Thermodynamic modeling and phase diagram prediction of salt lake brine systems. I. Aqueous Mg2+-Ca2+-Cl- binary and ternary systems

doi:10.1016/j.cjche.2020.03.039

中国化学工程学报 ›› 2020, Vol. 28 ›› Issue (9): 2391-2408.DOI: 10.1016/j.cjche.2020.03.039

• Chemical Engineering Thermodynamics • 上一篇下一篇

Thermodynamic modeling and phase diagram prediction of salt lake brine systems. I. Aqueous Mg²⁺-Ca²⁺-Cl^- binary and ternary systems

Huan Zhou, Xiaolong Gu, Yaping Dai, Jingjing Tang, Jian Guo, Guangbi Li, Xiaoqin Bai

College of Chemical Engineering and Materials Science, Tianjin Key Laboratory of Marine Resources and Chemistry, Tianjin University of Science and Technology, Tianjin 300457, China

收稿日期:2020-02-10 修回日期:2020-03-25 出版日期:2020-09-28 发布日期:2020-10-21
通讯作者: Huan Zhou
基金资助:
The authors gratefully thank the financial support of the National Natural Science Foundation of China (U1407204, U1707602) and also the Yangtze Scholars and Innovative Research Team in University of Education of China; the Innovative Research Team of Tianjin Municipal Education Commission (TD12-5004), and the Foundation of Tianjin Key Laboratory of Marine Resources and Chemistry (201602).

Thermodynamic modeling and phase diagram prediction of salt lake brine systems. I. Aqueous Mg²⁺-Ca²⁺-Cl^- binary and ternary systems

Huan Zhou, Xiaolong Gu, Yaping Dai, Jingjing Tang, Jian Guo, Guangbi Li, Xiaoqin Bai

College of Chemical Engineering and Materials Science, Tianjin Key Laboratory of Marine Resources and Chemistry, Tianjin University of Science and Technology, Tianjin 300457, China

Received:2020-02-10 Revised:2020-03-25 Online:2020-09-28 Published:2020-10-21
Contact: Huan Zhou
Supported by:
The authors gratefully thank the financial support of the National Natural Science Foundation of China (U1407204, U1707602) and also the Yangtze Scholars and Innovative Research Team in University of Education of China; the Innovative Research Team of Tianjin Municipal Education Commission (TD12-5004), and the Foundation of Tianjin Key Laboratory of Marine Resources and Chemistry (201602).

摘要/Abstract

摘要： Salt lake brine is a complex salt-water system under natural environment. Although many models can express the thermodynamic properties and phase equilibrium of electrolyte aqueous solution, the multi-temperature characteristics and predictability are still the goals of model development. In this study, a comprehensive thermodynamic model system is re-established based on the eNRTL model and some improvements: (1) new expression of long-range electrostatic term with symmetrical reference state is proposed to handle the electrolyte solution covering entire concentration range; (2) the temperature dependence of the binary interaction parameters is formulated with a Gibbs Helmholtz expression containing three temperature coefficients, the liquid parameters, which associated with Gibbs energy, enthalpy, and heat capacity contribution; and (3) liquid parameters and solid species data are regressed from properties and solubility data at full temperature range. Together the activity coefficient model, property models and parameters of liquid and solid offer a comprehensive thermodynamic model system for the typical bittern of MgCl₂-CaCl₂-H₂O binary and ternary systems, and it shows excellent agreement with the literature data for the ternary and binary systems. The successful prediction of complete phase diagram of ternary system shows that the model has the ability to deal with high concentration and high non-ideality system, and the ability to extrapolate the temperature.

关键词: Aqueous electrolytes, Comprehensive thermodynamic model, MgCl₂-CaCl₂-H₂O, Phase diagram, Thermodynamic properties

Abstract: Salt lake brine is a complex salt-water system under natural environment. Although many models can express the thermodynamic properties and phase equilibrium of electrolyte aqueous solution, the multi-temperature characteristics and predictability are still the goals of model development. In this study, a comprehensive thermodynamic model system is re-established based on the eNRTL model and some improvements: (1) new expression of long-range electrostatic term with symmetrical reference state is proposed to handle the electrolyte solution covering entire concentration range; (2) the temperature dependence of the binary interaction parameters is formulated with a Gibbs Helmholtz expression containing three temperature coefficients, the liquid parameters, which associated with Gibbs energy, enthalpy, and heat capacity contribution; and (3) liquid parameters and solid species data are regressed from properties and solubility data at full temperature range. Together the activity coefficient model, property models and parameters of liquid and solid offer a comprehensive thermodynamic model system for the typical bittern of MgCl₂-CaCl₂-H₂O binary and ternary systems, and it shows excellent agreement with the literature data for the ternary and binary systems. The successful prediction of complete phase diagram of ternary system shows that the model has the ability to deal with high concentration and high non-ideality system, and the ability to extrapolate the temperature.

Key words: Aqueous electrolytes, Comprehensive thermodynamic model, MgCl₂-CaCl₂-H₂O, Phase diagram, Thermodynamic properties

Huan Zhou, Xiaolong Gu, Yaping Dai, Jingjing Tang, Jian Guo, Guangbi Li, Xiaoqin Bai. Thermodynamic modeling and phase diagram prediction of salt lake brine systems. I. Aqueous Mg²⁺-Ca²⁺-Cl^- binary and ternary systems[J]. 中国化学工程学报, 2020, 28(9): 2391-2408.

参考文献

[1] T.L. Deng, H. Zhou, C. Xia, Salt Water System Phase Diagram and Its Application, Chemical Industry Press, Beijing, 2013(in Chinese).
[2] C. Christov, Isopiestic determination of the osmotic coefficients of an aqueous MgCl₂+CaCl₂ mixed solution at (25 and 50)℃, chemical equilibrium model of solution behavior and solubility in the MgCl₂+H₂O and MgCl₂+CaCl₂+H₂O systems to high concentration at (25 and 50)℃, J. Chem. Eng. Data 54(2009) 627-635.
[3] J.H. van't Hoff, F.B. Kenrick, H.L. Silcock (Eds.), Solubilities and inorganic and organic compounds, Pergamon Press (1979), p. 196.
[4] W.R. Cooling, J.J. Shafer, in:W. Engelhardt, J. Zemann (Eds.), Formation and Substance of Salt deposits in Mineralogy and Petrography in Individual Presentations, Springer-Verlag, Berlin 1962, p. 3046.
[5] C.F. Prutton, W.J. Lightfoot, Equilibria in saturated solutions, J. Am. Chem. Soc. 68(1946) 1001.
[6] N.S. Kurnakov, H.L. Silcock (Eds.), Solubilities and inorganic and organic compounds, Pergamon Press, New York 1979, pp. 258-262.
[7] W.J. Lightfoot, C.F. Prutton, The ternary system CaCl₂-MgCl₂-H₂O CaCl₂-KCl-H₂O and MgCl₂-KCl-H₂O at 35℃ and 75℃, J. Am. Chem. Soc. 69(1947) 2098-2011.
[8] G.O. Assarsona, Equilibria in aqueous systems containing K⁺, Na⁺, Ca²⁺,Mg²⁺ and Cl-. III. The ternary system CaCl₂-MgCl₂-H₂O, J. Am. Chem. Soc. 72(1950) 1442-1444.
[9] G.C. Sinke, E.H. Mossner, J.L. Curnutt, Enthalpies of solution and solubilities of calcium chloride and its lower hydrates, J. Chem. Thermodyn. 17(1985) 893-899.
[10] W. Voigt, What we know and still not know about oceanic salts, Pure Appl. Chem. 87(11-12) (2015) 1099-1126.
[11] K.S. Pitzer, Thermodynamics of electrolytes. I. Theoretical basis and general equations, J. Phys. Chem. 77(1973) 268-277.
[12] K. Thomsen, Modeling electrolyte solutions with the extended universal quasichemical (UNIQUAC) model, Pure Appl. Chem. 77(3) (2005) 531-542.
[13] P. Wang, A. Anderko, R.D. Springer, Modeling phase equilibria and speciation in mixed-solvent electrolyte systems:II. Liquid-liquid equilibria and properties of associating electrolyte solutions, J. Mol. Liquids 125(2006) 37-44.
[14] P. Wang, A. Anderko, R.D. Young, A speciation-based model for mixed-solvent electrolyte systems, Fluid Phase Equilib. 203(2002) 141-176.
[15] C.-C. Chen, H.I. Britt, J.F. Boston, Local composition model for excess Gibbs energy of electrolyte systems. Part I:Single solvent, single completely dissociated electrolyte systems, AIChE J. 28(4) (1982) 588-596.
[16] C.-C. Chen, L.B. Evans, A local composition model for the excess Gibbs energy of aqueous electrolyte systems, AIChE J. 32(3) (1986) 444-454.
[17] Y. Song, C.-C. Chen, Symmetric electrolyte nonrandom two-liquid activity coefficient model, Ind. Eng. Chem. Res. 48(2009) 7788-7799.
[18] K.S. Pitzer, P. Wang, J.A. Rard, S.L. Clegg, Thermodynamics of electrolytes. 13. Ionic strength dependence of higher-order terms; equations for CaCl₂ and MgCl₂, J. Solu. Chem. 28(4) (1999) 265-282.
[19] M.S. Gruszkiewicz, J.M. Simonson, Vapor pressures and isopiestic molalities of concentrated CaCl₂(aq),CaBr₂(aq), and NaCl(aq) to T=523 K, J. Chem. Thermodyn. 37(2005) 906-930.
[20] D.W. Zeng, H.Y. Zhou, W. Voigt, Thermodynamic consistency of solubility and vapor pressure of a binary saturated salt + water system II. CaCl₂+H₂O, Fluid Phase Equilibria. 253(2007) 1-11.
[21] N. Hossain, S.K. Bhattacharia, C.-C. Chen, Temperature dependence of interaction parametersin electrolyte NRTL model, AIChE J. 62(4) (2016) 1244-1253.
[22] Yizhuan Yan, C.-C. Chen, Thermodynamic representation of the NaCl+Na₂SO₄+H₂O system with electrolyte NRTL model, Fluid Phase Equilib. 306(2011) 149-161.
[23] S.K. Bhattacharia, C.-C. Chen, Thermodynamic modeling of KCl+H₂O and KCl+NaCl+H₂O systems using electrolyte NRTL model, Fluid Phase Equilib. 387(2015) 169-177.
[24] S. Tanveer, C.-C. Chen, Thermodynamic modeling of aqueous Ca²⁺-Na⁺-K⁺-Cl^- quaternary system, Fluid Phase Equilib. 409(2016) 193-206.
[25] S. Tanveer, H. Zhou, C.-C. Chen, Thermodynamic model of aqueous Mg²⁺-Na⁺-K⁺-Cl- quaternary system, Fluid Phase Equilibria 437(2017) 56-68.
[26] K.S. Pitzer, J.M. Simonson, Thermodynamics of multicomponent, miscible, ionic systems:theory and equations, J. Phys. Chem. 90(1986) 3005-3009.
[27] Novotnyp Sohnelo, Densities of Aqueous Solutions of Inorganic Substances, ELSEVIER, Amsterdam, 1985.
[28] H.Y. Afeefy, J.F. Liebman, S.E. Stein, Neutral thermochemical data, in:P.J. Linstrom, W.G. Mallard (Eds.), NIST Chemistry WebBook, NIST Standard Reference Database Number 69, National Institute of Standards and Technology, Gaithersburg MD, 2014, p.20899. (retrieved 23.7.2014).
[29] D.D. Wagman, W.H. Evans, V.B. Parker, The NBS Tables of chemical thermodynamic properties. Selected Values for inorganic and C1 and C2 organic substances in SI Units, (Suppl. no. 2) J. Phys. Chem. Ref. (1982) 11.
[30] J.M. Prausnitz, R.N. Lichtenthaler, E.C. Azevedo, Molecular Thermodynamics of FluidPhase Equilibria (3th), Prentice Hall, Englewood Cliffs, New Jersey, 1999.
[31] F. Kuschel, J. Seidel, Osmotic and activity coefficients of aqueous K₂SO₄-MgSO₄ and KCl-MgCl₂ at 25℃, J. Chem. Eng. Data 30(1985) 440-445.
[32] T. Sako, T. Hakuta, H. Yoshitome, Vapor pressures of binary (water-hydrogen chloride,-magnesium chloride, and-calcium chloride) and ternary (water-magnesium chloride-calcium chloride) aqueous solutions, J. Chem. Eng. Data 30(2) (1985) 224-228.
[33] K.R. Patil, A.D. Tripathi, G. Pathak, S.S. Katti, Thermodynamic properties of aqueous electrolyte solutions.2.Vapor pressure of aqueous solutions of NaBr, NaI, KCl, KI, RbCl, CsCl, CsBr, CsI, MgCl₂, CaCl₂, CaBr₂, CaI₂, SrCl₂, SrBr₂, SrI₂, BaCl₂, and BaBr₂, J. Chem. Eng. Data 36(2) (1991) 225-230.
[34] X. Xu, Y. Hu, L. Wu, S. Zhang, Experimental and modeling of vapor-liquid equilibria for electrolyte solution systems, J. Chem. Eng. Data 59(11) (2014) 3741-3748.
[35] I.D. Zaytsev, G.G. Aseyev, Properties of Aqueous Solutions of Electrolytes, CRC Press, Boca Raton, 1992.
[36] L. Zeng, Z. Li, A new process for fuel ethanol dehydration based on modeling the phase equilibria of the anhydrous MgCl₂ ethanol water system, AICHE J. 61(2) (2015) 664-676.
[37] A. Seidell, Solubilities of Inorganic and Metal Organic Compounds, Fourth ed.vol. 1, D.Van Nostrand Company, Inc., Princeton, NJ, 1940387.
[38] G. Perron, J.E. Desnoyers, Apparent molar volumes and heat capacities of alkaline earth chlorides in water at 25℃, Can. J. Chem. 52(1974) 3738-3741.
[39] G. Perron, A. Roux, J.E. Desnoyers, Heat capacities and volumes of NaCl, MgCl₂, CaCl₂, and NiCl₂ up to 6 molal in water, Can. J. Chem. 59(1981) 3049-3054.
[40] S. Likke, L.A. Bromley, Heat capacities of aqueous NaCl, KCl, MgCl₂, MgSO₄ and Na₂SO₄ solutions between 80℃ and 200℃, J. Chem. Eng. Data 18(2) (1973) 189-195.
[41] P.P. Saluja, J.C. LeBlanc, Apparent molar heat capacities and volumes of aqueous solutions of MgCl₂, CaCl₂, and SrCl₂ at elevated temperatures, J. Chem. Eng. Data 32(1) (1987) 72-76.
[42] M.E. Guendouzi, A. Dinane, A. Mounir, Water activities, osmotic and activity coefficients in aqueous chloride solutions at T=298.15 K by the hygrometric method, J. Chem. Thermodyn. 33(2001) 1059-1072.
[43] J.S. Baabor, M.A. Gilchrist, E.J. Delgado, Isopiestic study of (calcium chloride C water) and (calcium chloride C magnesium chloride C water) at T=313.15 K, J. Chem. Thermodyn. 33(2001) 405-411.
[44] R.A. Robinson, R.H. Stokes, Electrolyte Solutions, Dover Publications, Inc., Mineola, NY, 2002.
[45] J.A. Rard, D.G. Miller, Isopiestic determination of the osmotic and activity coefficients of aqueous MgCl₂ solutions at 25℃, J. Chem. Eng. Data 26(1) (1981) 38-43.
[46] M. Jelena, Milica, Osmotic and activity coefficients of[yKCl+(1-y)MgCl₂] (aq) at T=298.15 K, J. Solution Chem 36(2007) 1401-1419.
[47] H.F. Holmes, R.E. Mesmer, Aqueous solutions of the alkaline-earth metal chlorides at elevated temperatures. Isopiesti cmolalities and thermodynamic properties, J. Chem. Thermodyn. 28(1996) 1325-1358.
[48] W.R. Harrison, E.P. Perman, Vapour pressure and heat of dilution of aqueous solutions, Trans. Faraday Soc. 23(1927) 1-22.
[49] J. Ananthaswamy, G. Atkinson, Thermodynamics of concentrated electrolyte mixtures. 5. A review of the thermodynamic properties of aqueous calcium chloride in the temperature range 273.15-373.15 K, J. Chem. Eng. Data. 30(1) (1985) 120-128.
[50] P.P.S. Saluja, D.J. Jobe, J.C. LeBlanc, Apparent molar heat capacities and volumes of mixed electrolytes:[NaCl(aq)+CaCl₂(aq)],[NaCl(aq)+MgCl₂(aq)], and[CaCl₂(aq)+MgCl₂(aq)], J. Chem. Eng. Data 40(2) (1995) 398-406.
[51] J.J. Spitzer, P.P. Singh, K.G. McCurdy, L.G. Hepler, Apparent molar heat capacities and volumes of aqueous electrolytes:CaCl₂, Cd(NO₃)₂, CoCl₂, Cu(ClO₄)₂, Mg(ClO₄)₂, and NiCl₂, J. Solut. Chem. 7(2) (1978) 81-86.
[52] H.F. Holmes, C.F. Baes, R.E. Mesmer, Isopiestic studies of aqueous solutions at elevated temperatures I. KCl,CaCl₂, and MgCl₂, J. Chem. Thermodyn. 10(1978) 983-996.
[53] C.T. Liu, W.T. Lindsay, Thermodynamic Properties of Aqueous Solutions at High temperatures. Final Report to Office of saline Water under Contract 14(01-00D1), OSW Res. And Dev. Prog. Rep. No.722, Washington, 1971(2126).
[54] A.B. Zdanovskii, E.F. Soloveva, E.I. Lyakhovskaya, Experimental Solubility Data on Salt-water systems, Vol. 1:Three-Component Systems, Book 2, 2nd ed, 1973 Khimia, Leningrad.
[55] R.T. Pabalan, K.S. Pitzer, Thermodynamics of concentrated electrolyte mixtures and the prediction of mineral solubilities to high temperatures for mixtures in the system Na-K-Mg-Cl-SO₄-H₂O, Geochim. Cosmochim. Acta 51(9) (1987) 2429-2443.
[56] C. Held, L.F. Cameretti, G. Sadowski, Measuring and modeling activity coefficients in aqueous amino-acid solutions, Ind. Eng. Chem. Res. 50(2011) 131-141.
[57] R.F. Platford, Experimental Methods:Isopiestic, in:Activity Coeffcients in Electrolyte Solutions, CRC Press, Inc., McGraw-Hill, New York, 1995.
[58] M.S. Gruszkiewicz, D.A. Palmer, R.D. Springer, Phase behavior of aqueous Na-K-MgCa-Cl-NO₃ mixtures:Isopiestic measurements and thermodynamic modeling, J. Solut. Chem. 36(6) (2007) 723-765.
[59] K.F. Voitkovskii, Translation of:"the Mechanical Properties of Ice" (in English from Russian), Academy of Sciences (USSR), Archived (PDF) from the Original on 10, February 2017.
[60] I. Barin, O. Knacke, Thermochemical Properties of Inorganic Substances, Springer, Berlin, 1973(Supplement, 1997).
[61] D. Garvin, V.B. Parker, H.J. White Jr., CODATA Thermodynamic Tables. Selections for some Compounds of Calcium and Related Mixtures:A Prototype Set of Tables, Hemisphere, Washington, DC, 1987.
[62] K.S. Pitzer, C.S. Oakes, Thermodynamics of calcium chloride in concentrated aqueous solutions and in crystals, J. Chem. Eng. Data 39(1994) 553-559.
[63] M.E. Guendouzi, R. Azougen, A. Benbiyi, Thermodynamic properties of the mixed electrolyte systems{yMgCl₂+(1-y)NaCl}(aq)and{yMgCl₂+(1-y)CaCl₂}(aq)at 298.15 K, Calphad 29(2005) 114-124.

Thermodynamic modeling and phase diagram prediction of salt lake brine systems. I. Aqueous Mg²⁺-Ca²⁺-Cl^- binary and ternary systems

Thermodynamic modeling and phase diagram prediction of salt lake brine systems. I. Aqueous Mg²⁺-Ca²⁺-Cl^- binary and ternary systems

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