Calculation and application of model-free methods in vapor-liquid phase equilibrium

doi:10.11949/j.issn.0438-1157.20161302

Abstract

Abstract:

Calculation of vapor-liquid phase equilibrium was the foundation for development and design optimization of chemical processes.Focal point of the calculation was to determine relationship between four variables of temperature T, pressure p, liquid phase composition x and vapor phase composition y in any vapor-liquid phase equilibrium system.Among these four variables, it was difficult to accurately measure vapor phase composition y, especially at low vapor concentration.Therefore, y was generally calculated by thermodynamic methods after experimental determination of p, T and x.Such methods could be divided into model and model-free methods, which model-free methods got academic attractions as a result of no need to consider application limitations of various activity coefficient models.Through analysis of principles of model-free methods, recent progress with an emphasis on applicable system, convergence rate and calculation accuracy was summarized and compared from the viewpoint of direct and indirect technique.The application of several common methods was discussed and the future research of model-free methods was forecasted.

Key words: phase equilibrium, composition, thermodynamics, model-free method, prediction

摘要：

汽液相平衡计算是化工过程开发及优化设计的基础。汽液相平衡计算的核心是确定体系处于平衡状态时，温度T、压力p、液相组成x及汽相组成y 4个变量之间的关系。在这4个变量中，汽相组成一般难以准确测定，低浓度汽相组成的测定偏差更为明显，因此一般实验测定T、p、x，用热力学方法推算y。由T、p、x数据推算y的方法分为模型法和无模型法两种，无模型法由于不需要考虑各种活度系数模型的使用限制条件而备受国内外学者的关注。通过分析无模型法的原理，按照直接法和间接法两部分对目前无模型法的发展历程进行归纳综述，着重比较了各方法的适用体系、收敛速度和计算精度等方面，总结了几种常用方法的应用情况，并对无模型法未来的研究方向进行了展望。

关键词: 相平衡, 组成, 热力学, 无模型法, 预测

CLC Number:

TQ013.1

XIANG Shuguang, YU Mengmeng, WANG Jianping, SUN Xiaoyan. Calculation and application of model-free methods in vapor-liquid phase equilibrium[J]. CIESC Journal, 2017, 68(1): 1-7.

项曙光, 于萌萌, 王建平, 孙晓岩. 汽液相平衡中无模型法的计算及应用[J]. 化工学报, 2017, 68(1): 1-7.

References 39

[1]	郭克群. 相平衡数据库软件开发[D]. 青岛:青岛科技大学, 2012. GUO K Q. The development of phase equilibrium database software[D]. Qingdao:Qingdao University of Science and Technology, 2012.
[2]	胡萍, 俞慧芳, 崔秀丽, 等. 汽液相平衡研究进展[J]. 化工科技, 2006, 14(2):70-74. HU P, YU H F, CUI X L, et al. Research advance on the vapor-Iiquid equilibrium[J]. Science & Technology in Chemical Industry, 2006, 14(2):70-74.
[3]	胡英. 近代化工热力学应用研究的新进展[M]. 上海:上海科学技术文献出版社, 1994. HU Y. New Progress in Research of Modern Chemical Engineering Thermodynamics[M]. Shanghai:Shanghai Scientific and Technological Literature Press, 1994.
[4]	HALA E, PICK J, FRIED V, et al. Vapor Liquid Equilibrium[M]. New York:Pergamon Press, 1958.
[5]	LJUNGLIN J J, VANNESS H C. Calculation of vapour-liquid equilibria from vapour pressure data[J]. Chemical Engineering Science, 1962, 17(7):531-539.
[6]	BARNER H E, ADLER S B. Calculation of solution nonideality from binary T-x data[J]. Industrial & Engineering Chemistry Process Design and Development, 1973, 12(1):71-75.
[7]	POLAK J, LU C Y. A direct method for calculating ternary vapor compositions from total-pressure measurements[J]. Canadian Journal of Chemical Engineering, 1974, 52(1):88-91.
[8]	MARTINEZ-ORTIZ J A, MANLEY D B. Direct solution of the isothermal Gibbs-Duhem equation by an iterative method for binary systems[J]. AIChE Journal, 1977, 23(3):393-395.
[9]	SAYEGH S G, VERA J H. Model-free methods for vapor-liquid equilibria calculations binary systems[J]. Chemical Engineering Science, 1980, 35(11):2247-2256.
[10]	胡英, 英徐根. 由溶液蒸汽压或沸点确定平衡汽相组成的直接法[J]. 化工学报, 1980, 31(1):27-36. HU Y, YING X G. Determination of equilibrium vapor composition from the vapor pressure or boiling point of the solution by direct method[J]. Journal of Chemical Industry and Engineering(China), 1980, 31(1):27-36.
[11]	王利生. 一种由等压下的沸点-液相组成实测数据计算多组分汽液相平衡数据的方法[J]. 青岛科技大学学报(自然科学版), 1986, (2):112-122. WANG L S. A method for multicomponent vapor-liquid equilibrium calculations by using boiling point temperature-liquid composition data[J]. Journal of Qingdao University of Science and Technology (Natural Science Edition), 1986, (2):112-122.
[12]	周星风, 李浩然, 韩世钧. 流体相平衡中Gibbs-Duhem方程的求解问题研究[J]. 计算机与应用化学, 1989, 6(4):272-278. ZHOU X F, LI H R, HAN S J.Study on computation method for solving Gibbs-Duhem equation in fluid phase equilibrium[J]. Computer and Applied Chemistry, 1989, 6(4):272-278.
[13]	BARKER J A. Determination of activity coefficients from total pressure measurements[J]. Australian Journal of Chemistry, 1953, 6(3):207-210.
[14]	ISLAM A W, RAHMAN M H. A review of Barker's activity coefficient method and VLE data reduction[J]. The Journal of Chemical Thermodynamics, 2012, 44(1):31-37.
[15]	WON K W, PRAUSNITZ J M. High-pressure vapor-liquid equilibria calculation of partial pressures from total pressure data. Thermodynamic consistency[J]. Industrial & Engineering Chemistry Fundamentals, 1973, 12(4):459-463.
[16]	FONSECA I M A, LOBO L Q. Error analysis in Barker's method:extension to ternary systems[J]. Fluid Phase Equilibria, 1999, 154(2):205-211.
[17]	TAO L C. How to compute binary vapor-liquid equilibrium compositions from experimental p-x or T-x data[J]. Industrial & Engineering Chemistry, 1961, 53(4):307-309.
[18]	GAO D, ZHANG H, LUCKING P, et al. Computation of isobaric vapor-liquid equilibrium data for binary and ternary mixtures of methanol, water and ethanoic acid from T, P, x and HmE measurements[J]. Journal of Thermodynamics, 2012, (1):1-13.
[19]	MIXON F O, GUMOWSKI B, CARPENTER B H. Computation of vapor-liquid equilibrium data from solution vapor pressure measurements[J]. Industrial & Engineering Chemistry Fundamentals, 1965, 4(4):455-459.
[20]	贺利中, 吴兆立, 侯虞钧. 用p-x法测定和计算环丁砜-苯二元物系的汽液平衡[J]. 化学工程, 1985, (2):46-49. HE L Z, WU Z L, HOU Y J. Measured and calculated vapor-liquid equilibrium for binary mixtures of sulfolane-benzene by p-x method[J]. Chemical Engineering(China), 1985, (2):46-49.
[21]	刘洪来, 英徐根, 胡英. 在汽液平衡中由T, p, x数据推算y的样条函数法(Ⅰ):二元系[J]. 化工学报, 1991, 42(4):393-399. LIU H L, YING X G, HU Y. Calculation of y from T, p and x data in vapor-liquid equilibrium using spline function method (Ⅰ):Binary system[J]. Journal of Chemical Industry and Engineering(China), 1991, 42(4):393-399.
[22]	刘洪来, 英徐根, 胡英. 在汽液平衡中由T, p, x数据推算y的样条函数法(Ⅱ):三元系[J]. 化工学报, 1991, 42(4):400-406. LIU H L, YING X G, HU Y. Calculation of y from T, p and x data in vapor-liquid equilibrium using spline function method (Ⅱ):Ternary system[J]. Journal of Chemical Industry and Engineering(China), 1991, 42(4):400-406.
[23]	李浩然韩世钧. 四元体系汽液平衡的热力学一致性逐点检验[J]. 化工学报, 1994, 45(2):236-240. LI H R, HAN S J. Point-to-point thermodynamic consistency test of vapor-liquid equilibrium for quaternary system[J]. Journal of Chemical Industry and Engineering(China), 1994, 45(2):236-240.
[24]	LAM E, MEJIA A, SEGURA H, et al. A model-free approach data treatment of vapor-liquid equilibrium data in ternary systems(Ⅰ):Theory and numerical procedures[J]. Industrial & Engineering Chemistry Research, 2001, 40(9):2134-2148.
[25]	LAM E, MEJIA A, SEGURA H, et al. A model-free approach data treatment of vapor-liquid equilibrium data in ternary systems(Ⅱ):Applications[J]. Industrial & Engineering Chemistry Research, 2001, 40(9):2149-2159.
[26]	陈钟秀, 沈新华, 秦泽杭. 环氧丙烷-苯乙酮二元系的恒温汽液平衡研究[J]. 化学工程, 2003, 31(1):51-59. CHEN Z X, SHEN X H, QIN Z H. Study on isothermal vapor-liquid equilibrium for binary system propylene oxide-acetophenone[J]. Chemical Engineering(China), 2003, 31(1):51-59.
[27]	SALAVERA D, CHAUDHARI S K, ESTEVE X, et al. Vapor-liquid equilibria of ammonia+ water+ potassium hydroxide and ammonia+ water+ sodium hydroxide solutions at temperatures from (293.15 to 353.15) K[J]. Journal of Chemical & Engineering Data, 2005, 36(24):471-476.
[28]	BELABBACI A, GHEZOUALI C, VILLAMANAN R M, et al. Isothermal vapor-liquid equilibrium and molar excess Gibbs energies of two ternary systems containing either 1-butanol or 2-butanol+1-hexene+ methylbenzene at 313.15 K[J]. Fluid Phase Equilibria, 2015, 386(11):1-6.
[29]	王琨, 傅金彦, 刘洪来, 等. 静态蒸汽总压法研究二氟二氯甲烷-乙醚, 乙醚-丙酮二元系的恒温汽液平衡[J]. 化工学报, 1992, 43(6):652-657. WANG K, FU J Y, LIU H L, et al. Isothermal vapor-liquid equilibria for dichlorodifluoromethane diethylether and diethylether-acetone binary systems by static total-vapor-pressure method[J]. Journal of Chemical Industry and Engineering(China), 1992, 43(6):652-657.
[30]	SUN Y H, LIU H L, WANG K, et al. Measurements of isothermal vapor-liquid equilibrium of binary methanol/dimethyl carbonate system under pressure[J]. Fluid Phase Equilibria, 2005, 234(1):1-10.
[31]	MOODLEY K, NAIDOO P, RAAL J D, et al. Vapor-liquid equilibrium data for the morpholine-4-carbaldehyde+n-hexane or n-heptane binary systems using a static-synthetic apparatus[J]. Journal of Chemical & Engineering Data, 2013, 58(9):2552-2566.
[32]	MEJÍA A, SEGURA H, CARTES M, et al. Phase equilibria and interfacial tensions in the systems methyl tert-butyl ether+ acetone+ cyclohexane, methyl tert-butyl ether+acetone and methyl tert-butyl ether+ cyclohexane[J]. Fluid Phase Equilibria, 2008, 273(1/2):68-77.
[33]	MEJÍA A, SEGURA H, CARTES M. Vapor-liquid equilibrium and interfacial tensions of the system ethanol+hexane+tetrahydro-2H-pyran[J]. Fluid Phase Equilibria, 2014, 361(11):229-236.
[34]	DRAGOESCU D, TEODORESCU M, GHEORGHE D. Isothermal vapor-liquid equilibria and excess Gibbs free energies in some binary nitroalkane+ chloroalkane mixtures at temperatures from 298.15 K to 318.15 K[J]. Fluid Phase Equilibria, 2013, 338(10):16-22.
[35]	ZAOUI-DJELLOUL-DAOUADJI M, NEGADI A, MOKBEL I, et al. (Vapor-liquid) equilibria and excess Gibbs free energy functions of (ethanol+ glycerol), or (water+ glycerol) binary mixtures at several temperatures[J]. The Journal of Chemical Thermodynamics, 2014, 69(10):165-171.
[36]	BENDIAF L, NEGADI A, MOKBEL I, et al. Isothermal vapor-liquid equilibria of binary systems containing green solvents derived from biomass:(furfuryl alcohol+ toluene), (furfuryl alcohol+ ethanol), or (furfural+ toluene)[J]. Fuel, 2014, 122(1):247-253.
[37]	BOUZINA Z, NEGADI A, DERGAL F, et al. Vapor-liquid equilibria of N, N, N', N' tetramethylethylenediamine (TMEDA), tetramethylpropylenediamine (TMPDA) and their aqueous solutions[J]. Journal of Molecular Liquids, 2015, 201(11):83-89.
[38]	BOUZINA Z, DERGAL F, MOKBEL I, et al. Liquid-vapor equilibria of pure and aqueous solutions of diethylenetriamine or dipropylenetriamine[J]. Fluid Phase Equilibria, 2016, 414(1):164-169.
[39]	TAGUCHI H, NAKAKUBO J, MATSUDA H, et al. Determination of vapor-liquid equilibria at elevated pressures using ebulliometer[J]. Journal of Chemical Engineering of Japan, 2016, 49(4):317-323.