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A Computer Program to Solve Aqueous Inorganic Equilibrium Systems Using Pitzer's Method to Determine Activity Coefficients

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A Computer Program to Solve Aqueous Inorganic Equilibrium Systems Using Pitzer's Method to Determine Activity Coefficients AN ABSTRACT OF THE THESIS OF Barry Kelly for the degree of Master of Science in Chemical Engineering/Forest Products presentedon August 12, 1988. Title: A Computer Program to Solve Aqueous Inorganic Equilibrium Systems Using Pitzer's Method to Determine Activity Coefficients. Abstract approved: Redacted for Privacy W. J. FredericK/ Redacted for Privacy r 6/ R. V. Mrazek Chemical equilibrium is a major factor inmany natural and industrial systems. The ability to predict ionic equilibrium is extremely valuable in industry in solvingproblems without the costs involved in full scale experiments. An example of an application in the pulp and paper industry is the predictionof non-process element solubility in process streams. A computer program, ISIS, was developed to estimate the solubil- ity of inorganic salts in aqueous, inorganic solutions. The model incorporates a two step Gibbs free energy minimization algorithmand Pitzer's method for ionic activity coefficient prediction. The program, ISIS, was tested on threecases. The test cases were: KC1 solubility in a NaC1 and water solution, NaC1 solubility in a MgC12 and water solution, and CaSO4 solubility ina NaC1 and water solution. The equilibrium predictions in the test caseswere very good, with the mean of the absolute value of the relativeerror ranging from 4.3% for the first case, 17% for the secondcase, to 3.8% in the third case. ISIS accurately predicted the solid phase amount and chemical composition in each of the test cases. A parametric study was conducted on the three testcases to examine the effects of the activity coefficient predictor, and of uncertainty in chemical potentials, and third virial coefficientsand mixing terms in the Pitzer activity coefficient prediction model. The effects of the activity coefficient predictorwere determined by comparing predictions made with the Pitzer modelversus an extended Debye-Huckel equation and an ideal solution assumption. The dif- ferences were great, with the other activity coefficientpredictors resulting in errors greater than five times theerror with the Pitzer activity coefficient model. The effect of the chemical potentials was large, especially in the trace species case, CaSO4 ina NaC1 and water solution. A relative change of less than a tenth ofa percent in the solid species chemical potential resulted inan increased error of ten times the original error. The effect of assuming the third virial coefficients and the mixingterms to be zero in the Pitzer activity coefficient predictor can be large. Errors up to 90% in the mean activity coefficient were found. It was concluded that the computer program ISIS couldpredict accurately the solubility of inorganic salts inaqueous, inorganic solutions. The accuracy of the prediction would be greatly affected by the accuracy of the chemical potentials and the availabilityof the third virial coefficient and mixing terms in the Pitzeractivity coefficient predictor. Future work is recommended in collecting accurate chemical potentials and Pitzer interaction terms to increase the database for ISIS and similar programs. The inclusion of ISIS into a steady state chemical process simulator is also recommended. A Computer Program to Solve Aqueous Inorganic Equilibrium Systems Using Pitzer's Method to Determine Activity Coefficients by Barry Kelly A THESIS Submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science Completed August 12, 1988 Commencement June 1989 APPROVED: Redacted for Privacy 13r/ofesdoVICh-e-mical Engineeringin charge of major Redacted for Privacy ProfeSZ;rof Forest Productsj4charge of major Redacted for Privacy HeadofOh,lical Engineering Department Redacted for Privacy Head of Forest/Products Department Redacted for Privacy e School1' Date thesis is presented: August 12. 1988 ACKNOWLEDGMENT The completion of this work represents the support and education I received from many individuals. I would like to acknowledge just a few of the many. Specifically, I wish to thank Dr. William J. Frederick and Dr. Robert V. Mrazek for their guidance and assistance throughout the research and writing of project. A special thanks goes to my family. The combination of support from my mother and father, constant harassment frommy brothers and sisters, and continual help from my fiance, JoAnne, createda driving force towards the completion of the project of incrediblemagnitude. I would also like to thank Dr. Biermann, Dr. Humphrey, Dr. Levien, and Dr. Nelson for having served on my committee, and Sadie Airth for her help with this manuscript. TABLE OF CONTENTS Ent INTRODUCTION 1 THEORY 5 A. Gibbs Free Energy Minimization 5 B. Activity Coefficient Calculation 9 RESULTS 21 A. Test Cases 22 B. Parametric Study 28 CONCLUSION 48 FUTURE WORK 50 BIBLIOGRAPHY 51 APPENDICES Appendix A: Calculation of the Electrostatic Mixing Terms 54 Appendix B: Average ISIS Run Times 56 Appendix C: ISIS User Manual 57 Appendix D: ISIS Operations Manual 86 Appendix E: ISIS Source Code 124 Appendix F: ISIS Database Files 199 Appendix G: PITZER Source Code 211 LIST OF FIGURES Figure Ent 1. Solubility of a slightly soluble salt, CaSO4, in NaC1 and water solutions (Silcock, 1979; Block and Waters, 1968; Marshel and Slusher, 1966) and calculated solubilities from several computer programs 3 2. Solubility of KC1 in NaC1 and water solutions at 25°C (Silcock, 1979) and calculated solubility from ISIS computer program 23 3. Solubility of NaCl in MgC12 and water solutions at 25°C (Silcock, 1979) and calculated solubility from ISIS computer program 24 4. Solubility of Nadi in MgC12 and water solutions at 25°C (Silcock, 1979) calculated solubility from ISIS computer program. Ionic strength, and absolute value of the relative deviations between the ISIS prediction and the experimental points versus MgC12 concentration 25 5. Solubility of CaSO4 in NaCl and water solutions at 25°C (Block and Waters, 1968; Marshel and Slusher, 1966; Silcock, 1979) and calculated solubility from ISIS computer program 27 6. Solubility of KC1 in NaCl and water solutions 15 25°C (Silcock, 1979) and calculated solubility from ISIS computer program using Pitzer, extended Dedye-Huckel, and ideal solution activity coefficient prediction models 29 7. Solubility of Nadi in MgC12 and water solutions at 25°C (Silcock, 1979) and calculated solubility from ISIS computer program using Pitzer, extended Dedye-Huckel, and ideal solution activity coefficient production models 30 8. Solubility of CaSO4 in NaC1 and water solutions at 25°C (Block and Waters, 1968; Marshel and Slusher, 1966; Silcock, 1979) and calculated solubility from ISIS computer program using Pitzer, extended Debye-Huckel, and ideal solution activity coefficient prediction models 32 9. Solubility of KC1 in NaC1 and water solutions at 25°C (Silcock, 1979) and calculated solubility from ISIS computer program using the Pitzer activity coefficient predictor and varying chemical potentials 34 Figure Page 10. Solubility of NaC1 in MgC12 and water solutions at 25°C (Silcock, 1979) and calculated solubility from ISIS computer program using the Pitzer activity coefficient predictor and varying chemical potentials 36 11. Solubility of CaSO4 in NaC1 and water solutions at 25°C (Block and Waters, 1968; Marshel and Slusher, 1966; Silcock, 1979) and calculated solubility from ISIS computer program using the Pitzer activity coefficient predictor and varying chemical potentials 39 12. Percent error in mean activity coefficient of NaC1 versus NaC1 ionic fraction for Case 1 45 13. Percent error in mean activity coefficient of KC1 versus KC1 ionic fraction for Case 1 45 14. Percent error in mean activity coefficient of NaC1 versus NaC1 ionic fraction for Case 2 46 15. Percent error in mean activity coefficient of MgC12 versus MgC12 ionic fraction for Case 2 46 16. Percent error in mean activity coefficient of NaC1 versus NaC1 ionic fraction for Case 3 47 17. Percent error in mean activity coefficient of CaSO4 versus CaSO4 ionic fraction for Case 3 47 LIST OF TABLES Table Page 1. Empirical Constants in the Pitzer Activity Coefficient Equations 16 2. Comparison of Chemical Potentials Used inCase1 35 3. Comparison of Chemical Potentials Used inCase2 37 4. Comparison of Chemical Potentials Used inCase3 37 NOMENCLATURE aw activity of water Actual actual solubility data from literature A, B, ai, bi constants in the extended Debye-Huckel equation (17) ai activity of species i Aki number of moles of element k in species i AS Pitzer-Debye-Huckel limiting slope of osmotic coefficient, Equation (31) b empirical parameter in Equation (30) B' MX derivative of BMXwith respect to ionic strength BOmx second virial coefficient term, Equation (22) MX second virial coefficient term, Equation (23) COmx third virial coefficient constant for salt MX dw density of water at 25 °C D dielectric constant of water at 25 °C e charge of electron Ek total moles of element k in system f(I) Debye-Huckel term, Equation (19) F sum of Debye-Huckel term and derivatives of the second virial coefficient terms with respect to ionic strength, Equation (30) G Gibbs free energy CEx excess Gibbs free energy AGj Gibbs free energy change of reaction j I ionic strength, Equation (18) Ifmx ionic fraction of salt MX, Equation (56) total number of all species ISIS value calculated by program ISIS Boltzmann constant kt total number of elements K search parameter m molality of salt mi molality of species i n number of data points compared ni number of moles of species i nw number of moles of water No Avogadro
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