Calculation of Azeotropic Properties for Ternary Mixtures with the PC-SAFT Equation of State

Abstract

In this study, a novel approach employing the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) Equation of State was introduced to investigate azeotropic behavior in ternary mixtures and explore their liquid-vapor equilibria. The temperature range spans (243.15323.5) K, covering a broad spectrum of conditions relevant to industrial and chemical processes. Our analysis focuses on six different ternary mixtures: Difluoromethane (R32) + 1,1-difluoroethane (R152a) + 2,3,3,3-tetrafluoropro-1-ene (R1234yf); Isobutane (R600a) + 1,1-difluoroethane (R152a) + 1,1,2,2-tetrafluoroethane (R134); 1,1,1,2-tetrafluoroethane (R134a) + 2,3,3,3-tetrafluoropro-1-ene (R1234yf) + isobutane (R600a); 1,1,1,2-tetrafluoroethane (R134a) + 2,3,3,3-tetrafluoropro-1-ene (R1234yf) + dimethyl ether (DME); isobutene (R600a) + 1,3,3,3-tetrafluoropropene (R12345ze(E)) + trifluoroiodomethane (R13I1); and difluoromethane (R32) + fluoroethane (R161) + 1,3,3,3-tetrafluoropropene (R1234ze(E)). Among these, only three mixtures exhibit azeotropic behavior. The PC-SAFT equation of state, incorporating an expansion form tailored for Vapor-Liquid Equilibrium (VLE) calculations within ternary mixtures, determined azeotropic composition and pressure based on the Gibbs-Konovalov theorem, which characterizes azeotropic behavior under constant temperature. Our estimations of the VLE and azeotropic composition and pressure closely align with experimental data. The maximum relative error in pressure does not exceed 4.2% for the R600a + R152a + R134 mixture and remains less than 6.56% for the liquid composition of R1234ze(E) within the (R600a + R1234ze(E) + R13I1) ternary mixture. These results underscore the reliability and accuracy of the PC-SAFT equation of state in modeling azeotropes within ternary mixtures.

Keywords

• Ternary mixture
• Azeotrope
• PC-SAFT
• Equation of state.

References

1. J. Gross and G. Sadowski, “Application of perturbation theory to a hard-chain reference fluid: an equation of state for square-well chains,” Fluid Phase Equilib., 168, 183–199, 2000, doi: 10.1016/S0378-3812(00)00302-2.
2. J. Gross and G. Sadowski, “Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules,” Ind. Eng. Chem. Res., 40, 1244–1260, 2001, doi: 10.1021/ie0003887.
3. S. H. Huang and M. Radosz, “Equation of state for small, large, polydisperse, and associating molecules,” Ind. Eng. Chem. Res., 29, 2284–2294, 1990, doi:10.1021/ie00107a014.
4. S. H. Huang and M. Radosz, “Equation of state for small, large, polydisperse, and associating molecules: extension to fluid mixtures,” Ind. Eng. Chem. Res., 30, 1994–2005, 1991, doi: 10.1021/ie00056a050.
5. T. Kraska and K. E. Gubbins, “Phase Equilibria Calculations with a Modified SAFT Equation of State. 1. Pure Alkanes, Alkanols, and Water,” Ind. Eng. Chem. Res., 35, 4727–4737, 1996, doi: 10.1021/ie9602320.
6. A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, “Statistical associating fluid theory for chain molecules with attractive potentials of variable range,” J. Chem. Phys., 106, 4168–4186, 1997, doi: 10.1063/1.473101.
7. A. G. Lowri, A. D. Alej, “The thermodynamics of mixtures and the corresponding mixing rules in the SAFT-VR approach for potentials of variable range,” Mol. Phys., 93, 241–252, 1998, doi: 10.1080/002689798169249.
8. J. B. Felipe, F. V. Lourdes, “Prediction of Binary and Ternary Diagrams Using the Statistical Associating Fluid Theory (SAFT) Equation of State,” Ind. Eng. Chem. Res., 37, 660–674, 1998.

9. Y.-H. Fu, S. I. Sandler, “A Simplified SAFT Equation of State for Associating Compounds and Mixtures,” Ind. Eng. Chem. Res., 34, 1897–1909, 1995, doi: 10.1021/ie00044a042.
10. G. M. Kontogeorgis, E. C. Voutsas, I. V. Yakoumis, D. P. Tassios, “An Equation of State for Associating Fluids,” Ind. Eng. Chem. Res., 35, 4310–4318, 1996, doi: 10.1021/ie9600203.
11. Ii. Polishuk, “Generalization of SAFT + Cubic equation of state for predicting and correlating thermodynamic properties of heavy organic substances,” J. Supercrit. Fluids, 67, 94–107, 2012, doi: 10.1016/j.supflu.2012.02.009.
12. E. K. Karakatsani, T. Spyriouni, and I. G. Economou, “Extended statistical associating fluid theory (SAFT) equations of state for dipolar fluids,” AIChE Journal, 51, 2328–2342, 2005, doi: 10.1002/aic.10473.
13. J. A. Barker, D. Henderson, “Perturbation Theory and Equation of State for Fluids. II. A Successful Theory of Liquids,” J. Chem. Phys., 47, 4714–4721, 1967, doi: 10.1063/1.1701689.
14. Y. Maalem, A. Zarfa, Y. Tamene, S. Fedali, H. Madani, “Prediction of thermodynamic properties of the ternary azeotropic mixtures,” Fluid Phase Equilib., 517, 112613, 2020, doi: 10.1016/j.fluid.2020.112613.
15. B. Bentama, H. Grine, I. Anoune, H. Madani, C. Bougriou, “Calculation of azeotropic properties for binary mixtures with the PC-SAFT equation of state,” Fluid Phase Equilib., 565, 113631, 2023, doi: 10.1016/j.fluid.2022.113631.
16. L. A. Serafimov, O. B. Razova, A. V. Frolkova, T. V. Chelyuskina, “The Gibbs-Konovalov law at simple singular points of two-phase multicomponent system diagrams,” Russ. J. of Phys. Chem. A, 82, 946–950, 2008, doi: 10.1134/S0036024408060149.
17. I. Anoune, Z. Mimoune, H. Madani, A. Merzougui, “New modified PC-SAFT pure component parameters for accurate VLE and critical phenomena description,” Fluid Phase Equilib., 532, 112916, 2021, doi: 10.1016/j.fluid.2020.112916.
18. T. Yang, X. Hu, X. Meng, J. Wu, “Vapor–Liquid Equilibria for the Binary and Ternary Systems of Difluoromethane (R32), 1,1-Difluoroethane (R152a), and 2,3,3,3-Tetrafluoroprop-1-ene (R1234yf),” J. Chem. Eng. Data, 63, 771–780, 2018, doi: 10.1021/acs.jced.7b00950.
19. X. Hu, T. Yang, X. Meng, J. Wu, “Isothermal vapor liquid equilibrium measurements for difluoromethane (R32) + fluoroethane (R161) + trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) ternary mixtures,” Int. J. Refrig., 79, 49–56, 2017, doi: 10.1016/j.ijrefrig.2017.04.019.
20. Y. Zhao et al., “Vapor Liquid Phase Equilibrium for Azeotropic Isobutane + trans -1,3,3,3-Tetrafluoropropene + Trifluoroiodomethane System at Temperatures from 243.150 to 283.150 K,” J. Chem. Eng. Data, 63, 812–821, 2018, doi: 10.1021/acs.jced.7b00964.
21. P. Hu, W.-B. Zhu, L.-X. Chen, X.-D. Cai, Z.-S. Chen, “Vapor–liquid equilibria measurements of 1,1,1,2-tetrafluoroethane (HFC-134a)+2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf)+isobutane (HC-600a) ternary system,” Fluid Phase Equilib., 414, 111–116, 2016, doi: 10.1016/j.fluid.2016.01.028.
22. X. Han, Z. Gao, J. Lei, B. Yang, Y. Zhao, G. Chen, “Isothermal Vapor–Liquid Equilibrium of the Ternary Mixture of 1,1,1,2-Tetrafluoroethane + 2,3,3,3-Tetrafluoroprop-1-ene + Dimethyl Ether at Temperatures from 253.15 K to 323.15 K,” J. Chem. Eng. Data, 60, 2219–2225, 2015, doi: 10.1021/je501167d.
23. Y. Zhao, M. Gong, X. Dong, H. Guo, J. Wu, “The investigation on the vapor + liquid equilibrium for the ternary mixture isobutene (R600a) + 1,1-difluoroethane (R152a) + 1,1,2,2-tetrafluoroethane (R134) at temperatures from 253.150 to 273.150 K,” Fluid Phase Equilib., 408, 72–78, 2016, doi: 10.1016/j.fluid.2015.08.020.