Modeling of the Vapor-Liquid Equilibria Properties of Binary Mixtures for Refrigeration Machinery

Abstract

The presence of both critical and azeotropic states in the vapor-liquid equilibria (VLE) is a very important issue in the chemical and refrigeration engineering. The knowledge of the phase behavior (subcritical phase/supercritical phase) of refrigerant allows designing and optimizing the refrigeration industrials processes. However, it is rare to find data for this information, which poses a great challenge for researchers to develop predictive and correlative thermodynamic models. The present study proposes the computation of the compositions and pressures of critical and azeotropic points of the isothermal VLE as well as the correlation of experimental VLE data. Firstly, experimental data (PTxy) was used to predict the vapor-liquid phase of both critical and azeotropic behaviors and to determine their properties using the relative volatility model. Secondly, the thermodynamic model (PR-MC-WS-NRTL) was applied to correlate the data of the binary refrigerant systems and describe their isothermal (VLE) behavior. The results proved that there is good agreement between predicted values obtained by the developed model and the experimental reference data. The relative error of both critical and azeotropic properties does not exceed 4.3 % for the molar fraction and 7.5 % for the pressure using relative volatility model. On other hand the relative deviation is respectively less than 2.60 % and 2.58 % for the liquid and vapor mole fractions using (PR-MC-WS-NRTL) model. This shows the ability of these models to give a reliable solution to predict and modulate the phase behavior of the binary refrigerant systems.

Keywords

• Binary mixtures
• critical point
• azeotropic point
• relative volatility
• mixing rules

References

1. C. Coquelet, A. Chareton, and D. Richon, “Vapour–liquid equilibrium measurements and correlation of the difluoromethane (R32) + propane (R290) + 1,1,1,2,3,3,3-heptafluoropropane (R227ea) ternary mixture at temperatures from 269.85 to 328.35K,” Fluid Phase Equilib., 218, 209–214, 2004, doi:10.1016/j.fluid.2003.12.009.
2. Y. Maalem, A. Zarfa, Y. Tamene, S. Fedali, and H. Madani, “Prediction of thermodynamic properties of the ternary azeotropic mixtures,” Fluid Phase Equilib., 517, 112613, 2020, doi:10.1016/j.fluid.2020.112613.
3. JM. Calm, “The next generation of refrigerants – Historical review, considerations, and outlook,” Int. J. Refrig., 31,1123–1133, 2008, doi:10.1016/j.ijrefrig.2008.01.013.
4. S. Kato and D. Bluck, “Practical Applications of a Pure Prediction Method for Binary VLE to the Establishment of a High-Precision UNIFAC,” J. Chem. Eng. Data., 61, 4236–4244, 2016, doi:10.1021/acs.jced.6b00593.
5. A. Jakob, H. Grensemann, J. Lohmann, and J. Gmehling, “Further Development of Modified UNIFAC (Dortmund):  Revision and Extension 5,” Ind. Eng. Chem. Res., 45,7924–7933, 2006, doi:10.1021/ie060355c.
6. K. Zheng, H. Wu, C. Geng, G. Wang, Y. Yang, and Y. Li, “ A Comparative Study of the Perturbed-Chain Statistical Associating Fluid Theory Equation of State and Activity Coefficient Models in Phase Equilibria Calculations for Mixtures Containing Associating and Polar Components,” Ind. Eng. Chem. Res., 57, 3014–3030, 2018, doi:10.1021/acs.iecr.7b04758.
7. P. Anila, K. Rayapa Reddy, G. Srinivasa Rao, PVS. Sai Ram, D. Ramachandran, and C. Rambabu, “ Activity coefficients and excess Gibbs energy functions of acetophenone with 1,2-dichloroethane and 1,1,2,2-tetrachloroethane binary mixtures by using NRTL, UNIQUAC, UNIFAC and VAN LAAR models at a local atmospheric pressure of 95.3 kPa,” Karbala Int. J. Mod Sci ., 2, 211–218, 2016, doi:10.1016/j.kijoms.2016.07.001.
8. H. Mokarizadeh, S. Moayedfard, and M. Mozaffarian, “Comparison of MOSCED (NRTL) model results with regular correlative and predictive models based on vapor-liquid equilibrium calculations for azeotropic systems,” Fluid Phase Equilib., 516, 112592, 2020, doi:10.1016/j.fluid.2020.112592.

9. G. Yu, C. Dai, and Z. Lei, “Modified UNIFAC-Lei Model for Ionic Liquid–CH4 Systems,” Ind. Eng. Chem. Res., 57, 7064–7076, 2018, doi:10.1021/acs.iecr.8b00986.
10. AS. Teja and JS. Rowlinson, “The prediction of the thermodynamic properties of fluids and fluid mixtures — IV. Critical and azeotropic states,” Chem. Eng. Sci., 28, 529–538, 1973, doi:10.1016/0009-2509(73)80050-8.
11. S. Artemenko and V. Mazur, “Azeotropy in the natural and synthetic refrigerant mixtures,” Int. J. Refrig.,30,831839,2007,doi:10.1016/j.ijrefrig.2006.11.010.
12. ZT. Fidkowski, MF. Malone, and MF. Doherty, “Computing azeotropes in multicomponent mixtures,” Comput. Chem. Eng.,17,1141–1155, 1993, doi:10.1016/0098-1354(93)80095-5.
13. JE. Tolsma and PI. Barton, “Computation of heteroazeotropes. Part I: Theory,” Chem. Eng. Sci., 55, 3817–3834, 2000, doi:10.1016/S0009-2509(00)00032-4.
14. P. Kolář and K. Kojima, “Prediction of critical points in multicomponent systems using the PSRK group contribution equation of state,” Fluid Phase Equilib., 118,175–200,1996, doi:10.1016/0378 3812(95)02850-1.
15. XQ. Dong, MQ. Gong, Y. Zhang, and JF. Wu, “Prediction of homogeneous azeotropes by Wilson equation for binary HFCs and HCs refrigerant mixtures,” Fluid Phase Equilib., 269, 6–11, 2008, doi:10.1016/j.fluid.2008.04.012.
16. RA. Heidemann and AM. Khalil, “The calculation of critical points,” AIChE .J ., 26, 769–779, 1980, doi:10.1002/aic.690260510.
17. DV. Nichita, “Calculation of critical points using a reduction method,” Fluid Phase Equilib., 228–229, 223–231,2005, doi:10.1016/j.fluid.2004.09.036.
18. RW. Maier, JF. Brennecke, and MA. Stadtherr, “Reliable computation of homogeneous azeotropes,” AIChE. J., 44,1745–1755,1998, doi:10.1002/aic.690440806. M. He, Y. Liu, and X. Liu, “Prediction of critical temperature and critical pressure of multi-component mixtures,” Fluid Phase Equilib., 441, 2–8,2017, doi:10.1016/j.fluid.2016.11.017.
19. P. Hu, Z-S. Chen, and W-L. Cheng, “Prediction of vapor–liquid equilibria properties of several HFC binary refrigerant mixtures,” Fluid Phase Equilib., 204,75–84, 2003, doi: 10.1016/S0378-3812(02)00216-9.
20. X. Dong, M. Gong, Y. Zhang, J. Liu, and J. Wu, “Prediction of Homogeneous Azeotropes by the UNIFAC Method for Binary Refrigerant Mixtures,” J. Chem \& Eng. Data., 55, 52–57, 2010, doi:10.1021/je900693q.
21. S. Fedali, H. Madani, and C. Bougriou, “Prediction method of both azeotropic and critical points of the binary refrigerant mixtures,” J. Appl. Eng. Sci. & Technol., Vol 3 No 1, 2017.
22. G. Silva-Oliver and LA. Galicia-Luna, “Vapor–liquid equilibria for carbon dioxide + 1,1,1,2-tetrafluoroethane (R-134a) systems at temperatures from 329 to 354 K and pressures upto 7.37 MPa,” Fluid Phase Equilib., 199, 213–222, 2002, doi:10.1016/S0378-3812(01)00816-0.
23. D-Y. Peng and DB. Robinson, “A New Two-Constant Equation of State,” Ind. Eng. Chem. Fundam., 15, 59–64, 1976, doi:10.1021/i160057a011.
24. PM. Mathias and TW. Copeman, “Extension of the Peng-Robinson equation of state to complex mixtures: Evaluation of the various forms of the local composition concept,” Fluid Phase Equilib., 13, 91–108, 1983, doi:10.1016/0378-3812(83)80084-3.
25. Dortmund Data Bank (DDB), Version 97, “DDBST Software and Separation Technology GmbH,” Oldenburg, Germany, 1997.
26. DSH. Wong and SI. Sandler, “A theoretically correct mixing rule for cubic equations of state,” AIChE .J., 38, 671–680, 1992, doi:10.1002/aic.690380505.
27. H. Renon and JM. Prausnitz, “Local compositions 1 in thermodynamic excess functions for liquid mixtures,” AIChE .J., 14, 135–144, 1968, doi:10.1002/aic.690140124.
28. S. Wang, R. Fauve, C. Coquelet, A. Valtz, C. Houriez, P-A. Artola, E. El Ahmar, B. Rousseau, and H. Haitao, “Vapor–liquid equilibrium and molecular simulation data for carbon dioxide (CO2) + trans-1,3,3,3-tetrafluoroprop-1-ene (R-1234ze(E)) mixture at temperatures from 283.32 to 353.02 K and pressures up to 7.6 MPa,” Int. J. Refrig., 98, 362–371, 2019, doi:10.1016/j.ijrefrig.2018.10.032.
29. Q. Zhong, X. Dong, Y. Zhao, H. Li, H. Zhang, H. Guo,and M. Gong , “Measurements of isothermal vapour–liquid equilibrium for the 2,3,3,3-tetrafluoroprop-1-ene + propane system at temperatures from 253.150 to 293.150 K,” Int. J. Refrig., 81, 26–32, 2017, doi:10.1016/J.IJREFRIG.2017.05.016.
30. P. Hu, L-X. Chen, and Z-S. Chen, “Vapor–liquid equilibria for binary system of 2,3,3,3-tetrafluoroprop-1-ene (HFO-1234yf) +isobutane (HC-600a),” Fluid Phase Equilib., 365,1–4, 2014, doi:10.1016/j.fluid.2013.12.015.
31. X. Hu, T. Yang, X. Meng, S. Bi, and J. Wu, “Vapor liquid equilibrium measurements for difluoromethane (R32) + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) and fluoroethane (R161) + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf),” Fluid Phase Equilib., 438, 10–17, 2017, doi:10.1016/j.fluid.2017.01.024.
32. T. Yang, X. Hu, X. Meng, and 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.
33. H. Madani, A. Valtz, F. Zhang, J. El Abbadi, C. Houriez, P. Paricaud, and C.Coquelet, “Isothermal vapor-liquid equilibrium data for the trifluoromethane (R23) + 2,3,3,3-tetrafluoroprop-1-ene (R1234yf) system at temperatures from 254 to 348 K,” Fluid Phase Equilib., 415, 158–165, 2016, doi:10.1016/j.fluid.2016.02.005.