流体汽液相平衡混合规则研究进展
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摘要
混合工质汽液相平衡学术内涵丰富且应用广泛,而混合规则是决定混合物性描述准确与否的关键因素。综述了具有代表性的混合规则,包括原始的二次型、非二次型、密度型、状态方程-超额自由能型等混合规则,评价了其在流体汽液相平衡的描述能力,辅以数学推导介绍了其发展的动机及存在的优劣,以期对将来混合规则发展提供思路。
The vapor-liquid phase equilibrium data are the critical thermophysical property in chemistry industry.Since the mixing rules are the key factor to calculate the vapor-liquid equilibrium property of mixtures, they have been studied for more than one hundred years. The representative mixing rules are summarized, including the original quadratic form, non-quadratic type, density type, state equation-excess free energy type and other mixing rules. The ability to describe the vapor-liquid equilibrium in the fluid is evaluated. The mathematical derivation of these mixing rules are given in an understandable way and the motivation of their development and their strengths and weaknesses are analyzed.
The vapor-liquid phase equilibrium data are the critical thermophysical property in chemistry industry.Since the mixing rules are the key factor to calculate the vapor-liquid equilibrium property of mixtures, they have been studied for more than one hundred years. The representative mixing rules are summarized, including the original quadratic form, non-quadratic type, density type, state equation-excess free energy type and other mixing rules. The ability to describe the vapor-liquid equilibrium in the fluid is evaluated. The mathematical derivation of these mixing rules are given in an understandable way and the motivation of their development and their strengths and weaknesses are analyzed.
引文
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[2] Buck E. Applications of phase equilibrium thermodynamics in a US chemical company[C]//Proceedings of Joint CIESC/AIChE Meeting. Beijing:AIChE, 1982.
[3] Van der Waals J. Molekulartheorie eines K?rpers, der aus zwei verschiedenen Stoffen besteht[J]. Z. Phys. Chem(Leipzig)., 1890,5:133-173.
[4] Sengers J V, Kayser R, Peters C, et al. Equations of State for Fluids and Fluid Mixtures[M]. Amsterdam:Elsevier, 2000.
[5] van Laar J. The vapor pressure of binary mixtures[J]. Z. Phys.Chem., 1910, 72:723-751.
[6] Wilson G M. Vapor-liquid equilibrium(Ⅺ):A new expression for the excess free energy of mixing[J]. Journal of the American Chemical Society, 1964, 86(2):127-130.
[7] Renon H, Prausnitz J M. Local compositions in thermodynamic excess functions for liquid mixtures[J]. AIChE Journal, 1968, 14(1):135-44.
[8] Tassios D. Applied Chemical Engineering Thermodynamics[M].Berlin:Springer, 2013.
[9] van der Waals J D. Over de Continuiteit van den Gas-en Vloeistoftoestand[D]. Leiden:Leiden University, 1873.
[10] Peng D Y, Robinson D B. A new two-constant equation of state[J].Industrial&Engineering Chemistry Fundamentals, 1976, 15(1):59-64.
[11] Patel N C, Teja A S. A new cubic equation of state for fluids and fluid mixtures[J]. Chemical Engineering Science, 1982, 37(3):463-473.
[12] Good R J, Hope C J. New combining rule for intermolecular distances in intermolecular potential functions[J]. The Journal of Chemical Physics, 1970, 53(2):540-543.
[13] Lee K H, Sandler S I. The generalized van der Waals partition function(Ⅳ):Local composition models for mixtures of unequalsize molecules[J]. Fluid Phase Equilibria, 1987, 34(2):113-47.
[14] Lorentz H. Ueber die Beziehung zwischen der Fortpflan zungsgesch windigkeit des Lichtes und der K?rperdichte[J].Annalen der Physik, 1880, 245(4):641-665.
[15] Smith W R. Perturbation theory and one-fluid corresponding states theories for fluid mixtures[J]. The Canadian Journal of Chemical Engineering, 1972, 50(2):271-274.
[16] Leland T. Recent Developments in the Theory of Fluid Mixtures[M]//Advances in Cryogenic Engineering. Boston, MA:Springer,1960:466-484.
[17] Leland T, Rowlinson J, Sather G. Statistical thermodynamics of mixtures of molecules of different sizes[J]. Transactions of the Faraday Society, 1968, 64:1447-1460.
[18] Leland T, Rowlinson J, Sather G, et al. Statistical thermodynamics of two-fluid models of mixtures[J]. Transactions of the Faraday Society, 1969, 65:2034-2043.
[19] Kontogeorgis G M, Folas G K. Thermodynamic Models for Industrial Applications:from Classical and Advanced Mixing Rules to Association Theories[M]. Hoboken:John Wiley&Sons,2009.
[20] Hildebrand J H, Prausnitz J M, Scott R L. Regular and Related Solutions:the Solubility of Gases, Liquids, and Solids[M]. New York:Van Nostrand Reinhold, 1970.
[21] Han S, Lin H, Chao K. Vapor-liquid equilibrium of molecular fluid mixtures by equation of state[J]. Chemical Engineering Science, 1988, 43(9):2327-2367.
[22] Zhao Y X, Dong X Q, Zhong Q, et al. Modeling vapor liquid phase equilibrium for Cx Hy+Cx Hy Fz using Peng-Robinson and perturbed-chain SAFT[J]. Industrial&Engineering Chemistry Research, 2017, 56(25):7384-7389.
[23] Adachi Y, Sugie H. Effects of mixing rules on phase equilibrium calculations[J]. Fluid Phase Equilibria, 1985, 24(3):353-362.
[24] Iwai Y, Margerum M R, Lu B C Y. A new three-parameter cubic equation of state for polar fluids and fluid mixtures[J]. Fluid Phase Equilibria, 1988, 42:21-41.
[25] Robinson D B, Peng D Y, Chung S Y. The development of the Peng-Robinson equation and its application to phase equilibrium in a system containing methanol[J]. Fluid Phase Equilibria, 1985,24(1):25-41.
[26]赵延兴.含氨混合工质相平衡及溶油特性研究[D].北京:中国科学院大学, 2017.Zhao Y X. Phase equilibrium and solubility in lubricants for mixed refrigerants of ammonia+hydrocarbon/hydrofluorocarbon[D]. Beijing:University of Chinese Academy of Scienecs, 2017.
[27] Trebble M. Correlation of VLE data for binary mixtures of 1-alkanols and normal hexane with the Trebble-Bishnoi equation of state[J]. Fluid Phase Equilibria, 1988, 42:117-128.
[28] Georgeton G K, Smith R L, Teja A S. Application of cubic equations of state to polar fluids and fluid mixtures[J]. Equations of State, American Chemical Society, 1986:434-451.
[29] Flory P J, Krigbaum W R. Thermodynamics of high polymer solutions[J]. Annual Review of Physical Chemistry, 1951, 2(1):383-402.
[30] Hildebrand J H. The term‘Regular Solution’[J]. Nature, 1951,168(4281):868.
[31] Schwartzentruber J, Renon H, Watanasiri S. Development of a new cubic equation of state for phase equilibrium calculations[J].Fluid Phase Equilibria, 1989, 52:127-134.
[32] Adachi Y, Sugie H. A new mixing rule-modified conventional mixing rule[J]. Fluid Phase Equilibria, 1986, 28(2):103-118.
[33] Panagiotopoulos A, Reid R. New mixing rule for cubic equations of state for highly polar, asymmetric systems[C]//In Equations of State Theories and Applications, ACS Symposium Series 300.Washington:American Chemical Society, 1986:571-582.
[34] Sandoval R, Wilczek-Vera G, Vera J. Prediction of ternary vaporliquid equilibria with the PRSV equation of state[J]. Fluid Phase Equilibria, 1989, 52:119-126.
[35] Stryjek R, Vera J. PRSV-an improved Peng-Robinson equation of state with new mixing rules for strongly nonideal mixtures[J]. The Canadian Journal of Chemical Engineering, 1986, 64(2):334-340.
[36] Stryjek R, Vera J. PRSV2:a cubic equation of state for accurate vapor-liquid equilibria calculations[J]. The Canadian Journal of Chemical Engineering, 1986, 64(5):820-826.
[37] Michelsen M L, Kistenmacher H. On composition-dependent interaction coefficeints[J]. Fluid Phase Equilibria, 1990, 58(1):229-230.
[38] Schwartzentruber J, Renon H. Equations of state:how to reconcile flexible mixing rules, the virial coefficient constraint and the“Michelsen-Kistenmacher syndrome”for multicomponent systems[J]. Fluid Phase Equilibria, 1991, 67:99-110.
[39] Twu C H, Bluck D, Cunningham J R, et al. A cubic equation of state with a new alpha function and a new mixing rule[J]. Fluid Phase Equilibria, 1991, 69:33-50.
[40] Mathias P M, Klotz H C, Prausnitz J M. Equation of state mixing rules for multicomponent mixtures:the problem of invariance[J].Fluid Phase Equilibria, 1991, 67:31-44.
[41] Luedecke D, Prausnitz J M. Phase equilibria for strongly nonideal mixtures from an equation of state with density-dependent mixing rules[J]. Fluid Phase Equilibria, 1985, 22(1):1-19.
[42] Panagiotopoulos A Z. High pressure phase equilibria:experimental and Monte Carlo simulation studies[D].Massachusett:Massachusetts Institute of Technology, 1986.
[43] Wilczek-Vera G, Vera J. A comparative study of mixing rules for cubic equations of state[J]. Fluid Phase Equilibria, 1987, 37:241-253.
[44] Orbey H, Sandler S I. Modeling Vapor-Liquid Equilibria:Cubic Equations of State and Their Mixing Rules[M]. Cambridge:Cambridge University Press, 1998.
[45] Mohamed R S, Holder G D. High pressure phase behavior in systems containing CO2and heavier compounds with similar vapor pressures[J]. Fluid Phase Equilibria, 1987, 32(3):295-317.
[46]左有祥.具有局部组成混合规则的PT状态方程:超临界CO2流体分离分离乙醇水溶液的相平衡计算[J].石油大学学报(自然科学版), 1990, 14(5):56-65.Zuo Y X. P-T equation of state with local composition mixing rules:phase equilibrium calculations for ethanol extraction with supercritical carbon dioxide[J]. Journal of the University of Petroleum, China, 1990, 14(5):56-65.
[47] Melhem G A, Saini R, Goodwin B M. A modified Peng-Robinson equation of state[J]. Fluid Phase Equilibria, 1989, 47(2):189-237.
[48] Huron M J, Vidal J. New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures[J]. Fluid Phase Equilibria, 1979, 3(4):255-271.
[49] Wong D S H, Sandler S I. A theoretically correct mixing rule for cubic equations of state[J]. AIChE Journal, 1992, 38(5):671-680.
[50] Michelsen M L. A method for incorporating excess Gibbs energy models in equations of state[J]. Fluid Phase Equilibria, 1990, 60(1/2):47-58.
[51] Gupte P A, Rasmussen P, Fredenslund A. A new groupcontribution equation of state for vapor-liquid equilibria[J].Industrial&Engineering Chemistry Fundamentals, 1986, 25(4):636-645.
[52] Gani R, Tzouvaras N, Rasmussen P, et al. Prediction of gas solubility and vapor-liquid equilibria by group contribution[J].Fluid Phase Equilibria, 1989, 47(2):133-152.
[53] Huang H, Sandler S I. Prediction of vapor-liquid equilibria at high pressures using activity coefficient parameters obtained from low-pressure data:a comparison of two equation of state mixing rules[J]. Industrial&Engineering Chemistry Research, 1993, 32(7):1498-1503.
[54] Orbey H, Sandler S I. A comparison of various cubic equation of state mixing rules for the simultaneous description of excess enthalpies and vapor-liquid equilibria[J]. Fluid Phase Equilibria,1996, 121(1):67-83.
[55] Lee M T, Lin S T. Prediction of mixture vapor-liquid equilibrium from the combined use of Peng-Robinson equation of state and COSMO-SAC activity coefficient model through the Wong–Sandler mixing rule[J]. Fluid Phase Equilibria, 2007, 254(1):28-34.
[56] Hu P, Chen L X, Chen Z S. Vapor-liquid equilibria for binary system of 2, 3, 3, 3-tetrafluoroprop-1-ene(HFO-1234yf)+isobutane(HC-600a)[J]. Fluid Phase Equilibria, 2014, 365:1-4.
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