chemicallytechFine Chemical TechnologiesТонкие химические технологии2410-65932686-7575MIREA – Russian Technological University (RTU MIREA).10.32362/2410-6593-2020-15-1-46-54chemicallytech-1587Research ArticleTHEORETICAL BASIS OF CHEMICAL TECHNOLOGYТЕОРЕТИЧЕСКИЕ ОСНОВЫ ХИМИЧЕСКОЙ ТЕХНОЛОГИИDrawing PT-phase envelopes and calculating critical points for multicomponent systems using flash calculationsПостроение PT-фазовых диаграмм и расчет критических точек для многокомпонентных систем с использованием флэш-вычисленийhttps://orcid.org/0000-0002-6706-8179ТороЛ. А.ToroL. A.latoroc@unal.edu.coНациональный университет Колумбии; Автономный университет МанизалесаРоссияNational University of Colombia; Autonomous University of ManizalesRussian Federation2020210320201514654Copyright © Toro L.A., 20202020Торо Л.А.Toro L.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.finechem-mirea.ru/jour/article/view/1587Objectives

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

Methods

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

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

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.

Цели

Цели. Построение PT-фазовых диаграмм и расчет критических точек для многокомпонентных систем с использованием флэш-вычислений.

Методы

Методы. Для построения фазовых диаграмм многокомпонентных систем использовали флэш-вычисления на основе уравнения состояния и правила смешения. В общем случае методология использует уравнение состояния Соаве–Редлиха–Квонга и правило смешения Ван дер Ваальса; уравнение состояния Пенга–Робинсона и правило смешения ВонгаСэндлера, а также неслучайная двужидкостная модель активных коэффициентов. Результаты. Метод был применен к следующим смесям: этан (1)–бутан (2) (четыре разных состава); этан (1)–пропан (2) (четыре разных состава); бутан (1)–диоксид углерода (2) (три разных состава); C2C3C4C5C6 (один состав); изобутан–метанол–метил-трет-бутиловый эфир–1-бутен (один состав); и пропилен–вода–изопропиловый спирт–диизопропиловый эфир (ДИПЭ) (один состав).

Выводы

Выводы. Согласно нашим результатам, метод флэш-вычислений, базирующийся на уравнении состояния и правилах смешения, используемый для построения фазовых диаграмм, на основе которых проводится оценка критических точек для многокомпонентных смесей, хорошо согласуется с экспериментальными данными, имеющимися в литературе. Для смесей, содержащих CO2 , лучшие результаты получены с использованием уравнения состояния Пенга–Робинсона и правила смешения Вонга–Сэндлера.

флэш-вычислениякритические точкифазовые диаграммыflash calculationscritical pointsphase envelopesThis article has been edited for English language and spelling by Enago, an editing brand of Crimson Interactive Inc.ReferencesMichelsen 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-XMichelsen 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-XStradi 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.690470121Stradi 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.690470121Heidemann R.A., Khalil A.M. The Calculation of Critical Points. AIChE J. 1980;26(5):769-779. https://doi.org/10.1002/aic.690260510Heidemann R.A., Khalil A.M. The Calculation of Critical Points. AIChE J. 1980;26(5):769-779. https://doi.org/10.1002/aic.690260510Henderson 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.10119Henderson 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.10119Freitas 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.2004.06.063Freitas 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.2004.06.063Justo-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).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).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).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).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)90038-8Goffe 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)90038-8Corana 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/10.1145/29380.29864Corana 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/10.1145/29380.29864Tabrizi 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.2009.12.005Tabrizi 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.2009.12.005Cardona C.A., Sánchez C.A., Gutiérrez L.F. Destilación Reactiva: Análisis y Diseño Básico. Manizales, Colombia: Universidad Nacional de Colombia; 2007 (in Spanish).Cardona C.A., Sánchez C.A., Gutiérrez L.F. Destilación Reactiva: Análisis y Diseño Básico. Manizales, Colombia: Universidad Nacional de Colombia; 2007 (in Spanish).Reid R.C., Prausnitz J.M., Poling B.E. The Properties of Gases and Liquids. 4th Edition. New York: McGraw-Hill; 1987. 741 p.Reid R.C., Prausnitz J.M., Poling B.E. The Properties of Gases and Liquids. 4th Edition. New York: McGraw-Hill; 1987. 741 p.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.2007.12.006Justo-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.2007.12.006Jun 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.2009.11.024Jun 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.2009.11.024Akasaka 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.2007.10.007Akasaka 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.2007.10.007Alfradique 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.2007.05.012Alfradique 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.2007.05.012Horstman 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-LHorstman 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-LChien-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.2010.10.022Chien-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.2010.10.022Holland Ch.D. Fundamentos de destilación de mezclas multicomponentes. Limusa, Noriega Editores; 1992. 200 p. (in Spanish).Holland Ch.D. Fundamentos de destilación de mezclas multicomponentes. Limusa, Noriega Editores; 1992. 200 p. (in Spanish).Seader J.D, Henley E.J. Separation Process Principles. 2nd Edition. John Wiley and Sons, Inc; 2006. 800 p.Seader J.D, Henley E.J. Separation Process Principles. 2nd Edition. John Wiley and Sons, Inc; 2006. 800 p.Smith J.M., Van Ness H.C., Abbott M.M. Introducción a la Termodinámica en Ingeniería Química. McGraw-Hill; 2007. 836 p. (in Spanish).Smith J.M., Van Ness H.C., Abbott M.M. Introducción a la Termodinámica en Ingeniería Química. McGraw-Hill; 2007. 836 p. (in Spanish).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/i160057a011Peng 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/i160057a011Tester J.W., Modell M. Thermodynamics and Its Applications, 3rd Edition. Prentice Hall. 1996; 960 p.Tester J.W., Modell M. Thermodynamics and Its Applications, 3rd Edition. Prentice Hall. 1996; 960 p.

The authors declare that there are no conflicts of interest present.