UNIFAC参数的回归及其在汽液平衡中的应用
|
摘要
原始的UNIFAC模型中基团相互作用能量参数不是温度的依变函数,它的相互作用参数仅为amn和anm两个常数,因而适用的温度范围很小。为了适应化工生产的不断发展的要求,Gmehling(Dortmund)等提出了新改进,并建立了DDB数据库(Dortmund data bank),极大扩展了UNIFAC的应用范围。但是数据库中的参数矩阵还存在很多空缺,有待进一步的深入研究发展。本文在前人的研究基础上采用PR状态方程与MDUNIFAC活度系数模型,并与HVOS混合规则相结合,建立了HVOS-PR/MDUNIFAC模型。
为了使DDB数据库中基团相互作用能量参数的矩阵更为完整,本文选取了吡啶(1)/1,-氯丁烷(2)、吡啶(1)/1,1-二氯乙烷(2)、吡啶(1)/乙酸(2)、四氢呋喃(1)/环己烷(2)、吡啶(1)/氯仿(2)、吡啶(1)/溴乙烷(2)、环己烷(1)/三氯乙烯(2)等7个二元体系进行了汽液平衡数据的测定,对它们进行了热力学一致性检验,作出了部分相图。并将这些汽液平衡数据用于基团相互作用参数的回归。
本文利用Nelder-Mead扩展单纯形求极值法选取了原模型参数(MDUNIFAC)预测能力较差的33个二元汽液平衡体系(共计2727个实验数据点,数据来源于本课题实验测定的7个二元体系的汽液平衡数据以及“清华大学膜中心数据库”、“工程化学数据库”)进行重新回归,得到了15组修正的基团相互作用参数;用同样方法对原模型没有的基团参数的22个体系(共计1039个实验点,数据来源于“清华大学膜中心数据库”和“工程化学数据库”)进行了回归,得到了17组基团相互作用参数。利用上述修正后的和补充的相互作用参数对28个二元汽液平衡体系(共计739个实验点)进行了预测。结果表明,用修正的和补充的基团相互作用参数构建的汽液平衡模型对含醇、酸的非水极性体系预测精度显著提高,汽相组成的绝对偏差在0.05以内,压力的相对偏差≤6%;对含水极性体系的汽液平衡,预测精度也略有提高。这在一定程度上扩充了原MDUNIFAC模型的基团参数矩阵,扩大了这一模型的预测范围。在化学反应工程,分离工程,化工过程研究,开发和设计当中具有极强的实用价值。
The group interaction parameter a mn and a nm, are not functions dependesd on temperature in original UNIFAC model, and just the constants. The suitable temperature ranges are very narrow. In order to adapt the uninterrupted development of chemical industry, Gmehling (Dortmund) had brought forward the new improvement to the model and had established the DDB data base (Dortmund data bank), but the parameters’matrix is not perfectly. So, the further study is very important. In this paper, the prediction model of HVOS-PR/MDUNIFAC has been proposed by using PR Equation of state, MDUNIFAC activity coefficient combined with the mixing rule of HVOS.
In order to make the parameters’matrix more perfectly, the vapor-liquid phase equilibrium data of seven binary systems include Pyridine/1-Chlorobutane, Pyridine/1, 1-Dichloroethane, Pyridine/Acetic, Tetrahydrofuran/Cyclohexane, Pyridine/Chloroform, Pyridine/Ethyl bromide and Cyclohexane/Trichloroethylene have been measured in this paper, and the thermodynamic consistency checks have been made. And those binary vapor-liquid equilibrium data were applied to the regression of group interaction parameters.
The group interaction parameters for 15 group combinations were refitted with Nelder-Mead simplex method by predicting 33 binary vapor-liquid equilibrium systems (2727 experimental data,the data from the seven binary system which have been determined in this paper,“Center of tsinghua membrane’s Database”and "scientific Database"). Additionally, 17 new group interaction parameters were fitted by 22 binary vapor-liquid equilibrium systems (1039 experimental data, the data from the“Center of tsinghua membrane’s Database”and“scientific Database’); the parameters wer applied to predict the vapor-liquid equilibria for 28 binary systems(739 experimental data) at different temperature and pressure to test the accuracy of modified and supplemented group interaction parameters. Compared results calculated by using this new parameters and original parameters with the experimental data, it shows that the new parameters are much better than original parameters in these systems include alcohol and acid none-polar. The absolute deviation of vapor-composition is less than 0.05 and the relative deviation of bubble-pressure is less than 6%; the results of prediction for the binary and ternary water-polar systems were improved slightly because of the existing hydrogen-bonding and association effect for polar systems with water.
According to the result, the original MDUNIFAC group interaction parameters matrix and the range of application of this model are extended. The new group interaction parameters in this paper were proved that have important practical application values in chemical reaction engineering, separating engineering and chemical engineering processes.
为了使DDB数据库中基团相互作用能量参数的矩阵更为完整,本文选取了吡啶(1)/1,-氯丁烷(2)、吡啶(1)/1,1-二氯乙烷(2)、吡啶(1)/乙酸(2)、四氢呋喃(1)/环己烷(2)、吡啶(1)/氯仿(2)、吡啶(1)/溴乙烷(2)、环己烷(1)/三氯乙烯(2)等7个二元体系进行了汽液平衡数据的测定,对它们进行了热力学一致性检验,作出了部分相图。并将这些汽液平衡数据用于基团相互作用参数的回归。
本文利用Nelder-Mead扩展单纯形求极值法选取了原模型参数(MDUNIFAC)预测能力较差的33个二元汽液平衡体系(共计2727个实验数据点,数据来源于本课题实验测定的7个二元体系的汽液平衡数据以及“清华大学膜中心数据库”、“工程化学数据库”)进行重新回归,得到了15组修正的基团相互作用参数;用同样方法对原模型没有的基团参数的22个体系(共计1039个实验点,数据来源于“清华大学膜中心数据库”和“工程化学数据库”)进行了回归,得到了17组基团相互作用参数。利用上述修正后的和补充的相互作用参数对28个二元汽液平衡体系(共计739个实验点)进行了预测。结果表明,用修正的和补充的基团相互作用参数构建的汽液平衡模型对含醇、酸的非水极性体系预测精度显著提高,汽相组成的绝对偏差在0.05以内,压力的相对偏差≤6%;对含水极性体系的汽液平衡,预测精度也略有提高。这在一定程度上扩充了原MDUNIFAC模型的基团参数矩阵,扩大了这一模型的预测范围。在化学反应工程,分离工程,化工过程研究,开发和设计当中具有极强的实用价值。
The group interaction parameter a mn and a nm, are not functions dependesd on temperature in original UNIFAC model, and just the constants. The suitable temperature ranges are very narrow. In order to adapt the uninterrupted development of chemical industry, Gmehling (Dortmund) had brought forward the new improvement to the model and had established the DDB data base (Dortmund data bank), but the parameters’matrix is not perfectly. So, the further study is very important. In this paper, the prediction model of HVOS-PR/MDUNIFAC has been proposed by using PR Equation of state, MDUNIFAC activity coefficient combined with the mixing rule of HVOS.
In order to make the parameters’matrix more perfectly, the vapor-liquid phase equilibrium data of seven binary systems include Pyridine/1-Chlorobutane, Pyridine/1, 1-Dichloroethane, Pyridine/Acetic, Tetrahydrofuran/Cyclohexane, Pyridine/Chloroform, Pyridine/Ethyl bromide and Cyclohexane/Trichloroethylene have been measured in this paper, and the thermodynamic consistency checks have been made. And those binary vapor-liquid equilibrium data were applied to the regression of group interaction parameters.
The group interaction parameters for 15 group combinations were refitted with Nelder-Mead simplex method by predicting 33 binary vapor-liquid equilibrium systems (2727 experimental data,the data from the seven binary system which have been determined in this paper,“Center of tsinghua membrane’s Database”and "scientific Database"). Additionally, 17 new group interaction parameters were fitted by 22 binary vapor-liquid equilibrium systems (1039 experimental data, the data from the“Center of tsinghua membrane’s Database”and“scientific Database’); the parameters wer applied to predict the vapor-liquid equilibria for 28 binary systems(739 experimental data) at different temperature and pressure to test the accuracy of modified and supplemented group interaction parameters. Compared results calculated by using this new parameters and original parameters with the experimental data, it shows that the new parameters are much better than original parameters in these systems include alcohol and acid none-polar. The absolute deviation of vapor-composition is less than 0.05 and the relative deviation of bubble-pressure is less than 6%; the results of prediction for the binary and ternary water-polar systems were improved slightly because of the existing hydrogen-bonding and association effect for polar systems with water.
According to the result, the original MDUNIFAC group interaction parameters matrix and the range of application of this model are extended. The new group interaction parameters in this paper were proved that have important practical application values in chemical reaction engineering, separating engineering and chemical engineering processes.
引文
[1] Gmehling J, Onken U, Vapor-liquid equilibrium data collection, Frankfurt: DECHEMA, 1977~1995
[2] Wichterle I, Linke T, Hala E, Vapor-liquid equilibrium data bibliography, 1973, Supple. 1, 1976, Supple. 2, 1979, Supple. 4, 1982, Supple. 4, 1985
[3] Maczynski A, Verified vapor-liquid equilibrium data, vol. 1~7, Warszawa: PMN, 1976~1983
[4] Ohe S, Vapor-liquid equilibrium data-salt effect, Amsterdam: Elsevier, 1991
[5] 姚加.缔合体系分子热力学(博士后学位论文)[D].杭州:浙江大学,2000
[6] Redlich O,Kwong JNS.On the Thermodynamics of Solutions.V.An Equation of State. Fugacities of Gaseous Solutions.Chem Rev,1949,44(1):233-244
[7] Soave G.Equilibrium conslant form a modified Redlick-Kwong equation of state.Chem Eng Sci,1972,37:1197-1211
[8] Peng DY,Robinson DB.A New Tow-Constant Equation of State.Ind Eng Chem Fundam, 1976,15(1):59-64
[9] 陈新志,蔡振云,胡望明 化工热力学[M]. 北京:化学工业出版社,2005
[10] 物性定数,东京:丸善,1-10 集,1963-1972
[11] Knapp H, Doring R, Oeirch L, et al., Vapor-liquid equilibria for mixtures of low boiling substances, Frankfurt: DECHEMA, 1982, 1989
[12] Marsh N Kenneth, Niamskul Prin, Gmehling Jurgen, et al., Review of thermophysical property measurements on mixture containing MTBE, TAME,and other ethers with non-polar solvents, Fluid phase equilibria, 1999,156:207~227
[13] Suojiang Zhang, Toshihiko Hiaki, Masaru Hongo, Kazuo Kojima. Prediction of infinite dilution activity coefficients in aqueous solutions by group contribution model.A critical evaluation [J]. Fluid Phase Equilibria. 1998, 144.:97-112
[14] Suojiang Zhang, Toshihiko Hiaki, Kazuo Kojima. Prediction of infinite dilution activity coefficients for systems including water based on the group contribution model with mixture-type groupsⅠ . Alkane-H2O and alkanol - H2O mixtures [J]. Fluid Phase Equilibria. 1998,149:27-40
[15] Suojiang Zhang, Toshihiko Hiaki, Kazuo Kojima. Prediction of infinite dilution activity coefficients for systems including water based on the group contribution model with mixture-type groups.Ⅱ . Extension and application [J]. Fluid Phase Equilibria. 2002,198:15-27
[16] T. Oishi, J. M. Prausnitz. Estimation of solvent Activities in Polymer Solutions Using a Group-Contribution Method [J]. Ind.Eng. Chem. Proc. Des. Dev. 1978,17:333-339
[17] H. S. Elbro, A. Fredenslund, P. Rasmussen. A new simple equation for the prediction of solvent activities in polymer solutions [J]. Macromolecules. 1990,23: 4707-4714.
[18] Zhong Chongli, Sato Yoshiyuki, Masuoka Hirokatsu, Chen Xiaoning. Improvement of predictive accuracy of the UNIFAC model for vapor-liquid equilibria of polymer solutions [J]. Fluid Phase Equilibria. 1996,123:97-106
[19] Kikic. I, Fredenslund. On the combinatorial part of the UNIFAC and UNIQUAC models [J]. The Candian Journal of chemical Engineering. 1980,58: 253-258
[20] Rgen Gmehling, Jiding Li, Martin Schiller.A Modified UNIFAC Model.2.Present Parameter Matrix and Results for Different Thermodynamic Properties [J]. Ind. Eng. Chem. Res. 1993,32:178-193
[21] Bent L. Larsen, Peter Rasmussen, Aage Fredenslund. A modified UNIFAC group-contribution model for prediction of phase equilibria and heats of mixing [J]. Ind. Eng. Chem. Res. 1987,26:2274-2286
[22] Fredenslund, As., Gmehling, J. Rasmussen, P. Vapor-Liquid Equilibra Using UNIFAC-A Group Contribution [M]. Elsevier. Amsterdam. 1977
[23] Roland witti. Jürgen Lohmann. Jürgen Gmehling. Vapor-Liquid Equilibria by UNIFAC Contribution. 6. Revision and Extension [J]. Ind. Eng. Chem. Res. 2003,42: 183-188
[24] Jürgen Gmehling, Jiding Li, Martin Schiller.A Modified UNIFAC Model.2.Present Parameter Matrix and Results for Different Thermodynamic Properties [J]. Ind. Eng. Chem. Res. 1993,32: 178-193
[25] Jürgen Gmehling, Jürgen Lohmann, Antje Jakob, Jiding Li, Ralph Joh. A Modified UNIFAC (Dortmund) Model. 3. Revisionand Extension [J]. Ind. Eng. Chem. Res. 1998,37:4876-4882
[26] Jürgen Lohmann, Ralph Joh, Jürgen Gmehling. From UNIFAC to Modified UNIFAC (Dortmund) [J]. Ind. Eng. Chem. Res. 2001,40:957-964
[27] Jürgen Lohmann, Roland wittig , Jürgen Lohmann, Ralph Joh. A Modified UNIFAC (Dortmund) Model. 4. Revision and Extension[J]. Ind. Eng. Chem. Res. 2002,41: 1678-1688
[28] Jürgen Lohmann, Ralph John, Bernd Nienhaus, Jürgen Gmehling. Revision and Extension of the Group Contribution Method Modified UNIFAC (Dortmund)[J]. Chem. Eng. Technol.1998,21: 245-248
[29] Thomas Magnussen, Peter Rasmussen, Aage Fredenslund. UNIFAC parameter table for prediction of liquid-liquid equilibriums [J]. Ind. Eng. Chem. Proc. Des. Dev. 1981, 20: 331-339
[30] Herbert H. Hooper, Stefan Michel, John M. Prausnitz. Correlation of liquid-liquid equilibria for some water-organic liquid systems in the region 20-250.degree. C [J]. Ind. Eng. Chem. Res. 1988, 27: 2182-2187
[31] Bondi. A.Physical Properties of Molecular Crystals, Liquids and Glasses [M]. John Wiley. New York. 1968
[32] Iwai Y, Anai Y, Arai Y. Prediction of Solublities for Volable Hydrocarbons in low-Density Polythylene Using UNIFAC-FV Model[J]. Polym. Eng. Sci. 1981, 21: 1015-1018
[33] Pappa, G. D., Voutsas, E. C., Tassios, D. P. Prediction of Activity Coefficients in Polymer and Copolymer Solutions Using Simple Activity Coefficient Models [J]. Ind. Eng. Chem. Res. 1999, 38: 4975-4984
[34] Wibawa Gede, Takishima Shigeki, Sato Yoshiyuki, Masuoka, Hirokatsu. Revision of UNIFAC group interaction parameters of group contribution models to improve prediction results of vapor-liquid equilibria for solvent-polymer systems [J]. Fliud Phase Equilibria. 2002, 202: 367-383
[35] 周浩,刘洪来,胡英. 基团贡献法预测高分子溶液汽液平衡[J]. 高校化学工程学报. 1997,11(3).231-237
[36] Lindvig Thomas, Michelsen Michael L., Kontogeorgis Georgios. A Flory–Huggins model based on the Hansen solubility parameters [J]. Fluid Phase Equilibria. 2002, 203: 247-260
[37] Kikic. I, Fermeglia. M, Rasmussen. P. UNIFAC prediction of vapor-liquid equilibria in mixed solvent-salt systems [J]. Chem. Eng. Sci. 1991, 46: 2775-2780
[38] Achar. C, Dussap. C. G, Gros. J. B. Representation of vapour-liquid equilibria in water-alcohol-electrolyte mixtures with a modified UNIFAC group-contribution method [J]. Fluid Phase Equilibria. 1994, 98: 71-89
[39] Peiming Wang, Andrzej, Anderko, Robort D. Young. A speciation-based model for mixed-solvent electrolyte systems [J]. Fluid Phase Equilibria. 2002, 203: 141-176
[40] Fredenslund, As, Jones. R. L., Prausnitz. J. M. Group contribution estimation of activity coefficients in nonideal liquid mixtures [J]. AIChE J. 1975, 21: 1086-1099
[41] Holderbaum T, Gmehling J, PSRK: a group contribution equation of state basedon UNIFAC. Fluid phase equilibria, 1991,70: 251~265
[42] 于养信,陈中,高光华.用 PR 方程新的混合规则预测高压汽液平衡[J].清华大学学报.2002,42(5):595-598
[43] Michelsen, Michael L. Modified huron-vidal mixing rule for cubic equations of state [J]. Fluid Phase Equilibria. 1990,60: 213-219
[44] Orbey, H., Sandler, S. I. On the combination of equation of state and excess free energymodels [J]. Fluid Phase Equilibria. 1995, 111: 53-70
[45] Dahl Soren, Michelsen, Michael L. High-pressure vapor-liquid equilibrium with a UNIFAC-based equation of state [J]. AIChE J. 1990, 36: 1829-1836
[46] Boukouvalas, C., Spiliotis, N., Coutsikos, P., Tzouvaras, N., Tassios, D. Prediction of vapor-liquid equilibrium with the LCVM model: a linear combination of the Vidal and Michelsen mixing rules coupled with the original UNIFAC and the t-mPR equation of state[J]. Fluid Phase Equilibria. 1994, 92: 75-106
[47] Wong, D. S. H., Sandler, Stanley I. Theoretically correct mixing rule for cubic equations of state [J]. AIChE J. 1992, 38: 671-680
[48] David. H. Wong, Hasen Obey, Stanley I. Sandler. Equation of State Mixing Rule for Nonideal Mixtures Using Available Activity Coefficient Model Parameters and That Allows Extrapolation over Large Range of Temperature and Pressure [J]. Ind. Eng. Chem. Res. 1992, 31: 2033-2039
[49] Mariana Teodorescu, Peter Rasmussen. High-Pressure Vapor-Liquid Equilibria in the Systems Nitrogen + Dimethyl Ether, Methanol + Dimethyl Ether, Carbon Dioxide + Dimethyl Ether + Methanol, and Nitrogen + Dimethyl Ether + Methanol [J]. Chem. Eng. Data. 2001, 46: 640-64
[50] Weidong Yan, Magnus Topphoff, Christian Rose, Jürgen Gmehling. Prediction of vapor-liquid equilibria in mixed-solvent electrolyte systems using the group contribution concept [J]. Fluid Phase Equilibria. 1999, 162; 97-113
[51] Jiding Li, Magnus Topphoff, Kai Fischer, Jürgen Gmehling. Prediction of Gas Solubilities in Aqueous Electrolyte Systems Using the Predictive Soave-Redlich-Kwong Model [J]. Ind. Eng. Chem. Res. 2001, 40: 3703-3710
[52] Hala E, Pick J, Fried V, Vapour-liquid equilibrium, London: Pergamon Press,1967, 7~14
[53] Malanowski S, Experimental methods for vapor-liquid equilibria, Part ICirculaiton methods, Fluid Phase Equilibria, 1982, 8: 197~219
[54] 马沛生.化工数据[M].北京:中国石化出版社.2003,7:81-82
[55] 《化学工程手册》编辑委员会.《化学工程手册》[M].北京:化学工业出版社,1989,10.
[56] http://mole.ipe.ac.cn/phase_transition/phase_transition_query.aspx
[57] http://db.membrane.org.cn/data_view.asp?data_type=t13
[58] http://mole.ipe.ac.cn/nedb/Binary.htm
[2] Wichterle I, Linke T, Hala E, Vapor-liquid equilibrium data bibliography, 1973, Supple. 1, 1976, Supple. 2, 1979, Supple. 4, 1982, Supple. 4, 1985
[3] Maczynski A, Verified vapor-liquid equilibrium data, vol. 1~7, Warszawa: PMN, 1976~1983
[4] Ohe S, Vapor-liquid equilibrium data-salt effect, Amsterdam: Elsevier, 1991
[5] 姚加.缔合体系分子热力学(博士后学位论文)[D].杭州:浙江大学,2000
[6] Redlich O,Kwong JNS.On the Thermodynamics of Solutions.V.An Equation of State. Fugacities of Gaseous Solutions.Chem Rev,1949,44(1):233-244
[7] Soave G.Equilibrium conslant form a modified Redlick-Kwong equation of state.Chem Eng Sci,1972,37:1197-1211
[8] Peng DY,Robinson DB.A New Tow-Constant Equation of State.Ind Eng Chem Fundam, 1976,15(1):59-64
[9] 陈新志,蔡振云,胡望明 化工热力学[M]. 北京:化学工业出版社,2005
[10] 物性定数,东京:丸善,1-10 集,1963-1972
[11] Knapp H, Doring R, Oeirch L, et al., Vapor-liquid equilibria for mixtures of low boiling substances, Frankfurt: DECHEMA, 1982, 1989
[12] Marsh N Kenneth, Niamskul Prin, Gmehling Jurgen, et al., Review of thermophysical property measurements on mixture containing MTBE, TAME,and other ethers with non-polar solvents, Fluid phase equilibria, 1999,156:207~227
[13] Suojiang Zhang, Toshihiko Hiaki, Masaru Hongo, Kazuo Kojima. Prediction of infinite dilution activity coefficients in aqueous solutions by group contribution model.A critical evaluation [J]. Fluid Phase Equilibria. 1998, 144.:97-112
[14] Suojiang Zhang, Toshihiko Hiaki, Kazuo Kojima. Prediction of infinite dilution activity coefficients for systems including water based on the group contribution model with mixture-type groupsⅠ . Alkane-H2O and alkanol - H2O mixtures [J]. Fluid Phase Equilibria. 1998,149:27-40
[15] Suojiang Zhang, Toshihiko Hiaki, Kazuo Kojima. Prediction of infinite dilution activity coefficients for systems including water based on the group contribution model with mixture-type groups.Ⅱ . Extension and application [J]. Fluid Phase Equilibria. 2002,198:15-27
[16] T. Oishi, J. M. Prausnitz. Estimation of solvent Activities in Polymer Solutions Using a Group-Contribution Method [J]. Ind.Eng. Chem. Proc. Des. Dev. 1978,17:333-339
[17] H. S. Elbro, A. Fredenslund, P. Rasmussen. A new simple equation for the prediction of solvent activities in polymer solutions [J]. Macromolecules. 1990,23: 4707-4714.
[18] Zhong Chongli, Sato Yoshiyuki, Masuoka Hirokatsu, Chen Xiaoning. Improvement of predictive accuracy of the UNIFAC model for vapor-liquid equilibria of polymer solutions [J]. Fluid Phase Equilibria. 1996,123:97-106
[19] Kikic. I, Fredenslund. On the combinatorial part of the UNIFAC and UNIQUAC models [J]. The Candian Journal of chemical Engineering. 1980,58: 253-258
[20] Rgen Gmehling, Jiding Li, Martin Schiller.A Modified UNIFAC Model.2.Present Parameter Matrix and Results for Different Thermodynamic Properties [J]. Ind. Eng. Chem. Res. 1993,32:178-193
[21] Bent L. Larsen, Peter Rasmussen, Aage Fredenslund. A modified UNIFAC group-contribution model for prediction of phase equilibria and heats of mixing [J]. Ind. Eng. Chem. Res. 1987,26:2274-2286
[22] Fredenslund, As., Gmehling, J. Rasmussen, P. Vapor-Liquid Equilibra Using UNIFAC-A Group Contribution [M]. Elsevier. Amsterdam. 1977
[23] Roland witti. Jürgen Lohmann. Jürgen Gmehling. Vapor-Liquid Equilibria by UNIFAC Contribution. 6. Revision and Extension [J]. Ind. Eng. Chem. Res. 2003,42: 183-188
[24] Jürgen Gmehling, Jiding Li, Martin Schiller.A Modified UNIFAC Model.2.Present Parameter Matrix and Results for Different Thermodynamic Properties [J]. Ind. Eng. Chem. Res. 1993,32: 178-193
[25] Jürgen Gmehling, Jürgen Lohmann, Antje Jakob, Jiding Li, Ralph Joh. A Modified UNIFAC (Dortmund) Model. 3. Revisionand Extension [J]. Ind. Eng. Chem. Res. 1998,37:4876-4882
[26] Jürgen Lohmann, Ralph Joh, Jürgen Gmehling. From UNIFAC to Modified UNIFAC (Dortmund) [J]. Ind. Eng. Chem. Res. 2001,40:957-964
[27] Jürgen Lohmann, Roland wittig , Jürgen Lohmann, Ralph Joh. A Modified UNIFAC (Dortmund) Model. 4. Revision and Extension[J]. Ind. Eng. Chem. Res. 2002,41: 1678-1688
[28] Jürgen Lohmann, Ralph John, Bernd Nienhaus, Jürgen Gmehling. Revision and Extension of the Group Contribution Method Modified UNIFAC (Dortmund)[J]. Chem. Eng. Technol.1998,21: 245-248
[29] Thomas Magnussen, Peter Rasmussen, Aage Fredenslund. UNIFAC parameter table for prediction of liquid-liquid equilibriums [J]. Ind. Eng. Chem. Proc. Des. Dev. 1981, 20: 331-339
[30] Herbert H. Hooper, Stefan Michel, John M. Prausnitz. Correlation of liquid-liquid equilibria for some water-organic liquid systems in the region 20-250.degree. C [J]. Ind. Eng. Chem. Res. 1988, 27: 2182-2187
[31] Bondi. A.Physical Properties of Molecular Crystals, Liquids and Glasses [M]. John Wiley. New York. 1968
[32] Iwai Y, Anai Y, Arai Y. Prediction of Solublities for Volable Hydrocarbons in low-Density Polythylene Using UNIFAC-FV Model[J]. Polym. Eng. Sci. 1981, 21: 1015-1018
[33] Pappa, G. D., Voutsas, E. C., Tassios, D. P. Prediction of Activity Coefficients in Polymer and Copolymer Solutions Using Simple Activity Coefficient Models [J]. Ind. Eng. Chem. Res. 1999, 38: 4975-4984
[34] Wibawa Gede, Takishima Shigeki, Sato Yoshiyuki, Masuoka, Hirokatsu. Revision of UNIFAC group interaction parameters of group contribution models to improve prediction results of vapor-liquid equilibria for solvent-polymer systems [J]. Fliud Phase Equilibria. 2002, 202: 367-383
[35] 周浩,刘洪来,胡英. 基团贡献法预测高分子溶液汽液平衡[J]. 高校化学工程学报. 1997,11(3).231-237
[36] Lindvig Thomas, Michelsen Michael L., Kontogeorgis Georgios. A Flory–Huggins model based on the Hansen solubility parameters [J]. Fluid Phase Equilibria. 2002, 203: 247-260
[37] Kikic. I, Fermeglia. M, Rasmussen. P. UNIFAC prediction of vapor-liquid equilibria in mixed solvent-salt systems [J]. Chem. Eng. Sci. 1991, 46: 2775-2780
[38] Achar. C, Dussap. C. G, Gros. J. B. Representation of vapour-liquid equilibria in water-alcohol-electrolyte mixtures with a modified UNIFAC group-contribution method [J]. Fluid Phase Equilibria. 1994, 98: 71-89
[39] Peiming Wang, Andrzej, Anderko, Robort D. Young. A speciation-based model for mixed-solvent electrolyte systems [J]. Fluid Phase Equilibria. 2002, 203: 141-176
[40] Fredenslund, As, Jones. R. L., Prausnitz. J. M. Group contribution estimation of activity coefficients in nonideal liquid mixtures [J]. AIChE J. 1975, 21: 1086-1099
[41] Holderbaum T, Gmehling J, PSRK: a group contribution equation of state basedon UNIFAC. Fluid phase equilibria, 1991,70: 251~265
[42] 于养信,陈中,高光华.用 PR 方程新的混合规则预测高压汽液平衡[J].清华大学学报.2002,42(5):595-598
[43] Michelsen, Michael L. Modified huron-vidal mixing rule for cubic equations of state [J]. Fluid Phase Equilibria. 1990,60: 213-219
[44] Orbey, H., Sandler, S. I. On the combination of equation of state and excess free energymodels [J]. Fluid Phase Equilibria. 1995, 111: 53-70
[45] Dahl Soren, Michelsen, Michael L. High-pressure vapor-liquid equilibrium with a UNIFAC-based equation of state [J]. AIChE J. 1990, 36: 1829-1836
[46] Boukouvalas, C., Spiliotis, N., Coutsikos, P., Tzouvaras, N., Tassios, D. Prediction of vapor-liquid equilibrium with the LCVM model: a linear combination of the Vidal and Michelsen mixing rules coupled with the original UNIFAC and the t-mPR equation of state[J]. Fluid Phase Equilibria. 1994, 92: 75-106
[47] Wong, D. S. H., Sandler, Stanley I. Theoretically correct mixing rule for cubic equations of state [J]. AIChE J. 1992, 38: 671-680
[48] David. H. Wong, Hasen Obey, Stanley I. Sandler. Equation of State Mixing Rule for Nonideal Mixtures Using Available Activity Coefficient Model Parameters and That Allows Extrapolation over Large Range of Temperature and Pressure [J]. Ind. Eng. Chem. Res. 1992, 31: 2033-2039
[49] Mariana Teodorescu, Peter Rasmussen. High-Pressure Vapor-Liquid Equilibria in the Systems Nitrogen + Dimethyl Ether, Methanol + Dimethyl Ether, Carbon Dioxide + Dimethyl Ether + Methanol, and Nitrogen + Dimethyl Ether + Methanol [J]. Chem. Eng. Data. 2001, 46: 640-64
[50] Weidong Yan, Magnus Topphoff, Christian Rose, Jürgen Gmehling. Prediction of vapor-liquid equilibria in mixed-solvent electrolyte systems using the group contribution concept [J]. Fluid Phase Equilibria. 1999, 162; 97-113
[51] Jiding Li, Magnus Topphoff, Kai Fischer, Jürgen Gmehling. Prediction of Gas Solubilities in Aqueous Electrolyte Systems Using the Predictive Soave-Redlich-Kwong Model [J]. Ind. Eng. Chem. Res. 2001, 40: 3703-3710
[52] Hala E, Pick J, Fried V, Vapour-liquid equilibrium, London: Pergamon Press,1967, 7~14
[53] Malanowski S, Experimental methods for vapor-liquid equilibria, Part ICirculaiton methods, Fluid Phase Equilibria, 1982, 8: 197~219
[54] 马沛生.化工数据[M].北京:中国石化出版社.2003,7:81-82
[55] 《化学工程手册》编辑委员会.《化学工程手册》[M].北京:化学工业出版社,1989,10.
[56] http://mole.ipe.ac.cn/phase_transition/phase_transition_query.aspx
[57] http://db.membrane.org.cn/data_view.asp?data_type=t13
[58] http://mole.ipe.ac.cn/nedb/Binary.htm