Drawing PT-phase envelopes and calculating critical points for multicomponent systems using flash calculations

Objectives. This study aims to draw PT-phase envelopes and calculate the critical points for multicomponent systems using flash calculations.

Methods. Flash calculations with an equation of state and a mixing rule were used to construct phase envelopes for multicomponent systems. In general, the methodology uses the Soave–RedlichKwong equation of state and Van der Waals mixing rules; and the Peng–Robinson equation of state with Wong–Sandler mixing rules and the non-random two-liquid activity coefficient model.

Results. The method was applied to the following mixtures: ethane (1)–butane (2) (four different compositions); ethane (1)–propane (2) (four different compositions); butane (1)–carbon dioxide (2) (three different compositions); C2C3C4C5C6 (one composition); isobutane–methanol–methyl tertbutyl ether–1-butene (one composition); and propylene–water–isopropyl alcohol–diisopropyl ether (one composition).

Conclusions. Our results agreed to a large extent with the experimental data available in the literature. For mixtures that contained CO₂ , the best results were obtained using the PengRobinson equation of state and the Wong–Sandler mixing rules. Our methodology, based on flash calculations, equations of state, and mixing rules, may be viewed as a shortcut procedure for drawing phase envelopes and estimating critical points of multicomponent systems.

1. Michelsen M.L. Calculation of Phase Envelopes and Critical Points for Multicomponent Mixtures. Fluid Phase Equilib. 1980;4(1-2):1-10. https://doi.org/10.1016/0378-3812(80)80001-X

2. Stradi A.B., Brennecke F.J., Khon P.J., Stadtherr A.M. Reliable Computation of Mixture Critical Points. AIChE J. 2001;47(1):212-221. https://doi.org/10.1002/aic.690470121

3. Heidemann R.A., Khalil A.M. The Calculation of Critical Points. AIChE J. 1980;26(5):769-779. https://doi.org/10.1002/aic.690260510

4. Henderson N. Freitas L. Platt M.G. Prediction of Critical Points: a new methodology using global optimization. A. I. Ch. E. Journal. 2004;50(6):1300-1314. https://doi.org/10.1002/aic.10119

5. Freitas L., Platt G., Hénderson N. Novel approach for the calculation of critical points in binary mixtures using global optimization. Fluid Phase Equilib. 2004;225:29-37. https://doi.org/10.1016/j.fluid.2004.06.063

6. Justo-García D.N., García-Sanchez F. Cálculo de Puntos Críticos de sistemas multicomponentes utilizando optimización golbal. XX Congreso Nacional de Termodinámica. Apizaco, Tlaxcala, 5–9 de Septiembre de 2005. P. 342-366 (in Spanish).

7. Sánchez-Mares F., Bonilla-Petriciolet A. Cálculo de Puntos Críticos empleando una estrategia de optimización global estocástica. Afinidad. 2005;63(525):396-403 (in Spanish).

8. Goffe W.L, Ferrier G.D., Rogers J. Global Optimization of statistical functions with simulated annealing. J. Econometrics. 1994;60(1-2):65-99. https://doi.org/10.1016/0304-4076(94)90038-8

9. Corana A., Marchesi M., Martini C., Ridella S. Minimizing multimodal functions of continuous variables with simulated annealing algorithm. ACM Trans. Math. Software. 1987;13(3):262-280. http://dx.doi.org/10.1145/29380.29864

10. Tabrizi F.F., Nasrifar Kh. Application of predictive equations of state in calculating natural gas phase envelopes and critical points. Journal of Natural Gas Science and Engineering. 2010;2(1):21-28. https://doi.org/10.1016/j.jngse.2009.12.005

11. Cardona C.A., Sánchez C.A., Gutiérrez L.F. Destilación Reactiva: Análisis y Diseño Básico. Manizales, Colombia: Universidad Nacional de Colombia; 2007 (in Spanish).

12. Reid R.C., Prausnitz J.M., Poling B.E. The Properties of Gases and Liquids. 4th Edition. New York: McGraw-Hill; 1987. 741 p.

13. Justo-García D.N., García-Sánchez F., Díaz-Ramírez N.L., Romero-Martínez A. Calculation of critical points for multicomponent mixtures containing hydrocarbon and nonhydrocarbon components with the PC-SAFT equation of state. Phase Fluid Equilib. 2008;265:192-194. https://doi.org/10.1016/j.fluid.2007.12.006

14. Jun Cai, Ying Hu, Prausnitz J.M. Simplified critical-point criteria for some multicomponent systems. Chem. Eng. Sci. 2010;65(8):2443-2453. https://doi.org/10.1016/j.ces.2009.11.024

15. Akasaka R. Calculation of the critical point for mixtures using mixture models based on Helmholtz energy equations of state. Fluid Phase Equilib. 2008;263(1):102-108. https://doi.org/10.1016/j.fluid.2007.10.007

16. Alfradique M.F., Castier M. Critical points of hydrocarbon mixtures with the Peng-Robinson, SAFT, and PC-SAFT equations of state. Fluid Phase Equilib. 2007;257(1):78-101. https://doi.org/10.1016/j.fluid.2007.05.012

17. Horstman S., Fisher K., Gahmeling J. Experimental determination of critical points of pure components and binary mixtures using a flow apparatus. Chem. Eng. Technol. 1999;22(10):839-842. https://doi.org/10.1002/(SICI)1521-4125(199910)22:10<839::AID-CEAT839>3.0.CO;2-L

18. Chien-Bin Soo, Thévenau P., Coqulet C., Ramjugernath D., Richon D. Determination of critical points of pure and multicomponent mixtures using a “dynamic-synthetic” apparatus. J. of Supercritical Fluids. 2010;55(2):545-553. https://doi.org/10.1016/j.supflu.2010.10.022

19. Holland Ch.D. Fundamentos de destilación de mezclas multicomponentes. Limusa, Noriega Editores; 1992. 200 p. (in Spanish).

20. Seader J.D, Henley E.J. Separation Process Principles. 2nd Edition. John Wiley and Sons, Inc; 2006. 800 p.

21. Smith J.M., Van Ness H.C., Abbott M.M. Introducción a la Termodinámica en Ingeniería Química. McGraw-Hill; 2007. 836 p. (in Spanish).

22. Peng D., Robinson D.D. A New Two-Constant Equation of State. Ind. Eng. Chem. Fund. 1976;15(1):59-64. https://doi.org/10.1021/i160057a011

23. Tester J.W., Modell M. Thermodynamics and Its Applications, 3rd Edition. Prentice Hall. 1996; 960 p.