Document Type: Research Paper

**Authors**

Persian Gulf University

**Abstract**

In this work, an equation of state has been utilized for thermodynamic modeling of aqueous electrolyte solutions. The proposed equation of state is a combination of simplified statistical associating fluid theory (SAFT) equation of state (similar to simplified PC-SAFT) to describe the effect of short-range interactions and mean spherical approximation (MSA) term to describe the effect of long-range interactions. In this model, the salt- based approach or restricted primitive model has been used to adjust the four parameters of the model. The salt (ion) parameters have been estimated through simultaneous fitting to experimental mean ionic activity coefficient and liquid density data of strong electrolytes. Four strong electrolytes, three 1:1 and one 1:2 electrolytes have been used. Using adjusted ion parameters, osmotic coefficient of solvent has been predicted with 0.79% average relative deviation (ARD%). Results show that simplified SAFT, in combination with the MSA term has ARD% about 1% and less for correlating of density and mean ionic activity coefficient of electrolyte solutions.

**Keywords**

Full Text

[1] P. Debye, E. HuÌˆckel, “Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen,” *Phys. Z.*, vol. 24, pp. 185−206, 1923.

[2] L. Blum, “Mean Spherical Model for Asymmetric Electrolytes I. Method of Solution,” *Mol. Phys.*, vol. 30, pp. 1529−1535, 1975.

[3] L. Blum, J.S. Hoye, “Mean Spherical Model for Asymmetric Electrolytes. 2. Thermodynamic Properties and the Pair Correlation Function,”* J. Phys. Chem.*, vol. 81, pp. 1311−1316, 1977.

[4] C.-C. Chen, H.I. Britt, J.F. Boston, L.B. Evans, “Local composition model for excess Gibbs energy of electrolyte systems. Part I: Single solvent, single completely dissociated electrolyte systems,”* AIChE Journal*, vol. 28, pp. 588-596, 1982.

[5] A. Haghtalab, S.H. Mazloumi, “A nonelectrolyte local composition model and its application in the correlation of the mean activity coefficient of aqueous electrolyte solutions,”* Fluid Phase Equilibria*, vol. 275, pp. 70-77, 2009.

[6] A. Haghtalab, K. Peyvandi, “Electrolyte-UNIQUAC-NRF model for the correlation of the mean activity coefficient of electrolyte solutions,”* Fluid Phase Equilibria*, vol. 281, pp. 163-171, 2009.

[7] C.-C. Chen, P.M. Mathias, H. Orbey, “Use of hydration and dissociation chemistries with the electrolyte–NRTL model,”* AIChE Journal*, vol. 45, pp. 1576-1586, 1999.

[8] C.-C. Chen, L.B. Evans, “A local composition model for the excess Gibbs energy of aqueous electrolyte systems,”* AIChE Journal*, vol. 32, pp. 444-454, 1986.

[9] J. Li, Y. Lin, J. Gmehling, “gE Model for Single- and Mixed-Solvent Electrolyte Systems. 3. Prediction of Salt Solubilities in Aqueous Electrolyte Systems,”* Industrial & Engineering Chemistry Research*, vol. 44, pp. 1602-1609, 2005.

[10] B. Mock, L.B. Evans, C.-C. Chen, “Thermodynamic representation of phase equilibria of mixed-solvent electrolyte systems,”* AIChE Journal*, vol. 32, pp. 1655-1664, 1986.

[11] C.S. Lee, S.B. Park, Y.S. Shim, “A Unified and Predictive Model for Mixed-Electrolyte, Aqueous Mixed-Solvent Systems Using Parameters for Ions and Solvents,”* Industrial & Engineering Chemistry Research*, vol. 35, pp. 4772-4780, 1996.

[12] A. Rastogi, D. Tassios, “Thermodynamics of a single electrolyte in a mixture of two solvents,”* Industrial & Engineering Chemistry Research*, vol. 26, pp. 1344-1351, 1987.

[13] A. Mohs, J. Gmehling, “A revised LIQUAC and LIFAC model (LIQUAC*/LIFAC*) for the prediction of properties of electrolyte containing solutions,”* Fluid Phase Equilibria*, vol. 337, pp. 311-322, 2013.

[14] H. Planche, H. Renon, “Mean Spherical Approximation Applied to a Simple but Non-primitive Model of Interaction for Electrolyte Solutions and Polar Substances,”* J. Phys. Chem.*, vol. 5, pp. 3924−3929, 1981.

[15] W. Fürst, H. Renon, “Representation of excess properties of electrolyte solutions using a new equation of state,”* AIChE Journal*, vol. 39, pp. 335-343, 1993.

[16] J.A. Myers, S.I. Sandler, R.H. Wood, “An Equation of State for Electrolyte Solutions Covering Wide Ranges of Temperature, Pressure, and Composition,”* Industrial & Engineering Chemistry Research*, vol. 41, pp. 3282-3297, 2002.

[17] M.A. Clarke, P.R. Bishnoi, “Development of a new equation of state for mixed salt and mixed solvent systems, and application to vapour–liquid and solid (hydrate)–vapour–liquid equilibrium calculations,”* Fluid Phase Equilibria*, vol. 220, pp. 21-35, 2004.

[18] A. Haghtalab, S.H. Mazloumi, “A square-well equation of state for aqueous strong electrolyte solutions,”* Fluid Phase Equilibria*, vol. 285, pp. 96-104, 2009.

[19] J. Wu, J.M. Prausnitz, “Phase Equilibria for Systems Containing Hydrocarbons, Water, and Salt: An Extended Peng−Robinson Equation of State,”* Industrial & Engineering Chemistry Research*, vol. 37, pp. 1634-1643, 1998.

[20] Y. Lin, K. Thomsen, J.-c. de Hemptinne, “Multicomponent equations of state for electrolytes,”* AIChE Journal*, vol. 53, pp. 989-1005, 2007.

[21] R. Inchekel, J.-C. de Hemptinne, W. Fürst, “The simultaneous representation of dielectric constant, volume and activity coefficients using an electrolyte equation of state,”* Fluid Phase Equilibria*, vol. 271, pp. 19-27, 2008.

[22] E. Collinet, J. Gmehling, “Prediction of phase equilibria with strong electrolytes with the help of the volume translated Peng-Robinson group contribution equation of state (VTPR),”* Fluid Phase Equilibria*, vol. 246, pp. 111-118, 2006.

[23] A. Galindo, A. Gil-Villegas, G. Jackson, A.N. Burgess, “SAFT-VRE: Phase Behavior of Electrolyte Solutions with the Statistical Associating Fluid Theory for Potentials of Variable Range,”* The Journal of Physical Chemistry B*, vol. 103, pp. 10272-10281, 1999.

[24] B.H. Patel, P. Paricaud, A. Galindo, G.C. Maitland, “Prediction of the Salting-Out Effect of Strong Electrolytes on Water + Alkane Solutions,”* Industrial & Engineering Chemistry Research*, vol. 42, pp. 3809-3823, 2003.

[25] B. Behzadi, B.H. Patel, A. Galindo, C. Ghotbi, “Modeling electrolyte solutions with the SAFT-VR equation using Yukawa potentials and the mean-spherical approximation,”* Fluid Phase Equilibria*, vol. 236, pp. 241-255, 2005.

[26] S.P. Tan, H. Adidharma, M. Radosz, “Statistical Associating Fluid Theory Coupled with Restricted Primitive Model To Represent Aqueous Strong Electrolytes,”* Industrial & Engineering Chemistry Research*, vol. 44, pp. 4442-4452, 2005.

[27] X. Ji, S.P. Tan, H. Adidharma, M. Radosz, “SAFT1-RPM Approximation Extended to Phase Equilibria and Densities of CO2−H2O and CO2−H2O−NaCl Systems,”* Industrial & Engineering Chemistry Research*, vol. 44, pp. 8419-8427, 2005.

[28] S.P. Tan, X. Ji, H. Adidharma, M. Radosz, “Statistical Associating Fluid Theory Coupled with Restrictive Primitive Model Extended to Bivalent Ions. SAFT2: 1. Single Salt + Water Solutions,”* The Journal of Physical Chemistry B*, vol. 110, pp. 16694-16699, 2006.

[29] X. Ji, S.P. Tan, H. Adidharma, M. Radosz, “Statistical Associating Fluid Theory Coupled with Restrictive Primitive Model Extended to Bivalent Ions. SAFT2: 2. Brine/Seawater Properties Predicted,”* The Journal of Physical Chemistry B*, vol. 110, pp. 16700-16706, 2006.

[30] X. Ji, H. Adidharma, “Ion-Based SAFT2 to Represent Aqueous Single- and Multiple-Salt Solutions at 298.15 K,”* Industrial & Engineering Chemistry Research*, vol. 45, pp. 7719-7728, 2006.

[31] X. Ji, H. Adidharma, “Ion-Based Statistical Associating Fluid Theory (SAFT2) to Represent Aqueous Single-Salt Solutions at Temperatures and Pressures up to 473.15 K and 1000 bar,”* Industrial & Engineering Chemistry Research*, vol. 46, pp. 4667-4677, 2007.

[32] L.F. Cameretti, G. Sadowski, J.M. Mollerup, “Modeling of Aqueous Electrolyte Solutions with Perturbed-Chain Statistical Associated Fluid Theory,”* Industrial & Engineering Chemistry Research*, vol. 44, pp. 3355-3362, 2005.

[33] C. Held, L.F. Cameretti, G. Sadowski, “Modeling aqueous electrolyte solutions: Part 1. Fully dissociated electrolytes,”* Fluid Phase Equilibria*, vol. 270, pp. 87-96, 2008.

[34] J. Rozmus, J.-C. de Hemptinne, A. Galindo, S. Dufal, P. Mougin, “Modeling of Strong Electrolytes with ePPC-SAFT up to High Temperatures,”* Industrial & Engineering Chemistry Research*, vol. 52, pp. 9979-9994, 2013.

[35] N. Von Solms, M.L. Michelsen, G.M. Kontogeorgis, “Computational and Physical Performance of a Modified PC-SAFT Equation of State for Highly Asymmetric and Associating Mixtures,”* Ind. Eng. Chem. Res.*, vol. 42, pp. 1098-1105, 2003.

[36] G.A. Mansoori, N.F. Carnahan, K.E. Starling, T.W. Leland, “Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres,”* J. Chem. Phys.*, vol. 54, pp. 1523-1525, 1971.

[37] S.S. Chen, A. Kreglewski, “Applications of the Augmented van der Waals Theory of Fluids. I. Pure Fluids.,”* Ber. Bunsen-Ges. Phys. Chem.*, vol. 81, pp. 1048-1052, 1977.

[38] W.G. Chapman, K.E. Gubbins, G. Jackson, M. Radosz, “New reference equation of state for associating liquid,”* Ind. Eng. Chem. Res.*, vol. 29, pp. 1709-1721, 1990.

[39] S.P. Tan, H. Adidharma, M. Radosz, “Statistical Associating Fluid Theory Coupled with Restricted Primitive Model To Represent Aqueous Strong Electrolytes,”* Ind. Eng. Chem. Res.*, vol. 44, pp. 4442− 4452, 2005.

[40] J.P. Wolbach, S.I. Sandler, “Using Molecular Orbital Calculations To Describe the Phase Behavior of Hydrogen-Bonding Fluids,”* Ind. Eng. Chem. Res.*, vol. 36, pp. 4041-4051, 1997.

[41] D. Archer, “Thermodynamic Properties of the NaCl+H2O System. II. Thermodynamic Properties of the NaCl(aq), NaCl-H2O(cr), and Phase Equilibria.,”* J. Phys. Chem. Ref. Data*, vol. 21, 1992.

[42] 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*, vol. 30, 1985.

[43] W.J. Hamer, Y.C. Wu, “Osmotic coefficients and mean activity coefficients of uni-univalent electrolytes in water at 25°C,”* J. Phys. Chem. ref. Data*, vol. 1, pp. 1047-1110, 1972.

[44] D. Archer, “Thermodynamic Properties of the NaBr+H2O System,”* J. Phys. Chem. Ref. Data*, vol. 20, 1992.

Volume 4, Number 1

Summer and Autumn 2017

Pages 69-84