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record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd leader nam 2200313Ia 4500 controlfield tag 001 002221017 005 20100714120701.0 007 cr cn 008 100714s1999 flua sb 000 0 eng d datafield ind1 8 ind2 024 subfield code a E14SFE0003511 040 FHM c FHM 035 (OCoLC)647765372 049 FHMM 090 TP145 (ONLINE) 1 100 Abutayeh, Mohammad. 0 245 Thermodynamic model and the controlling variables of phosphate lattice loss h [electronic resource] / by Mohammad Abutayeh. 260 [Tampa, Fla.] : b University of South Florida, 1999. 300 x, 72 leaves : ill. ; 29 cm. 500 Title from PDF of title page. Document formatted into pages; contains 72 pages. 502 Thesis (M.S.Ch. E.)University of South Florida, 1999. 504 Includes bibliographical references. 538 Mode of access: World Wide Web. 590 Advisor: J. Carlos Busot, Ph.D. 650 Phosphoric acid. Phosphoric acid industry. 690 Dissertations, Academic z USF x Chemical Engineering Masters. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.3511 PAGE 1 Graduate School University of South Florida Tampa, Florida CERTIFICATE OF APPRO V AL Master's Thesis This is to certify that the Master's Thesis of MOHAMMAD ABUTAYEH with a major in Chemical Engineering has been approved by the Examining Committee on November 22, 1999 as satisfactory for the thesis requirement for the Master of Science in Chemical Engineering degree Examining Committee : Major 9fofessor : J. Ph D CoMajor LtH's H. GarciaRubio Ph D Member Professor : Scott W Campbell Ph.D PAGE 2 THERMODYNAMIC MODEL AND THE CONTROLLING VARIABLES OF PHOSPHATE LATTICE LOSS by MOHAMMAD ABUTAYEH A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Chemical Engineering Department of Chemical Engineering College of Engineering University of South Florida December 1999 Major Professor : 1. Carlos Busot, Ph.D PAGE 3 ACKNOWLEDGEMENTS I would like to first thank God for giving me the patience and the strength to complete this work. Then, I wish to express my deepest appreciation to my major professor, Dr J. Carlos Busot, for his valuable criticism and professional guidance I would also like to express my gratitude to my comajor professor, Dr. L. GarciaRubio, for encouraging and providing me with the opportunity to continue my graduate studies I must also thank my committee member professor, Dr. Scott W Campbell, for his support and tremendous knowledge that guided me throughout my academic years Last but not least, I like to extend my deepest appreciation to my family and friends for their support and motivation throughout my years of education in general and to Cargill Fertilizer, Inc. for generously supporting this project. PAGE 4 T ABLE OF CONTENTS LIST OF TABLES .......... .... ............ ....... .......... .......... ..... ........... ..... .... ... ..... . . ............... iii LIST OF FIGURES ................................ ............. .... ...... ....... ........ .... .... ........ .................... iv LIST OF SYMBOLS ................................ ...... ... ......... ......... ......... .................................. vi ABSTRACT .... ........... .............................. .... ............. ... ................................. ....... ...... ..... ix CHAPTER 1 INTRODUCTION ............ .... .................. ..... ................ .... . .......... .............. 1 1.1 Phosphoric Acid Manufacturing ................ ... ...................... ................... .......... 1 1.2 Phosphate Losses ....... ...... ....... .... ................... ...... ........... .................. .............. 2 1.3 Thennodynamic Model of Phosphate Lattice Loss ....... ................ ............. ..... 4 CHAPTER 2. THERMODYNAMICS OF ELECTROLYTE SOLUTIONS .... ......... ..... . 5 2.1 Ionic Equilibrium ........ ...... .... ...................... ... ...... ..... ............ ........... . ......... .... 5 2 2 Ionic Activity .. ......... ........... ... ...... .... ...... ........... ..... ...................................... . 9 2.3 Ionic Activity Coefficient Models ............ ......... ...... ........................... ...... ..... 10 2.4 SolidLiquid Equilibria in Aqueous Solutions . ............. ..... ................. .... ...... 15 2.5 VaporLiquid Equilibria in Aqueous Solutions .............................................. 16 CHAPTER 3. THERMODYNAMIC MODEL OF PHOSPHATE LATTICE LOSS ... ... 17 3.1 Model Description ..... ..... ............... ........ ............. ..... ... ...................... ... .......... 17 3.2 Model Simulation ................................ .... ........ ................... . ............. ............ 18 CHAPTER 4 RESULTS AND DISCUSSION ................................ .... ............ . .... ........ 27 4.1 Temperature Effect on Equilibrium ............................ ...................... ........... 27 4.2 Temperature Effect on System Variables ......... .......... .......... . . ............. ......... 32 4.3 Sulfuric Acid Effect on System Variables ............ . .... ...... .......... ... ...... ........ .40 4.4 Model Validation ... ............ .... ........ ... ...................... ...... ......... .................... .48 CHAPTER 5. SUMMARY, CONCLUSION, AND RECOMMENDATIONS ......... ...... 52 5.1 Summary ..... ....... ..... . ........... ............................................... . . .................. .... 52 5.2 Conclusion ................. ....... ......... ..... ................................ ...... ......... "., ...... ... PAGE 5 5 3 Recommendations ......................... ..... .................. . ... ....................... ..... ... ..... 54 REFERENCES ................. ...... .......................... ....... . . . ... ..... ............... ............. ...... .... 55 APPENDICES ..... ....... . .... . ....... ............................... ..... ............ ........... ......... ..... ........... 57 Appendix 1. Literature and Experimental Data ...... ......................... ... ................ 5 8 Appendix 2 Matlab Code for Regression of A and f3 Literature Data .... ........... 60 Appendix 3 Matlab Code for Regression of KH S04 Experimental Data ......... ...... 61 Appendix 4 Matlab Code for Regression of KH3P04 Experimental Data ... . ....... 62 Appendix 5 Matlab Code for Regression of KH2P04 Experimental Data ... ..... . .... 63 Appendix 6. Matlab Code for Regression of K Gypsum Experimental Data ...... ...... 64 Appendix 7 Matlab Code for Regression of KD CPD Experimental Data .......... ..... 65 Appendix 8 TK Solver Code of Thermodynamic Model .... . ............ . ....... .... ..... 66 11 PAGE 6 LIST OF TABLES Table 1. Approximate Effective Ionic Radii in Aqueous Solutions at 25 C .................... 11 Table 2. Bromley's Parameters for Different Electrolytes at 25 C .... ..... .... ..... ........... .... 14 Table 3 Literature and Regressed Values of Thermodynamic Functions ........ . ............. 27 Table 4. Debye Hiickel Parameters Data ......... . . .... ...... ....... . ........ ............. .... ............. 58 Table 5 Equilibrium Constants and Solubility Products at Various Temperatures ....... . 58 Table 6 Physical and Reference State Properties .... ......... ..... ................ ... ...... ............. 59 Table 7. Janikowski' s Data .. ... . . ...... .......... ..... .......... ....... ........... .......... ....... ........ ........ 59 1lI PAGE 7 LIST OF FIGURES Figure 1. Flowsheet of a Phosphoric Manufacturing Process ............ .......... ...... ... .... 2 Figure 2 Gypsum Crystals. Shown Bar s Length is 100 microns ... ... .... . .... . ......... ......... 3 Figure 3 DebyeHuckel Parameter A as a Function of Temperature ............... ....... ....... 12 Figure 4 DebyeHuckel Parameter f3 as a Function of Temperature ... .... ........................ 12 Figure 5 KHS04 as a Function of Temperature .......... ............ ......... .... .... . .... ............. ...... 29 Figure 6 KH3P 0 4 as a Function of Temperature ............... ....... ... .................... ........ ... ...... 30 Figure 7 KH2P04 as a Function of Temperature ...... ..... .... ....... ... ... .......... .... .... .............. 30 Figure 8. Kr,y p sum as a Function of Temperature .... .......... ... . .............. ... ....... .......... ....... 31 Figure 9. KD C PD as a Function of Temperature ........ . ... ........ .... .... ... ... ...... ....... .... ..... ... 31 Figure 10. Ionic Strength Versus Temperature Ideal Solution Model.. ... ... . ....... ..... ... 34 Figure 11. Ionic Strength Versus Temperature DebyeHuckel Model .................... ..... 34 Figure 12. Ionic Strength Versus Temperature RobinsonGuggenheimBates Model .. 35 Figure 13. Ionic Strength at 1.5 % H2S04 as a Function of Temperature . ........... . ....... 35 Figure 14. pH Versus Temperature Ideal Solution Model ...... .......... ....... .... . . ........... 36 Figure 15. pH Versus Temperature DebyeHuckel Model... ............ .... ... .......... .......... 36 Figure 16. pH Versus Temperature RobinsonGuggenheimBates Model ...... ........ .... 37 Figure 17. pH at 1.5 % H2S04 as a Function of Temperature ...... . ... ... .... .... ... ..... ... .... ... 37 Figure 18. Lattice Loss Versus Temperature Ideal Solution Model.. ... . .... ......... ... . .... 38 Figure 19. Lattice Loss Versus Temperature DebyeHuckel Model . ..... . ... ... ........ .. .. 3 8 IV PAGE 8 Figure 20. Lattice Loss Versus Temperature RobinsonGuggenheimBates Model ..... 39 Figure 21. Lattice Loss at 1.5 % H2S04 as a Function of Temperature .... ............. ..... ..... 39 Figure 22. Ionic Strength Versus % H2S04 Ideal Solution Model ................. . .... ........ .42 Figure 23. Ionic Strength Versus % H2S04 DebyeHiickel Model .... ....... .... ... ..... ...... 42 Figure 24 Ionic Strength Versus % H2S04 RobinsonGuggenheimBates Model... ... .43 Figure 25 Ionic Strength at 25C as a Function of % H2S04 ......... ...... ..... .................. .43 Figure 26 pH Versus % H2S04 Ideal Solution Model... ............... .... ......... . ..... .......... .44 Figure 27. pH Versus % H2S04 DebyeHiickel Model ......... .................. ... .... . ....... ..... 44 Figure 28. pH Versus % H2S04 RobinsonGuggenheimBates Model ................ .... .... .45 Figure 29. pH at 25C as a Function of% H2S04 ........................................................... 45 Figure 30. Lattice Loss Versus % H2S04 Ideal Solution Model .................................. .46 Figure 31. Lattice Loss Versus % H2S04 DebyeHiickel Model... ........ ....... ................ .46 Figure 32. Lattice Loss Versus % H2S04 RobinsonGuggenheimBates Model... ........ 47 Figure 33. Lattice Loss at 25C as a Function of% H2S04 .................................. .. ....... .47 Figure 34. Griffith Prediction of Lattice Loss at 25C ...... ................... ............ .... ........ .49 Figure 35. Model Prediction of Lattice Loss at 25 C .................. ........... ... .................. .49 Figure 36 Model Prediction of Lattice Loss at 78 5 C ..... .................................. .......... 51 Figure 37. Adjusted Model Prediction of Lattice Loss at 78.5 C ............ ........ ........ ........ 51 v PAGE 9 %H2S04 %P205 %P20P) A I K Kaq Ksp LIST OF SYMBOLS Percent H2S04 Equivalence by Mass in Liquid [Kg H2SOJl(g Liquid] Percent P20S Equivalence by Mass in Liquid [Kg P20sIKg Liquid] Percent P20S Equivalence by Mass in Solid [Kg P20sIKg Solid] DebyeHuckel Constant Activity of Species i [mol i/Kg H20] Bromley's Interaction Parameter Components Bromley's Interaction Parameter of Species i Bromley's Interaction Parameter of Species i Partial Molar Specific Heat of Species i [J/(mol iK)] Summation of Bromley's Interaction Parameters of Species i Fugacity of Vapor Species i Partial Molar Gibbs Free Energy of Species i [J/mol i] Partial Molar Enthalpy of Species i [J/mol i] Ionic Strength [mollKg H20] Dissolution Equilibrium Constant VaporLiquid Equilibrium Constant Solubility Product Mass of Species i Per Mass of Water [Kg i/Kg H20] Molality of Species i [mol i/Kg H20] VI PAGE 10 MWi Molecular Weight of Species i [Kg ilmol i] ni Number of Moles of Species i [mol i] P Total Pressure [Pal Pi Partial Pressure of Species i [Pal pH Liquid Phase pH R Ideal Gas Constant [J/(mol'K)] ri Effective Ionic Radius of Species i [I] T Temperature [K] TPM Total Phosphate Molality [mol TPMlKg H20] TSM Total Sulfate Molality [mol TSMlKg H20] Xi Mole Fraction of Species i in Solid [mol ilmol Solid] ZiJ Bromley's Interaction Parameter of Species i Zi Ionic Charge of Species i [e] f3 DebyeHiickel Constant "Ii Activity Coefficient of Species i S, 5 Bromley's Interaction Parameter Components J1i Chemical Potential of Species i [J/mol i] Vi Stoichiometric Coefficient of Species i [J/mol i] PH20 Reference State Density of Water [Kg H20IL] Wi Mass Fraction of Species i in Solid [Kg i/Kg Solid] iJ.Cp Molar Specific Heat of Dissolution or Solubility [J/(mol'K)] iJ.G Molar Gibbs Free Energy of Dissolution or Solubility [J/mol] iJ.H Molar Enthalpy of Dissolution or Solubility [J/mol] Vll PAGE 11 eP205 rtJH20 1Jfp205 + o L S v Moles H2S04 Equivalence Per Moles ofTSM [mol H2SO,Jmol TSM] Moles P205 Equivalence Per Moles ofTPM [mol P205/mol TPM] Mass Fraction of Water in Liquid [Kg H20IKg Liquid] Moles P20S Equivalence Per Moles ofDCPD [mol P205/mol DCPD] Superscripts Proton Charge [+ e = + 1.60217733(49) 3 1019 C] Electron Charge [e = 1.60217733(49) 3 1019 C] Reference State Property Liquid Phase Property Solid Phase Property Vapor Phase Property Vlll PAGE 12 THERMODYNAMIC MODEL AND THE CONTROLLING V ARlABLES OF PHOSPHATE LATTICE LOSS by MOHAMMAD ABUTAYEH An Abstract Of a thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Chemical Engineering Department of Chemical Engineering College of Engineering University of South Florida December 1999 Major Professor: J. Carlos Busot, Ph .D. IX PAGE 13 A thermodynamic model was developed based upon five equilibrium reactions to predict the limits of distribution of phosphates between the liquid and the solid phases in a reactor used to e x tract phosphoric acid from phosphate rock. A computer code was generated to carry out different simulations of the model using several inputs of temperatures and liquid phase sulfuric acid contents Ideal Solution DebyeHuckel and RobinsonGuggenheimBates electrolyte activ i ty coefficient models were employed alternately in each simulation to complete the thermodynamic model and the outputs were compared to one another. Experimental data of equilibrium constants were regressed to adjust the values of LlC p 0 and m O used in the simulations to obtain a more accurate representation of the thermodynamic equilibrium Results for ionic strength liquid phase pH, and phosphate lattice loss were used to analyze temperature and liquid phase sulfuric acid content effects on the reacting system. Completing the thermodynamic model with Ideal Solution and DebyeHuckel electrolyte activity coefficient models was found to bind all predictions of phosphate latt i ce loss The model prediction of phosphate losses was found to give a lower bound to the real phosphate losses Furthermore, decreasing temperature and increasing liquid phase sulfuric acid content w,as found to min i mize phosphate lattice loss AbstractApproved : ______________________________________________ __ Major Professor : 1. Carlos Busot, Ph D Professor, Department of Chemical Engineering Date Approved : __________________________________ x PAGE 14 CHAPTER 1. INTRODUCTION 1.1 Phosphoric Acid Manufacturing According to the Dictionary of Chemistry (1), phosphoric acid, also known as orthophosphoric acid, is a watersoluble transparent crystal melting at 42C. It is used in fertilizers, soft drinks, flavor syrups, pharmaceuticals, animal feeds, water treatment, and to pickle and rustproof metals. The dihydrate process is the most common process in the industrial manufacture of phosphoric acid used by the Florida fertilizer plants. As shown in Figure 1, phosphate rock (Ca3(P04h) is grounded into small granules to facilitate its transport and to increase its reaction surface area. The granules are then sent to a large Continuous Stirred Tubular Reactor (CSTR) along with sulfuric acid (H2S04) and water (H20) where the following reaction is carried out: Ca3(P04)2 + 3H2S04 + 6H20+2H3P04 + 3CaS04 H20 The reaction products, phosphoric acid (H3P04) and gypsum (CaS0402H20) as well as the unreacted reactants and bypro ducts, are sent to a filter then to a clarifier to separate phosphoric acid from the solid gypsum. Excess water is used in the filter to wash off phosphoric acid from gypsum and to obtain the desired concentration of phosphoric acid. Some of the reactor slurry is recycled back to the reactor from the clarifier for further extraction of phosphoric acid (2). 1 PAGE 15 F il1:er Tabl e Figure 1. Flowsheet of a Phosphoric Acid Manufacturing Process 1 2 Phosphate Losses The optimization of the process of manufacturing phosphoric acid can take several paths, one of which is the minimization of phosphate loss Phosphate loss can occur in many ways and is mainly attributed to the formation of gypsum crystals. The extraction of phosphoric acid from phosphate rock in the dihydrate process involves the formation of gypsum crystals, shown in Figure 2, as a reaction product in the CSTR. 2 PAGE 16 Figure 2. Gypswn Crystals. Shown Bar's Length is 100 microns One type of phosphate loss takes place during the filtering of the reaction slurry where some of the phosphoric acid fails to wash away from the solid filter cake This type of loss can be avoided by increasing the filter size or by using excess washing water to improve the filtering process. A second type of phosphate loss occurs due to poor rruxmg of the reactor contents When phosphate rock encounters a local high concentration of sulfuric acid, gypswn will crystallize very rapidly because of the very fast reaction between phosphate rock and sulfuric acid Gypswn will precipitate covering the unreacted rock granules and forming crystals with an inner core of unutilized phosphates, which is lost as a solid waste. This problem can be overcome by improving the mixing mechanism to eliminate the local overconcentrated zones in the reactor 3 PAGE 17 A third type of loss arises from the formation of dicalcium phosphate dihydrate or DCPD (CaHP04H20). Gypsum and DCPD have almost the same molecular weight and density; moreover, they share the same monoclinic crystal lattice structure, which will facilitate the formation of a solid solution of both crystals Frochen and Becker (3) confirmed the existence of the DCPDGypsum solid solution in 1959 This lattice loss is thermodynamically controlled and the controlling variables will be investigated to determine their effect on that loss. 1.3 Thermodynamic Model of Phosphate Lattice Loss Thermodynamics can not yield any information about the intermediate states of a given reacting system. These intermediate states are the subject matter of chemical kinetics, which studies reaction rates and mechanisms. Chemical kinetics will predict what chemicals are present while thermodynamics will predict the limits of distribution of those chemicals in the different phases (4) The objective of this study is to produce a thermodynamic model that will predict the limits of distribution of phosphates between the liquid and the solid phases in the reactor used to extract phosphoric acid from phosphate rock. Different electrolyte activity coefficient models will be employed alternately to complete the model and to carry out different simulations using several inputs of temperatures and liquid phase sulfuric acid contents to study their effect on the distribution of phosphates The results will then be compared to other literature data to validate the model and assess its accuracy. 4 PAGE 18 CHAPTER2.THERMODYNANITCSOFELECTROLYTESOLUTIONS 2 1 Ionic Equilibrium It is generally more convenient in aqueous solution thermodynamics to describe the chemical potential of a species i in terms of its activity, ai. G. N. Lewis (5) defined the chemical potential of species i in terms of its activity as f.1j(T) = j(T)+ RTln(aJ (1) A criterion for any given reaction occurring at equilibrium is the minimization of the stoichiometric sum of the chemical potential of the reacting species. This can be represented in a generalized form as (2) By substituting (1) into (2) (3) Further simplification yields (4) But )n(aJ is the same as In Il;(aJ Substituting (5) Solving for Il;(a J" Il ()' (LjV;f.1;(T)) a '=exp 'j I RT (6) 5 PAGE 19 The thermodynamic equilibrium constant for a specific reaction is defined as K = exp ', [ LYP; (T)] RT (7) The partial molar Gibbs free energy is defined as the reference state chemical potential. Using this defmition Equation (6) and Equation (7) can be equated and the thermodynamic equilibrium constant becomes K IT ( )Y [L;VP;(T)] = a = exp =='; RT (8) Values of the partial molar Gibbs free energy for different chemicals are available in the literature as tabulations of the standard Gibbs free energy of formation To study the temperature effect on the equilibrium constant, Equation (8) is rewritten to simplify its differentiation "vG' (T) lnK= RT (9) Differentiating (10) By defmition dG = aG dT + aG dP + aG dn aT ap a n;' (II) At constant pressure and composition vP ; (T)] = vP ; (T)] a T T dT T (12) 6 PAGE 20 The GibbsHelmholtz relationship (5) is used frequently to show the temperature dependencies of various derived properties It is given by (13) Using Equations (12) and (13), Equation (10) can be restated as RdInK = LiViHJT) dT T2 (14) This is known as the Van't Hoff Equation (6). The expression 1:; Vi H;(F) can be written as a function of temperature in terms of the heat capacity of the reacting species T LYiHi(T) = LiViHiO(r)+ (15) TO Values of H/(F) and Cp/(F) for different chemicals are available in the literature as tabulations of the standard Enthalpy of formation and the standard heat capacity. Assuming a constant 1:; Vi Cp;{T) value, which equals .Ei Vi Cp/(F) (16) Substituting Equation (16) in (14) (17) Integrating between T O and T gives Where K O is given by InKo = I I RT" (19) 7 PAGE 21 The reference state thermodynamic functions of the chemical reactions, L1Cp 0 &l, and L1Go are defined in terms of the reference state thermodynamic properties of the reacting species as follows (20) (21) (22) Equations (18) and (19) can now be rewritten using newly defmed reference state thermodynamic functions of the chemical reactions as In K = l!.G' RT' (23) (24) Equations (23) and (24) can be used to obtain the equilibrium constant of a chemical reaction as a function of temperature given the reference state thermodynamic properties of the reacting species A more accurate version of Equation (23) can be obtained by substituting a temperaturedependent heat capacity function i.e Cp/F), in Equation (15), integrating it, and then proceeding with the same steps to get to Equation (23) Another alternative can be used to obtain a more accurate version of Equation (23) if experimental data of the equilibrium constant at various temperatures is available. L1Cpo and iJHo can be used as adjustable parameters to fit the data to Equation (23) by means of nonlinear regression This will compensate for the temperatureindependent heat capacity assumption used to develop that equation, which will result in better estimates of the equilibrium constants 8 PAGE 22 2 2 Ionic Activity In 1887 Svante Arrhenius ( 5) presented his theory of electrolytic dissociation of solute into negatively and positively charged ions He assumed that the distribution and motion of ions in a solution is independent of the ionic interaction forces Experimental work showed that Arrhenius' theory holds only for weak electrolytes, and that electrostatic forces between ions must be considered especially for strong electrolytes. In 1923, Peter Debye and Erich Huckel (5) presented their theory of interionic attractions in electrolyte solutions As electrolyte dissociation in solutions increases ion concentration also increases resulting in smaller distance and greater electrostatic force between ions The strength of this coulombic interaction between ions must therefore be considered in modeling thermodynamic equilibrium of electrolyte systems. Ionic strength is a measure of the average electrostatic interactions among ions in an electrolyte Lewis and Randall (1) defined the ionic strength as onehalf the sum of the terms obtained by multiplying the molality of each ion by its valence squared 1 mz2 2L...i I I (25) As previously mentioned, the chemical potential of species i in terms of its activity is (1) Where the standard state is a hypothetical solution with molality m for which the activity coefficient is unity. The activity is related to molality by (26) Note that the activity can be related to other concentration scales such as molarity and mole fraction scales The units of activity are the same as those of the chosen concentration scale and the activity coefficient remains dimensionless always. 9 PAGE 23 2 3 Ionic Activity Coefficient Models Activity coefficient models for nonelectrolyte binary and multicomponent systems are available in the literature as Excess Gibbs Energy models. Different models handle different systems and one should be very careful when choosing a model to work with. Most of these models contain adjustable parameters that can be manipulated. DebyeHuckel theory that was presented over seventy years ago provides the cornerstone for most models of electrolyte solutions. Classical Electrostatics and statistical mechanics are used to linearize the PoissonBoltzmann distribution of charges, which will then approximate the ionion interaction energy allowing for the derivation of an expression for the mean ionic activity coefficient. Below are some ionic activity coefficient models for aqueous multicomponent electrolyte solutions. 1. DebyeHuckel model (7) (27) Approximated values of ri, the ion size parameter or the effective ionic radius, at 25C are given in Table 1 (7) A and fJ are temperaturedependent parameters and can be estimated from the following polynomials that were obtained by fitting literature data found at temperatures between 0 and 100C (7) A = (0.69725708) (0 0021544338)T + (5. 134952E 6)T2 (28) fJ = (0 34905962) (0.00032917649)T + (8.8002615E 7)T2 (29) The DebyeHuckel model is satisfactory for weak electrolyte solutions of ionic strength of 0.1 molal or less but it gets progressively worse as ionic strength increases to practical engineering levels 10 PAGE 24 Table 1. Approximate Effective Ionic Radii in Aqueous Solutions at 25C r (A) Inorganic Ions r (A) Organic Ions 2 5 b + + + t + R ,Ag 3.5 HCOO, H 2Cif, CH3NH3 + (CH3)zNH 2 + 3 K + cr, B(, r, CN, N02, N03 4 H 3 N +CH2 COOH, (CH3hNW, C 2 HsNH3 + 3.5 OK, F, SCN, OCN, HS, CI03, 4.5 CH3 COO, CICH 2 COO, CI04, Br03, 104, Mn04 (C 2 H shNH2 + H 2NCH2 COO, oxalate 2, HCie4 Na+ CdCt, Hg/+ CI02, 103, 5 ChCHCOO, ChCOO, HC03, H 2P04, HS03, H 2As04, (C2Hs)3NW, C3H7NH3 + Cie, SO/, S20/, S20{, SeO/, succinate 2, malonate 2, tartrate 2 C 0 2HPO 2S 0 2PO 3r4, 4,26,4, Fe(CN)6 3, Cr(NH3)l+ CO(NH3)63 + Co(NH3)sH 2 0 3 + 4.5 Pb + CO/, SO/, MoO/, 6 benzoate, hydroxybenzoate, Co(NH3)sCI 2 + Fe(CN)sN02 chlorobenzoate, phenylacetate, vinylacetate, (CH3 )zC=CHCOO, (C 3 H 7)zNH/, phthalate 2, glutarate 2, adipate 2 5 S 2 + B 2 + R 2 + Cd 2 + H 2 + S27 trinitrophenolate, (C 3H7hNW, r a a, ,g" S20/, WO/, Fe(CN)6 4 methoxybenzoate, pimelate 2, suberate 2, Congo red anion 2 6 L' + C 2 + C 2 + Z 2 + S 2 + Mn2 + l,a,u,n,n, 8 2 + 2 + 2 + C ( ) 3 + Fe ,Nl ,Co 0 en 3 CO(S203)(CN)s 48 M 2 + B 2 + g e 9 H + Al3 + F 3 + C 3 + S 3 + y3 + ,e, r c, L 3 + In 3 + C 3 + P 3 + N d 3 + S 3 + a, ,e, r, ,m, Co(S03)z(CN)t 11 Th 4 + Z 4 + C 4 + S 4 + r e n 11 PAGE 25 0.62 0 6 0.58 0 .56 Q; Gi E PAGE 26 2. RobinsonGuggenheimBates model (7) 10 = (0.51 U 0. 2I)Z2 gr, 1+1.51 (30) The model is essentially a modified version of the Debye Huckel model. The effective ionic radius is assumed to be 4 6 A. This model is relatively successful for solutions up to 1 molal ionic strength and it is more convenient to implement than the DebyeHuckel model. 3 Bromley s model (5) Az2JI log r = 'iT F l+vI (31) A is the DebyeHuckel parameter defined in Equation (28) and F i is' a summation of interaction parameters (32) Where j can either indicate all anions in the solution if i were a cation, or all cations in the solution ifi were an anion Z ij and B if are defined by' Z +z, Z .. =' J IJ 2 B is Bromley s parameter defined as (33) (34) (35) Values for B + H 0 5 are available in Table 2 ( 5) Bromley s model gives adequate results for strong electrolyte solutions up to ionic strengths of 6 molal 13 PAGE 27 Table 2 Bromley's Parameters for Different Electrolytes at 25C Cation B+ 8+ Anion B8H+ 0.0875 0.103 F0.0295 0 930 Lt 0 0691 0 138 cr 0 0643 0 067 Na+ 0.0000 0.028 Bf 0 0741 0 064 K+ 0 0452 0 079 r 0 0890 0 196 Rb+ 0 0537 0 100 CI03 0.0050 0.450 Cs + 0 0710 0.138 CI04 0 0020 0 790 0 0420 0 020 Br030 0320 0.140 TI+ 0 1350 0.020 103 0 0400 0.000 Ag+ 0.0580 0.000 N03 0.0250 0 270 Be2 + 0 1000 0 200 H 2P04 0.0520 0 200 Mg2 + 0 0570 0 157 H 2As04 0.0300 0 050 Ca2 + 0 0374 0 119 CNS0 0710 0 160 si+ 0 0245 0.110 OK 0 0760 1.000 Ba2 + 0.0022 0 098 Formate 0 0720 0 700 Mn2 + 0.0370 0 210 Acetate 0 1040 0 730 Fe2 + 0 0460 0.210 Propionate 0 1520 0.700 Co 2 + 0 0490 0.210 Butyrate 0 1670 0 700 Ni2 + 0 0540 0.210 Valerate 0.1420 0 700 Cu2 + 0 0220 0 300 Caproate 0.0680 0 700 Zn2 + 0 1010 0 090 Heptylate 0 0270 0.700 Cd 2 + 0 0720 0.090 Caprylate 0.1220 0 700 Pb2 + 0 1040 0 250 Pelargonate 0 2840 0 700 U02 2 + 0 0790 0.190 Caprate 0.4590 0 700 Cr3 + 0 0660 0 150 HMalonate 0 0050 0.220 Al 3 + 0 0520 0 120 H Succinate 0 0210 0.270 Sc 3 + 0.0460 0.200 H Adipate 0.0530 0 260 y3+ 0.0370 0 200 Toluate 0.0220 0.160 La3 + 0 0360 0 270 CrO/0 0190 0.330 Ce3 + 0 0350 0 270 SO/0.0000 0.400 Pr3 + 0.0340 0 270 S20 / 0.0190 0 700 Nd3+ 0.0350 0.270 HPO/0 0100 0.570 Sm3 + 0 0390 0 270 HAsO/0 0210 0 670 Eu3 + 0 0410 0 270 C 0 3 2 0 0280 0.670 Ga3 + 0.0000 0 200 Fumarate 0 0560 0 700 Co(en) 3 + 0 0890 0 000 Maleate 0 0170 0 700 Th4+ 0.0620 0.190 pol0 0240 0 700 Asol0.0380 0.780 Fe(CN)6 3 0 0650 0 000 Mo(CN)6 3 0 0560 0 000 14 PAGE 28 Many other ionic activity coefficient models for electrolyte solutions are also available in the literature such as Guggenheim's Equation (5), Davies' Equati,on (5), Meissner's Equation (5), Pitzer's Equation (5), Chen's Equation (5) and National Bureau of Standards' Parametric Equations (5). Most of these models predict the mean ionic activity coefficient of single and multicomponent electrolyte solutions but not the ionic activity coefficient of individual ions 2.4 SolidLiquid Equilibria in Aqueous Solutions Electrolytes dissolve in some solvents until they form a saturated solution of their constituent ions in equilibrium with the undissolved electrolytes In a saturated solution electrolytes continue to dissolve and an equal amount of ions in the solution keep combining to precipitate as a solid. Simple dissociation reactions can be represented as Dissoluticn CmAn(s) mCc+(aq)+nAa(aq) Pr ecipitaticn The equilibrium constant for a dissolution reaction is called the solubility product, and is given by Equation (8). The solubility product of the given arbitrary dissolution reaction is (36) The activity of the undissolved electrolytes or any other solid is obtained by (37) For slightly soluble electrolytes, deviation from ideality is minimum and the value of the activity coefficient approaches unity. Equation (36) can be rewritten as (38) 15 PAGE 29 Notice that Ksp at the standard conditions can be calculated by usmg the definition of the equilibrium constant given by Equation (7) or by using Van't Hoff's relationship (6) given by Equation (14) 2 5 VaporLiquid Equilibria in Aqueous Solutions Some gases dissolve in electrolyte solutions and become in equilibrium with the undissolved gas. As before, this can be represented by (39) al can be obtained using Equation (26), where a t is related to the partial pressure ofi by aV = f.,F (40) Notice that Kaq at the standard conditions can be calculated by using the definition of the equilibrium constant given by Equation (7) or by using Van't Hoff's relationship (6) given by Equation (14). 16 PAGE 30 CHAPTER 3 THERMODYNAMIC MODEL OF PHOSPHATE LATIICE LOSS 3 1 Model Description The large reactor used to extract phosphoric acid from phosphate rock in the dihydrate process contains the three distinct phases The vapor phase can be safely considered an inert phase due to the low volatility of the reacting species and the small solubility of gases in the condensed phases The liquid phase is mainly water along with phosphoric acid and small amounts of sulfuric acid The solid phase is primarily gypsum with small quantity of phosphate present as dicalcium phosphate dihydrate or DCPD In a thermodynamic analysis, only major components and major reactions need to be considered. Trace components and reactions affect chemical kinetics but not to a great deal the thermodynamic equilibrium. The thermodynamic model of phosphate lattice loss mentioned earlier will be developed based upon the following equilibrium reactions +SO; H3P04 + HPO;CaHP04 + HPO;+2H2 0 CaS04 +SO;+2H2 0 Very slow chemical reactions, such as the dissolution of H20 and HPOl, and very fast chemical reactions such as the dissolution of H2S04, do not disturb the equilibrium and thus will not be considered in the model. 17 PAGE 31 3.2 Model Simulation A thermodynamic model will be developed to predict the limits of distribution of phosphates between the liquid and the solid phases in the reactor used to extract phosphoric acid from phosphate rock. To track down the degrees of freedom, each equation in the model will be followed by a set of two numbers, a Roman number and an Arabic number, that will work as a counter. The first number will count the number of equations while the second number will count the number of unknowns and the difference between the two numbers is the degree of freedom of the model. Defining the liquid phase properties : total phosphate molality (TPM) and total sulfate molality (TSM) TSM = m HSO' + m SO:(i,4) (ii, 7) The total phosphates content of the liquid phase is a known parameter and can be expressed as percent P205 equivalence by mass (Kg P205 / Kg Solution) (iii, 8) The effective sulfuric acid content of the liquid phase is a manipulated parameter and can be expressed as percent H2 S04 equivalence by mass (Kg H2 S04 / Kg Solution) %H 2S0 4 = (TSM x 0 H2S04 X MW H2S04 X H20 )x 100 (iv, 8) %P205 is taken to be 28% mass, while %H2S04 will be varied to study its effect on the distribution of phosphates. The variable ei indicates the moles of species i equivalence per 1 mole of its prospective compounds; therefore, eP205 is equal to 112 and eH2S04 is equal to 1. 18 PAGE 32 The variable PAGE 33 aSOZx aH+ K =_,4 __ HSO' aHSOi (xii, 19) (xiii, 22) aHPOZx a H + K =_"4 __ HzPOi (xiv, 24) The solidliquid equilibria are included in the model by the solubility product relations. The solubility product relations for gypsum and DCPD are z asozx a c z + x a H 0 Ks 4 a Z PGypsum XGypsum z aHPot x aCaz+ xaHzO KSPDCPD = "X D CPD (xv, 28) (xvi, 30) Neglecting the presence of impurities and assuming that the solid phase consists of only gypsum and DCPD XGYPsllm + X DCPD = 1 (xvii, 30) Mass fraction ofDCPD in the solid solution can be obtained by OJD CPD = ( + MW J xGypsum X MWG),psum X DCPD X DCPD (xviii, 31) The phosphate lattice loss, %P20P), can be expressed as percent P205 equivalence by mass (Kg P205 / Kg Solid) %PzOs(S) = [OJD C PD x( 1 ]X'PPZOl XMWpzol]XI00 MWD CPD (xix, 32) The variable 'Fno5 is defined in a similar way to the variable en 05. It indicates the moles ofP205 equivalence per 1 mole ofDCPD; therefore, 'FP 205 is equal to 112. 20 PAGE 34 Temperaturedependent equilibrium constants of the model reactions can be captured using Equation (23) developed in Chapter 2 Mr ( I:!.C 0 ( 0 0 ) inK = InKo HS04 __ I_JPHSO, InI..I..+ 1 HS 04 HS04 R T r R T T (xx, 35) (xxi, 38) (xxii, 41) inK = InKo Gypsu m ___ PGy psum InI..I..+ 1 Ml 0 ( 1 1 J I:!.C 0 ( 0 0 ) Gypsu m Gypsum R T T O R T T (xxiii, 44) (xxiv 47) Temperature of the medium is a manipulated parameter that will be varied to study its effect on the distribution of phosphates. The reference state equilibrium constants can be obtained using Equation (24) defined in Chapter 2 (xxv 48) (xxvi, 49) (xxvii 50) _I:!.GO In KO = Gy p sum Gypsum RTo (xxviii 51) (xxix, 52) 21 PAGE 35 The reference state thermodynamic functions of the model reactions, LJ.Cp 0 &l, and LJ.Go can be easily computed using the reference state thermodynamic properties of the reacting species available in the literature LJ.Cp expressions for this model are defined as follows (xxx 52) (xxxi 52) (xxxii 52) (xxxiii, 52) (xxxiv 52) Similarly, &l e x pressions for this model are (xxxv, 52) MrH PO =" .Y; H ; = HHo po+ HHo + PO 3 4 L..J, Z 4 3 4 (xxxvi 52) (xxxvii, 52) (xxxviii 52) (xxxix, 52) If e x perimental data of the equilibrium constant at vanous temperatures IS available, LJ.Cp and LJ.H0 can be used as adjustable parameters to fit the data to Equation (23) by means of nonlinear regression This will compensate for the temperatureindependent heat capacity assumption used to develop that equation which will result in better estimates of the temperaturedependent equilibrium constants. 22 PAGE 36 Likewise, AG o expressions for this model are (xxxx, 52) (xxxxi, 52) (xxxxii, 52) (xxxxiii, 52) (xxxxiv, 52) Equation (26) gives the defmition of activity and how it is related to molality by the activity coefficient. Expanding Equation (26) to define the activities of the reacting specIes aH20 =YH2 0 xmH20 (xxxxv, 53) a H3PO, = Y H3PO, x m H3PO, (xxxxvi, 54) (xxxxvii, 55) (xxxxviii, 56) a Y xm HSO:; HSO, HSO, (xxxxix, 57) a S02= Y S02 x m S02, 4 4 (xxxxx, 58) (xxxxxi, 59) (xxxxxii, 60) The degree of freedom of the model is now 8 and it needs to be brought down to zero to run the simulation. The last set of equations contains eight activity coefficients that are not yet defined 23 PAGE 37 Before defining those activity coefficients, an expression for the ionic strength of the aqueous solution is needed Using Equation (25), the ionic strength of the solution can be written as (xxxxxiii, 61) The hydrogen ion activity in a solution is an important concept in many chemical and biological processes. The magnitude of this activity is measured by the pH, where (xxxxxiv, 62) Note that the mass density of water was used to convert the activity concentration scale from molality to molarity as required by the pH definition In other words, pH is the negative base 10logarithm of the hydrogen ion activity given by molarity units. Finally, activity coefficients of the reacting species must be defined to bring this model to completion The following correlations (14) for the activity coefficients of phosphoric acid and water were determined from vapor pressure data of pure solutions of phosphoric acid and water at 25C and they will be used in the simulation rHO = (0. 87979) + (0.75533)%P20S (0.0012084)%P20s 2 + (15.258) (xxxxxv, 62) 2 2 (159 56) r H PO = (22 676) (1.01 92)%P20S + (0 .01 89l)%P20s (xxxxxvi, 62) 3 4 Three sets of electrolyte activity coefficients will be employed to complete the model. Ideal solution, DebyeHuckel, and RobinsonGuggenheimBates models (7) will be used alternately to write the activity coefficients of the remaining electrolytes. The simulation will be carried out utilizing each model and the three outputs will then be compared to one another. 24 PAGE 38 Ideal solution model assumes that the physical properties of the mixture are not influenced by temperature or concentration and that there are no interactions between components ; therefore, in an ideal solution the activity of a substance is equal to its concentration This corresponds to activity coefficients that equal unity YH P O = Y HPO'= Y H SO= yso'= Y H + = Yc '+ = 1 2 4 4 4 4 a (xxxxxviiaxxxxxxiia, 62) The ideal solution model provides a limiting case for the behavior of an actual solution. The model can describe real solutions at low concentrations In 1923 and for the first time ionion and ionsolvent interactions were accounted for in an electrolyte model proposed by Debye and Hucke!. The DebyeHuckel model also accounts for temperature and ionic radius effects on solution behavior. Activity coefficients based on this model are obtained using Equation (27) Az! po.JI logy = H,PO;; 1 + f3r .JI H,PO, (xxx x xviib 62) (xxxxxviiib 62) AZ!SO;; .JI logy = __ .2....= HSO' 1 + fJr .JI HSO;; (xxxxxixb 62) (xxxxxxb 62) (xxxxxxib, 62) (xxxxxxiib 62) 25 PAGE 39 Values of rj, A, and fJ are available in the literature Values of rj for many common electrolytes are given in Table 1 (7) while Equations (28) and (29) provide estimates for A and fJ as functions of temperature The DebyeHiickel model generates adequate results for weak electrolyte solutions up to 0 1 molal ionic strength The third set of electrolyte activity coefficients that will be used is given by the RobinsonGuggenheimBates model. The model adds a considerable improvement to the DebyeHiickel model by subtracting an adjustable parameter term that will increase the range of adequacy up to 1 molal ionic strength Activity coefficients based on this model are obtained using Equation (30) 1 =(0.51U 021) 2 o Z gr H,PO. 1 + l.5I H,PO. (xxxxxviic, 62) ( 0 .51 U ) 2 logr HPO'= 0 .21 Z HPO'  1 + l.5I (xxxxxviiic, 62) 10 = ( 0 .51 U 2I)Z2 gr HSO;; 1 + l.5I HSO;; (xxxxxixc 62) ( 0 .51 U I) 2 logr ,_ = 0 2 zsazsa. 1 + 1.51 (xxxxxxc, 62) ( 0.51U ) 2 logr + = 0.21 ZH+ H 1 + 1.51 (xxxxxxic, 62) ( 0.51 U ) 2 logr 2+ = 0 .21 Z c 2+ Ca 1 + l.5I a (xxxxxxiic, 62) The model is now complete with 62 unknowns to solve using 62 equations A computer code will be used to solve the model using different inputs of temperatures, liquid phase sulfuric acid contents, and electrolyte activity coefficient models 26 PAGE 40 CHAPTER 4 RESULTS AND DISCUSSION 4 1 Temperature Effect on Equilibrium Experimental data of equilibrium constants (7) and solubility products (8) (9) (10) of model reactions were found at various temperatures Least squares regression was used to fit the data points to Equation (23) by manipulating the values of .t1Cp 0 and &l. (23) Table 3 displays two values of .t1Cp 0 and &l for each equilibrium reaction One of those two values is the stoichiometric sum of the reference state thermodynamic properties of the reacting species found in the literature (7) (11) (12) (13) The other value is the adjusted value by least squares regression to fit the data points to Equation (23) Table 3. Literature and Regressed Values of Thermodynamic Functions L1Cp' ( llmol K ) &i' (llmol) Equilibrium Reaction literature regression literature regression +SO;209.00 310 .01 21930 16928 155.00 155.41 7950 7663 + HPO;226 00 248 97 +4150 +4034 CaS04 +SO;+2H2 O 365 30 493 59 1160 +4338 CaHP04 + HPO ; +2H2 O 399.30 878.73 3050 3050 27 PAGE 41 Equation 23 was developed assuming a temperatureindependent heat capacity to simplify the integration of the heat capacity function; therefore, the difference between the two values of iJCp o and &l for each reaction given in Table 3 shows the magnitude of heat capacity dependence on temperature The closer the adjusted values to the reference state values of iJCp and LJ}l are, the more independent from temperature heat capacity is likely to be and vice versa It is noteworthy to mention that the two values of iJCp o and iJH o for each reaction given in Table 3 are presented to show the degree of heat capacity dependence on temperature and not to compare both values to one another. The heat capacity of dissolution for H3P04 is almost independent of temperature, while for H2P04 is slightly dependent on temperature. On the other hand, the heat capacity of dissolution for HS04 is most likely a strong function of temperature The heat capacity of solubility for gypsum is probably dependent on temperature to a great extent. The adjusted iJHGYPsumo value was considerably different from the reference state value of iJHGypsumo in order to account for that dependence Only two data points of DCPD solubility product (9) (10) were found and used in the regression The reference state value of iJHDCPD was kept the same and iJCPDCPD was adjusted to fit a straight line through the two data points The heat capacity of solubility for DCPD seems to have significant temperature dependence. Temperature effect on equilibrium and the results of Table 3 can be illustrated by Figures 5 through 9. Equilibrium constants and solubility products were computed and plotted versus temperature using both values of iJCp o and iJH o given in Table 3. Experimental data were also plotted with both computed values to show the degree of accuracy or the degree of deviation of the computed values 28 PAGE 42 The adjusted values of LJCp 0 and Ml were used in the simulation rather than the reference state values because they give a more accurate representation of the thermodynamic equilibrium as demonstrated by Figures 5 through 9. However If calculations are to be carried out at the reference state temperature of 25 C, Equation (23) reduces to Equation (24) and the values of LJCp 0 and Ml become irrelevant. Equation (24) was developed earlier in chapter two and is given by InKO = AGo RT" (24) Generally, LJCp 0 and LJll for any constant temperature simulation become insignificant provided that the equilibrium constants or the partial molar Gibbs free energy for the different species are available at that temperature 0 022 ,_,_,_.,_,_,_,_._._r_, 0 02 0 .018 0 .016 0", a" I 0 .014 Ii '0, .s 0 .012 ..,. o (J) ':;I 0 .01 0.008 0 .006 o = data .... = regression = literature 0.004 L"''...L:'::::3':;5:4:::.04:.5::.5'0 o 5 10 15 20 25 30 Temperature ("C) Figure 5 KHso4 as a Function of Temperature 29 PAGE 43 X 10 3 9 5 9 8 5 08 N J: 7.5 0 .s 7 .... I( '" 6 5 5 5 0 X 10 6 6.8 6 6 6.4 6.2 0N J: 6 Cl 0 5 8 .s .... 1(5 6 N I 5.4 5 2 5 4 8 0 5 10 15 20 25 30 Temperature ("C) o = data .... = regression = literature 35 40 45 Figure 6 KH3P04 as a Function of Temperature 00o = data .... = regression = literatu re 5 10 15 20 25 30 35 40 45 Temperature ("C) Figure 7 KH2P04 as a Function of Temperature 30 50 50 PAGE 44 X 105 4 5irr,,..... ..a '" J: Ol o g E II) a. 4 <9'3.5 o o = data .... = regression = literature Temperature (OC) Figure 8 KGypsum as a Function of Temperature X 107 2 5 2.45 ..0", 2.4 J: Ol 2 35 g o g 2.3 2 25 2.2 o = data = regression = literature 2 15 L__ '__ '___ '__ "__ '_ _ '_ ' 24 26 28 30 32 34 36 38 Temperature (OC) Figure 9. KDCPD as a Function of Temperature 31 PAGE 45 4.2 Temperature Effect on System Variables Using temperature as an input list that varied from 0 to 100C, the simulation was ran using three different activity coefficient models : ideal solution, DebyeHuckel, and RobinsonGuggenheimBates. Each simulation run was carried out with five different inputs of the effective sulfuric acid content of the liquid phase Ionic strength decreased linearly with increasing temperature. This result shows that the average degree of ionization, and thus the electrostatic interactions among ions, tends to decrease with increasing temperature The ideal solution model predicted the lowest values for ionic strength while the DebyeHuckel model predicted the highest RobinsonGuggenheimBates model predicted intermediate values for ionic strength but closer to those predicted by the ideal solution model. Furthermore, DebyeHuckel and RobinsonGuggenheimBates models prediction of ionic strength becomes closer to the ideal solution model prediction as ionic strength value decreases This is expected since both models reduce to the ideal solution model at an ionic strength of zero The liquid phase pH increased almost lineady with increasing temperature This result shows that the activity, and thus the molality, of the hydrogen ion tends to decrease with increasing temperature This observation is in agreement with the previous one concerning ionic strength. As temperature increases, the average degree of ionization decreases which will decrease the molality and activity of the hydrogen ion. For most of the temperature range, the ideal solution model predicted the lowest values while the RobinsonGuggenheimBates model predicted the highest. The DebyeHuckel model on the other hand, predicted intermediate pH values for temperatures between 20 and 70C, lowest for temperatures below 20 C, and highest for temperatures above 70C. 32 PAGE 46 The solid phase content of DCPD expressed as % P 2 05 also known as the phosphate lattice loss is the variable of most interest. Simulation results indicated that phosphate lattice loss increased rapidly with increase in temperature As was shown earlier the solubility product of DCPD decreases as temperature increases which is in agreement with increasing phosphate losses at elevated temperatures The ideal solution model predicted the lowest values for phosphate lattice loss while the DebyeHuckel model predicted the highest. RobinsonGuggenheimBates model predicted intermediate values for phosphate lattice loss but closer to those predicted by the ideal solution model. Furthermore DebyeHuckel and Robinson GuggenheimBates models prediction of phosphate lattice loss becomes closer to the ideal solution model prediction as temperature decreases According to the Equilibrium constants and the solubility products plots low reactor temperatures will increase the dissolution of DCPD and decrease the d i ssolution of gypsum This will increase the solid content of gypsum and decrease its content of DCPD Low reactor temperatures will also increase the dissociation of HS04 which will increase the concentration of S04 2 ions in the aqueous solution This will sh i ft the equilibrium of gypsum towards more precipitation On the contrary low reactor temperatures will decrease the dissociation of H 2 P04, which will decrease the concentration of HPOl ions in the aqueous solution This will shift the equilibrium of DCPD towards more dissolution. Before deciding on how low of a temperature the reactor should be operated at more equilibrium data is needed to perform more meticulous regression and obtain more precise values of the equilibrium constants especially for gypsum and DCPD 33 PAGE 47 0.9 0.8 00. 7 N I 0.6 o .s 0 5 .<: D. c: 0.4 (J) 2 0 3 c: .2 0 2 0 1 .___________________ % H 2 SO 4 = 2 5 __ % H 2S04 = 2 0 % H2S04 = 1 5 % H 2S04 = 1 0 __ ____ ____ L ____ ______ ____ o 20 40 60 80 100 120 Temperature (OC) Figure 10 Ionic Strength Versus Temperature Ideal Solution Model 0 9 0 8 00. 7 N I Cl 5 0 6 o .s 0.5 .<: D. c: 0.4 (J) 0 3 .2 0 2 0 1 ............ ....._____ % H SO = 2 5 _______ 2 4 ____________ % H 2 S 4 = 2 0 % H 2S 04 = 1 5 % H 2S04 = 1 0 OL____ ______ ______ L_ ____ _L ______ ____ __ o 20 40 60 80 100 120 Temperature (OC) Figure 11. Ionic Strength Versus Temperature DebyeHiickel Model 34 PAGE 48 0.9 0.8 00.7 '" J: 0.6 o .. 0.5 .<: ;;, I: 0.4 (I) 0.3 .2 0 2 0.1 % H 2S04 = 2.5 H 2S04 = 2 0 % H2S04 = 1 5 % H 2S04 = 1 0 _ __'_ __ __ _'_ __ ___' __' o 20 40 60 80 100 120 Temperature (OC) Figure 12. Ionic Strength Versus Temperature RobinsonGuggenheimBates Model 0.8 ,...,.r,.,,, 0 7 00.65 '" J: 0.6 o .. 0 .55 .<: ;;, I: 0.5 (I) 2 0.45 I: .2 0.4 0 .35 OebyeHuckel RGB Ideal Solution 0.3 L. __ L.. _ '_ '_ ___' ___ '_ '__ __' o 20 40 60 80 100 120 140 Temperature rC) Figure 13. Ionic Strength at 1.5 % H2S04 as a Function of Temperature 35 PAGE 49 J: Q. '" .Q :; 0 U) J: Q. 0 9 0 8 0 7 0 6 0 5 0.4 0 3 0 2 0 1 0 0 .....____% H 2S04 = 1 0 % H 2S04 = 1 5 __ % H2S04 = 2 0 _.% H 2S04 = 2 5 20 40 60 80 100 120 Temperature (OC) Figure 14. pH Versus TemperatureIdeal Solution Model 0 9 0 8 0 7 0.6 :5 0 5 :;: o U) 0.4 0 3 0 1 OL____ ______ ______ L_ ____ _L ______ i_ ____ __ o 20 40 60 80 100 120 Temperature ( OC) Figure 15. pH Versus Temperature DebyeHuckel Model 36 PAGE 50 I Il. 0 9 0 8 0 7 0.6 I:: 2 0 5 :; "0 I/) 0.4 0 3 0 20 1 % H 2S04 = 1.0 % H 2S04 = 1.5 % H 2S04 = 2 0 ______ % H 2S04 = 2 5 OL____ ______ ____ __ __ __ _L ______ ____ _J __ o 20 40 60 80 100 120 Temperature (OC) Figure 16. pH Versus Temperature RobinsonGuggenheimBates Model I Il. 0.45 0.4 0 35 :;; ::J "0 I/) 0 3 o 20 40 60 80 100 120 140 Temperature (OC) Figure 17. pH at l.5 % H2S04 as a Function of Temperature 37 PAGE 51 1.41,.,,_,.__ ., ., ., 1.2 .. ::! >R 0 8 o on o '" 0.. 0 6 C> iii ....I 0.4 0 2 20 40 60 80 100 120 Temperature (OC) Figure 18. Lattice Loss Versus Temperature Ideal Solution Model 2 .5r..,,..,, ., ., '" 2 ::! 1 5 <0 o 0..'" Q) o ....I 0 5 20 40 60 80 100 120 Tern perature ("C) Figure 19 Lattice Loss Versus Temperature DebyeHuckel Model 38 PAGE 52 1 .6rr... ______ ,____ . __ I/) I/) IV :! 1 4 1 2 0"'0. 8 N a. ., o 0 6 ...J 0 4 0 2 20 40 60 80 100 120 Tern perature ( OC) Figure 20 Lattice Loss Versus Temperature RobinsonGuggenheimBates Model '" o N a. ., o DebyeH Ockel RG8 Ideal Solution 0 5 f ...J o 20 40 60 80 100 120 140 Tern perature ( OC) Figure 21. Lattice Loss at 1.5 % H2S04 as a Function of Temperature 39 PAGE 53 4 3 Sulfuric Acid Effect on System Variables Using sulfuric acid content of the liquid phase as an input list that varied from 0 .01 to 2.50 % by mass, the simulation was ran using three different activity coefficient models: ideal solution, DebyeHuckel, and RobinsonGuggenheimBates Each simulation run was carried out with five different inputs of temperature Ionic strength increased almost linearly with increasing % H2S04 This result shows that the average degree of ionization, and thus the electrostatic interactions among ions, tends to increase with increasing % H2S04 The ideal solution model predicted the lowest values for ionic strength while the DebyeHuckel model predicted the highest. RobinsonGuggenheimBates model predicted intermediate values for ionic strength but closer to those predicted by the ideal solution model. Furthermore, DebyeHuckel and RobinsonGuggenheimBates models prediction of ionic strength becomes closer to the ideal solution model prediction as ionic strength value decreases This is expected since both models reduce to the ideal solution model at an ionic strength of zero. The liquid phase pH decreased linearly with increasing % H2S04 This result shows that the activity, and thus the molality, of the hydrogen ion tend to increase with increasing % H2S04 This observation is in agreement with the previous one concerning ionic strength. As % H2S04 increases, the average degree of ionization increases which will increase the molality and activity of the hydrogen ion. For most of the % H2S04 range, the ideal solution model predicted the lowest values while the Robinson GuggenheimBates model predicted the highest. The DebyeHuckel model on the other hand, predicted intermediate pH values between 1.15 and 1.75 % H2S04 lowest pH values below 1.15 % H2S04, and highest pH values above 1. 75 % H2S04 40 PAGE 54 The phosphate lattice loss decreased significantly with increase in % H2S04 As was shown earlier, sulfuric acid is used to extract phosphoric acid from phosphate rock while gypsum crystals will precipitate as a byproduct. Increasing precipitation of gypsum, due to increasing sulfuric acid concentration, will increase its concentration in the solid solution bringing the solid phase content ofDCPD down The ideal solution model predicted the lowest values for phosphate lattice loss while the DebyeHilckel model predicted the highest. RobinsonGuggenheimBates model predicted intermediate values for phosphate lattice loss but closer to those predicted by the ideal solution model. Furthermore, DebyeHuckel and Robinson GuggenheimBates models prediction of phosphate lattice loss becomes closer to the ideal solution model prediction as % H2S04 increases Sulfuric acid dissociates instantaneously forming HS04 and W ions in the liquid phase; therefore high concentration of sulfuric acid also means high concentrations of HS04and W ions in the aqueous solution. According to the Equilibrium reactions of the thermodynamic model, increasing concentration of HS04 will increase its dissociation rate to form more sol ions Increasing concentration of SO/ions will shift the equilibrium of gypsum towards more precipitation, which will decrease the concentration of Ca2+ ions in the aqueous solution. Increasing concentration of W ions due to increasing dissociation of sulfuric acid and HS04 ions will slow down the dissociation of phosphoric acid and H2P04ions which will reduce the concentration of HPO/in the aqueous solution. Decreasing concentrations of Ca2+ and HP04 2 ions will shift the equilibrium ofDCPD towards more dissolution and the phosphate losses will decrease as a consequence 41 PAGE 55 0 9 0 8 00. 7 T=O'C IN T=25'C 0 6 T = 50'C ;" T = 75'C E T = 100 c 0 5 t c ____________ 0 4 ____ " II) ___ .0 3 .2 0 2 0 1 ____ ______ L__ __ __ __ __ L__ __ __ __ o 0 5 1 5 2 2 5 3 % H 2S04 (% mass) Figure 22. Ionic Strength Versus % H 2S04 Ideal Solution Model 0 9 0 8 00. 7 N I 0 6 o E 0 5 .c m _c ..___0.4 _II) 0 3 ..Q 0 2 0 1 ......... _.... T = O'C T = 25'C T = 50'C T = 75 C .... T = 100 c OL____ ______ _L ______ J_ ______ L_ ____ ______ o 0 5 1 5 2 2 5 3 % H 2S04 (% mass) Figure 23. Ionic Strength Versus % H 2 S04 DebyeHiickel Model 42 PAGE 56 0 9 0 8 00.7 N I T = OC T = 25C T = 50 C ;t 0 6 T = 75 C _________ T = 100 C 50 5 . c: _____ 0.4 _____ .;::: 0.3 ..e 0 2 0 1 OL__ __ ______ _L ______ __ __ __ __ __ _J __ __ __ o 0 5 1 5 2 2 5 3 % H 2S04 (% mass) Figure 24. Ionic Strength Versus % H2S04 RobinsonGuggenheimBates Model 0 9 ,..,,.r,.,..,, 0 8 o I N O 7 0 .3L__ __ i__ __ _L __ __ o 0 5 1 5 2 2 5 3 3 5 Figure 25 Ionic Strength at 25C as a Function of % H2S04 43 PAGE 57 J: CL <: 2 :; 0 en J: CL <: 0 :;: 0 en 0 7 0.6 0 5 0.4 ..... ........., ...... ..... .......... 0 3 0.2 ...... T= 100'C .......... 75'C T = 50'C T = 25'C T = O'C 0 .1L____ ______ _L __ __ __ ______ __ __ ______ 0 7 0 6 0 5 0.4 0 3 0 2 0 1 o 0 5 1 5 2 2 5 % H 2S04 (% mass) Figure 26 pH Versus % H2S04 Ideal Solution Model 0 0 5 1 5 % H 2S04 (% mass) 2 T = 50'C T = 25 'C T = O'C 2 5 Figure 27 pH Versus % H2S04 DebyeHiickel Model 44 3 3 PAGE 58 0 .7,, ___ ,___ .___ ,__ , ___ , 0 6 0 5 J: Q. Q 0.4 :l "0 II) 0 3 0 2 ".. _ T = 75 C T = 50 C T = 25 C T = OC 0 1 ''''''' o 0 5 1 5 2 2 5 3 % H 2S04 (% mass) Figure 28 pH Versus % H2S04 RobinsonGuggenheimBates Model 0.45 0 4 0.35 J: Q. c:: 0 3 0 :;; :::I "0 II) 0 .25 0 2 0 15 0 0 5 1 5 2 2.5 3 3 5 Figure 29 pH at 25C as a Function of% H2S04 45 PAGE 59 7 6 T = 100 C 5 'ii) III co ::! 4 '" 0 '" a. 3 CIl 0 T = 75 C ...J \ 2 T = 50 C T = 25 C T =O C 0 0 0 5 1 5 2 2 5 % H 2S04 (% Mass) Figure 30 Lattice Loss Versus % H 2 S04 Ideal Solution Model 9 8 7 'ii) 6 III co ::! 5 '" 0 a.'" 4 CIl 0 3 ...J 2 0 T = 100 C T = 75 C \ T = 50 C T = 2 5 C T = 0 C 0 0.5 1 5 % H 2S04 ( % Mass) 2 2 5 Figure 31. Lattice Loss Versus % H 2 S04 DebyeHuckel Model 46 PAGE 60 7 T = 100 C 6 5 U> en '" ::! 4 '" 0 N [l. 3 Q) T = 75' C iU ...J 2 T = 50 C T = 25 C T = O C 0 o \ \ \ 0.5 1 5 % H 2S04 (% Mass) 2 2 5 Figure 32 Lattice L oss Versus % H2S 04 Robinson GuggenheimBates Model 0 6 DebyeHOcke l 0 5 \ U> 0 4 RGB en '" ::! Ideal Solution 0"'0. 3 N [l. Q) iU 0 2 ...J 0 1 0 0 0 5 1 5 2 2 5 Figure 33. Lattice Loss at 25C as a Function of % H2S04 47 PAGE 61 4.4 Model Validation The model can be val i dated by comparing its results to literature data Only two sets of phosphate lattice loss data were found in the literature The thermodynamic model developed in the previous chapter was used to run two different simulations analogous to the literature data Simulation results and literature data were then compared to each other to determine the validity of the developed thermodynamic model. Griffith (14) predicted the DCPD concentrations in the solid phase at a constant temperature of 25C and a 28 % liquid content of P20S for a specified rarlge of liquid phase % H2S04 Griffith employed ideal solution, DebyeHiickel, and Bromley activity coefficient models to compute phosphate losses. Figure 34 shows Griffith s results and Figure 35 shows simulation results when ran at the same conditions The model predicts slightly more phosphate losses than what Griffith had computed when ideal solution model is employed but it predicts less phosphate losses than what Griffith had computed when DebyeHiickel model is employed Griffith used different values for L1Cp 0 and M l to estimate the equil i brium constants of model reactions but that was unimportant since the simulation was run at the reference state temperature of25 C which will reduce equation (23) to equation (24) and the values of L1C p 0 and .Ml become irrelevant. The difference between the two predictions, even though minor can be attributed to different factors Griffith used different values for the reference state equilibrium constants and solubility products than those used in the simulation In addition Griffith assigned a value of unity to the second DebyeHiickel parameter /3, whereas Equation ( 2 9) presented earlier in Chapter 2 was used in the simulation to estimate that parameter. 48 PAGE 62 3.0r2.5 2.0 Lat":i.e % P20S 1.5 LO 0.5 "DebyeHv.eke1 Ideal 0.5 Liqui.d Phase %P205 = 28_0 2.0 Figure 34. Griffith Prediction of Lattice Loss at 25 DC 3 2 5 0'" 1 5 N [l. Cll :;::; ro 0 5 o o \ DebyeH ockel RG B Ideal Solution 0 5 1 5 % H 2S04 (% Mass) 2 Figure 35. Model Prediction of Lattice Loss at 25 DC 49 2 5 PAGE 63 The only real data found in the literature was that reported by Janikowski et al (15) The solid phase content of DCPD expressed as % P205 was measured at different liquid phase % H2S04 Janikowski's data was collected from an isothermal CSTR with a temperature of 78 5 C and a 31 % liquid content of P205 A simulation was run at the same conditions to compare the results with the data Figure 36 shows that the model prediction of phosphate losses is much lower than those depicted by Janikowski s data. This discrepancy can be credited to electrolytes and other impurities unaccounted for by the thermodynamic model. These overlooked substances can substantially affect the thermodynamic equilibrium if present in large quantities Another reason for this discrepancy can be attributed to mechanical malfunctions mentioned earlier in Chapter 1, e g poor filtering and insufficient mixing since Janikowski s data is a real industrial data representing practical circumstances. Busot and Griffith ( 16 ) hypothesized that an unattained equilib rium in the reactor would result in greater phosphate losses than predicted by thermodynamic models that are developed assuming global equilibrium Values of L1CPDCPDo and L1HDCP D o used in the model were adjusted using only two data points as was mentioned earlier This can result in an inaccurate calculation of the solubility product of DCPD which can affect the model prediction of phosphate lattice loss The model and Janikowski's data were employed to obtain a KSPDCPD at 78 5 0c. KSPDCPD at 78.5 C was used along with the other two values found for K SPDCPD at 25 and 37.5 C to adjust the values of L1CPDcPD o and L1HDCPD o using Equation (23) A L1CPDCPDo of1415.45 [J/(molK)] and aL1HDcPDo of+258. 55 [J/mol] were found to yield the best fit of Janikowski s data as illustrated by Figure 37 Simulation input and output for the RobinsonGuggenheimBates curve in Figure 37 is included in Appendix 8 50 PAGE 64 0 9 0 8 en '" 0 7 0"'0. 6 o.N Q) () 0 5 ...J 0 4 0 3 a a a a a a 00 a = Janikowski's Data a a DebyeH Ockel RGB Ideal Soluti on ____ L ____ ____ 1 3 1.4 1.5 1 6 1 7 2 1.8 1 9 Figure 36 Model Prediction of Lattice Loss at 78.5 C 1.5 1.4 a = Janikowski' s Data 1 3 en 1 2 '" os :! 1.1 '" 1 0 DebyeHockel N 0. Q) 0 9 0 ...J 0 8 0 7 R G B 0 6 Ideal Sol u t ion 0 5 1 3 1 4 1 5 1 6 1 7 1.8 1 9 2 Figure 37. Adjusted Model Prediction of Lattice Loss at 78 5 C 51 PAGE 65 CHAPTER 5. SUMMARY, CONCLUSION, AND RECOMMENDATIONS 5 1 Summary Phosphoric acid manufacturing by the dihydrate process involves inevitable phosphate losses due to the formation of gypsum crystals. One type of these losses is triggered by the crystallization of DCPD that has the same lattice structure as that of gypsum As a result, gypsum and DCPD form a solid solution of a composition that can be controlled thermodynamically Thermodynamics of electrolyte solutions such as equilibrium and activity were reviewed. Two relationships, Equations (28) and (29), were developed to estimate the value of the two temperaturedependent DebyeHiickel parameters used in many ionic activity coefficient models. Experimental data of equilibrium constants were regressed to introduce new values of L1Cp 0 and &l of model reactions to be used in Equation 23 as adjustable parameters (Table 3) to better represent the thermodynamic equilibrium A thermodynamic model was developed based upon five equilibrium reactions to predict the limits of distribution of phosphates between the liquid and the solid phases in a reactor used to extract phosphoric acid from rock. Ideal Solution DebyeHiickel and RobinsonGuggenheimBates electrolyte activity coefficient models were employed alternately to complete the model and to carry out different simulations using several inputs of temperatures and liquid phase sulfuric acid contents The results were then compared to other literature data to validate the model. 52 PAGE 66 5.2 Conclusion The developed relationships to estimate the value of the two temperature dependent DebyeHiickel parameters yielded excellent results that can be shown by Figures 3 and 4 The adjusted fitting parameter values of .t1Cpo and Nt of model reactions resulted in a more accurate representation of the thermodynamic equilibrium as illustrated by Figures 5 through 9 The adjusted fitting parameter values of .t1Cp" and &t for the dissolution of DCPD may not be very reliable since they were obtained by regressing only two experimental data points due to the scarcity of such data Decreasing temperature and increasing liquid phase sulfuric acid content was found to minimize phosphate lattice loss. The ideal solution model predicted the lowest values for phosphate lattice loss and the DebyeHiickel model predicted the highest, while RobinsonGuggenheimBates model predicted intermediate values Completing the thermodynamic model with Ideal Solution and DebyeHiickel electrolyte activity coefficient models was found to bind all predictions of phosphate lattice loss. The model predicts slightly more phosphate losses than what Griffith had computed when ideal solution model is employed, but it predicts less phosphate losses than what Griffith had computed when DebyeHiickel model is employed Both models assume the formation of an ideal gypsumDCPD solid solution The difference between the two predictions can be attributed to different values of equilibrium constants, solubility products, and DebyeHiickel parameters used by Griffith The model prediction of phosphate losses gave a lower bound to the real industrial data reported by Janikowski. Discrepancy can be accredited to the presence of impurities, mechanical inefficiencies, and unattained equilibrium in addition to the thermodynamically controlled lattice losses 53 PAGE 67 5 3 Recommendations The two correlations for the activity coefficients of phosphoric acid and water used in the simulation were determined from vapor pressure data of pure solutions of phosphoric acid and water at 25C. The two relationships, Equations (xxxxxv, 62) and (xxxxxvi, 62), incorporate neither the temperature effect nor the effect of the other electrolytes present in the aqueous solution. The activity coefficients of both phosphoric acid and water need to be investigated and more rigorous relationships need to be developed to predict their values More research is recommended to identify the most common operating conditions in industry such as the temperature range and the liquid phase content of phosphates and sulfuric acid. Regression calculations and model simulations need to be performed within those operating conditions to better represent real situations. Moreover, more equilibrium data of gypsum and DCPD is needed to perform a more precise regression to adjust the values of ,1Cp 0 and &l. Finally, sensitivity analyses need to be conducted on the effects of ,1Cp", ,11t, and other adjusted parameters on phosphate lattice losses It is also suggested to place a 95% upper and lower confidence limit on the adjusted parameters' prospective figures 54 PAGE 68 REFERENCES 1. Parker, S P., 1997, Dictionary of c hemistry, McGrawHill New York. 2 Van Der Sluis, S Meszaros, Y, Wesselingh 1. A, and Van Rosmalen, G M 1986, A Clean Technology Phosphoric Acid Process, The Fertiliser Society, London 3 Frochen, 1. and Becker P 1959, Crystallization and Cocrystallization in the Manufacture of WetProcess Phosphoric Acid" Proceedings of the I S. M A Technical Confer e nce, No. LE/59/59 4 Connors, K. A, 1990, Chemical kinetics, VCH Publishers, New York. 5 Zemaitis ,1. F Jr., Clark D M Rafal, M and Scrivner N c., 1986 Handbook of Aqueous Electrolyt e Thermodynamics American Institute of Chemical Engineers New York. 6. Smith 1. M and Van Ness H. C., 1987 Introduction to Che mical Engin e ering Thermodynamics, Fourth Edition, McGrawHill, New York. 7 Dean, 1. A 1992, Lange s Handbook of Che mistry, Fourteenth Edition, McGraw Hill New York. 8 Marshall, W L., Slusher R, and Jones E V.,1963, Aqueous Systems at High Temperature. XIV ", Journal of Che mical and Engine e ring Data 9 Patel, P R, Gregory T. M and Brown W E., 1974 "Solubility ofCaHP04 2H 2 0 in the Quaternary System Ca(OHhH 3P04 NaCIH 2 0 at 25C", Journal of R e s e arch National Bureau of Standards 78A(6) pp 675681. 10 Moreno, E C. and Gregory T. M 1966, Solubility of CaHP04 2H20 and Formation of Ion Pairs in the System Ca(OHhH 3 P04H20 at 37 5 C", Journal of Res e arch, National Bureau of Standards 70A(6), pp. 545552 11. Atkins, P W., 1994, Physical C h e mistry, Fifth Edition, W. H. Freeman and Company New York. 12 Lewis G. N and Randall M., 1961, The rmodynamics, Second Edition McGraw Hill, New York. 55 PAGE 69 . 13 Franks, F 1973, Water, Plenum Press, London 14 Griffith, D. J. Jf., 1985, Thermodynamic Bounds on Composition of Calcium S ulfate Chlcium Phosphate Solid Solutions in Equilibrium with Phosphoric Acid Solutions, M S. Thesis, University of South Florida, Tampa, Florida 15. Janikowski, S. M Robinson, N and Sheldrick, W F., 1961, "Insoluble Phosphate Losses in Phosphoric Acid Manufacture by the Wet Process Proceedings of the Fertilizer Society No. 81. 16 Busot, J. C and Griffith, J., 1987, ''Thermodynamic Bounds and Composition of Calcium SulfateCalcium Phosphate Sol i d Solutions in Acid EquilibtiUfii with Phosphoric Acid Solutions" Proceedings of the Second International Conference on Thermodynamics of Aqueous Electrolyte Solutions Warrenton, Virginia 56 PAGE 70 APPENDICES 57 PAGE 71 Appendix 1 Literature and Experimental Data Table 4. DebyeHiickel Parameters Data o 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 0.4918 0.4952 0.4989 0.5028 0.5070 0 5115 0.5161 0.5211 0.5262 0 5317 0.5373 0 5432 0.5494 0.5558 0 5625 0 5695 0 5767 0.5842 0 5920 0 6001 0.6086 0.3248 0.3256 0.3264 0 3273 0 3282 0 3291 0 3301 0.3312 0.3323 0 3334 0 3346 0 3358 0.3371 0.3384 0 3397 0 3411 0 3426 0 3440 0.3456 0 3471 0.3488 Table 5 Equilibrium Constants and Solubility Products at Various Temperatures (7) (7) (7) Tree) KHS04 KH3P04 KH2P04 KG!!I2.sum (8) K (9) (10 ) DCPD 0 0 016672 0 00879 0.486407 4.3 0.015417 5 0 008453 0.522396 10 0.008166 0.557186 15 0 012764 0 007816 0 587489 20 0 007464 0.612350 25 0.010304 0.007112 0.633870 4 22E05 2.51 E07 30 0.008913 0.006745 0.647143 4 36E05 35 0.008035 0 006368 0 653131 37.5 2 19E07 40 0.006761 0.005970 0 659174 4.25E05 50 0 005675 0.005284 0 656145 60 3.57E05 58 PAGE 72 Appendix 1 (Continued) Table 6 Physical and Reference State Properties MW( 7 ) (Kg / mole2 P20S 0 141945 H2SO 4 0 098080 H2O 0 018015 H3P04 0.097995 H2P04 0.096987 HP04 0.095979 HS04 0 097072 S04 0.096064 H 0 001008 Ca 0 040078 Gypsum 0 172172 DCPD 0.172088 Cpa (7) (J 1 ) (12) (J 3) Ho(7) (J / mol K2 (J / mol2 75 .35 285830 65 1288340 90 1296290 316 1292140 84 887340 293 909270 0 0 37 542830 186 2022600 197 2403580 Table 7. Janikowski s Data 1.350 1.370 1 385 1.455 1.460 1.515 1 540 1 550 1 655 1.660 1 665 1.680 1.710 1 715 59 0.960 0 920 0 890 0 850 0 830 0 740 0 765 0 765 0.710 0 670 0 720 0 660 0 670 0 690 GO (7) (J / mol2 237140 1142650 1130390 1089260 755910 744530 0 553540 1797500 2154750 Z r (7) (e) ( A ) NA NA NA NA 1 4 2 4 1 4 2 4 +1 9 +2 6 NA NA PAGE 73 Appendix 2. Matlab Code for Regression of A and f3 Literature Data T = [0 5 101520253035404550556065707580859095 100] ; A = [0.4918 0.4952 0.4989 0 5028 0.50700.5115 0 5161 0 5211 0.52620.5317 ... 0 5373 0.54320.54940. 55580.5625 0.5695 0 5767 0.5842 0 5920 0.6001 0 6086] ; B = [0 3248 0.3256 0 3264 0 3273 0 3282 0 3291 0.3301 0.3312 0.3323 0.3334 ... 0 .33460.33580. 3371 0.33840.33970. 3411 0 34260.34400.34560.3471 0 3488] ; TK = T + 273.15 ; polyfit(TK,A,2) ans= 0.00000513495200 0.00215443376623 0.69725708453699 polyfit(TK,B,2 ) ans = 0.00000088002615 0.00032917648667 0.34905962443669 Ar = (0.69725708453699)(0.00215443376623). *(TK)+(0.00000513495200). (TK). /\2 ; Br = (0.34905962443669)(0 00032917648667). *(TK)+(0.00000088002615). *(TK) ./\2 ; plot(T ,A, 'ko', T ,Ar, 'k '),xlabel('TemperatureeC),),ylabel('Parameter A') gtext('o = data'),gtext('= fit') plot(T,B,'ko',T,Br,'k'),xlabel('Temperature(C)'),ylabel(,Parameter Beta') gtext('o = data'),gtext('= fit') 60 PAGE 74 Appendix 3. Matlab Code for Regression of KHS04 Experimental Data R=8.314; Tr = 298 15 ; T = [273 .15 277.45 288 .15 298.15 303.15 308 .15 313 .15 323.15]'; pK_HS04 = [1.778 1.812 1.894 1.9872.0502.0952.1702. 246] ; K_HS04 = 10 /' (pK_HS04); % Global Variables Initial Guesses, & Options global T K_HS04 ; parameters =[21930 209] ; OPTIONS(l) = 0 ; % The Fun Function (An mFile) % function f= fun(parameters) ; % global T K_HS04; % Delta_H_HS04 = parameters(I,I) ; % Delta_Cp_HS04 = parameters(l,2) ; % Kc_HS04 = 0 01030386120442 exp ((Delta_H_HS04/R).*.IT). . % (l/Tr)) (DeJta_Cp_HS04/R).*(log(Tr./T)(Tr.lT)+I)) ; % f= sumKc_HS04K_HS04)/'2) ; % Regression & Results, Kc HS04 = Calculated Equilibrium Constant x = fmins('fun(x)',parameters,OPTIONS); Delta_H_HS04 = x(l,I); ans = 1.692832807144829e+004 ; Delta_Cp_HS04 = x(l,2); ans = 3.100073820743674e+002 ; Delta_Hr_HS04 = 21930 ; Delta_Cpr_HS04 = 209 ; Kcl HS04 = 0 01030386120442 exp ((Delta_H_HS04/R).*./T)(l/Tr)) ... (Delta Cp HS04/R). *(log(Tr./T)(Tr./T)+ 1) ) ; Kc2 HS04 = 0 01030386120442 exp ((Delta_Hr_HS04/R).*./T)(l/Tr)) ... (Delta_Cpr HS04/R). (log(Tr./T)(Tr./T)+ 1) ) ; plot(T 273 15,K_ HS04,'ko',T273 15,Kc1_HS04,'k:',T273 15 ,Kc2 HS04,'k'), . xlabel(Temperature (OC)'),ylabel(K H S _0_4_/\(mol/Kg H 20),), ... title(K H S _0 4 "'Versus T'), ... gtext('o = data'), gtext(' /\./\./\./\. = regression') ,gtext('= literature') 61 PAGE 75 Appendix 4 Matlab Code for Regression ofKH3P 0 4 Experimental Data R=8.314; Tr = 298 .15 ; T= [273.15 278 .15 283.15 288 .15 293 .15 298 .15 303 .15 308 .15 313.15 323 .15]'; pK IDP04 = [2.056 2 073 2 088 2.107 2.127 2.148 2 .171 2 196 2.224 2 277] ; K_IDP04 = 10 /'( pK_IDP04); % Global Variables, Initial Guesses, & Options global T K IDP04 ; parameters =[7950 155] ; OPTIONS(l) = 0 ; % The Fun Function (An mFile) % function f= fun(parameters) ; % global T K _H3P04 ; % DeltaJI_IDP04 = parameters(l,I); % Delta_Cp_IDP04 = parameters(l,2) ; % Kc_IDP04 = 0 00711213513653 exp ((DeltaJI_H3P041R).*./T)... % (l/Tr (Delta Cp H3P041R). *(log(Tr /T)(Tr./T)+ 1) ) ; % f= sumKc_IDP04KJf3P04)/'2) ; % Regression & Results, Kc IDP04 = Calculated Equilibrium Constant x = fmins(,fun(x)',parameters,OPTIONS) ; Delta_H_IDP04 = x(l,I) ; ans = 7.663321868430035e+003 ; Delta_Cp_H3P04 = x(l,2); ans = 1.554144573028516e+002 ; Delta_Hr_IDP04 = 7950 ; Delta_Cpr H3P04 = 155 ; Kcl_IDP04 = 0 00711213513653 exp ((Delta_H_IDP041R).*./T)(l/Tr ... (Delta Cp IDP041R). *(log(Tr./T) (Tr./T)+ 1) ) ; Kc2 IDP04 = 0 00711213513653 exp ((Delta_Hr_IDP041R). *(l'/T)(l/Tr ... (Delta_Cpr IDP041R). *(log(Tr./T)(Tr /T)+ 1) ) ; plot(T273 15,K_IDP04,'ko',T273 .15,Kcl_H3P04,'k',T273.15,Kc2_IDP04,'k'), ... xlabel('Temperature (OC)'),ylabel('K_H_3 _P 0_4 (mollKg H_20)'), ... title('K_H_3_P _0_4 Versus T'), ... gtext('o = data') gtext('/\. /\. /\. /\. = regression'),gtext('= literature') 62 PAGE 76 Appendix 5 Matlab Code for Regression of KH2P04 Experimental Data R=8.314; Tr = 298 .15 ; T = [273 .15 278 .15 283 .15 288 .15 293 .15 298.15303 .15308. 15313 .15323.15]'; pK _H2P04 = [7.313 7 .2827. 2547.231 7 213 7.198 7 189 7 .1857.181 7 .183]'; K_H2P04 = 10 /'( pK_H2P04); % Global Variables, Initial Guesses & Options global T K H2P04 ; parameters = [4150 226] ; OPTIONS(l) = 0 ; % The Fun Function (An m File) % function f = fun(parameters) ; % global T K H2P04 ; % Delta H H2P04 = parameters(l 1) ; % Delta_Cp_H2P04 = parameters(l 2) ; % Kc_H2P04 = 6 338697112569273e8 *exp ((Delta_H_H2P041R) .*.rr)... % (Irrr (Delta Cp_H2P041R) *(log(Tr rr)(Tr.rr)+I ; % f= sumKc H2P04K_H2P04)/'2) ; % Regression & Results Kc H2P04 = Calculated Equilibrium Constant x = fmins('fun( x )"parameters OPTIONS) ; Delta_H_H2P04 = x(l I) ; ans = 4 033524375681814e+003 ; Delta_Cp_H2P04 = x(l,2) ; ans = 2 489728900252766e+002 ; Delta_Hr_H2P04 = 4150 ; Delta_Cpr _H2P04 = 226 ; KclJUP04 = 6 338697112569273e8 *exp ((Delta_H_H2P041R) *(l .rr)(lrrr ... (Delta Cp H2P041R) *(log(Tr rr)(Tr.rr)+ 1) ) ; Kc2_H2P04 = 6 338697112569273e8 .*exp ((Delta_Hr_H2P041R) .*.tr)(lrrr ... (Delta_Cpr H2P041R) (log(Tr.rr)(Tr .rr)+ 1) ) ; plot(T273 .15, K_H2P04,'ko' T273 .15, Kcl_H2P04,'k:' T273 .15, Kc2_H2P04,'k') ... xlabel('Temperature ( O C)'),ylabel('K H 2 _P 0_4_ A (mollKg H 20),) ... title('K H 2 _P _0_4_ A Versus T') ... gtext('o = data'),gtext('A. A A. A. = regression '),gtext('= literature') 63 PAGE 77 Appendix 6 Matlab Code for Regression of Koypsum Experimental Data R=8.314; Tr=298.15; T = [298.15 303.15 313.15 333 .15]'; K_Gypsum = [42.2e6 43.6e6 42.5e6 35 .7e6]'; % Global Variables, Initial Guesses, & Options global T K _Gypsum ; parameters = [1160 365.3] ; OPTIONS (1 ) = 0 ; % The Fun Function ( An mFile ) % function f= fun(parameters) ; % global T K_ Gypsum ; % Delta H _Gypsum = parameters(l, 1) ; % Delta Cp _Gypsum = parameters(1,2) ; % Kc_ Gypsum = 42.2e6 exp ( (Delta_H_ Gypsum!R) *((l.ff)(lffr)) ... % (Delta Cp Gypsum!R) *(log(Tr.ff)(Tr.ff)+ 1) ) ; % f= sum((Kc_GypsumK_Gypsum)/'2); % Regression & Results, Kc _Gypsum = Calculated Solubility Product x = finins(,fun(x)',parameters OPTIONS) ; Delta_H_Gypsum = x(l,l); ans = 4.338149706356578e+003 ; Delta Cp _Gypsum = x(l,2) ; ans = 4 935892366111605e+002 ; Delta_Hr_Gypsum = 1160 ; Delta_Cpr_Gypsum = 365 3 ; Kcl_Gypsum = 42 2e6 exp ((Delta_H_Gypsum!R) .*((l.ff)(l/Tr)) ... (Delta Cp Gypsum!R) *(log(Tr./T)(Tr /T)+ 1) ) ; Kc2_Gypsum= 42.2e6 exp ((DeltaJIr_Gypsum!R).*((l.ff)(l/Tr)) ... (Delta_Cpr Gypsum!R). *(log(Tr./T)(Tr .ff)+ 1) ) ; plot(T273 15,K_Gypsum,'ko',T273 15,Kc1_Gypsum,'k',T273 15,Kc2_Gypsum,'k'), ... xlabel(Temperature COC)'), ylabel('K G 3 .p s u m (mol/Kg H 20),,4') ... title('K_G3'p_s_u_m Versus T'), ... gtext('o = data'),gtext('l\. 1\. 1\. 1\. = regression'),gtext('= literature') 64 PAGE 78 Appendix 7. Matlab Code for Regression of KDCPD Experimental Data R=8.314; Tr=298.15 ; T = [298 .15310.65]'; K_DCPD = [2.512663370009572e7 2 1ge7] '; % Global Variables, Initial Guesses & Options global T K_DCPD ; Delta_Cp_bCPD = [399 .3] ; OPTIONS(l) = 0 ; % The Fun Function ( An mFile ) % function f= fun(Delta_Cp_DCPD) ; % globat T K DCPD ; % Kc_DCPD = 2.512663370009572e7 exp ( (30501R).*l.ff)(lffr ... % (Delta Cp DCPDIR) *(log(Tr.ff)(Tr .ff)+ 1) ) ; % f= surnKc bCPDKDCPD)/'2) ; % Regression & Results Kc DCPD = Calculated Solubility Product Delta_Cp_DCPD = ftnins('fun(x)' Delta_Cp_DCPD,OPTIONS) ; ans = 8.787345583534251e+002 ; Delta_Cpr_DCPD = 399 3 ; Kcl_DCPD = 2 512663370009572e7 exp ((30501R).*./T)(lffr ... (Delta Cp DCPDIR) *(log(Tr /T)(Tr .ff)+ 1) ) ; Kc2 _DCPD = 2 512663370009572e7 exp ( ( 30501R). *l.ff)(lffr . (Delta_Cpr .J)CPDIR). *(log(Tr.ff)(Tr./T)+ 1) ) ; plot(T 273 15,K _DCPD,'ko' T 273 15,Kcl DCPD,'k:',T 273 15, Kc2 DCPD,'k') ... xlabel('Temperature eC)'), ylabel('K.J) C _P _D (mollKg H _20)" 4') ... title('K_D_C_P_D Versus T') ... gtext('o = data') gtext(' ''. ". ". ". = regression'),gtext('= literature') 65 PAGE 79 Appendix 8 TK Solver Code of Thermodynamic Model ; Liquid phase properties TPM = m H3P04 + m H2P04 + m HP04 TSM = m HS04 + m S04 %P20S = (TPMe_P20sMW_P20SI_H20) .100 %H2S04 = (TSMe_H2S04MW_H2S04_H20) .100 A. M H 2 0 'I' M Total 1 m H20 =MW H20 ; Total mass balance in the liquid phase M TPM = m H3P04MW H3P04 + m H2P04MW H2P04 + m HP04MW HP04 M TSM = m HS04MW HS04 + m S04MW S04 MOther = m HMW H + m CaMW Ca M Total =M H20 +M TPM +M TSM +M Other ; Electroneutrality z H2P04m H2P04 + z HP04m HP04 + z HS04m HS04 + z S04m S04 + z Hm H + Z Cam Ca = a ; Phenomenological assumptions ; 1) Liquid phase acid equilibria K HS04 = K H3P04 K H2P04 a S04a H a HS04 a H2P04a H a H3P04 a HP04a H a H2P04 ; 2) Solidliquid equilibria Ksp_Gypsum 2 a S04a Ca a H20 x_Gypsum 2 a HP04a Ca a H 2 0 x DCPD x_Gypsum + x DCPD = 1 ; Solid phase properties x DCPDMW DCPD w DCPD x GypsumMW_Gypsum + x_DCPDMW_ DCPD %P20Ss = [WDCPD[ 1 Jp P20S MW P 20S] 100 MW DCPD 66 PAGE 80 Appendix 8. (Continued) ; Temperaturedependent equilibrium constants K HS04 = Kr HS04 e [ I t.H H3P04 [ + :r J R K H3P04 = Kr H3P04 e [ t.H H2 P04 [_1 ___ l_J R T Tr K H2P04 = Kr H2P04 e Ksp Gypsum = Kspr Gypsum e [ t.H ;psum Ksp_DCPD = Kspr_DCPDe [ t.H RDCPD [ + :r J ; Reference state equilibrium constants Kr HS04 = e [ t.Gr HS04 J RTr Kr H3P04 = e Kr H2P04 = e [ t.Gr H3P04 J RTr [ t.Gr H2 P04 J RTr [ t.Gr Gypsum J RTr Kspr_Gypsum = e [ t.Gr DCPD J RTr Kspr_DCPD = e t.Cp H3P04 R t.Cp H2P04 R t.Cp DCPD R ; Reference state heat capacities of reaction ..1Cpr_HS04 = Cpr_S04 + Cpr_H Cpr_HS04 ..1Cpr_H3P04 = Cpr_H2P04 + Cpr_H Cpr_H3P04 ..1Cpr_H2P04 = Cpr_HP04 + Cpr_H Cpr_H2P04 [ In[ + J +lJJ [ In[ + J +lJJ ..1Cpr_Gypsum = Cpr_Ca + Cpr_S04 + 2Cpr_H20 Cpr_Gypsum ..1Cpr_DCPD = Cpr_Ca + Cpr_HP04 + 2Cpr_H20 Cpr_DCPD ; Reference state enthalpies of reaction ..1Hr HS04 = Hr S04 + Hr H Hr HS04 ..1Hr H3P04 = Hr H2P04 + Hr H Hr H3P04 ..1Hr H2P04 = Hr HP04 + Hr H Hr H2P04 ..1Hr_Gypsum = Hr_Ca + Hr_S04 + 2Hr_H20 Hr_Gypsum ..1Hr DCPD = Hr Ca + Hr HP04 + 2Hr H20 Hr DCPD 67 PAGE 81 Appendix 8 (Continued) ; Reference state Gibbs free energies of reaction LiGr_HS04 = Gr_S04 + Gr_H Gr_HS04 LiGr H3P04 = Gr H2P04 + Gr H Gr H3P04 LiGr=H2P04 = Gr=HP04 + Gr H Gr H2P04 LiGr _Gypsum = Gr Ca + Gr S04 + 2Gr H20 Gr Gypsum LiGr DCPD = Gr C;. + Gr HP04 + 2Gr H20 Gr DCPD ; Defining activities a_H20 = m_H20r _H20 a_H3P04 = r _H3P04 a_H2P04 = m_H2P04 r _H2P04 a_HP04 = m_HP04 r _HP04 a_HS04 = m_HS04 r _HS04 a_S04 = m_S04 r _S04 a_H =m_Hr_H a Ca = m Ca r Ca ; Defining solution's ionic strength and pH ; Nonelectrolyte activity coefficients + m S04 z S04 r_H20=(0.87979) + (0.75533%P205) [0.0012084 %P2052 ] +[ 15.258 ] %P205 r_H3P04 = (22.676) (1.0192%P205) +[0.01891 %P2052 ] _[ 159.56 ] %P205 ; Electrolyte activity coefficients ; a) Ideal solution model r H2P04 = 1 r _HP04 = 1 r _HS04 = 1 r _S04 = 1 r_H= 1 r _Ca = 1 ; b) DebyeHuckel model 2 A = (0.69725708453699 ) (0.00215443376623 ) T + (0.00000513495200 ) T 2 f3 = (0.34905962443669 ) (0.00032917648667 ) T + (0.00000088002615 ) T 68 2 + ... PAGE 82 Appendix 8. (Continued) [ 2 0.5 ] Az H2P04 1 1 + 1.5 ] y_H2P04 = 10 [ 2 0.5 ] Az_HP04 I 1 + 1.5 ] Y _HP04 = 10 [ 2 0.5 ] Az_HS04 1 1 + 1 5 ] Y _HS04 = 10 [ 2 0.5 ] Az_ S04 1 1 + ] y_S04 = 10 [ "'] Az H 1 1 + y_H= 10 [ 2 0 5 ] Az Ca 1 1 + .5 ] y_Ca= 10 ; c) RobinsonGuggenheimBates model [[ .5111 ( .21;] Z_H2P042J 1 +1.51 y _H2P04 = 10 [[ .5111 ( .21;] Z HP042J 1 + 1 .51 Y _HP04 = 10 [[ .5111 (.2I;] Z_HS042J 1 + 1 .51 Y _HS04 = 10 [[ .5111 ( .21;] Z _S042J 1 + 1 .51 y_S04 = 10 [[ .5111 ( .21;] Z_H2J 1 + 1. 51 y_H=10 [[ .5111 (.21;] z_Ca 2 J 1 + 1 .51 y_Ca = 10 69 PAGE 83 A ppe n d ix 8 (C o ntinued) ; Programming: list guess TPM = place ( TPM el t () + 1) TSM = place ( 'TSM elt () + 1) PAGE 84 Appendix 8. (Continued) Status Inp u t Name Output Unit Commen t 4 T_H2P04 A D effective ionic radius 4 r _HP04 AD effectivei onic radius 4 r _HS04 A D effec tiv e i onic radius 4 T_S04 A D effective ionic radius 9 r H A D effective ionic radius 6 r Ca A D effective ionic radius .1419446 MW_P205 Kg/ mole molecular weight of phosphate equivalence .0980796 MW_H2S04 Kg/ mole molecular weight of sulfuric acid equivalence .0180154 MW_H20 Kg/ mole mo l ecular weight of water .0979954 MW_lDP04 Kg/mole molecular weight of phosphoric acid 0969874 MW_H2P04 Kg/ mole molecular weight of phosphate dihydrate ion 0959794 MW_HP04 Kg/ mole molecular weight of hydrated phospha te ion .0970716 MW_HS04 Kg/ mole molecular weight of hydrated sulfate ion 0960636 MW_S04 Kg/ mole molecular weight of sulfate ion .001008 MW_H Kg/ mole molecular weight of hydrogen ion 040078 MW_Ca Kg/ mole molec u lar weight of calcium ion .172172 MW_Gypsum Kg/ mole molecular weight of gypsum 172088 MW_DCPD Kg/mole molecular weight ofDCPD I z_H2P04 Charge of phosphate dihydrate ion 2 z _HP04 Charge of sulfate dihydrate ion I z_HS04 Charge of sulfate hydrat e ion 2 z_S04 Charge of sulfate ion I z_H Charge of hydrogen ion 2 z _Ca Charge of calcium ion m_H20 55.50806532 mol /Kg H2O molality of water L m_lDP04 7.549047485 mol /Kg H2O molality of phosphoric acid L m_H2P04 .2652079088 mol/KgH20 motaIity of phosphate dihydrate ion L m_HP04 4.427943E8 mol /KgH20 molality of sulfat e dihydrate ion LGuess 2355200522 m_HS04 mol /Kg H2O molality of sulfate hydrate ion LGuess 0016061009 m_S04 mol /KgH20 motaIity of sulfate ion LGuess .5039402022 m_H mol /Kg H2O molality of hydrogen ion L m_Ca 2.455495E 8 mol /Kg H2O molality of calcium ion a_H2O 1 213. 759403 mol /KgH20 acti vi ty of water L a_H3P04 30.99799863 mol /Kg H2O activity of phosphoric acid L a_H2P04 2386572731 mol /Kg H2O activity of phosphate dihydrate ion L a_HP04 2 90372E 8 mol /Kg H2O activity of sulfate dihydrate ion L a_HS04 2119415431 mol /KgH20 activity ofsulfate hydrate ion L a _S04 0010532359 mol/Kg H2O activity of sulfate ion L a_H 4534894719 mol /Kg H2O activ ity of hydrogen ion L a_Ca 1 610244E8 mol /Kg H2O activity of calcium ion LH20 21.86636115 activity coefficient of water LlDP04 4 106213226 activity coefficient of phosphoric acid LH2P04 8998874666 activity coefficient of phosphate dihydrate ion y _HP04 6557719142 activity coefficient of sulfate dihydrate ion Guess .8998874666 LHS04 activity coefficient of sulfate hydrate ion Guess 6557719142 LS04 activity coefficient of sulfate jon Guess .8998874666 LH activity coefficient of hydrogen ion LCa 6557719142 activity coefficient of calcium ion 75 35 Cpr_H2O J/moiK reference state heat capacity of water 65 Cpr_IDP04 J /molK reference state heat capacity of phosphoric acid 90 Cpr_H2P04 J /molK reference state heat capacity of phosphate dihydrate ion 316 Cpr_HP04 J /moiK reference state heat capacity of sulfate dihydrate ion 84 Cpr _HS04 J /molK reference state heat capacity of sulfate hydrate ion 293 Cpr_S04 J /molK reference state heat capacity of sulfate ion 0 Cpr_H J /molK reference state heat capacity of hydrogen ion 37 Cpr_ea J /molK reference state heat capacity of calcium ion 186 Cpr Gypsum J /molK reference state heat capacity of gypsum 197 Cpr_DCPD J /molK reference state heat capacity of DCPD 71 PAGE 85 Appendix 8. (Continued) Status Input Name Output Unit Comment 285830 Hr_H20 J I mol reference stat e enthalpy of water 1288340 Hr_H3P04 J I mol reference stat e enthalpy of phosphoric acid 1296290 Hr_H2P04 J I mol reference state enthalpy of phosphate dihydrate ion 1292140 Hr_HP04 J I mol r e ference state enthalpy of sulfate dihydrate ion 887340 Hr_HS04 J I mol refe rence state enthalpy of sulfate hydrate ion 909270 Hr_S04 J I mol reference state enthalpy of sulfate ion 0 Hr_ H J Imol reference state enthalpy of hydrogen ion 542830 Hr_Ca J I mol reference state enthalpy of calcium ion 2022600 Hr_Gypsum J I mol reference state enthalpy of gypsum 2403580 Hr_DCPD J I mol reference state enthalpy of DCPD 237140 Gr_H20 J I mol reference state Gibbs free energy of water 1142650 Gr_IDP04 J I mol reference state Gibbs free energy of phosphoric acid 1130390 Gr_H2P04 J I mol reference state Gibbs free energy of phosphate dihydrate ion 1089260 Gr_HP04 J I mol reference state Gibbs free energy of sulfate dihydrate ion 755910 Gr_HS04 J I mol reference stat e Gibbs free energy of sulfate hydrate i on 744530 Gr_S04 J I mol reference state Gibbs free energy of sulfate ion 0 Gr_H J I mol reference state Gibbs free energy of hydrogen ion 553540 Gr_Ca J I mol reference stat e Gibbs free energy of calcium ion 1797500 Gr_Gypsum J Imol reference state Gibbs free energy of gypsum 2154750 Gr_DCPD J I mol referenc e state Gibbs free energy ofDCPD ilCpr_HS04 209 J ImolK reference state heat capacity ofHS04 dissolution ilCpr _H3P04 155 J ImolK reference state heat capacity ofH3P04 dissolution ilCpr_H2P04 226 J ImolK reference state heat capacity ofH2P04 dissolution ilCpr _Gypsum 365.3 J /molK reference state heat capacity of gypsum solubility ilCpr_DCPD 399.3 J ImolK referenc e state heat capacity ofDCPD solubility LlHr_HS04 21930 J I mol reference state enthalpy of HS04 dissolution LlHr_H3P04 7950 J I mol reference state enthalpy ofH3P04 dissolution LlHr_H2P04 4150 J I mol reference state enthalpy ofH2P04 dissolution LlHr_Gypsum 1160 J I mol reference state enthalpy of gypsum solubility LlHr_DCPD 3050 J Imol reference state enthalpy of DCPD solubility ilGr_HS04 11380 J I mol reference state Gibbs free energy ofHS04 dissolution ilGr_H3P04 12260 J I mol reference state Gibbs free energy ofH3P04 dissolution ilGr_H2P04 41130 J I mol reference state Gibbs free energy of H2P04 dissolution ilGr_Gypsum 25150 J Imol reference state Gibbs fre e energy of gypsum solubility ilGr_DCPD 37670 J I mol reference state Gibbs free energy ofDC PD solubility 310 007382 ilCp _HS04 J ImolK adjusted reference state heat capacity ofHS04 dissolution 155.414457 ilCp_IDP04 J /molK adjusted reference state heat capacity ofIDP04 dissolution 248 97289 ilCp_H2P04 J ImolK adjusted reference state heat capacity of H2P04 dissolution 493 589237 ilCp Gypsum J ImolK adjusted reference state heat capacity of gypsum solubility 1415.45 ilCp D CPD J ImolK adjusted reference state heat capacity ofDCPD solubility 16928.3281 LlH_HS04 J I mol adjusted reference state enthalpy of HS04 dissolution 7663.32187 LlH_IDP04 J I mol adju s ted reference state enthalpy of IDP04 dissolution 4033 524376 LlH_H2P04 J I mol adjusted reference state enthalpy ofH2P04 dissolution 4338 149706 LlH_Gypsum J I mol adjusted reference state enthalpy of gypsum solubility 258.55 LlH_DCPD J I mol adjusted reference state enthalpy ofDCPD solubility 0103038612 Kr_HS04 mol /KgH20 reference state equilibrium constant ofHS04 dissolution 0071121351 Kr_H3P04 mol /KgH20 reference state equilibrium constant ofH3P04 dissolution 6.338697E8 Kr_H2P04 mol I Kg H2O reference state equilibrium constant of H2P04 dissolution .0000422 Kspr_Gypsum (mol IKg H20)A 4 refe rence state solubility product of gypsum 2.512663E7 Kspr_DCPD ( mol I Kg H2O ) A 4 reference state solubility product ofDCPD L K_HS04 0022535996 mol /KgH20 equilibrium constant of HS04 dissolution L K _IDP04 0034914693 mol /KgH20 equilibrium constant ofIDP04 dissolution L K_H2P04 5 517563E8 mol /KgH20 equilibrium constant of H2P04 dissolution L Ksp Gypsum 2.5606315 ( mol I Kg H2O ) A 4 solubility product of gyp s um L Ksp D C PD 2 8395018 ( mol IKgH20)A 4 s olubility product ofDCPD 72 PAGE 86 UNIVERSITY OF SOUTH FLORIDA 1 \11\111111\11\1111\111\111\\111111\\111\111\11111\11\11111\111\ 32102036399182 r 