pitzer, 1998)
Wang and Pitzer (1998) developed a general model that describes the thermodynamic properties
of MgCl2(aq) based on an ion-interaction treatment of a variety of thermodynamic properties. The
equations for calculating the ion interaction parameters (π½ππ(0)
, π½ππ(1)
,πΆππ(0)
, πΆππ(1)
) are given below,
π(π, π) = πΉ0 + πΉ1 (π
10) + πΉ2 (
π
10)2
/2 (B.7)
where P is the system pressure in bar. F0, F1 and F2 are functions of temperature only and given by Eqs.
(B.8) to (B.11)
πΉ0 = π1 + π2πππ + π3π + π4π2 + π5π
3 + π6π10 + π7 (
1
π1βπ)2
(B.8)
πΉ1 = π8 + π9πππ + π10π + π11π2 + π12π
3 + π13π10 + π14 (
1
π1βπ)2
(B.9)
πΉ2 = π15 + π16πππ + π17π + π18π2 + π19π
3 + π20π10 + π21 (
1
π1βπ)2
(B.10)
πΆπππ= 2[πΆππ
(0)+ πΆππ
(1)ππ₯π(βπ₯π1) + πΆππ
(2)ππ₯π(βπ₯π2)] (B.11)
where π₯π1 = πΌπ1πΌ; π₯π2 = πΌπ2πΌ, πΌπ1 = 0.4πππππβ1, πΌπ2 = 0.28πππππ
β1, and T1 = 647K. The constants
q1~q21 are shown in Table B 3.
140
4. KCl-H2O system (Holmes and Mesmer, 1983)
π(π) = π1 + π1 (1
πβ
1
ππ ) + π3 ππ (
π
ππ )
+π4(π β ππ ) + π5(π2 β ππ
2) + π6ππ(π β 260) (B.12)
where π1-π6 are constants listed in Table B 4, and ππ is 298.15 K.
141
Table B 1 Constants of Eqs. (B.1) β (B.4) for calculating Pitzer ion-interaction parameters (π·ππ(π)
, π·ππ(π)
and
πͺπππ
) of CaCl2(aq) (Holmes et al., 1994).
Const. π(π», π·) = π·ππ(π)
π(π», π·) = π·ππ(π)
π(π», π·) = πͺπππ
π1 0 0 -1.3455 10-1
π2 4.9213 10-3 -1.3814 10-1 0
π3 -3.5512 10-5 1.6522 10-2 3.0401 10-4
π4 4.7629 10-8 6.3784 10-6 1.3136 10-7
π5 0 -3.1030 10-3 -5.8863 10-5
π6 0 -2.0329 10-2 -6.4986 10-4
π7 -3.5549 10-4 0 0
π8 1.1021 10-3 0 -9.0317 10-7
π9 -1.3924 10-1 0 0
π10 -2.8663 10-6 1.0935 10-6 0
π11 2.9609 10-9 -4.0084 10-9 5.9573 10-12
π12 2.3285 10-3 0 0
π13 -2.1508 10-2 0 0
π14 0 0 -5.5630 10-9
π15 0 0 1.7685 10-6
π16 -1.2534 10-10 0 0
π17 3.5462 10-13 0 0
142
Table B 2 Constants in Eqs. (B.5) β (B.6) for calculating Pitzer ion-interaction parameters (π·ππ(π)
, π·ππ(π)
and
πͺπππ
) of Na2SO4(aq) (Rumpf and Maurer, 1993).
Const. π(π») = π·ππ(π)
π(π») = π·ππ(π)
* π(π») = πͺπππ
π1 1.869 10-2 1.0994 5.54900 10-3
π2 -1.03611 10-5 -3.2355 10-4 0
π3 3.00299 10-2 5.76552 10-1 5.14316 10-5
π4 -1.43441 10+1 -1.88769 10+2 0
π5 -6.66894 10-1 -2.05974 10-1 0
π6 0 -1.46744 10+3 3.45791 10-1
π7 -2.081437 10+2 -5.29421 10+2 4.25799 10+1
π8 -1.43441 10+1 -1.88769 10+2 0
π9 3.00299 10-2 5.76552 10-1 5.14316 10-5
π10 -2.07222 10-5 -6.471 10-4 0
π11 6.66894 10-1 2.05974 10-1 -3.45791 10-1
π12 0 1.46744 10+3 0
*When calculating π½ππ(1)
, T2 in Eqs. (B.5) and (B.6) is 680K, otherwise T2 is 263K
143
Table B 3 Constants of Eqs. (B.7) β (B.10) for calculating Pitzer ion-interaction parameters (π·ππ(π)
, π·ππ(π)
and πͺπππ
) of MgCl2(aq) (Wang and Pitzer, 1998).
Coeff. π(π», π·) = π·ππ(π)
π(π», π·) = π·ππ(π)
πͺπππ= π[πͺππ
(π)+ πͺππ
(π)πππ(βπππ) + πͺππ
(π)πππ(βπππ)] (Eq. A11)
π(π», π·) = πͺππ(π)
π(π», π·) = πͺππ(π)
π(π», π·) = πͺππ(π)
π1 -5.50111455 10+1 7.21220552 10+1 5.92428240 0 0
π2 1.50130326 10+1 -1.77145085 10+1 -1.65126386 -1.02256042 0
π3 -1.58107430 10-1 1.14397153 10-1 1.89399822 10-2 3.77018617 10-2 -2.28040769 10-3
π4 2.30409919 10-4 0 -2.99972128 10-5 -7.91682934 10-5 1.37425889 10-5
π5 -1.31768095 10-7 -1.43588435 10-7 1.89174291 10-8 5.91314258 10-8 -1.94821902 10-8
π6 -1.26699609 10-28 1.72952766 10-27 0 0 1.04649784 10-28
π7 2.82197499 10+2 3.41920714 10+3 5.49030201 10+1 -2.28493084 10+2 0
π8 0 0 4.50114048 10-2 0 0
π9 0 2.28440612 10-4 -1.08427926 10-2 0 0
π10 8.39661960 10-5 0 7.41041864 10-5 -7.79259941 10-5 0
π11 -4.60207270 10-7 0 -5.99961498 10-8 4.28675876 10-7 0
π12 6.21165614 10-10 0 0 -5.77509662 10-10 0
π13 8.43555937 10-31 -1.77573402 10-29 0 0 0
π14 0 -2.29668879 10+2 -4.60562847 0 0
π15 0 0 0 -5.13962051 10-4 0
π16 0 0 0 9.30761142 10-5 0
π17 0 -2.71485086 10-7 0 0 0
π18 0 0 0 0 0
π19 0 0 -1.39016981 10-15 -7.43350922 10-13 0
π20 0 0 0 0 0
π21 -1.11176553 1.01000272 10+1 1.40556304 10-1 1.12721557 0
144
Table B 4 Constants of Eq. (B.12) for calculating Pitzer ion-interaction parameters (π·ππ(π)
, π·ππ(π)
and πͺπππ
) of
KCl(aq) (Holmes and Mesmer, 1983).
Const. π(π») = π·ππ(π)
π(π») = π·ππ(π)
π(π») = πͺπππ
π1 4.808 10-2 4.76 10-2 -7.88 10-4
π2 -7.5848 10+2 3.039 10+2 9.127 10+1
π3 -4.7062 1.066 5.8643 10-1
π4 1.0072 10-2 0 -1.298 10-3
π5 -3.7599 10-6 0 4.9567 10-7
π6 0 4.7 10-2 0
145
Appendix C: Experimental Error Estimation
2-D interpolation of scatter experimental data. Multiple measurements (usually 3 to 6
measurements) were made at each target experimental P-T-x point. The inverse distance weighted 2-D
interpolation method (Shepard, 1968) was used to get an approximation of the real value based on scattered
data generated by measurements at each interpolation point. Based on this approach, the value of the
interpolation point in a set, f(x, y), is defined as:
π(π₯, π¦) = β ππ(π₯π , π¦π)ππ=1 ππ(π₯π , π¦π) (C.1)
where n is the number of scatter (experimental) points in the set, fi(xi, yi) is the value of the i-th scatter
point, and Wi(xi, yi) is the weight function assigned to the i-th scatter point.
The weight function is defined as,
ππ(π₯π , π¦π) =βπβ2
β βπβ2π
π=1
(C.2)
where hi is the distance from the interpolation point to the i-th scatter point and is defined as:
βπ = β(π₯ β π₯π)2 + (π¦ β π¦π)
2 (C.3)
Error estimation. The CO2 solubility in the aqueous phase is commonly expressed by either
molality (ππΆπ2) or mole fraction (π₯πΆπ2). The error estimation is performed on the mole fraction scale, but
the obtained results can be converted to the molality scale. The mole fraction of CO2 in an aqueous sample
is defined as,
π₯πΆπ2 =
ππΆπ2πππΆπ2
ππΆπ2πππΆπ2
+ππ πππππβππΆπ2
βππ πππ‘
πππ»2π+ππ πππ‘πππ πππ‘
(ππ+ππ)
(C.4)
146
whereππΆπ2 is the mass of CO2 in the sample, ππ πππππ is the total mass of sample, ππ πππ‘ is the mass of
salt in the sample;πππΆπ2, πππ»2πand πππ πππ‘ are the molar masses of CO2, H2O and NaCl, respectively;
ππ and ππ are, respectively, the stoichiometric numbers of the anion and cation of the dissolved salt.
The error propagation theory described by Taylor (1997) is used to determine the instrumental
error of each measured point. From Eq. (C.4), the error in π₯πΆπ2 due to the pressure variation in the pressure
cell is:
πΏπ₯ππππ = |
ππ₯πΆπ2
ππππππ π π’ππππππ| πΏπ = |
ππ₯πΆπ2
πππΆπ2
πππΆπ2
ππππππ π π’ππππππ| πΏπ (C.5)
The error in π₯πΆπ2 due to the temperature variation of pressure cell is:
πΏπ₯ππππ = |
ππ₯πΆπ2
ππππππ π π’ππππππ| πΏπ = |
ππ₯πΆπ2
πππΆπ2
πππΆπ2
ππππππ π π’ππππππ| πΏπ (C.6)
The error in π₯πΆπ2 due to the volume variation is:
πΏπ₯ππππ = |
ππ₯πΆπ2
ππππππ π π’ππππππ| πΏπ = |
ππ₯πΆπ2
πππΆπ2
πππΆπ2
ππππππ π π’ππππππ| πΏπ (C.7)
The error in π₯πΆπ2 due to the sample mass variation is:
πΏπ₯ππππ πππππ
= |ππ₯πΆπ2
πππ πππππ| πΏππ πππππ (C.8)
The error in π₯πΆπ2 due to the salt mass variation is:
πΏπ₯ππππ πππ‘ = |
ππ₯πΆπ2
πππ πππ‘| πΏππ πππ‘ (C.9)
147
From Eq. (C.4), the derivative of π₯πΆπ2 with respect to ππΆπ2 is,
ππ₯πΆπ2
πππΆπ2=
1
πππΆπ2(ππΆπ2πππΆπ2
+ππ πππππβππΆπ2
βππ πππ‘
πππ»2π+ππ πππ‘πππ πππ‘
(ππ+ππ))βππΆπ2πππΆπ2
(1
πππΆπ2β
1
πππ»2π)
(ππΆπ2πππΆπ2
+ππ πππππβππΆπ2
βππ πππ‘
πππ»2π+ππ πππ‘πππ πππ‘
(ππ+ππ))
2 (C.10)
ππΆπ2 = ππΆπ21 +ππΆπ2
2 +ππΆπ23 = (ππΆπ2
1 + ππΆπ22 + ππΆπ2
3 )πππππ π π’ππππππ (C.11)
In Eq. (C.11) ππΆπ21 , ππΆπ2
2 and ππΆπ23 represent the CO2 amount by mass, as well as ππΆπ2
1 , ππΆπ22 , and
ππΆπ23 represent the CO2 density in the pressure cell, due to the 1st, 2nd and 3rd expansion during sample
analysis process, respectively. Also, the Ppressure cell, Tpressure cell, and Vpressure_cell in Eqs. (C.5- C.11) denote the
pressure (bar), temperature (K) and volume (cm3) of the pressure cell. Other partial derivatives are obtained
as follows:
(πππΆπ2
ππ)π,ππΏπ = β((
πππΆπ21
ππ)π,π1
πΏπ1)
2
+ ((πππΆπ2
2
ππ)π,π2
πΏπ2)
2
+ ((πππΆπ2
3
ππ)π,π3
πΏπ3)
2
(C.12)
(πππΆπ2
ππ)π,ππΏπ = β((
πππΆπ21
ππ)π,π1
πΏπ1)
2
+ ((πππΆπ2
2
ππ)π,π2
πΏπ2)
2
+ ((πππΆπ2
3
ππ)π,π3
πΏπ3)
2
(C.13)
where π1, π2, π3and π1, π2, π3 are the equilibrium temperatures and pressures of the pressure cell during 1st,
2nd and 3rd expansion; πΏπ1, πΏπ2, πΏπ3 and πΏπ1, πΏπ2, πΏπ3 are the temperature and pressure changes of the
pressure cell during 1st, 2nd and 3rd expansion, respectively. The terms (πππΆπ2
1
ππ)π,π1
, (πππΆπ2
2
ππ)π,π2
, (πππΆπ2
3
ππ)π,π3
are determined by the slope of the isothermal curve generated by the EoS of Span and Wagner (1996).
Similarly, the terms (πππΆπ2
1
ππ)π,π1
, (πππΆπ2
2
ππ)π,π2
, (πππΆπ2
3
ππ)π,π3
are determined by the slope of isobaric curve
generated by the same EoS.
148
Substituting (C.10) and (C.12) into (C.5), (C.10) and (C.13) into (C.6), (C.10) and (C.11) into
(C.7), respectively, the πΏπ₯ππππ , πΏπ₯πππ
π , πΏπ₯ππππ can be calculated. By differentiation of Eq. (C.4) with respect to
ππ πππππ and ππ πππ‘, the Eqs. (C.14) and (C.15) can be obtained as:
ππ₯πΆπ2
πππ πππππ= β
1
πππ»2π
ππΆπ2πππΆπ2
(ππΆπ2πππΆπ2
+ππ πππππβππΆπ2
βππ πππ‘
πππ»2π+ππ πππ‘πππ πππ‘
(ππ+ππ))
2 (C.14)
ππ₯πΆπ2
πππ πππ‘=
(1
πππ»2πβππ+πππππ πππ‘
)ππΆπ2πππΆπ2
(ππΆπ2πππΆπ2
+ππ πππππβππΆπ2
βππ πππ‘
πππ»2π+ππ πππ‘πππ πππ‘
(ππ+ππ))
2 (C.15)
Substituting (C.14) into (C.8), and (C.15) into (C.9), respectively, the πΏπ₯ππππ πππππ
and πΏπ₯πππ
π πππ‘ can be
calculated. Thus, the calculated instrumental error of the sample analysis can be estimated by the error
propagation as follows:
πΏπ₯πππ π‘π = β(πΏπ₯ππππ )2 + (πΏπ₯πππ
π )2 + (πΏπ₯ππππ )2 + (πΏπ₯πππ
ππππππ)2+ (πΏπ₯πππ
π πππ‘)2 (C.16)
In this study, the calculated instrumental error (Ξ΄xinstr) is found to be below 0.7 % of the mole
fraction of CO2 in the aqueous phase. The instrumental error on the molality scale (πΏππππ π‘π ) can be
converted from the mole fraction scale as below:
πΏππππ π‘π =55.509πΏπ₯πππ π‘π+(ππ+ππ)ππ πππ‘πΏπ₯πππ π‘π
1βπΏπ₯πππ π‘π (C.17)
and πΏππππ π‘π
ππΆπ2< 0.77% for all experimental CO2 solubility.
149
The random errors were estimated from direct repetitions of the measurement results. The standard
deviation between 2-D interpolation point and measured experimental value represents the random error of
the value during the experiment:
πΏπ₯ππππππ =β1
πβ1β (π₯π β π₯2βπ·)
2ππ=1 (C.18)
where π₯2βπ·is 2-D interpolation value of the measured solubility data. The random error based on molality
scale (πΏπππππππ) can also be converted from πΏπ₯ππππππ in the same manner as Eq. (C.17) does.
Symbols
hi distance between scattered (experimental) and interpolation points
π₯2βπ· 2-D interpolation value of scattered measured CO2 solubility, mole fraction
ππΆπ2 mass of CO2 in the sample cell, g
ππ πππ‘ mass of dissolved salt in the sample
ππ πππππ mass of sample, g
ππΆπ21 , ππΆπ2
2 , ππΆπ23 mass of CO2 of 1st, 2nd, and 3rd CO2 expansion
πππ molecular weight of a component, g mol-1
πππππ π π’ππππππ pressure of the pressure cell during sample analysis process, bar
π1, π2, π3 equilibrium pressure of pressure cell during 1st, 2nd, and 3rd CO2 expansion
π1, π2, π3 equilibrium temperature of pressure cell during 1st, 2nd, and 3rd CO2 expansion, K
πππππ π π’ππππππ temperature of the pressure cell, K
πππππ π π’πeππππ volume of the stainless steel vessel for measuring the CO2 solubility during sample
analysis process, 297.27 cm3
πΏπ1, πΏπ2, πΏπ3 pressure difference of pressure cell during 1st, 2nd, and 3rd CO2 expansion
πΏπ1, πΏπ2, πΏπ3 temperature difference of pressure cell during 1st, 2nd, and 3rd CO2 expansion
πΏπ estimated error for the pressure cell volume
150
Appendix D: The PSUCO2 Web-Computational Interface
Figure D. 1 User-interface of CO2-brine phase equilibria model. Part I: CO2 solubility in pure H2O and in
single-salt brine; Part II: CO2 solubility in mixed-salt brine.
Can be accessed at: http://carbonlab.org/psuco2/index.php.
151
Figure D. 2 User-interface of pure CO2 model, developed based on Span and Wagnerβs (1996) EoS.
Can be accessed at: http://carbonlab.org/CO2eos/index.php.
Figure D. 3 User-interface of brine density model.
Can be accessed at: http://carbonlab.org/density/index.php.
152
Appendix E. Original Experimental Data Records
The experimental CO2 solubility data recorded herein were measured during the periods of August
2011- February 2014. The experimental apparatus is located in the Room 114, Academic Projects Building,
The Energy Institute, The Pennsylvania State University, University Park. The correction factor 0.992
should be applied to all obtained raw experimental data listed here to compensate water vapor error. Please
refer to Section 2.3.4 for the explanation of the error caused by water vapor during the sample analysis
process.
153
Table E 1 Original Experimental CO2 solubility data record at 1453-2190 psia and 322.15-423.15 K for the CO2-H2O system.
Run No #. P / psia T / K πππππ
/ mol kg-1
ππͺπΆπβ²
/ mol kg-1 ππͺπΆπ
INVERSE
DISTANCE,
1/πππ, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
1 2181 323.15 0 1.2550 2.2109 0.0339 0.5120
2 2170 323.15 0 1.2616 2.2223 0.0323 0.4880
3 2178 323.15 0 1.2642 2.2268 NA NA Discarded
4 2176 374.15 0 1.0342 1.8290 NA NA Discarded
5 2163 373.15 0 1.0297 1.8212 0.0063 0.4142
6 2165 373.15 0 1.0265 1.8157 0.0090 0.5858
7 2190 423.15 0 1.0168 1.7988 0.0048 0.0862
8 2180 423.15 0 1.0148 1.7954 0.0509 0.9138
9 2190 423.15 0 1.0254 1.8138 NA NA Discarded
10 1448 323.15 0 1.1296 1.9944 0.1770 0.4569
11 1453 322.15 0 1.1738 2.0707 0.1269 0.3276
12 1447 322.15 0 1.1626 2.0515 0.0806 0.2081
13 1469 323.15 0 1.1683 2.0612 0.0029 0.0074
14 2172 352.15 0 1.0789 1.9066 - -
15 2136 352.65 0 1.1158 1.9705 - -
Note: ππΆπ2β² means the original measured data, the real CO2 solubility (ππΆπ2) obtained in this study equals to ππΆπ2 = 0.992ππΆπ2
β²
154
Table E 2 Original Experimental CO2 solubility data record at 2150-2200 psia, 322.65-427.15 K, and from 1-6 mol kg-1 NaCl for the CO2-NaCl-H2O system.
Run No #. P / psia T / K ππ΅ππͺπ
/ mol kg-1
ππͺπΆπβ²
/ mol kg-1 ππͺπΆπ
INVERSE
DISTANCE,
1/πππ, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
14 2177 323.15 1 1.0418 1.7793 NA NA Discarded
15 2173 323.15 1 1.0257 1.7523 0.1519 0.6589
16 2172 323.15 1 1.0216 1.7454 0.0786 0.3411
17 2153 373.15 1 0.8421 1.4432 0.0020 0.0004
18 2193 376.15 1 0.8269 1.4175 0.0032 0.0006
19 2181 374.15 1 0.8387 1.4374 0.0328 0.0061
20 2188 373.65 1 0.8447 1.4476 0.0065 0.0012
21 2176 373.15 1 0.8425 1.4438 5.3091 0.9917
22 2154 422.15 1 0.7970 1.3669 0.0021 0.0043
23 2161 424.15 1 0.8299 1.4226 0.0047 0.0095
24 2150 423.15 1 0.7918 1.3581 0.0015 0.0031
25 2177 423.15 1 0.8060 1.3821 0.4863 0.9831
26 2178 322.65 2 0.8772 1.4527 0.1620 0.0488
27 2170 323.15 2 0.8736 1.4468 0.0323 0.0097
28 2175 323.15 2 0.8651 1.4329 3.1215 0.9414
29 2174 373.15 2 0.7121 1.1825 0.4078 0.7579
30 2200 373.15 2 0.7236 1.2013 0.0017 0.0031
31 2171 373.15 2 0.7089 1.1772 0.0480 0.0892
32 2172 373.15 2 0.7097 1.1785 0.0786 0.1462
33 2153 371.15 2 0.7161 1.1890 0.0019 0.0036
34 2162 426.15 2 0.6654 1.1058 0.0052 0.2578
35 2163 426.15 2 0.6257 1.0405 0.0060 0.2982
36 2192 427.15 2 0.6581 1.0938 0.0035 0.1740
37 2162 422.65 2 0.6644 1.1041 0.0054 0.2701
38 2181 323.15 3 0.7167 1.1517 0.0339 0.0727
39 2165 323.15 3 0.7325 1.1768 0.0090 0.0192
40 2174 322.65 3 0.7434 1.1942 0.3700 0.7949
155
Run No #. P / psia T / K ππ΅ππͺπ
/ mol kg-1
ππͺπΆπβ²
/ mol kg-1 ππͺπΆπ
INVERSE
DISTANCE,
1/πππ, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
41 2171 323.15 3 0.7279 1.1695 0.0480 0.1030
42 2161 323.15 3 0.7267 1.1677 0.0047 0.0101
43 2192 373.15 3 0.6192 0.9966 0.0037 0.0291
44 2200 373.15 3 0.6208 0.9992 0.0017 0.0132
45 2172 373.15 3 0.6260 1.0075 0.0786 0.6185
46 2168 374.15 3 0.6223 1.0016 0.0172 0.1350
47 2181 376.15 3 0.6134 0.9874 0.0260 0.2041
48 2175 426.15 3 0.5739 0.9244 0.1073 0.0656
49 2175 422.15 3 0.5495 0.8855 0.7574 0.4630
50 2200 424.15 3 0.6030 0.9708 0.0017 0.0010
51 2195 426.15 3 0.5968 0.9609 0.0026 0.0016
52 2190 425.15 3 0.5921 0.9534 0.0047 0.0029
53 2190 424.15 3 0.5992 0.9648 0.0048 0.0029
54 2175 422.15 3 0.5903 0.9506 0.7574 0.4630
55 2178 322.65 4 0.6272 0.9780 0.1620 0.8513
56 2160 323.15 4 0.6347 0.9895 0.0041 0.0217
57 2182 323.15 4 0.6323 0.9857 0.0242 0.1270
58 2175 374.15 4 0.5316 0.8301 0.7574 0.2853
59 2175 373.65 4 0.5306 0.8285 1.7533 0.6604
60 2178 374.15 4 0.5380 0.8400 0.1444 0.0544
61 2176 422.15 4 0.5018 0.7839 0.8415 0.8228
62 2196 427.15 4 0.4744 0.7414 0.0023 0.0023
63 2173 423.65 4 0.5032 0.7861 0.1463 0.1431
64 2182 424.15 4 0.5042 0.7877 0.0236 0.0231
65 2165 423.15 4 0.5008 0.7824 0.0090 0.0088
66 2191 323.15 5 0.5483 0.8301 0.0042 0.0171
67 2172 323.15 5 0.5580 0.8445 0.0786 0.3212
68 2178 323.65 5 0.5544 0.8391 0.1620 0.6616
156
Run No #. P / psia T / K ππ΅ππͺπ
/ mol kg-1
ππͺπΆπβ²
/ mol kg-1 ππͺπΆπ
INVERSE
DISTANCE,
1/πππ, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
69 2183 374.15 5 0.4696 0.7117 0.0178 0.0803
70 2173 374.15 5 0.4756 0.7208 0.1319 0.5959
71 2173 376.15 5 0.4687 0.7104 0.0642 0.2900
72 2164 373.15 5 0.4658 0.7060 0.0075 0.0338
73 2181 424.15 5 0.4367 0.6622 0.0328 0.0179
74 2195 423.65 5 0.4457 0.6758 0.0026 0.0014
75 2175 423.65 5 0.4433 0.6722 1.7533 0.9558
76 2171 422.15 5 0.4435 0.6725 0.0458 0.0250
77 2176 323.15 6 0.4979 0.7321 5.3091 0.3333
78 2176 323.15 6 0.5056 0.7434 5.3091 0.3333
79 2176 323.15 6 0.5030 0.7395 5.3091 0.3333
80 2174 374.15 6 0.4182 0.6157 0.2897 0.0368
81 2176 373.65 6 0.4267 0.6281 2.2813 0.2895
82 2176 373.15 6 0.4320 0.6358 5.3091 0.6737
83 2176 424.15 6 0.3857 0.5681 0.8415 0.1472
84 2175 423.65 6 0.3993 0.5880 1.7533 0.3067
85 2175 423.15 6 0.3913 0.5763 3.1215 0.5461
Note: ππΆπ2β² means the original measured data, the real CO2 solubility (ππΆπ2) obtained in this study equals to ππΆπ2 = 0.992ππΆπ2
β²
157
Table E 3 Original Experimental CO2 solubility data record at 2171-2179 psia, 322.65-426.15 K, and from 0.3333-2.0000 mol kg-1 CaCl2 for the CO2-CaCl2-
H2O system.
Run No #. P / psia T / K ππͺππͺππ
/ mol kg-1
ππͺπΆπβ²
/ mol kg-1 ππͺπΆπ
INVERSE
DISTANCE,
1/πππ, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
86 2176 323.15 0.3333 1.0969 1.9041 5.3091 0.4851
87 2177 324.15 0.3333 1.0742 1.8655 0.3272 0.0299
88 2176 323.15 0.3333 1.1115 1.9290 5.3091 0.4851
89 2174 373.15 0.3333 0.9106 1.5859 0.4078 0.7286
90 2173 373.15 0.3333 0.8909 1.5521 0.1519 0.2714
91 2176 425.65 0.3333 0.8486 1.4795 0.1553 0.1596
92 2173 423.15 0.3333 0.8652 1.5080 0.1519 0.1561
93 2177 424.65 0.3333 0.8452 1.4736 0.2322 0.2387
94 2177 423.65 0.3333 0.8986 1.5653 0.4336 0.4456
95 2177 323.15 0.6667 0.9640 1.6486 0.4863 0.4649
96 2173 323.15 0.6667 0.9513 1.6273 0.1519 0.1452
97 2174 323.15 0.6667 0.9915 1.6949 0.4078 0.3899
98 2177 373.15 0.6667 0.7758 1.3311 0.4863 0.5165
99 2174 373.15 0.6667 0.7923 1.3590 0.4078 0.4331
100 2171 372.65 0.6667 0.7838 1.3446 0.0474 0.0503
101 2178 425.15 0.6667 0.7240 1.2433 0.1008 0.4137
102 2172 423.15 0.6667 0.7367 1.2648 0.0786 0.3229
103 2173 426.15 0.6667 0.7277 1.2496 0.0642 0.2634
104 2173 322.65 1.0000 0.8502 1.4323 0.1463 0.4303
105 2171 323.65 1.0000 0.8532 1.4373 0.0474 0.1394
106 2173 323.65 1.0000 0.8720 1.4685 0.1463 0.4303
107 2173 373.15 1.0000 0.7019 1.1854 0.1519 0.3384
108 2177 375.15 1.0000 0.6826 1.1532 0.1651 0.3679
109 2173 374.15 1.0000 0.6812 1.1509 0.1319 0.2938
110 2174 425.15 1.0000 0.6365 1.0762 0.1550 0.2373
111 2174 423.15 1.0000 0.6357 1.0748 0.4078 0.6243
158
Run No #. P / psia T / K ππͺππͺππ
/ mol kg-1
ππͺπΆπβ²
/ mol kg-1 ππͺπΆπ
INVERSE
DISTANCE,
1/πππ, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
112 2177 426.15 1.0000 0.6416 1.0847 0.0904 0.1385
113 2173 323.15 1.3333 0.7493 1.2435 0.1519 0.2714
114 2174 323.15 1.3333 0.7525 1.2487 0.4078 0.7286
115 2174 373.15 1.3333 0.6116 1.0173 0.4078 0.3690
116 2174 372.15 1.3333 0.6219 1.0342 0.2897 0.2621
117 2174 373.15 1.3333 0.6247 1.0389 0.4078 0.3690
118 2175 423.15 1.3333 0.5543 0.9229 3.1215 0.8480
119 2174 423.15 1.3333 0.5515 0.9182 0.4078 0.1108
120 2173 423.15 1.3333 0.5627 0.9367 0.1519 0.0413
121 2176 323.15 1.6667 0.6684 1.0926 5.3091 0.8927
122 2173 323.15 1.6667 0.6712 1.0971 0.1519 0.0255
123 2177 323.15 1.6667 0.6668 1.0900 0.4863 0.0818
124 2176 372.65 1.6667 0.5490 0.8991 2.2813 0.8780
125 2176 375.15 1.6667 0.5406 0.8805 0.2388 0.0919
126 2179 374.15 1.6667 0.5524 0.9046 0.0782 0.0301
127 2177 423.65 1.6667 0.4878 0.7997 0.4336 0.5339
128 2173 423.65 1.6667 0.5022 0.8231 0.1463 0.1802
129 2177 424.65 1.6667 0.5015 0.8220 0.2322 0.2859
130 2176 323.15 2.0000 0.6226 1.0021 5.3091 0.8559
131 2177 323.15 2.0000 0.6344 1.0208 0.4863 0.0784
132 2174 323.15 2.0000 0.6169 0.9929 0.4078 0.0657
133 2176 374.15 2.0000 0.4937 0.7963 0.8415 0.8988
134 2171 372.65 2.0000 0.4974 0.8022 0.0474 0.0506
135 2171 372.65 2.0000 0.5053 0.8147 0.0474 0.0506
136 2174 423.15 2.0000 0.4447 0.7178 0.4078 0.2922
137 2173 423.65 2.0000 0.4398 0.7099 0.1463 0.1048
138 2176 422.15 2.0000 0.4469 0.7213 0.8415 0.6030
Note: ππΆπ2β² means the original measured data, the real CO2 solubility (ππΆπ2) obtained in this study equals to ππΆπ2 = 0.992ππΆπ2
β²
159
Table E 4 Original Experimental CO2 solubility data record at 1420-2178 psia, 322.15-425.15 K, and from 0.3333-2.0 mol kg-1 Na2SO4 for the CO2-Na2SO4-
H2O system.
Run No #. P / psia T / K ππ΅πππΊπΆπ
/ mol kg-1
ππͺπΆπβ²
/ mol kg-1 ππͺπΆπ
INVERSE
DISTANCE,
1/πππ, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
139 2175 323.15 0.3333 1.0154 1.7652 3.1215 0.3333
140 2175 323.15 0.3333 1.0138 1.7624 3.1215 0.3333
141 2175 323.15 0.3333 1.0287 1.7879 3.1215 0.3333
142 2176 372.15 0.3333 0.8477 1.4779 0.8415 0.2015
143 2174 371.65 0.3333 0.8714 1.5186 0.2127 0.0509
144 2175 373.15 0.3333 0.8553 1.4910 3.1215 0.7475
145 2176 422.65 0.3333 0.8311 1.4494 2.2813 0.7126
146 2177 423.15 0.3333 0.8684 1.5135 0.4863 0.1519
147 2177 423.65 0.3333 0.8195 1.4295 0.4336 0.1354
148 2175 323.15 0.6667 0.8241 1.4127 3.1215 0.3065
149 2176 323.15 0.6667 0.8663 1.4840 5.3091 0.5213
150 2175 323.65 0.6667 0.8361 1.4330 1.7533 0.1722
151 2175 323.15 0.6667 0.8731 1.4955 NA NA Discarded
152 2175 374.65 0.6667 0.6744 1.1591 NA NA Discarded
153 2174 371.65 0.6667 0.6713 1.1538 NA NA Discarded
154 2176 373.15 0.6667 0.6915 1.1881 5.3091 0.4932
155 2176 373.15 0.6667 0.7070 1.2144 5.3091 0.4932
156 2173 373.65 0.6667 0.7086 1.2172 0.1463 0.0136
157 2176 424.15 0.6667 0.6681 1.1484 0.8415 0.2809
158 2176 422.15 0.6667 0.6690 1.1499 0.8415 0.2809
159 2178 422.15 0.6667 0.6961 1.1959 0.1444 0.0482
160 2177 424.15 0.6667 0.7100 1.2195 0.3272 0.1092
161 2176 424.15 0.6667 0.7287 1.2513 0.8415 0.2809
162 2175 322.15 1.0000 0.6852 1.1575 0.7574 0.2194
163 2175 322.65 1.0000 0.7162 1.2093 1.7533 0.5079
164 2170 322.65 1.0000 0.6936 1.1716 0.0320 0.0093
165 2173 323.15 1.0000 0.6859 1.1587 0.1519 0.0440
160
Run No #. P / psia T / K ππ΅πππΊπΆπ
/ mol kg-1
ππͺπΆπβ²
/ mol kg-1 ππͺπΆπ
INVERSE
DISTANCE,
1/πππ, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
166 2175 324.15 1.0000 0.6867 1.1601 0.7574 0.2194
167 2175 373.65 1.0000 0.5614 0.9503 NA NA Discarded
168 2174 372.15 1.0000 0.5748 0.9728 NA NA Discarded
169 2173 372.65 1.0000 0.5463 0.9251 NA NA Discarded
170 2176 373.65 1.0000 0.6054 1.0241 2.2813 0.2676
171 2175 373.15 1.0000 0.5966 1.0094 3.1215 0.3662
172 2175 373.15 1.0000 0.6173 1.0440 3.1215 0.3662
173 2176 423.65 1.0000 0.5537 0.9374 NA NA Discarded
174 2176 422.65 1.0000 0.5477 0.9273 NA NA Discarded
175 2175 423.15 1.0000 0.5914 1.0007 3.1215 0.8047
176 2175 424.15 1.0000 0.6108 1.0332 0.7574 0.1953
177 2135 323.15 1.3333 0.5283 0.8799 NA NA Discarded
178 2155 323.15 1.3333 0.5563 0.9262 0.0024 0.0007
179 2174 323.15 1.3333 0.5841 0.9720 0.4078 0.1155
180 2175 323.15 1.3333 0.5585 0.9298 3.1215 0.8839
181 2175 374.65 1.3333 0.5241 0.8730 0.3891 0.3394
182 2175 374.15 1.3333 0.5060 0.8431 0.7574 0.6606
183 2173 424.15 1.3333 0.5154 0.8587 0.1319 0.0548
184 2175 424.15 1.3333 0.5338 0.8890 0.7574 0.3151
185 2175 424.15 1.3333 0.5032 0.8385 0.7574 0.3151
186 2175 424.15 1.3333 0.4888 0.8147 0.7574 0.3151
187 2175 323.15 1.6667 0.4661 0.7644 3.1215 0.3662
188 2175 323.15 1.6667 0.4839 0.7934 3.1215 0.3662
189 2176 323.65 1.6667 0.5016 0.8222 2.2813 0.2676
190 2176 373.65 1.6667 0.4767 0.7817 NA NA Discarded
191 2174 373.15 1.6667 0.4441 0.7286 0.4078 0.0370
192 2176 373.15 1.6667 0.4366 0.7164 5.3091 0.4815
193 2176 373.15 1.6667 0.4509 0.7397 5.3091 0.4815
161
Run No #. P / psia T / K ππ΅πππΊπΆπ
/ mol kg-1
ππͺπΆπβ²
/ mol kg-1 ππͺπΆπ
INVERSE
DISTANCE,
1/πππ, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
194 2175 425.15 1.6667 0.4302 0.7059 0.2315 0.0182
195 2175 423.15 1.6667 0.4346 0.7131 3.1215 0.2454
196 2175 423.15 1.6667 0.4390 0.7203 3.1215 0.2454
197 2176 422.15 1.6667 0.4518 0.7411 0.8415 0.0662
198 2175 423.15 1.6667 0.4331 0.7107 3.1215 0.2454
199 2176 422.65 1.6667 0.4314 0.7079 2.2813 0.1794
200 NA NA 2.0000 0.3643 0.5888 NA NA Discarded
201 2175 372.65 2.0000 0.3742 0.6047 1.7533 0.3597
202 2175 373.15 2.0000 0.3949 0.6379 3.1215 0.6403
203 2175 424.15 2.0000 0.3752 0.6063 0.7574 0.1345
204 2175 423.15 2.0000 0.3713 0.6000 3.1215 0.5542
205 2175 423.65 2.0000 0.3889 0.6283 1.7533 0.3113
206 1687 346.150 1.0000 0.6878 1.1618 - -
207 1687 346.150 1.0000 0.7148 1.2070 - -
208 1420 348.15 1.0000 0.5194 0.8798 - -
209 1420 348.15 1.0000 0.5367 0.9090 - -
210 1420 348.15 1.0000 0.5222 0.8847 - -
211 1419.9 348.15 1.0000 0.5261 0.8912 - -
Note: ππΆπ2β² means the original measured data, the real CO2 solubility (mCO2) obtained in this study equals to mCO2 = 0.992mCO2
β²
162
Table E 5 Original Experimental CO2 solubility data record at 2175-2176 psia, 323.15-424.15 K, and from 0.3333-2.0000 mol kg-1 MgCl2 for the CO2-MgCl2-
H2O system.
Run No #. P / psia T
/ K
π¦ππ ππ₯π
/ mol kg-1
π¦πππβ²
/ mol kg-1 π±πππ
INVERSE
DISTANCE,
1/π‘π’π, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
212 2175 323.15 0.3333 1.0709 1.8599 3.1215 0.3333
213 2175 323.15 0.3333 1.0842 1.8825 3.1215 0.3333
214 2175 323.15 0.3333 1.0832 1.8808 3.1215 0.3333
215 2175 374.65 0.3333 0.8919 1.5538 0.3891 0.1816
216 2175 373.65 0.3333 0.8801 1.5336 1.7533 0.8184
217 2175 424.15 0.3333 0.8009 1.3975 0.7574 0.5000
218 2175 424.15 0.3333 0.8180 1.4269 0.7574 0.5000
219 2175 323.15 0.6667 0.9566 1.6362 3.1215 0.2500
220 2175 323.15 0.6667 0.9622 1.6456 3.1215 0.2500
221 2175 323.15 0.6667 0.9690 1.6570 3.1215 0.2500
222 2175 323.15 0.6667 0.9853 1.6844 3.1215 0.2500
223 2175 373.15 0.6667 0.7693 1.3200 3.1215 0.5000
224 2175 373.15 0.6667 0.7770 1.3331 3.1215 0.5000
225 2175 423.15 0.6667 0.7005 1.2034 3.1215 0.6403
226 2175 423.65 0.6667 0.7112 1.2216 1.7533 0.3597
227 2175 323.15 1.0000 0.8267 1.1575 3.1215 0.5000
228 2175 323.15 1.0000 0.8547 1.2093 3.1215 0.5000
229 2176 373.15 1.0000 0.6688 1.1302 5.3091 0.6297
230 2175 373.15 1.0000 0.6709 1.1337 3.1215 0.3703
231 2175 423.65 1.0000 0.6023 1.0189 1.7533 0.3597
232 2175 423.15 1.0000 0.6349 1.0735 3.1215 0.6403
233 2175 323.15 1.3333 0.7442 1.2351 3.1215 0.5000
234 2175 323.15 1.3333 0.7530 1.2495 3.1215 0.5000
235 2175 373.15 1.3333 0.6170 1.0262 3.1215 0.2500
236 2175 373.15 1.3333 0.5970 0.9932 3.1215 0.2500
237 2175 373.15 1.3333 0.5889 0.9799 3.1215 0.2500
238 2175 373.15 1.3333 0.5907 0.9829 3.1215 0.2500
163
Run No #. P / psia T
/ K
π¦ππ ππ₯π
/ mol kg-1
π¦πππβ²
/ mol kg-1 π±πππ
INVERSE
DISTANCE,
1/π‘π’π, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
239 2175 373.15 1.3333 0.5650 0.9405 NA NA Discarded
240 2175 423.15 1.3333 0.5357 0.8922 3.1215 0.8047
241 2175 422.15 1.3333 0.5605 0.9331 0.7574 0.1953
242 2175 323.15 1.6667 0.6608 1.0803 3.1215 0.5000
243 2175 323.15 1.6667 0.6927 1.1318 3.1215 0.5000
244 2175 373.15 1.6667 0.5365 0.8789 3.1215 0.2500
245 2175 373.15 1.6667 0.5587 0.9149 3.1215 0.2500
246 2175 373.15 1.6667 0.5175 0.8480 3.1215 0.2500
247 2175 373.15 1.6667 0.5357 0.8776 3.1215 0.2500
248 2175 423.15 1.6667 0.4687 0.7686 3.1215 0.7877
249 2176 424.15 1.6667 0.4844 0.7942 0.8415 0.2123
250 2175 323.15 2.0000 0.6215 1.0003 3.1215 0.5000
251 2175 323.15 2.0000 0.6064 0.9762 3.1215 0.5000
252 2175 372.15 2.0000 0.4849 0.7822 0.7574 0.1953
253 2175 373.15 2.0000 0.4878 0.7868 3.1215 0.8047
254 2175 423.15 2.0000 0.4239 0.6063 3.1215 0.5000
255 2175 423.15 2.0000 0.4433 0.6000 3.1215 0.5000
Note: mCO2β² means the original measured data, the real CO2 solubility (mCO2) obtained in this study equals to mCO2 = 0.992mCO2
β²
164
Table E 6 Original Experimental CO2 solubility data record at 2175-2176 psia, 323.15-424.15 K, and from 0.5-4.5 mol kg-1 KCl for the CO2-KCl-H2O system.
Run No #. P / psia T / K π¦πππ₯
/ mol kg-1
π¦πππβ²
/ mol kg-1 π±πππ
INVERSE
DISTANCE,
1/π‘π’π, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
256 2175 323.15 0.5 1.1832 2.050884 3.121527 1
257 2175 374.65 0.5 0.9371 1.631268 0.389051 0.181601
258 2175 373.65 0.5 0.9505 1.654209 1.753291 0.818399
259 2175 424.15 0.5 0.8882 1.547462 0.757371 1
260 2175 323.15 1 1.0971 1.871989 3.121527 0.5
261 2175 323.15 1 1.1081 1.890404 3.121527 0.5
262 2175 373.15 1 0.8846 1.514892 3.121527 0.5
263 2175 373.15 1 0.8874 1.519614 3.121527 0.5
264 2175 423.15 1 0.8223 1.409706 3.121527 1
265 2175 323.15 2 1.0135 1.674584 3.121527 1
266 2175 373.15 2 0.7878 1.306537 3.121527 1
267 2175 423.15 2 0.7298 1.211512 3.121527 1
268 2175 323.15 3 0.9205 1.474463 3.121527 1
269 2175 373.15 3 0.7463 1.198773 3.121527 1
270 2175 422.15 3 0.6318 1.016723 0.757371 1
271 2175 323.15 3 0.9205 1.474463 3.121527 1
272 2175 373.15 3 0.7463 1.198773 3.121527 1
273 2175 422.15 3 0.6318 1.016723 0.757371 1
274 2175 323.15 4 0.8686 1.349227 3.121527 1
275 2175 373.15 4 0.6791 1.057984 3.121527 1
276 2176 424.15 4 0.5977 0.932352 0.841499 1
277 2175 323.15 4.5 0.84 1.284844 3.121527 1
278 2175 373.15 4.5 0.6368 0.9775 3.121527 1
279 2175 423.15 4.5 0.5477 0.841881 3.121527 0.930968
280 2175 421.15 4.5 0.5414 0.832278 0.231462 0.069032
Note: mCO2β² means the original measured data, the real CO2 solubility (mCO2) obtained in this study equals to mCO2 = 0.992mCO2
β²
165
Table E 7 Original Experimental CO2 solubility data record at 1450-2538 psia, 323.15-424.15 K, and total ionic strength from 1.712 to 4.984 mol kg-1 H2O for
the CO2-synthetic brine system. The chemical composition of the dissolved species (NaCl, Na2SO4, CaCl2, MgCl2, KCl, SrCl2, and NaBr) are listed in Table 4. 2.
Run No #. P / psia T / K π¦πππ₯
/ mol kg-1
π¦πππβ²
/ mol kg-1
INVERSE
DISTANCE,
1/π‘π’π, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
281 2538 422.15 1.712 0.7705 0.9750 0.5000
282 2538 424.15 1.712 0.7951 0.9750 0.5000
283 2538 373.15 1.712 0.8136 39.0625 0.5000
284 2538 373.15 1.712 0.8234 39.0625 0.5000
285 2538 323.15 1.712 0.9587 39.0625 0.5000
286 2538 323.15 1.712 0.9687 39.0625 0.5000
287 2175 423.15 1.712 0.6984 3.1215 0.5778
288 2176 423.65 1.712 0.7089 2.2813 0.4222
289 2175 373.15 1.712 0.7582 3.1215 0.5000
290 2175 373.15 1.712 0.765 3.1215 0.5000
291 2175 323.15 1.712 0.9331 3.1215 0.5000
292 2175 323.15 1.712 0.9433 3.1215 0.5000
293 1813 423.15 1.712 0.6147 1189.0606 0.5000
294 1813 423.15 1.712 0.6271 1189.0606 0.5000
295 1813 373.15 1.712 0.7043 1189.0606 0.5000
296 1813 373.15 1.712 0.6991 1189.0606 0.5000
297 1813 323.15 1.712 0.9015 1189.0606 0.5000
298 1813 323.15 1.712 0.9167 1189.0606 0.5000
299 1450 423.15 1.712 0.5051 7.0359 0.5000
300 1450 423.15 1.712 0.5149 7.0359 0.5000
301 1450 373.15 1.712 0.6019 7.0359 0.5000
302 1450 373.15 1.712 0.5979 7.0359 0.5000
303 1450 323.15 1.712 0.843 7.0359 0.5000
304 1450 323.15 1.712 0.8572 7.0359 0.5000
305 2538 423.15 4.984 0.4832 39.0625 0.5000
306 2538 423.15 4.984 0.4933 39.0625 0.5000
307 2538 373.15 4.984 0.5052 39.0625 0.5000
166
Run No #. P / psia T / K π¦πππ₯
/ mol kg-1
π¦πππβ²
/ mol kg-1
INVERSE
DISTANCE,
1/π‘π’π, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
308 2538 373.15 4.984 0.5151 39.0625 0.5000
309 2538 323.15 4.984 0.6062 39.0625 0.5000
310 2538 323.15 4.984 0.6132 39.0625 0.5000
311 2175 423.15 4.984 0.449 3.1215 0.5778
312 2176 423.65 4.984 0.4504 2.2813 0.4222
313 2175 373.15 4.984 0.4822 3.1215 0.5000
314 2175 373.15 4.984 0.4923 3.1215 0.5000
315 2175 323.15 4.984 0.5991 3.1215 0.5000
316 2175 323.15 4.984 0.6191 3.1215 0.5000
317 1813 423.15 4.984 0.374 NA NA Discarded
318 1813 423.15 4.984 0.397 1189.0606 1.0000
319 1813 373.15 4.984 0.4365 1189.0606 0.5000
320 1813 373.15 4.984 0.4372 1189.0606 0.5000
321 1813 323.15 4.984 0.5592 NA NA Discarded
322 1813 323.15 4.984 0.5732 1189.0606 1.0000
323 1450 423.15 4.984 0.3203 7.0359 0.5000
324 1450 423.15 4.984 0.3361 7.0359 0.5000
325 1450 373.15 4.984 0.3732 7.0359 0.5000
326 1450 373.15 4.984 0.3857 7.0359 0.5000
327 1450 323.15 4.984 0.5279 7.0359 0.5000
328 1450 323.15 4.984 0.5513 7.0359 0.5000
Note: mCO2β² means the original measured data, the real CO2 solubility (mCO2) obtained in this study equals to mCO2 = 0.992mCO2
β²
167
Table E 8 Original Experimental CO2 solubility data record at 1450-2538 psia, 323.15-424.15 K, and total ionic strength from 1.712 to 4.984 mol kg-1 H2O for
the CO2-synthetic brine system. The chemical composition of the dissolved species (NaCl and CaCl2) are listed in Table 4. 2.
Run No #. P / psia T / K π¦πππ₯
/ mol kg-1
π¦πππβ²
/ mol kg-1
INVERSE
DISTANCE,
1/π‘π’π, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
329 2538 423.15 1.712 0.7705 39.0625 0.5000
330 2538 423.15 1.712 0.8024 39.0625 0.5000
331 2538 373.15 1.712 0.826 39.0625 0.5000
332 2538 373.15 1.712 0.8224 39.0625 0.5000
333 2538 323.15 1.712 0.9431 39.0625 0.5000
334 2538 323.15 1.712 0.9741 39.0625 0.5000
335 2175 423.15 1.712 0.7037 3.1215 0.5778
336 2176 423.65 1.712 0.7165 2.2813 0.4222
337 2175 373.15 1.712 0.7597 3.1215 0.5000
338 2175 373.15 1.712 0.7714 3.1215 0.5000
339 2175 323.15 1.712 0.9212 3.1215 0.5000
340 2175 323.15 1.712 0.943 3.1215 0.5000
341 1813 423.15 1.712 0.6043 1189.0606 0.5000
342 1813 423.15 1.712 0.6209 1189.0606 0.5000
343 1813 373.15 1.712 0.691 1189.0606 0.5000
344 1813 373.15 1.712 0.7018 1189.0606 0.5000
345 1813 323.15 1.712 0.8907 1189.0606 0.5000
346 1813 323.15 1.712 0.9206 1189.0606 0.5000
347 1450 423.15 1.712 0.5068 7.0359 0.5000
348 1450 423.15 1.712 0.5117 7.0359 0.5000
349 1450 373.15 1.712 0.5886 7.0359 0.5000
350 1450 373.15 1.712 0.6004 7.0359 0.5000
351 1450 323.15 1.712 0.8484 7.0359 0.5000
352 1450 323.15 1.712 0.8663 7.0359 0.5000
353 2538 423.15 4.984 0.481 39.0625 0.5000
354 2538 423.15 4.984 0.5039 39.0625 0.5000
355 2538 373.15 4.984 0.5198 39.0625 0.5000
168
Run No #. P / psia T / K π¦πππ₯
/ mol kg-1
π¦πππβ²
/ mol kg-1
INVERSE
DISTANCE,
1/π‘π’π, Eq. (C.3)
WEIGHTING
FACTOR,
Eq. (C.2)
Note
356 2538 373.15 4.984 0.5308 39.0625 0.5000
357 2538 323.15 4.984 0.6085 39.0625 0.5000
358 2538 323.15 4.984 0.6181 39.0625 0.5000
359 2175 423.15 4.984 0.4386 3.1215 0.5778
360 2176 423.65 4.984 0.4608 2.2813 0.4222
361 2175 373.15 4.984 0.4852 3.1215 0.5000
362 2175 373.15 4.984 0.5019 3.1215 0.5000
363 2175 323.15 4.984 0.5969 3.1215 0.5000
364 2175 323.15 4.984 0.6121 3.1215 0.5000
365 1813 423.15 4.984 0.3943 1189.0606 0.5000
366 1813 423.15 4.984 0.4064 1189.0606 0.5000
367 1813 373.15 4.984 0.4378 1189.0606 0.5000
368 1813 373.15 4.984 0.4455 1189.0606 0.5000
369 1813 323.15 4.984 0.5769 1189.0606 0.5000
370 1813 323.15 4.984 0.5886 1189.0606 0.5000
371 1450 423.15 4.984 0.3268 7.0359 0.5000
372 1450 423.15 4.984 0.3345 7.0359 0.5000
373 1450 373.15 4.984 0.387 7.0359 0.5000
374 1450 373.15 4.984 0.3914 7.0359 0.5000
375 1450 323.15 4.984 0.5188 7.0359 0.5000
376 1450 323.15 4.984 0.5675 7.0359 0.5000
Note: mCO2β² means the original measured data, the real CO2 solubility (mCO2) obtained in this study equals to mCO2 = 0.992mCO2
β²
VITA
HAINING ZHAO
John and Willie Leone Family Department of
Energy and Mineral Engineering
The Pennsylvania State University, University Park, PA
E-mail: [email protected]; cell:(814) 954-2216
web: www.carbonlab.org
EDUCATION
The Pennsylvania State University, University Park, PA, USA
Ph.D. in Petroleum and Natural Gas Engineering, to be conferred 12/2014
Ph.D. Minor in Electrochemical Engineering, to be conferred 12/2014
Tianjin University, Tianjin, CHINA
M.S. in Mechanical Engineering 7/2010
Tianjin Institute of Urban Construction, Tianjin CHINA
B.S. in Gas Engineering 7/2004
PROFESSIONAL HISTORY
Beijing Fuhua Gas Co., Ltd. Beijing, CHINA
Compressed natural gas production & delivery 2004-2007
RESEARCH INTERESTS
Equation of State for reservoir fluid PVT modeling
CO2 Storage & EOR
Reservoir simulation; Description of flow through porous media
Electrochemical sensor/corrosion
Web-based computational interface
PUBLICATIONS
Haining Zhao, Mark Fedkin, Robert Dilmore, and Serguei N. Lvov (2014), Carbon dioxide
solubility in aqueous solutions of sodium chloride at geological conditions: Experimental results at
323.15, 373.15, 423.15 K and 150 bar and modeling up to 573.15 K and 2000 bar, Geochimica et
Cosmochimica Acta, doi: 10.1016/j.gca.2014.11.004.
Haining Zhao, Robert Dilmore, and Serguei N. Lvov (2014), Experimental studies and modeling
of CO2 solubility in high temperature aqueous CaCl2, MgCl2, Na2SO4, and KCl solutions,
Geochimica et Cosmochimica Acta, in review.
Haining Zhao, Robert Dilmore, Douglas E. Allen, Sheila W. Hedges, Yee Soong, and Serguei N.
Lvov (2014), Measurement and modeling of CO2 solubility in natural and synthetic reservoir
brines, Environmental Science & Technology, in review.