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record xmlns http:www.loc.govMARC21slim leader nam 22 Ka 4500 controlfield tag 007 crbnuuuuuu 008 s2010 flu s 000 0 eng d datafield ind1 8 ind2 024 subfield code a E14SFE0004815 035 (OCoLC) 040 FHM c FHM 049 FHMM 090 XX9999 (Online) 1 100 Thomas, Mark. 0 245 Geochemical modeling of co2 sequestration in dolomitic limestone aquifers h [electronic resource] / by Mark Thomas. 260 [Tampa, Fla] : b University of South Florida, 2010. 500 Title from PDF of title page. Document formatted into pages; contains X pages. 502 Thesis (MSEV)University of South Florida, 2010. 504 Includes bibliographical references. 516 Text (Electronic thesis) in PDF format. 538 Mode of access: World Wide Web. System requirements: World Wide Web browser and PDF reader. 3 520 ABSTRACT: Geologic sequestration of carbon dioxide (CO2) in a deep, saline aquifer is being proposed for a powergenerating facility in Florida as a method to mitigate contribution to global climate change from greenhouse gas (GHG) emissions. The proposed repository is a brinesaturated, dolomiticlimestone aquifer with anhydrite inclusions contained within the Cedar Keys/Lawson formations of Central Florida. Thermodynamic modeling is used to investigate the geochemical equilibrium reactions for the minerals calcite, dolomite, and gypsum with 28 aqueous species for the purpose of determining the sensitivity of mineral precipitation and dissolution to the temperature and pressure of the aquifer and the salinity and initial pH of the brine. The use of different theories for estimating CO2 fugacity, solubility in brine, and chemical activity is demonstrated to have insignificant effects on the predicted results. Nine different combinations of thermodynamic models predict that the geochemical response to CO2 injection is calcite and dolomite dissolution and gypsum precipitation, with good agreement among the quantities estimated. In all cases, CO2 storage through solubility trapping is demonstrated to be a likely process, while storage through mineral trapping is predicted to not occur. Over the range of values examined, it is found that net mineral dissolution and precipitation is relatively sensitive to temperature and salinity, insensitive to CO2 injection pressure and initial pH, and significant changes to porosity will not occur. 590 Advisor: Jeff Cunningham, Ph.D. 653 Carbon capture and storage Activity coefficient CO2 solubility model Mineral precipitation and dissolution Geochemistry Nonlinear 690 Dissertations, Academic z USF x Civil & Environmental Eng. Masters. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.4815 PAGE 1 Geochemical Modeling of CO 2 Sequestration in Dolomitic Limestone Aquifers by Mark W. Thomas A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Environmental Engineering Department of Civil and Environmental Engineering College of Engineering University of South Florida Major Professor: Jeff rey Cunningham, Ph.D. Mark Stewart, Ph.D. Maya Trotz, Ph.D. Date of Approval: Octo ber 2 5 2010 Keywords: carbon capture and storage, activity coefficient, CO 2 solubility model, mineral precipitation and dissolution, geochemistry non linear Copyright 2010, Mark W. Thomas PAGE 2 Acknowled gements The research leading to this thesis was funded by the State of Florida through the Florida Energy Systems Consortium (FESC). Any opinions, findings, conclusions, or recommendations are those of the author and do not necessarily reflect the views o f FESC. I would like to thank Dr. Jeffrey Cunningham at the University of South Florida for giving me the opportunity to join his research team and be come part of this project, and for the constructive comments mentoring, and advice given during the writ ing of this thesis. I would also like to thank the faculty o f the Department of Civil and Environmental Engineering at the University of South Florida for their teaching efforts a nd to all those who encouraged me during the preparation of this thesis PAGE 3 i Table of Contents List of Tables ................................ ................................ ................................ ..................... iii List of Figures ................................ ................................ ................................ .................... iv Abstract ................................ ................................ ................................ .............................. vi 1: Introduction ................................ ................................ ................................ ................ 1 2: Literature Review ................................ ................................ ................................ ....... 5 3: Estimatin g Thermodynamic Variables ................................ ................................ ...... 9 3.1: Equilibrium Constant, K ................................ ................................ ............... 9 3.2: Activity Coefficient, ................................ ................................ ................. 10 3.2. 1: Activity Coefficient for Neutral Aqueous Species ................................ .... 11 3.2.2: Activity Coefficient for Charged Aqueous Species ................................ ... 11 3.2.3: Activity Coefficient for Aqueous CO 2 ................................ ....................... 17 3.2.3.1:Method of Drummond (22) ................................ ................................ .. 18 3.2.3.2:Method of Rumpf et al. (23) ................................ ................................ 18 3.2.3.3:Method of Duan and Sun (25) ................................ ............................. 19 3.3: Estimating the Fugacity Coefficient for Gaseous and Supercritical CO 2 CO2 ................................ ................................ ................................ .... 20 3.3.1: Method of Spycher and Reed (26) ................................ ............................. 20 3.3.2: Method of Duan et al. (20) ................................ ................................ ......... 21 3.4: Estimating the Activity of Water, a W ................................ .......................... 21 3.5: Aqueous CO 2 Concentration, m CO2 ................................ ............................. 23 3.5.1: Equilibrium Constant ................................ ................................ ................. 23 3.5. 2: Method of Duan and Sun (25) ................................ ................................ ... 24 3.5.3: Method of Spycher and Pruess (21) ................................ ........................... 25 3.5.4: Spycher and Pruess (21) adaptation of the method of Duan and Sun (25) ................................ ................................ ..................... 27 3.6: Summary ................................ ................................ ................................ ..... 29 4: Model Development ................................ ................................ ................................ 30 PAGE 4 ii 4.1: Model Overview ................................ ................................ ......................... 30 4.2: System of Geochemical Equations ................................ ............................. 30 4.2.1: Rock Minerals ................................ ................................ ............................ 31 4.2.2: Carbonate System ................................ ................................ ...................... 32 4.2.3: Aqueous Complexes ................................ ................................ .................. 33 4.2.4: S alinity ................................ ................................ ................................ ....... 34 4.2.5: Water (H 2 O) System ................................ ................................ .................. 35 4.2.6: Charge Balance ................................ ................................ .......................... 36 4.3: Itera tive Solution Procedure ................................ ................................ ....... 36 4.3.1: Inner Iteration Loop ................................ ................................ ................... 37 4.3.2: Outer Iteration Loop ................................ ................................ .................. 40 4.4: Model Implementation ................................ ................................ ................ 41 4.5: M odel Limitations ................................ ................................ ....................... 42 4.6: Model Outputs ................................ ................................ ............................ 42 4.7: Comparison of Thermodynamic Sub models ................................ ............. 43 5: Model Results ................................ ................................ ................................ .......... 50 5.1: Effect of I nitial pH ................................ ................................ ...................... 50 5.2: Effect of CO 2 Injection Pressure ................................ ................................ 54 5.3: Effect of Salinity ................................ ................................ ......................... 58 5.4: Eff ect of Temperature ................................ ................................ ................. 62 5.5: Effects on Porosity, ................................ ................................ .................. 65 5.6: Choice of Thermodynamic Sub model for CO 2 Parameter Estimation ................................ ................................ ................................ ... 69 6: Summary and Conclusion ................................ ................................ ........................ 70 Works Cited ................................ ................................ ................................ ...................... 71 PAGE 5 iii List of Tables Table 1: Equilibrium Reactions for Mineral Dissolution and Precipitation ..................... 31 Table 2: Equilibrium Reactions for Carbonate Species ................................ .................... 32 Table 3: Equilibrium Reactions for Aqueous Complexes ................................ ................. 33 Table 4: Equilibrium Reactions for H 2 O Dissociation ................................ ...................... 35 Table 5: Combinations of Sub Models for CO 2 Thermodynamic Parameter Estimation ................................ ................................ .......................... 44 Table 6: Brine D ensities at V arious S alinities and T emperatures ................................ ..... 66 Table 7: Mineral D ensities ................................ ................................ ................................ 67 Table 8: Porosity and R esidual B rine S aturation S cenarios ................................ .............. 67 Table 9: Change in Porosity for S cenarios 1 3 U sing V arious C ombinations of I nitial pH, CO 2 I njection P ressure, S alinity, T emperature ................................ .. 68 PAGE 6 iv List of Figures Figure 1: Debye Huckel Parameter A as a Function of Temperature at Constant Pressures ................................ ................................ ........................... 13 Figure 2: Debye Huckel Parameter B as a Function of Temperature at Constant Pressures ................................ ................................ ........................... 13 Figure 3: Helgeson Interaction Parameter b NaCl as a Function of Temperature at Constant Pressures ................................ ................................ ........................... 16 Figure 4: Helgeson Interaction Parameter b Na+,Cl as a Function of Temperature at Constant Pressures ................................ ................................ ....................... 17 Figure 5: Inner Iteration Loop for Pre CO 2 Injection ................................ ...................... 37 Figure 6: Inner Iteration Loop for Post CO 2 Injection ................................ .................... 38 Figure 7: Outer Iteration Loop ................................ ................................ ........................ 41 Figure 8: Equilibrium pH for Various Choices of Thermodynamic Sub Models ........... 45 Figure 9: CO 2 Molality for Various Choices of Thermodynamic Sub Models .............. 45 Figure 10: Calcite Dissolution for Various Choices of Thermodynamic Sub Models ................................ ................................ ................................ ...... 46 Figure 11: Dolomite Dissolution for Various Choices of Thermodynamic Sub Models ................................ ................................ ................................ ...... 46 Figure 12: Gypsum Precipitation for Various Choices of Thermodynamic Sub Models ................................ ................................ ................................ ...... 47 Figure 13: N et CO 2 Storage for Various Choices of Thermodynamic Sub models ......... 47 Figure 14: Equilibrium pH as a Function of Initial pH ................................ ..................... 51 Figure 15: Calcite Dissolutio n as a Function of Initial pH ................................ ................ 51 Figure 16: Dolomite Dissolution as a Function of Initial pH ................................ ............ 52 Figure 17: Gypsum Precipitation as a Function of Initial pH ................................ ........... 52 PAGE 7 v Figure 18: Net CO 2 Storage as a Function of Initial pH ................................ .................... 53 Figure 19: Equilibrium pH as a Function of CO 2 Injection Pressure ................................ 54 Figure 20: Calcite Dissolution as a Function of CO 2 Injection Pressure .......................... 55 Figure 21: Dolomite Dissolution as a Function of CO 2 Injection Pressure ....................... 55 Figure 22: Gypsum Precipitation as a Function of CO 2 Injection Pressure ...................... 56 Figure 23: Net CO 2 Storage as a Function of CO 2 Injection Pressure .............................. 56 Figure 24: Equilibrium pH as a Function of Salinity ................................ ........................ 58 Figure 25: Calcite Dissolution as a Fun ction of Salinity ................................ ................... 59 Figure 26: Dolomite Dissolution as a Function of Salinity ................................ ............... 59 Figure 27: Gypsum Precipitation as a Function of Salinity ................................ .............. 60 Figure 28: Net CO 2 Storage as a Function of Salinity ................................ ....................... 60 Figure 29: Equilibrium pH as a Function of Temperature ................................ ................ 62 Figure 30: Calcite Dissolution as a Function of Temperature ................................ ........... 63 Figure 31: Dolomite Dissolution as a Function of Temperature ................................ ....... 63 Figure 32: Gypsum Precipitation as a Fun ction of Temperature ................................ ....... 64 Figure 33: Net CO 2 Storage as a Function of Temperature ................................ ............... 64 PAGE 8 vi Abstract Geologic sequestration of carbon dioxide (CO 2 ) in a deep, saline aquifer is being proposed for a power generating facility in Florida as a method to mitigate contri bution to global climate change from greenhouse gas (GHG) emissions. The proposed repository is a brine saturated dolomitic limestone aquifer with anhydrite inclusions contained within the Cedar Keys/Lawson formation s of Central Florida. Thermodynamic mod eling is used to investigate the geochemical equilibrium reactions for the minerals calcite, dolomite, and gypsum with 28 aqueous species for the purpose of determining the sensitivity of mineral precipitation and dissolution to the temperature and pressur e of the aquifer and the salinity and initial pH of the brine. The use of different theories for estimating CO 2 fugacity, solubility in brine, and chemical activity is demonstrated to have insignificant effects on the predicted results Nine different comb inations of thermodynamic models predict that the geochemical response to CO 2 injection is calcite and dolomite dissolution and gypsum precipitat ion with good agreement among the quantities estimated. In all cases, CO 2 storage through solubility trapping is demonstrated to be a likely process, while storage through mineral trapping is predicted to not occur. Over the range of values examined, it is found that net mineral dissolution and precipitation is relatively sensi tive to temperature and salinity, insensitive to CO 2 injection pressure and initial pH, and significant changes to porosity will not occur. PAGE 9 1 1: Introduction It is becoming increasingly accepted by the scientific community that global climate ch ange due to anthropogenic emissions of greenhouse gas es (GHG) is occurring. them, with a resulting net increase of GHG concentrations in the atmosphere (1) A greenhouse gas of pr imary concern is carbon dioxide ( CO 2 ) One of the major sources of CO 2 emissions is the combustion of fossil fuels for power generation and industrial processes in energy intensive global economy (1) Part of the long term solution to global climate change is widespread adoption of low carbon fuels for power generation and industrial processes ; however, in the near term, techniques to reduce CO 2 emissions are being inves tigated (1) O ne of the more promising mitigation techniques being investigated is captur ing CO 2 from large point source emitters and storing it to prevent release to the atmosphere (1; 2) This process, commonly referred to as carbon capture and storage ( CCS ) relies on technologies that have already been implemented at smaller scales by the oil and gas industr ies for enhanced oil recovery (EOR) and CO 2 disposal from natural gas refining (1; 2) Proposed repositories for large scale storage of captured CO 2 include depleted oil and natural gas fields coal beds the deep ocean and deep saline aquifers (1; 2) Deep saline aquifers are ideal candidates for storing CO 2 because they are commonly PAGE 10 2 found throughout the world often have large storage capacity and ideal geologic properties, are not used as drinking water sources, and are isolated from the biosphere (1; 3; 4) Injection of CO 2 into deep aquifers for geologic storage requires a compressed CO 2 stream recovered from industrial processes and an injection well drilled into the receiving formation (2) Typically, the CO 2 is injected into and maintained within the aquifer under supercritical conditions to take advantage of higher density of the CO 2 phase under these conditions; in other words, more mass of CO 2 is stored per bulk aquifer volume when it is supercritical versus when it is gaseous (1) As CO 2 injection into the aquifer continues, it will displace the native brine as it sweeps through the formation (2) As the native brine is being displaced by CO 2 sweeping some brine will remain trapped in pores due to capillary forces. This trapped brine is known as the residual brine saturation and may absorb CO 2 from the injected CO 2 phase Carbon dioxide storage in deep saline aquifers i nvolves many uncertainties from geochemical and geologic perspectives. Carbon dioxide storage in a deep saline aquifer results in numerous geochemical reactions between the n ative brine and the rock minerals that comprise the aquifer formation (2; 4) These reactions are expected to result in dissolution and precipitation of different minerals, and this can have consequences related to fo rmation integrity and storage efficiency (4) Excess mineral dissolution could weaken the aquifer formation, which could increase the risk of CO 2 escaping into other geologic formation s (1; 5) Conversely, excess mineral precipitation could decrease the porosity of the formation, potentially decreasing the permeability of the aquifer to injected CO 2 or decreasing the available volume for bulk CO 2 storage (6) PAGE 11 3 T he University of South Florida has been investigating the feasibility of capturing CO 2 from a power generating facility in Polk County, Florida and storing it in a deep, dolomitic limestone aquifer located with in the Cedar Keys/Lawson formation of Central Florida (7; 8; 9) Geochemical modeling of CCS in this formation has been previously performed by researchers at the University of South Florida using TOUGHREACT software (7) The previous models predicted that CO 2 injection in this formation would lower the pH of the native brine, resulting in the dissolution of calcite and dolomite and the precipitation of gypsum (7) Additionally, it was found that porosity increased very slightly due to excess mineral dissolution in areas where CO 2 saturated brine interacts with the mineral phase (7) H owever, further investigation into the methods used by the TOUGHREACT soft ware for estimating thermodynamic parameters (activity coefficients, fugacity coefficients, solubility) is deemed warranted. Alternative geochemical models of CCS in the Cedar Keys/Lawson injection zone that yield similar predictions to those of TOUGHREACT simulations would lend support to the results reported by Cunningham et al. (7) The first objective of this thesis is to develop a general thermodynamic framework for geochemical modeling of CO 2 injection in to a dolomitic limestone aquifer that is representative of the Cedar Keys/Lawson injection zone After developing a framework for geochemical modeling, the next objective is to examine the system sensitivity to different methods for estimating thermodynamic parameters for CO 2 The third objective is to investigate the system sensitivity to geophysical and chemical parameters like initial pH, CO 2 injection pressure, brine salinity, and temperature. The final objective of this PAGE 12 4 thesis is to use the results of th e geochemical model to estimate changes in porosity induced by CO 2 injection. T his thesis will first discuss existing knowledge of CO 2 injection into deep saline aquifers (Chapter 2) It will then explore the thermodynamic variables involved in describing the geochemical system and different methods for their estimation (Chapter 3) This will be followed by discussion o f the calculation methodology required to solve non linear geochemical equations that describe the chemistry induced by CO 2 dissolution into residual brine (Chapter 4) Finally, data obtained from the models related to mineral precipitation and dissolution and changes in porosity w ill be presented (Chapter 5), and appropriate conclusions will be drawn (Chapter 6) PAGE 13 5 2: Literature Revi ew A great deal of research on CO 2 injection into geologic formations is available in the literature for a wide variety of conditions and intended purpose of storage While the idea of widespread and large scale capture and storage of CO 2 from facilities like fossil fuel power plants is relatively new, the process and technologies of injecting CO 2 underground are not (1; 10) Carbon dioxide injection has been used primarily in the oil industry as a wa y to increase oil production from declining fields and in the gas industry as a way to dispose of CO 2 that is stripped from natural gas during refining operations though at a smaller scale than would be need ed for widespread adoption of CO 2 sequestration from power generation facilities (1; 10) M uch of the research has focused on CO 2 storage in sandstone formations because they often hold oil or natural gas and often include the possibility of mineral trapping due to the presence of aluminosilicate minerals (1; 11; 12) However, r ecent research has also considered the possibility of using carbonate formations as CO 2 storage repositories (5; 6; 13) S tudies have included both laboratory experiments and computer modeling of expected conditions for a CO 2 injection process into a carbonate aquifer (4; 5; 6; 13; 14) Carbon dioxide is trapped in a deep saline aquifer by several processes. Initially, CO 2 is trapped with in the pores of the aquifer formation due to capillary forces and underneath the aquifer confining layer by hydrodynamic forces due to buoyancy (1; 2) As time passes, CO 2 is further trapped in the aquifer by dissolution and speciation into PAGE 14 6 native brine through solubility and ionic trapping (1; 2) Finally, dissolved carbonate species can be further trapped by combining with dissolved cations to form solid mineral precipitates in thermodynamic equilibrium with the brine during a process known as mineral trapping (1; 2) It has been suggested that mineral trapping of CO 2 in a typical calcium carbonate aquifer (i.e. calcium or calcite is present in significant amounts ) is not a viable mechanism for CO 2 storage due to the increase in solubility of calcium carbonate minerals at low pH conditions resulting from CO 2 dissolution into native brine (4; 6; 13) This is in contrast to the precipitation of low solubility carbonate minerals tha t is expected in aluminosilicate rich, iron rich, or magnesium rich aquifer formations (3; 10; 11) M odeling performed by others typically predicts a pH around 4.8 as a result of CO 2 dissolution into brine contained within a carbonate aquifer (5; 7) Solution buffering by bicarbonate ion (HCO 3 ) due to dissolution of carbonate containing minerals is predicted to be the dominant mechanism for dete rmining the pH of CO 2 saturated brine in carbonate aquifers (4; 5; 7) Additionally, solution buffering enhances the dissolution of CO 2 and this can contribute to additional CO 2 storage by solubility trappin g (5; 15) Calcite, if present, is always predicted to dissolve locally when it is in contact with CO 2 saturated brine (5; 6; 7; 13) although some studies have found that it can precipitate downstream from areas of high dissolution due to particle trapping in pores and exposure to high bicarbonate concentration in displaced brine (6) The net calcite dissolution is predicted to be re latively low when compared to its abundance in the mineral phase (i.e., aquifer matrix) (5; 7) However, near the injection well, some have noted that calcite dissolution can be quite high, leading to large increases in porosity with high connectivity PAGE 15 7 i.e. channeling through the rock formation (4) Dolomite, if it is also present in the mineral phase has been predicted by some models to dissolve along with calcite when in contact with CO 2 saturated brine (5; 7) However, other models predict that dolomite can precipitate when magnesium saturated brine encounters a pure calcite phase (13) Cunningham et al. also suggest that gypsum precipitates due to increased Ca 2+ concentrations released by calcite and dolomite dissolution when sulfate ion (SO 4 2 ) is present (7) In the literature, most computer models of single phase CO 2 injection into c arbonate aquifers typically predict that that permeability and porosit y are not likely to be significantly affected (5; 7; 13) However, some research suggests that micro scale anisotrop ic features of the aquifer formation can influenc e mineral dissolution and precipitation and have a significant effect on changes in porosity and permeability (13; 14) This is consistent with lab experiments performed by Izgec et al. (6) Other s have explored the difference between injecting pure phase CO 2 versus CO 2 saturated brin e and found that injection of CO 2 saturated brine can damage the aquifer formation by excessive carbonate mineral dissoluti on This is a result of continuous refreshing of CO 2 saturated brine that is cation deficient near the wellhead (4) In general however most studies do not predict that changes in porosity and permeability due to geochemical effects of CO 2 injection into carbonate aquifers represent a significant impediment to implementation (4; 5; 7) Most research into the geochemical effects of CO 2 injection into a carbonate aquifer suggests that carbonate minerals will dissolve. However, there is some disagreement over the extent of carbonate mineral dissolution and the effects of this dissolution on porosity PAGE 16 8 and permeability. Furthermore, there is a lack of data comparing the effects of the choice s of different methods for estimating thermodynamic parameters on the geochemical system Finally, there is little information available in the literature on the sensitivity of the geochemistry involved with CO 2 injection into a carbonate aquifer to physical and chemical parameters like initial pH, CO 2 injection pressure, and brine salinity PAGE 17 9 3: Estimating Thermodynamic Variables To model the effects of CO 2 injection into a carbonate aquifer, the system must be describe d in a thermodynamic context. This thermodynamic description is based on solubility equilibrium relationships for minerals, aqueous complexes, and CO 2 with ions dissolved in the native brine of the aquifer formation. Deviations from ideal thermodynamic beha vior due to high pressure, salinity, and temperature are accounted for by activity coefficients for aqueous species and by a fugacity coefficient for the supercritical CO 2 phase 3.1: Equilibrium Constant K The equilibrium constant K represents the ratio of product activities to reactant activities that occurs when the forward and reverse rate s of a reaction are equal (i.e., the reaction is at equilibrium). Consider a chemical reaction where the reactants A and B are in equilibrium wi th the products C and D The reaction can be written in the following manner : Equation 1 where lowercase letters represent a stoichiometric coefficient and uppercase letters represent a chemical species. The equilibrium constant is given by the following expression: PAGE 18 10 Equation 2 w here a j represents the chemical activity of species j Equilibrium constant s for many reactions have been determined experimentally and values are available in the literature. For this study, equilibrium constant s are taken from the thermodynamic database include d with the TOUGHREACT geochemical modeling software (16) This database has equilibrium constant s for many geochemical reactions as functions of temperature and is considered valid over a temperature range of 0 300C (16) The equilibrium constant s for most reactions considered in this paper are calculated using an equation of the following form (16) : Equation 3 where K is the equilibrium constant T is the temperature in Kelvin and a through e are constants that are defined in the geochemical database for each equilibriu m reaction (16) Most of the geoche mical reactions considered in this thesis are analyzed using equilibrium constant s 3.2: Activity Coefficient, The activity coefficient , relates the activity of a chemical species to its concentration, and is a way to account for non ideal effects that occur at high ionic strength, temperature and pressure. The following equation describes the relationship between chemical activity and the activity coefficient: Equation 4 PAGE 19 11 where a i is the activity of chemical i and m i represents the molal concentration of i. The activity coefficient must be estimated for the following three types of aqueous species: neutral, ionic, and dissolved CO 2 Methods for estimating activity coefficients for these different types of aqueous species are described below. 3.2.1: Activity Coefficient for Neutral Aqueous Species A neutral species is a solvated complex containing positive and negative ions with a net charge of zero. Examples include NaHCO 3 (aq) NaCl (aq) C aCO 3(aq) etc. The activity of aqueous neutral species is assumed to be equal to unity (11; 16) 3.2.2: Activity Coefficient for Charged Aqueous Species Charged aqueous species includes ions and charged aqueous complexes. Wh en charged species are dissolved in a solvent that contains high concentrations of other charged species the effects of individual species are damp en ed due to ionic interactions. This damp en ing effect is quantified by the activity coefficient In general, charged aqueous species have activity coefficients that are less than unity. To calculate the activity coefficient for charged aqueous species the method presented by Helgeson et al. (17) is used. This method is ch osen because it is applicable for temperatures between 0 600 C pressure s up to 5 000 bar and chloride brines up to 6 molal ionic strength (16; 17) T his is the calculation method that is used in the TOUGHREACT software (16) The expression for estimating activity coefficients of charged aqueous species is as follows (16; 17) : PAGE 20 12 Equation 5 where A and B are Debye Huckel parameters; z j is the ionic charge for charged species j ; is the true ionic strength in molal units ; j is the ion distance of closest approach for ion j ; m is the sum of molal concentrations for all dissolved species ; abs ,j is the absolute Born coefficient for charged species j ; and b NaCl and b Na +, Cl a re parameters describing ionic interaction. The equations to estimate Debye Huckel parameters A and B we re regressed as functions of temperature and pressure using data given in Tables 1 and 2 of Helgeson et al. (18) These tables contain experimental data values for the se Debye Huckel parameters at different temperatures for the saturation pressure of water and five constant pressures ranges between 1 kilobar and 5 kilobar Linear interpolation is used for estimating values that lie between the constant pressure lines Plots of A and B as functions of temperature for the differ ent pressures are obtained using data from the literature (18) and are presented in the following figures: PAGE 21 13 Figure 1 : Debye Huckel P arameter A as a Function of Temperature at Constant Pressures Figure 2 : Debye Huckel P arameter B as a F unction of T emperature at C onstant P ressures 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0 100 200 300 400 A (kg 1/2 mole 1/2 ) Temperature ( C) Debye Huckel Parameter A SAT 1 kb 2 kb 3 kb 4 kb 5 kb 0.30 0.35 0.40 0.45 0 100 200 300 400 B (kg 1/2 mole 1/2 Ang 1 ) Temperature ( C) Debye Huckel Parameter B SAT 1kb 2kb 3kb 4kb 5kb PAGE 22 14 The true ionic strength is given by the following equation (17) : Equation 6 where m re presents molal concentration, subscript j represents free ionic species and subscript q represents aqueous complexes. This is different from the stoichiometric ionic strength, where the concentrations in the calculat ion do not take into account whether the ions are complexed with other ions Stoichiometric ionic strength is defined by the following equation (17) : Equation 7 where m j represents the molal concentration of the free ion j j is the stoichiometric coefficient of species j combined in aqueous complex q and m q,j represents the molal concentration of aqueous complex q containing ion j Note that in the aqueous comp lex summation operator, the charge of ion j is used for calculations, as opposed to the charge of aqueous complex q used in the true ionic strength calculation. The distance of closest approach j for charged species interactions is based on the assumpt ion that most ionic interaction s will involve Na + and Cl ions due to their high concentrations (16; 19) This implies that most charged species are shielded by surrounding Na + or Cl ions, depending on the respective charge s The distance of closest approach is calculated as follows (16; 17; 19) : PAGE 23 15 Equation 8 Equation 9 where r eff,j is the effective ionic radius of species j in Angstroms. Th ese expressions are based on simplifications of Equation 125 of Helgeson et al. (17) by Reed (19) as explained in the TOUGHREACT user guide (16) Values for r eff are taken from Table 3 of Helgeson et al. (17) Note that 1.91 and 1.81 are the ionic radii in Angstroms for Na + and Cl respectively. The absolute Born coefficient for ion j abs ,j is an ion solvation parameter and is calculated as follows (16; 17) : Equation 10 where = 1.66027 10 5 A ng cal / mole and r eff ,j is in Angstroms. It is related to the dielectric constant of the solution (17) Calculating the interaction parameters b NaCl and b Na +, Cl follows a procedure similar to that used for calculating the Debye Huckel parameters. Equations were regressed based on data given in Tables 29 and 30 of Helgeson et al. (17) as functions of temperature for the saturation vapor pressure for water and at five additional con stant pressures ranging from 1 kilobar to 5 kilobar Linear interpolation is used to estimate values for interaction PAGE 24 16 parameters that lie between constant pressure lines. Plots of b NaCl and b Na+,Cl are given in the following figures: Figure 3 : Helgeson I nteraction P arameter b NaCl as a Function of Temperature at Constant Pressures 12.0 10.0 8.0 6.0 4.0 2.0 0.0 2.0 4.0 0 100 200 300 400 500 b NaCl (kg mole 1 )*10 3 Temperature ( C) Parameter b NaCl SAT 1 kb 2 kb 3 kb 4 kb 5 kb PAGE 25 17 Figure 4 : Helgeson I nteraction P arameter b Na+,Cl as a Function of Temperature at Constant Pressures In summary, Equations 5 6, and 8 10 are used with data given in Figures 1 4 to estimate the activity coefficient for each species of dissolved ion and charged aqueous complex. 3.2.3: Activity Coefficient for Aqueous CO 2 The activity coefficient for aqueous (dissolved) CO 2 d escribes the non ideal effects of high temperature, pressure, and ionic strength on the chemical activity of CO 2(aq) This 15.0 10.0 5.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 0 100 200 300 400 500 b Na+Cl (kg mole 1 )*10 8 Temperature ( C) Parameter b Na+,Cl SAT 1 kb 2 kb 3 kb 4 kb 5 kb PAGE 26 18 2 solubility in high ionic strength solutions as compare d with pure water (16; 20) At low ionic strengths, the activity coefficient for dissolved CO 2 is considered to be unity (16; 21) However, the activity coefficient increases at high ionic strength as the solution becomes more crowded for dissolved CO 2 and dissolution is less than predicted based on ideal thermodynamic considerations. For this study, three different models are use d to estimate CO2 3.2.3.1: Method of Drummond (22) This model is a function of temperature and ionic strength and is given by the following expression (16; 22) : Equation 11 where T is the temperature in Kelvin; I is the molal ionic strength ; and C, F, G, E and H are constants tabulated by Drummond (16; 22) This model has been cited in numerous publications and has been incorporated into TOUGHREACT geochemical modeling software as well as others (16) This model is valid for a temperature range of 20 400 C and 0 6.5 molal NaCl concentration and yields the m olal scale activity coefficient for aqueous CO 2 (16; 22) 3.2.3.2: Method of Rumpf et al. (23) This model is a function of temperature and ionic strength and is given by the following expression (21; 23) : Equation 12 PAGE 27 19 where (21; 23) : Equation 13 and (21; 23) : Equation 14 where T is the temperature in Kelvin and m salt is the molal concentration of all dissolved salt species A variation presented by Spych er et al. (21) based on a simplification presented by Duan et al. (24) is included to yield the final form of the equation (21) : Equation 15 where m is the molal concentration of the indicated species. This method is valid for temperature from 313 433 K and 0 6 molal salt concentration and yields a molal scale activity coeff icient (21) 3.2.3.3: Method of Duan and Sun (25) This model is a function of temperature, pressure, and ionic strength and is given by the following expression (25) : Equation 16 where and are parameters calculated based on the following equation (25) : PAGE 28 20 Equation 17 where P is the pressure in bars T is the temperature in Kelvin and c 1 through c 11 are constants from Table 2 of Duan and Sun (25) Note that and use different sets of constants c 1 through c 11 This CO 2 activity coefficient model is valid for temperatures of 273 573 K, pressures of 0 2000 bar and ionic strengths of 0 4.3 m olal (25) 3.3: Estimating the Fugacity Coefficient for Gaseous and Supercritical CO 2 CO2 The fugacity coefficient CO2 is a parameter used to describe the deviation from ideal thermodynamic behavior of gaseous/supercritical CO 2 that is observed at high temperature and pressure. The fugacity coefficient is used to calculate the fugacity of the CO 2(g,sc) phase, a thermodynamic val ue that is akin to the activity of an aqueous species. Gas phase f ugacity is calculated as follows: Equation 18 where F is the fugacity is the fugacity coefficient, and P CO2 is the partial pressure of CO 2 in bars. For this study, two models are used to estimate CO2 as described below 3.3.1: Method of Spycher and Reed (26) This model, a function of temperature and pressure is given by the following expression (26) : Equation 19 PAGE 29 21 where T is the temperature in Kelvin ; P is the total gas pressure in bars ; and a, b, c, d, e and f are constants given by Spycher and Reed (26) This model is applicable for a temperature range of 50 350 C and pressure up to 500 bar s (26) It is report ed that there are significant discrepancies between the estimated compressibility factor Z using this model and experimentally observed values of Z at the P T ranges considered (26) This indicates that the method of Spycher and Reed (26) might not be the best method for estimating the CO 2 fugacity coefficient. However, this model has been incorporated into the geochemical modeling software TOUGHREA CT (16) and is thus considered in this thesis 3.3.2: Method of Duan et al. (20) This model, also a function of temperature and pressure, is given by the following expression (20) : Equation 20 where T is the temperature in Kelvin, P is the pressure in bar s, and c 1 c 15 are constants given in Table 1 of Duan et al. (20) This model has been fit ted to experimental data for six T P ranges ranging from 273 573K and 0 2 000 bar (20) 3.4: Estimating the Activity of Water a W The activit y of water a W is considered to be unity under ideal conditions. However, at elevated temperature, pressure and ionic strength, the activity of water begins to deviate from unity as a function of the osmotic coefficient, (16; 17) : PAGE 30 22 Equation 21 where m is the total molal concentration of all dissolved ions. The osmotic coefficient, is calculated as follows (16) : Equation 22 w here (16; 17) : Equation 23 where (16; 17) : Equation 24 where I is the stoichiometric ionic strength (see Equation 7 ) m t,j is the total molal concentration of ion j and m CHRG is the total molal concentration of all charged species in solution. This procedure for calculating the osmotic coefficient utilize s several modifications presented in the TOUGHREACT user manual (16) The original form of the osmotic coefficient equation is Equation 190 of Helgeson et al (17) ; and assuming NaCl dominance in so lution, would yield this expression (17) : PAGE 31 23 Equation 25 Note that this is a function of the true ionic strength, (see Equation 6 ) However, it is reported in the TOUGHREACT user guide (16) and implemented in the TOUGHREACT program that using the stoichiometric ionic strength and half the charged species molality more accurately matches experimentally obtained data than the original formulation based solely on the true ionic strength (16) 3.5: Aqueous CO 2 Concentration, m CO2 The molal concentration of dissolved CO 2 in brine is estimated using four methods. 3.5.1: Equilibrium Constant This method is based on the equilibrium expression for the following chemical reaction : Equation 26 Equation 27 where F CO2 is the fugacity of gaseous/supercritical CO 2 which is estimated using techniques discussed in Section 3.3 The activity of bicarbonate ion is constrained additionally by equilibrium with dissolved CO 2 according to the following equations: PAGE 32 24 Equation 28 Equation 29 The value for K CO2(aq) is taken from thermodynamic database included with TOUGHREACT geochemical modeling software and is calculated as a function of temperature. At 45 C, the log K CO2(aq) value is 6.273 (16) The activity of CO 2(aq) is related to the molal concentration of CO 2 by the following equation: Equation 30 The equations simplify to yield an expression for m CO2 as a function of CO 2 fugacity, equilibrium constants, and activity coefficient. The concentration of dissolved CO 2 along with the solution pH, is used to estimate the activity of bicarbonate, HCO 3 which all other geochemical species are functions of. The pH is then iterated until the geochemical system converges 3.5.2: Method of Duan and Sun (25) This model is a function of temperature, pressure and salt content and is given by Equation 9 of Duan and Sun (25) : Equation 31 PAGE 33 25 where y CO2 is the CO 2 mole fraction in the gaseous phase (assumed in this study to be unity) and CO2 1(0) is the difference between the chemical potentials of CO 2 in the gaseous phase and the liquid phase (20) The value of CO2 1(0) /RT is calculated similarly to and using constants given in Table 2 of Duan and Sun (2003). This CO 2 solubility model is valid for temperatures of 273 573K, pressures of 0 2000 bar and ionic strengths of 0 4.3 m, and yields values that are within 10% of experimentally observed values (20) 3.5.3: Method of Spycher and Pruess (21) This model is a function of temperature, pressure and salt content, and is given by Equation 2 of Spycher and Pruess (21) : Equation 32 where y H2O is the water mole fraction in the gaseous phase (assumed to be zero for this study) ; x is the mole fraction scale activity coefficient for a queous CO 2 ; K CO2 0 is the thermodynamic equilibrium constant for CO 2 dissolution ; P 0 is 1 bar ; and is the average partial molar volume of CO 2 over the P 0 P range which is assumed to be 32.6 cm 3 /mole based on data in Table 2 of Spycher and Pruess (21) To calculate K CO2 0 the following equation is used (21) : Equation 33 where a, b, c and d are constants given in Table 2 of Spycher and Pruess (21) and T is temperature in degrees Celsius. PAGE 34 26 The mole fraction activity coefficient for CO 2 can be converted from the molal scale activity coefficient (see Section 3. 2.3: ) with the following equation (21) : Equation 34 where m salt is the total molal concentration of all species that are not aqueous CO 2 and m is the molal scale activity coefficient that is calculated using methods presented earlier. It is reported by Spycher and Pruess (21) that more accurate results are obtained using the methodology of Duan and Sun (25) or Rumpf et al. (23) for calculating m The molal concentration of aqueous CO 2 can be determined from the mole f raction of aqueous CO 2 using the following relationship (21) : Equation 35 Unlike the previous two models for CO 2 aqueous solubility, this model requires an iterative solution. This is due to the need to convert between mole fraction and molal scales. The solution procedure is as follows: 1. 2. 3. 4. PAGE 35 27 5. 6. The methodology presented by Spycher and Pruess (21) is valid from 12 100C, 1 600 bar and 0 6 m olal NaCl concentration (21) However, the iterative procedure is slight ly cumbersome for calculations 3.5.4: Spycher and Pruess (21) adaptation of the method of Duan and Sun (25) This methodology is a combination of models presented in Spycher et al. (27) and Duan and Sun (25) that is present ed in Spycher and Pruess (21) If the CO 2 solubility model presented by Duan and Sun (25) is simplified into standard thermodynamic variables and the natural log terms are eliminated the following equation results (21) : Equation 36 where F CO2 is the fugacity of the gaseous CO 2 phase, K CO2 is the thermodynamic equilibrium constant and CO2 is the activity coefficient of aqueous CO 2 Now assume there are two systems that are identical except that one consists of pure water and the other system consists of a brine solution with known ionic concentrations For pure water (21) : Equation 37 PAGE 36 28 For brine (21) : Equation 38 The gas phase fugacity and thermodynamic equilibrium constant s are equal because they are function s of temperature and pressure but not salt content. Thus (21) : Equation 39 However, in pure water, CO2 approaches unity (16; 21; 27) Thus (21) : Equation 40 Solving for m CO2 (21) : Equation 41 To determine CO2 the activity co efficient expression presented by Duan and Sun (25) is used (21) although it appears that any suitable method for estimating CO2 could suffice To determine the solubility of CO 2 in pure water, m CO2 0 the methodology presented by Spycher et al. (27) is used. This model is given by the following equation (27) : Equation 42 PAGE 37 29 This model for determining solubility in pure water is identical to the model for determining CO 2 solubility (see Equation 32 ) in brine with the exception of the missing x term which is neglected because x approaches unity in pure water (21) Eliminating the x term makes the solution procedure non iterative because there is no conversion fro m mole fraction to molal scale. All other model parameters are calculated in an identical fashion to the procedure presented by Spycher and Pruess (21) 3.6: Summary The parameters discussed in this chapter are used to describe the thermodynamic environment of a geochemical system. These parameters include solubility equilibrium constants for mineral precipitation and dissolution, for the formation of aqueous complexes, and for dissolution of CO 2 In addition, non ideal effects due to high pressure, salinity, and temperature are accounted for using activity and fugacity coefficients. These parameters and their methods of estimation are then incorporated into the solution procedure discussed in Chapter 4 to describe pre and post injection conditions for CCS in a c arbonate aquifer. PAGE 38 30 4: Model Development 4.1: Model Overview Geochemical models are used to estimate the equilibrium concentrations of various dissolved ions for the purpose of quantifying mineral precipitation and dissolution in response to CO 2 injection. To accomplish this models were developed to describe both pre CO 2 injection and post CO 2 injection geochemical conditions For pre injection conditions, the brin e pH and salinity (salt mass fraction) and the aquifer temperature and pressure ar e specified parameters and are used to estimate the initial equilibrium concentrations of dissolved ions. For post injection conditions, CO 2 injection pressure aquifer temperature and pressure and brine salinity are specified parameters and are used to estimate the new equilibrium pH and ion concentrations. Then the difference between pre and post injection equilibrium ion concentrations is used to estimate the extent of mineral precipitation and dissolution and net CO 2 solubility trapping that occurs during thermodynamic equilibrium processes associated with CO 2 injection 4.2: S ystem of Geochemical Equations The geochemical model is used to solve for the equilibrium concentrations of 28 aqueous species the activity of water and the solution net charge. The geochemical system is non linear based on 30 equations and used to solve for 30 unknown values This system of equations includes 24 equilibrium expression s for ions and aqueous PAGE 39 31 complexes two total mass expressions for N a + and Cl ions three equations to describe the dissociation and the activity of water, and one charge balance equation that calculates the net charge of the solution. 4.2.1: Rock Minerals There are three solubility equilibrium expressions that describe the prec ipitation or dissolution of rock minerals assumed to be present in the aquifer. These rock minerals are calcite (CaCO 3 (s) ), dolomite (CaMg(CO 3 ) 2 (s) ), and gypsum (CaSO 4 2H 2 O (s) ). These three minerals are the source s of Ca 2+ Mg 2+ and SO 4 2 ions in solution that are available for geochemical reaction The precipitation/dissolution reactions and log K values from the TOUGHREACT database (16) for each mineral are given in the following table : Table 1 : Equil ibrium R eactions for M ineral D issolution and P recipitation Reaction log K 35 C 45 C 55 C Calcite 1.703 1.552 1.404 Dolomite 2.173 1.828 1.492 Gypsum 4.494 4.533 4.584 PAGE 40 32 4.2.2: Carbonate System There are three carbonate equilibrium expressions for CO 2(aq) HCO 3 and CO 3 2 that take into account reactions of CO 2 in the aqueous phase and dissolution from the gaseous phase. For pre injection conditions, the geochemical system is closed; i.e., there is no separate CO 2 gas phase that dissolved carbonate species must be in equilibrium with. Thus, the concentrations of aqueous carbona te species are constrained only by the assumed initial pH. For post injection conditions, the geochemical system is open; i.e., the co ncentrations of aqueous carbonate species must be in equilibrium with a separate CO 2 phase that can dissolve into or out of solution. The carbonate system reactions and log K values from the TOUGHREACT database (16) are given in the following table : Table 2 : Equilibrium R eactions for C arbonate S pecies Reaction log K 35 C 45 C 55 C 7.875 7.945 8.018 6.297 6.273 6.267 10.249 10.191 10.148 Note that that equilibrium relationship for CO 2(g,sc) and HCO 3 in Table 2 is not used when other methods (i.e., Duan and Sun (25) or Spycher and Pruess (21) ) are used to estimate the molal concentration of CO 2(aq) m CO2 In this case, m CO2 is estimated using other methods and the equilibrium relationship between CO 2(aq) and HCO 3 is assumed to be valid for remaining calculations PAGE 41 33 4.2.3: Aqueous Complexes There are 1 8 equil ibrium expressions that describe aqueous complex ing reactions that are combinations of the ions in solution made available by the previous six equilibrium r eactions given in Table 1 and Table 2 These aqueous complexes include both dissolved charged species (CaCl + MgHCO 3 + NaSO 4 etc) and dissolved neutral species (NaCl (aq) NaHCO 3(aq) etc) The following table contains the 18 aq ueous complex ing reactions considered and their respective log K values from the TOUGHREACT database (16) Table 3 : Equilibrium R eactions for A queous C omplexes Reaction log K 35 C 45 C 55 C 0.682 0.650 0.610 0.673 0.668 0.643 6.834 6.671 6.520 1.060 1.092 1.135 12.486 12.141 11.816 2.140 2.188 2.241 0.697 0.688 0.676 2.101 2.188 2.373 0.133 0.111 0.075 7.220 7.094 6.978 1.054 1.090 1.137 11.434 11.105 10.796 PAGE 42 34 Reaction log K 35 C 45 C 55 C 2.510 2.645 2.781 0.749 0.711 0.670 9.864 9.935 10.027 0.085 0.001 0.081 13.850 13.575 13.325 0.840 0.870 0.899 4.2.4: Salinity I t is assumed that the salinity (salt mass fraction) is a known parameter, and the salt mass fraction is considered to be only NaCl. The contribution to salinity due to other dissolved ions is assumed to be insignificant. Thus, the total mass of Na + and Cl available for reaction per unit volume is specified by the assumed salinity S alinity, S is defined by the following equation: Equation 43 where S is in percent. This is used to specify the total molal concentration of Na + and Cl ions: Equation 44 where ( m Na,Cl ) TOT is the total molal concentration of Na + and Cl ions respect ively, and PAGE 43 35 MW NaCl is the formula weight for NaCl (58.443 *10 3 kg/mole). Note that this equation is applied twice in the geochemical model to determine the concentrations of both Na + and Cl This is used as a constraint for all species containing Na + and Cl because the sum of concentration of Na + and Cl in all species containing Na + and Cl must equal the total concentration s for Na + and Cl specified by the known salt mass fraction 4.2.5: Water (H 2 O) System The dissociation of water (H 2 O) into H + and OH ions must be considered for any system contained with in the aqueous phase. The water dissociation reaction and log K values from the TOUGHREACT database (16) are given in the following table: Table 4 : Equilibrium R eactions for H 2 O D issociation Reaction log K 35 C 45 C 55 C 13.680 13.400 13.146 The activities of H + and OH are related to the activity of H 2 O (see Chapter 3.4) by the following expression: Equation 45 The pH of the brine is related to the chemical activity of H + by the following equation: Equation 46 PAGE 44 36 4.2.6: Charge Balance The charge balance equation quantifies the net charge o f the solution. It is the sum of the concentrations all ionic and complexed species multiplied by their respective overall charge: Equation 47 where m indicates molal concentration, z indicates charge, subscript j indicates ions and subscript q indicates aqueous complexes. 4.3: Iterative Solution Procedure Because the system of equations i s non linear, an iterative solution procedure is required. In this iterati ve procedure a basis species from the parent reaction s that appears often in the system of equilibrium equations is chosen. The basis species is chosen in such a way that all other geochemical species are functions of th is species and its value can be conveniently iterated unt il all equations are satisfied Essentially, this means picking a basis species that is not specified by any known parameters The molal concentration of this basis species is then iterated until th e net solution charge converges to zero (within an allowab le tolerance) For initial conditions (pre injection) the basis species is bicarbonate ion, HCO 3 because it is not constrained solely by any specified parameter (i.e. initial pH, aquifer pressure, salinity, or temperature) For calculations after CO 2 injection occurs, H + is the chosen basis species because the pH is no longer specified and the activity of HCO 3 is now constrained by equilibrium with the gaseous CO 2 phase The solution procedure consists of an inner iteration loop and an outer iteratio n loop which are discussed below PAGE 45 37 4.3.1: Inner Iteration Loop The purpose of the inner iteration loop is to estimate concentrations of all geochemical species given a particular starting estimate for the concentration of the basis species. The inner iteration lo op is necessary because thermodynamic parameters like activity coefficients, activity of water and aqueous CO 2 concentration are functions of the concentrations of all geochemical species, which are functions of thermodynamic parameters and the concentrat ion of the basis species. Figure 5 and Figure 6 are flow charts of the algorithms used for the inner iteration loop for pre and post injection conditions, respectively. Figure 5 : Inner Iteration Loop for Pre CO 2 Injection PAGE 46 38 Figure 6 : Inner Iteration Loop for Post CO 2 Injection I n order to generate initial estimates for the activities and molal concentrations of all geochemical species activity coefficients are initially assumed to equal unity. The initial estimates for activities and molal concentrations are then used to initialize the inner iteration loop. The molal concentrations of species j at iteration n are solved for using the following expression: Equation 48 where a j is the activit y of all other species in the j th equilibrium reaction raised to their PAGE 47 39 respective stoichiometric coefficient and K j is the equilibrium constant for the j th equilibrium reaction (as given in Tables 1 4). The activity of species j is used to estimate the concentration of species j at iteration n with the following expression: Equation 49 where j is the activity coefficient for species j The activity coefficient for the j th ion at iteration n is estimated using concentrations and the ionic strength from the previous iteration: Equation 50 The procedure is similar for estimating the activity of water at the n th iteration: Equation 51 To solve for the concentrations of free Na + and Cl ions at iteration n the following expression s are used: Equation 52 Equation 53 PAGE 48 40 where m indicates molal concentration and ( m Na+ ) q and ( m Cl ) q indicate molal concentration of Na + and Cl in aqueous complex q multiplied by their stoichiometric coefficient respectively. These concentrations for free Na + and Cl ions are then used to solve for the activities of aqueous complexes containing Na + and Cl ions for iteration n The inner iteration loop is considered to have converged when the change in ionic strength between successive iterations is less than a specified tolerance. A minimal change in ionic strength between iterations indicates that a stable solution has been determined for the given basis species activity 4.3.2: Outer Iteration Loop A t equilibrium, the solution cannot have a net charge. Thus, the model is solved in such a way as to drive the net charge of the brine to zero, and the charge balance equation is used as the convergence criteri on for the outer iteration process. An initial estimate is made for the concentration of the basis species and the inner iteration loop is solved to convergence. Then, t he outer iteration loop is used to iterate the concentration of the basis species until the calculated solution charge approaches zero (within a specified tolerance) Figure 7 is a flowchart demonstrating the algorithm used for the outer iteration loop. For each iteration of the outer loop, a new value for the pH (pre injection) or [HCO 3 ] (post injection) is tested. For each value of pH or [HCO 3 ] tested, the inner iteration loop must be solved to convergence. When the solution net charge approaches zero, the system has converged and the model yield s the equilibrium concentrations of the geochemical species. PAGE 49 41 Figure 7 : Outer I teration L oop 4.4: Model Implementation Computer programs were developed to calculate activity coefficients for ionic species charged aqueous complexes, and aqueous CO 2 ; the fugacity coefficient for CO 2(g,sc) ; aqueous CO 2 concentration ; and the activity of wat er These programs are written in Visual Basic so they can be implemented in a Microsoft Excel spreadsheet where inner and outer iterative calculations are performed. The inner iteration loop is written directly into the spreadsheet as sequential blocks of cells w h ere calculations are carried out and rele vant values are passed forward to the next block. In practice, a fixed number of inner iterations are written explicitly into the PAGE 50 42 structure of the spreadsheet. Excess iterations are written into the spreads heet to ensure that the inner loop will converge for a given estimate of the basis species concentration In most cases, fewer than ten inner iterations are required per outer iteration and 20 inner iterations are sufficient in all scenarios examined The outer loop is iterated using the SOLVER function that is included in Microsoft Excel. The SOLVER function iterate s the concentration of the basis species until the convergence criteri on of net solution charge approach ing zero is met 4.5: Model Limitations The geochemical model is based on the assumption of system equilibrium for both pre and post CO 2 injection conditions. The model only examines geochemistry in the residual brine saturation and does not address chemical processes that occur at the moving CO 2 brine interface. The model also assumes the presence of only three minerals: calcite, dolomite, and gypsum. The model is based on the assumption that only these three minerals are allowed to dissolve and/or precipitate. Finally, the model does not address advective/transport effects or chemical reaction rates. 4.6: Model Outputs Once solved, the geochemical model yields the concentrations and activity coefficients of all aqueous species included in the system, the activity of water, and the CO 2(g,sc) fugacity fo r post injection conditions. Next, t he amount of minerals that precipitate or dissolve due to CO 2 injection can be estimated by examining the difference in concentrations of calcium, magnesium, and sulfate ions in solution for pre and post injection condi tions. Positive concentration difference indicates that ions enter solution PAGE 51 43 due to mineral dissolution and negative concentration difference indicates that ions leave solution due to mineral precipitation. Thus: Equation 54 Equation 55 Equation 56 where m indicates molal concentration and subscripts pre and post refer to conditions before and after CO 2 injection, respectively. Changes in concentrations of carbonate species can also be used to estimate the net CO 2 storage via the solubility trapping mechanism : Equation 57 4.7: Comparison of Thermodynamic S ub models With three different models for estimating CO2 two models for estimating CO2 and four models for estimating m CO2 as describe d in Chapter 3 there are 24 possible combinations of thermodynamic sub models that could be studied. Initially, nine overall geochemical models were developed using different combinations of the thermodynamic models, as summarized in Table 5. PAGE 52 44 Table 5 : Combinations of S ub M odels for CO 2 T hermodynamic P arameter E stimation Model Sub models for CO 2 thermodynamic parameter estimation CO 2(aq) Activity Coefficient CO 2(g,sc) Fugacity Coefficient CO 2(aq) Solubility 1 Drummond (22) Spycher and Reed (26) Equilibrium Constant (16) 2 Drummond (22) Duan and Sun (20) Equilibrium Constant (16) 3 Rumpf et al. (23) Duan and Sun (20) Equilibrium Constant (16) 4 Rumpf et al. (1994) Spycher and Reed (20) Equilibrium Constant (16) 5 Duan and Sun (2003) Duan et al. (20) Duan and Sun (25) 6 Drummond (22) Duan et al. (20) Duan and Sun (25) 7 Drummond (22) Duan et al. (20) Spycher and Pruess (21) adaptation of Duan and Sun (25) 8 Rumpf et al. (23) Duan et al. (20) Spycher and Pruess (21) 9 Rumpf et al. (23) Spycher and Reed (26) Spycher and Pruess (21) These nine combinations of thermodynamic sub models were then used to examine a baseline geochemical scenario to determine the sensitivity of model outputs to the choice of thermodynamic sub models. The base line geochemical scenario has an initial pH of 7. 5, brine salinity of 10%, initial aquifer pressure of 100 bar, CO 2 injection pressure of 160 bar and aquifer temperature of 45 C. The equilibrium pH, equilibrium CO 2 molality, and mineral precipitation/dissolution for calcite, dolomite and gypsum were det ermined for each model after CO 2 injection and plotted along with their respective average values in the following figures: PAGE 53 45 Figure 8 : Equilibrium pH for V arious C hoices of T hermodynamic S ub M odels Figure 9 : CO 2 M olality for V arious C hoices of T hermodynamic S ub M odels 4.5 4.6 4.7 4.8 4.9 5.0 1 2 3 4 5 6 7 8 9 pH Model Equilibrium pH 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1 2 3 4 5 6 7 8 9 moles CO 2 per kg H 2 O Model CO 2(aq) molality PAGE 54 46 Figure 10 : Calcite D issolution for V arious C hoices of T hermodynamic S ub M odels Figure 11 : Dolomite D issolution for V arious C hoices of T hermodynamic S ub M odels 5000 5500 6000 6500 7000 1 2 3 4 5 6 7 8 9 mg Calcite per kg H 2 O Model Dissolved Calcite 300 350 400 450 500 1 2 3 4 5 6 7 8 9 mg Dolomite per kg H 2 O Model Dissolved Dolomite PAGE 55 47 Figure 12 : Gypsum P recipitation for V arious C hoices of T hermodynamic S ub M odels Figure 13 : Net CO 2 Storage for Various Choices of Thermodynamic Sub models 3000 3500 4000 4500 1 2 3 4 5 6 7 8 9 mg Gypsum per kg H 2 O Model Precipitated Gypsum 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 1 2 3 4 5 6 7 8 9 moles CO 2 per kg H 2 O Model Net CO 2 Storage PAGE 56 48 The average equilibrium pH is around 4.79, and this agrees closely with results in the literature (5; 7) The average CO 2 concentration is 1.0 molal, which also agree s generally well with results by others (5; 7) In general, the different combinations of thermodynamic models yield similar results. P recipitation of gypsum and dissolution of c alcite and dolomite also agree well with predictions by others (5; 7) The average estimated net CO 2 storage is around 2.1 molal. S everal trends can be observed based on the choices of CO 2 parameter sub models First, the choice of methodology for estimating the activity coefficien t for CO 2(aq) does not have significant effect on the model predictions. Next, it is observed that s ystem s using the equilibrium constant from the thermodynamic database for calculating the concentration of CO 2(aq) (i.e., models 1 4) predict higher values for mineral pr ecipitation and dissolution, CO 2(aq) concentration, and net CO 2 storage than systems using the Duan and Sun (25) or the Spycher and Pruess (21) solubility models (i.e., models 5 9) This is because the equilibrium constant method for estimating CO 2 solubility does not take into account the effects of high ionic strength, and probably over estimates the dissolved CO 2 concentration. In general, the models using more recent correlations for CO 2 solubility that include the effects of dissolved ions (models 5 9) are in good agreement. Using the CO 2 fugacity model as a distinguishing characteristic, it is observed that models using the Spycher and Reed (26) mode l for CO 2(g,sc) fugacity coefficient (i.e., models 1, 4, and 9) estimate higher values for mineral dissolution/precipitation CO 2(aq) concentration and net CO 2 storage, and estimate lower value s for equilibrium pH. The choice of fugacity coefficient model has the greatest effect on geochemical predictions. This is because the temperatures and pressures being considered are at the low end of the PAGE 57 49 recommended ranges for use with the Spycher and Reed model where inaccuracies are reported for fugacity coefficie nt estimation (26) The fugacity coefficient model presented by Duan et al. (20) is fitted to experimental data for six different T P regimes and probably a better choice for the conditions considered. However, the differences in geochemical predictions are generally low estimates from all models for the equilibrium pH agree to within 1% of the average, estimates from all models for mineral precipitation and dissolution agree to within 1 0% of the average, and estimates from all models for m CO2 and net CO 2 storage agree to within 2 5 % of the average T his suggests that the choice of thermodynamic sub models for estimating CO 2 paramete rs does not have a large effect on the solution to the geochemical system Additionally, these results suggest that variations in estimated CO 2 solubility have a limited effect on other estimated quantities like equilibrium pH and mineral precipitation or dissolution. From these nine geochemical systems three were chosen such that each model used different sub models for calculating m CO2 and CO2 The models chosen for furth er investigation are models 1, 5, and 8 from the preceding table. These models are used to examine the sensitivity of the system to key chemical and physical parameters as described in the next chapter. PAGE 58 50 5: Model Results Models 1, 5 and 8 are used to examine the effects of initial pH, CO 2 injection pressure, sali nity and temperature on the geochemical system. Simulations are performed such that one parameter varies while the other three are kept constant in order to evaluate the sensitivity of the geochemical system to the varying parameter. These simulations are variants o f the base case described in Chapter 4 where the initial pH is 7.5, aquifer pressure is 100 bar, CO 2 injection pressure is 160 bar, salini ty is 10% and temperature is 45 C. 5.1: Effect of Initial pH In these simulations, temperature, CO 2 injection pressure and salinity are co nstant at 45 C, 160 bar and 10%, respectively. Three sets of simulations using an i nitial pH of 6.5, 7.5 and 8.5 were performed PAGE 59 51 Figure 14 : Equilibrium pH as a F unction of I nitial p H Figure 15 : Calcite D issolution as a F unction of I nitial pH 4.70 4.75 4.80 4.85 4.90 6.0 7.0 8.0 9.0 Equilibrium pH Initial pH Equilibrium pH Model 1 Model 5 Model 8 4000 5000 6000 7000 8000 6.0 7.0 8.0 9.0 mg Calcite per kg H 2 O Initial pH Calcite Dissolution Model 1 Model 5 Model 8 PAGE 60 52 Figure 16 : Dolomite D issolution as a F unction of I nitial pH Figure 17 : Gypsum P recipitation as a F unction of I nitial pH 200 300 400 500 600 700 6.0 7.0 8.0 9.0 mg Dolomite per kg H 2 O Initial pH Dolomite Dissolution Model 1 Model 5 Model 8 2500 3000 3500 4000 4500 6.0 7.0 8.0 9.0 mg Gypsum per kg H 2 O Initial pH Gypsum Precipitation Model 1 Model 5 Model 8 PAGE 61 53 Figure 18 : Net CO 2 Storage as a Function of Initial pH Note that the geochemical system predicts slightly increas ing quantities for mineral dissolution and precipitation and very slightly increasing net CO 2 storage with increasing initial pH. However, the system is insensitive to initial pH. This is consistent with the findings by others (7) Insensitivity to initial pH is due to the fact that equilibrated pre injection brine ha s similar composition over the range of pH examined due to the dominance of bicarbonate ion in solution for pH 6 9 Note also that the initial pH has no effect on the equilibrium pH for post CO 2 injection conditions The initial pH does not influence the e quilibrium pH after CO 2 injection because the post injection system has excess CO 2 available, so the separate CO 2 phase will be the controlling phase for equilibrium. Because of these reasons, net mineral precipitation and dissolution is influenced very li ttle by the initial pH. 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 6.0 7.0 8.0 9.0 moles CO 2 per kg H 2 O Initial pH Net CO 2 Storage Model 1 Model 5 Model 8 PAGE 62 54 5.2: Effect of CO 2 Injection Pressure In these simulations, temperature, initial pH and salinity are constant at 45 C, 7.5 and 10%, respectively. Three sets of simulations are performed for CO 2 injection p ressure s of 120, 160 and 200 bars. Figure 19 : Equilibrium pH as a F unction of CO 2 I njection P ressure 4.70 4.75 4.80 4.85 4.90 100 120 140 160 180 200 220 Equilibrium pH CO 2 Injection Pressure (bar) Equilibrium pH Model 1 Model 5 Model 8 PAGE 63 55 Figure 20 : Calcite D issolution as a F unction of CO 2 I njection P ressure Figure 21 : Dolomite D issolution as a F unction of CO 2 I njection P ressure 4000 5000 6000 7000 8000 100 120 140 160 180 200 220 mg Calcite per kg H 2 O CO 2 Injection Pressure (bar) Calcite Dissolution Model 1 Model 5 Model 8 200 300 400 500 600 700 100 120 140 160 180 200 220 mg Dolomite per kg H 2 O CO 2 Injection Pressure (bar) Dolomite Dissolution Model 1 Model 5 Model 8 PAGE 64 56 Figure 22 : Gypsum P recipitation as a F unction of CO 2 I njection P ressure Figure 23 : Net CO 2 Storage as a Function of CO 2 Injection Pressure 2500 3000 3500 4000 4500 100 120 140 160 180 200 220 mg Gypsum per kg H 2 O CO 2 Injection Pressure (bar) Gypsum Precipitation Model 1 Model 5 Model 8 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 100 120 140 160 180 200 220 moles CO 2 per kg H 2 O CO 2 Injection Pressure (bar) Net CO 2 Storage Model 1 Model 5 Model 8 PAGE 65 57 Note that the geochemical system predicts slightly increas ing quantities of mineral dissolution and precipitation decreased equilibrium pH and increased net CO 2 storage in response to increas ing CO 2 inject ion pressure. However, the system is relatively insensitive to CO 2 injection pressure. This is due to the fact that the fugacity of the CO 2(g,sc) phase does not vary proportionally with pressure over the range of pressures examined. Using the baseline scen ario and the Spycher and Reed (26) methodology for estimating CO 2 fugacity, varying the pressure from 120 bar to 200 bar results in a change in fugacity from 70 to 88 bar; i.e. a 67% increase in pressure results in a 26% increa se in fugacity. Similarly, using the Duan et al. (20) methodology for estimating CO 2 fugacity, the same 67% increase in pressure results in a 19% increase in CO 2 fugacity This minimizes the effects of increased CO 2 pressure on the concentrations of carbonate species. PAGE 66 58 5.3: Effect of Salinity In these simulations, temperature, initial pH and CO 2 injection pressure are constant at 45 C, 7.5 and 160 bar, respectively. Three sets of simulations are performed for brine s alinit ies of 5%, 10% and 15%. Figure 24 : Equilibrium pH as a F unction of S alinity 4.70 4.75 4.80 4.85 4.90 0% 5% 10% 15% 20% Equilibrium pH Salinity (%) Equilibrium pH Model 1 Model 5 Model 8 PAGE 67 59 Figure 25 : Calcite D issolution as a F unction of S alinity Figure 26 : Dolomite D issolution as a F unction of S alinity 4000 5000 6000 7000 8000 0% 5% 10% 15% 20% mg Calcite per kg H 2 O Salinity (%) Calcite Dissolution Model 1 Model 5 Model 8 200 300 400 500 600 700 0% 5% 10% 15% 20% mg Dolomite per kg H 2 O Salinity (%) Dolomite Dissolution Model 1 Model 5 Model 8 PAGE 68 60 Figure 27 : Gypsum P recipitation as a F unction of S alinity Figure 28 : Net CO 2 Storage as a Function of Salinity 2500 3000 3500 4000 4500 0% 5% 10% 15% 20% mg Gypsum per kg H 2 O Salinity (%) Gypsum Precipitation Model 1 Model 5 Model 8 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 0% 5% 10% 15% 20% moles CO 2 per kg H 2 O Salinity (%) Net CO 2 Storage Model 1 Model 5 Model 8 PAGE 69 61 The geochemical system appears to be sensitive to salinity with increasing salinity resulting in increasing quantities of mineral dissolution and precipitation decreasing equilibrium pH and decreasing net CO 2 storage The sensitivity of mineral dissolution and precipitation and equilibrium pH to salinity is due to decreasing estimates for activity coefficients at higher ionic strengths. A lower activity coefficient means that more of a certain ion must be in solution for a given activity required for equilibrium than for a higher activity c oefficient; in other words, it takes more of a certain ion to exert the same thermodynamic influence on the solution with a lower activity coefficient than with a higher activity coefficient. These increased ion concentrations thus require proportionally m ore minerals dissolution. Salinity has the greatest effect on net CO 2 storage out of all the physical and chemical parameters examined. The sensitivity of net CO 2 storage to salinity is due to the decreasing solubility of CO 2 in higher salinity solutions b ecause of the salting out mechanism PAGE 70 62 5.4: Effect of Temperature In these simulations, initial pH, CO 2 injection pressure and salinity are constant at 7.5, 160 bar and 10%, respectively. Three sets of simulations are performed at t emperature of 35, 45 an d 55 C. Figure 29 : Equilibrium pH as a F unction of T emperature 4.70 4.75 4.80 4.85 4.90 30 35 40 45 50 55 60 Equilibrium pH Temperature ( C) Equilibrium pH Model 1 Model 5 Model 8 PAGE 71 63 Figure 30 : Calcite D issolution as a F unction of T emperature Figure 31 : Dolomite D issolution as a F unction of T emperature 4000 5000 6000 7000 8000 30 35 40 45 50 55 60 mg Calcite per kg H 2 O Temperature ( C) Calcite Dissolution Model 1 Model 5 Model 8 200 300 400 500 600 700 30 35 40 45 50 55 60 mg Dolomite per kg H 2 O Temperature ( C) Dolomite Dissolution Model 1 Model 5 Model 8 PAGE 72 64 Figure 32 : Gypsum P recipitation as a F unction of T emperature Figure 33 : Net CO 2 Storage as a Function of Temperature 2500 3000 3500 4000 4500 30 35 40 45 50 55 60 mg Gypsum per kg H 2 O Temperature ( C) Gypsum Precipitation Model 1 Model 5 Model 8 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 30 35 40 45 50 55 60 moles CO 2 per kg H 2 O Temperature, C Net CO 2 Storage Model 1 Model 5 Model 8 PAGE 73 65 The geochemical system appears to be relatively sensitive to temperature with increasing temperature resulting in decreasing quantities of mineral dissolution and precipitation decreasing equilibrium pH and decreasing net CO 2 storage Sensitivity to temperature is due to decreasing equilibrium constant s at highe r temperatures for the geochemical reactions considered (see Table 1 Table 4 ). This effect, known as retrograde solubility, is particularly pronounced with calcium carbonate (CaCO 3(s) ). This means that less free ions must be in solution to achieve equilibrium with the solid mineral phase and the injected CO 2 phase. The decrease in equilibrium pH associated with increased temperatures is also due to the decreased equilibrium constant for the dissociation of water. In other words, at elevated temperatures the activity of H + ions is increased relative to standard conditions. 5.5: Effects on Porosity, The formation porosity, is the ratio of void volume to bulk aquifer volume and can change as a result of mineral precipitation and dissolution due to CO 2 injection If significant amounts of minerals dissolve, then porosity will increas e. Conversely, if mineral precipitation is the dominant effect then porosity will decrease For simplicity, geochemical reactions occurring in the brine that is being displaced by the moving CO 2 interface are not considered. Rather, only the residual pore brine that is not displaced by the moving CO 2 interface i.e. it is held in place due to capillary forces is considered to reach equilibrium with the CO 2 phase. The change in porosity can be estimated as follows: PAGE 74 66 Equation 58 where initial is the initial porosity (i.e., before CO 2 injection), S RES is the residual brine saturation of the pore volume S is the salinity, BR INE is the density of the brine, and minerals is the change in mineral volume per kg of H 2 O To estimate minerals the following expression is used: Equation 59 where is the net mass of mineral precipitated/dissolved per kg H 2 O and mineral is the respective mineral density. Brine densit y is estimated and values are tabulated in the following table for various combinations of salinity and temperature (28) Table 6 : Brine D ensities at V arious S alinities and T emperatures Salinity (%) Density (kg/m 3 ) 35 C 45 C 55 C 5 1,031 1,027 1,022 10 1,069 1,065 1,060 15 1,109 1,104 1,099 Mineral densities are estimated using the molecular weights and molar volumes in the TOUGHREACT thermodynamic database (16) for each respective mineral using the following relationship: PAGE 75 67 Equation 60 where MW indicates the molecular weight in g/mole and MV indicates the molar volume in cm 3 /mole for respective mineral. Calculated d ensities for calcite, dolomite, and gypsum are listed in the following table: Table 7 : Mineral D ensities Mineral Density (g/cm 3 ) Calcite 2.71 Dolomite 2.86 Gypsum 2.31 The following three combinations of porosity and residual brine saturations are examined : Table 8 : Porosity and R esidual B rine S aturation S cenarios Scenario INITIAL S RES 1 0.1 0.1 2 0.2 0.3 3 0.3 0.5 Using the three scenarios of porosity and residual brine saturation listed in Table 8 the change in porosity is calculated for the base geochemical scenario described earlier in this chapter with varying initial pH, CO 2 injection pressure, salinity and temperature. Results ar e given in Table 9 PAGE 76 68 Table 9 : Change in Porosity for S cenarios 1 3 U sing V arious C ombinations of I nitial pH, CO 2 I njection P ressure, S alinity, T emperature Scenario INITIAL S RES Init. pH CO 2 Injection Pressure (bar) Salinity Temp. ( C) Model 1 Model 5 Model 8 1 0.1 0.1 6.5 160 10% 45 8.3E 06 6.9E 06 6.8E 06 1 0.1 0.1 7.5 160 10% 45 8.3E 06 6.9E 06 6.9E 06 1 0.1 0.1 8.5 160 10% 45 8.3E 06 6.9E 06 6.9E 06 1 0.1 0.1 7.5 120 10% 45 8.0E 06 7.3E 06 7.2E 06 1 0.1 0.1 7.5 200 10% 45 8.4E 06 6.6E 06 6.5E 06 1 0.1 0.1 7.5 160 5% 45 8.8E 06 7.3E 06 7.3E 06 1 0.1 0.1 7.5 160 15% 45 8.0E 06 6.8E 06 6.8E 06 1 0.1 0.1 7.5 160 10% 35 1.2E 05 9.4E 06 9.3E 06 1 0.1 0.1 7.5 160 10% 55 6.0E 06 5.2E 06 5.2E 06 2 0.2 0.3 6.5 160 10% 45 5.0E 05 4.1E 05 4.1E 05 2 0.2 0.3 7.5 160 10% 45 5.0E 05 4.2E 05 4.1E 05 2 0.2 0.3 8.5 160 10% 45 5.0E 05 4.2E 05 4.1E 05 2 0.2 0.3 7.5 120 10% 45 4.8E 05 4.4E 05 4.3E 05 2 0.2 0.3 7.5 200 10% 45 5.0E 05 4.0E 05 3.9E 05 2 0.2 0.3 7.5 160 5% 45 5.3E 05 4.4E 05 4.4E 05 2 0.2 0.3 7.5 160 15% 45 4.8E 05 4.1E 05 4.1E 05 2 0.2 0.3 7.5 160 10% 35 7.0E 05 5.7E 05 5.6E 05 2 0.2 0.3 7.5 160 10% 55 3.6E 05 3.1E 05 3.1E 05 3 0.3 0.5 6.5 160 10% 45 1.2E 04 1.0E 04 1.0E 04 3 0.3 0.5 7.5 160 10% 45 1.2E 04 1.0E 04 1.0E 04 3 0.3 0.5 8.5 160 10% 45 1.2E 04 1.0E 04 1.0E 04 3 0.3 0.5 7.5 120 10% 45 1.2E 04 1.1E 04 1.1E 04 3 0.3 0.5 7.5 200 10% 45 1.3E 04 9.9E 05 9.8E 05 3 0.3 0.5 7.5 160 5% 45 1.3E 04 1.1E 04 1.1E 04 3 0.3 0.5 7.5 160 15% 45 1.2E 04 1.0E 04 1.0E 04 3 0.3 0.5 7.5 160 10% 35 1.8E 04 1.4E 04 1.4E 04 3 0.3 0.5 7.5 160 10% 55 9.1E 05 7.8E 05 7.8E 05 Estimates for the change in porosity are positive (i.e., porosity increases ) for all models and are virtually identical for models 5 and 8 and model 1 agreeing within 20% PAGE 77 69 The change in porosity is strongly related to the initial porosity and residual brin e saturation, with estimates spanning three orders of magnitude for initial porosity ranging from 0.1 to 0.3 and residual brine saturation ranging from 0.1 to 0.5. Specifically, higher initial porosity and residual brine saturation results in larger estima ted changes in porosity for the geochemical system considered. This is because higher initial porosity and residual brine saturation implies that there is more brine available per unit aquifer volume for equilibration with surrounding minerals and the inje cted CO 2 resulting in larger net mineral dissolution and precipitation quantities per unit aquifer volume. However, the overall change in porosity is very small for all scenarios considered, with a maximum change that is three orders of magnitude less tha n the initial porosity. This agrees well with observations by others (5; 7) 5.6: Choice of Thermodynamic Sub model for CO 2 Parameter Estimation In every simulation, model 1 gave the largest net mineral reactions and chan ge in pH. This is most likely due to the greater fugacity coefficient predicted using the method of Spycher and Reed (26) and the higher aqueous CO 2 concentration predicted using the equilibrium constant method. Models 5 and 8 use more recently developed correlations that account for the effects of dissolved salts to estimate the equilibrium dissolved CO 2 concentration, and the lower estimated aqueous CO 2 concentrations result in slightly lower net mineral reactions and changes in pH as compared to model 1. However, estimates of mineral precipitation and dissolution are closely grouped within the same order of magnitude for all three models, indicating tha t the choice of thermodynamic sub models does not have a significant impact on the esti mated quantities. PAGE 78 70 6: Summary and Conclusion Different thermodynamic sub models are used to construct overall geochemical model s to describe pre and post CO 2 injection conditions in a deep, saline aquifer that is comprised of calcite, dolomite, and gypsum. It is found that the overall geochemical model s are relatively insensitive to appropriate choices for thermodynamic sub models for estimating such parameters as CO 2(aq) activity coefficient, CO 2(g,sc) fugacity coefficient and the solubility of CO 2(aq) These geochemical models are used to determine concentrations of ionic species and aqueous complexes and quantify the amount of minerals that are di ssolving into or precipitating out of solution so that the change in porosity due to CO 2 injection can be estimated. All of the models predict that calcite and dolomite will dissolve and gypsum will precipitate. 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