汽液相平衡计算混合法则中协体积项b的改进
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摘要
混合物汽液相平衡通常需要引入合适的混合法则才能更好地进行关联。针对目前混合法则中协体积项b的改进提出了一种新的修正协体积项b的方法。该方法以Mie势能理论、London色散力理论为基础,同时引入Leach等分子形状系数进行修正,这样协体积项b中的交互作用参数lij形式上是纯组分分子形状系数θ和φ及临界参数的函数,无需实验数据拟合得到,从而真实反映了二元混合物的实际混合情况。将修正的协体积项b运用于MHV1、LCVM及HV混合法则并结合PR+NRTL模型对不同种类的16个体系汽液相平衡进行了计算,并与采用b=∑xibi的MHV1、LCVM及HV混合法则结合PR+NRTL模型计算的结果进行比较,结果表明运用修正的协体积项b的混合法则+PR+NRTL模型所得的计算结果精度优于采用b=∑xibi的MHV1、LCVM及HV混合法则+PR+NRTL模型的计算结果。
To get better correlation results of vapor liquid equilibrium(VLE) of mixture systems, it is usually necessary to select the suitable mixing rule. The modifications of force parameter a have obtained good results in both theory and application. However, the research on co-volume parameter b is less and usually empirical. A new modified method for co-volume b was presented. In the revised mixing rule, the molecular shape factors obtained from Leach et al were introduced to amend co-volume b on the basis of Mie potential-energy and London dispersion theory. Thus, the interactive parameter lij in co-volume b was dependent on the molecular shape factors θ, φ, and critical parameters of the components. Without experimental data, molecular shape factors and interactive parameter lij could be obtained, which could be used to reflect the actual situations of mixture systems. The VLE calculation results for 16 kinds of different systems were given by using modified co-volume parameter b in MHV1/LCVM/HV mixing rules combined with PR EOS and NRTL models, and the results were compared with the results of using b = ∑xibi in MHV1/LCVM/HV mixing rule combined with PR EOS and NRTL models. The models with the modified co-volume b were better than those with b = ∑xibi to some extent.
To get better correlation results of vapor liquid equilibrium(VLE) of mixture systems, it is usually necessary to select the suitable mixing rule. The modifications of force parameter a have obtained good results in both theory and application. However, the research on co-volume parameter b is less and usually empirical. A new modified method for co-volume b was presented. In the revised mixing rule, the molecular shape factors obtained from Leach et al were introduced to amend co-volume b on the basis of Mie potential-energy and London dispersion theory. Thus, the interactive parameter lij in co-volume b was dependent on the molecular shape factors θ, φ, and critical parameters of the components. Without experimental data, molecular shape factors and interactive parameter lij could be obtained, which could be used to reflect the actual situations of mixture systems. The VLE calculation results for 16 kinds of different systems were given by using modified co-volume parameter b in MHV1/LCVM/HV mixing rules combined with PR EOS and NRTL models, and the results were compared with the results of using b = ∑xibi in MHV1/LCVM/HV mixing rule combined with PR EOS and NRTL models. The models with the modified co-volume b were better than those with b = ∑xibi to some extent.
引文
[1]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
[2]Michelsen M L.A modified Huron-Vidal mixing rule for cubic equations of state[J].Fluid Phase Equilibria,1990,60(1):213-219
[3]Boulouvalas C,Spiliotis N,Coutsikos P,Tzouvaras N,Tassios D.Prediction of vapor-liquid equilibrium with LCVM model.A linear combination of the Huron-Vidal and Michelsen mixing rules coupled with the original UNIFAC and the t-m PR equation of state[J].Fluid Phase Equilibria,1994,92:75-106
[4]Heidman J L,Tsonopoulos C,Brady C J,Wilson G M.High-temperature mutual solubilities of hydrocarbons and water(Ⅱ):Ethylbenzene,ethylcyclohexane,and n-octane[J].AICh E Journal,1985,31(3):376-384
[5]Wang Wenchuan,Zhong Chongli.Mixing rules for hydrogen-containing systems[J].Fluid Phase Equilibria,1989,47(1):103-114
[6]Coutinho J A P,Kontogeorgis G M,Stenby E H.Binary interaction parameters for nonpolar systems with cubic equations of state:a theoretical approach(Ⅰ).CO2/hydrocarbons using SRK equation of state[J].Fluid Phase Equilibria,1994,102(1):31-60
[7]Weber W,Petkov S,Brunner G.Vapour-liquid-equilibria and calculations using the Redlich-Kwong-Aspen-equation of state for tristearin,tripalmitin,and triolein in CO2 and propane[J].Fluid Phase Equilibria,1999,158-160:695-706
[8]Valderrama J O,Lopez C L,Arce P F.Mixing rules in equations of state applied to mixtures containing a supercritical fluid[J].Inf.Technol.,2000,11(2):59-64
[9]Chafer A,Fornari T,Berna A,Stateva R P.Solubility of quercetin in supercritical CO2+ethanol as a modifier:measurements and thermodynamic modelling[J].The Journal of Supercritical Fluids,2004,32(1):89-96
[10]Mc Farlane R A,Gray M R,Shaw J M.Evaluation of co-volume mixing rules for bitumen liquid density and bubble pressure estimation[J].Fluid Phase Equilibria,2010,293(1):87-100
[11]London F.The general theory of molecular forces[J].Trans.Faraday Soc.,1937,33:8-26
[12]Leach J W,Chappelear P S,Leland T W.Use of molecular shape factors in vapor-liquid equilibrium calculations with the corresponding states principle[J].AICh E Journal,1968,14(4):568-576
[13]Reid R C,Leland T W.Pseudocritical constants[J].AICh E Journal,1965,11(2):228-237
[14]Prausnitz J M,Gunn R D.Volumetric properties of nonpolar gaseous mixtures[J].AICh E Journal,1958,4(4):430-435
[15]Peng D Y,Robinson D B.A new two-constant equation of state[J].Industrial and Engineering Chemistry Fundamentals,1976,15(1):59-64
[16]Renon H,Prausnitz J M.Local compositions in thermodynamic excess functions for liquid mixtures[J].AICh E Journal,1968,14(1):135-144
[17]Li Xinru(李新如),Shen Yanshu(沈彦曙),Meng Xuelin(孟学林),Sheng Lei(圣磊),Zheng Danxing(郑丹星).Vapor-liquid equilibrium(VLE)for the system 1,1-difluoroethane-N,N-dimethylformamide[J].Journal of Engineering Thermophysics(工程热物理学报),2013,34(3):389-392
[18]Han X H,Xu Y J,Gao Z J,Wang Q,Chen G M.Vapor-liquid equilibrium study of an absorption heat transformer working fluid of(HFC-32+DMF)[J].J.Chem.Eng.Data,2011,56(4):1268-1272
[19]Han X H,Gao Z J,Xu Y J,Qiu Y,Min X W,Cui X L,Chen G M.Solubility of refrigerant 1,1,1,2-tetrafluoroethane in the N,N-dimethyl formamide in the temperature range from 263.15 to 363.15 K[J].J.Chem.Eng.Data,2011,56(5):1821-1826
[20]Wang Q,Xu Y J,Gao Z J,Qiu Y,Min X W,Han X H,Chen G M.Isothermal vapor-liquid equilibrium data for the binary mixture ethyl fluoride(HFC-161)+1,1,1,2,3,3,3-heptafluoroproane(HFC-227ea)over a temperature range from 253.15 K to 313.15 K[J].Fluid Phase Equilibria,2010,297(1):67-71
[21]Zhang Yu(张宇),Gong Maoqiong(公茂琼),Wu Jianfeng(吴剑峰).Vapor-liquid equilibrium measurement and correlation for R23+R116system[J].Journal of Chemical Industry and Engineering(China)(化工学报),2008,59(2):269-275
[22]Wang Q,Gao Z J,Xu Y J,Han X H,Chen G M.Isothermal vapor-liquid equilibrium data for the binary mixture trifluoroethane(HFC-143a)+ethyl fluoride(HFC-161)over the temperature range253.15 to 303.15 K[J].J.Chem.Eng.Data,2010,55(9):2990-2993
[23]Valtz A,Coquelet C,Richon D.Vapor-liquid equilibrium data for the sulfur dioxide(SO2)+1,1,1,2,3,3,3-heptafluoropropane(R227ea)system at temperatures from 288.07 to 403.19 K and pressures up to5.38 MPa:representation of the critical point and azeotrope temperature dependence[J].Fluid Phase Equilibria,2004,220(1):77-83
[24]Valtz A,Coquelet C,Richon D.Vapor–liquid equilibrium data for the sulfur dioxide(SO2)+difluoromethane(R32)system at temperatures from 288.07 to 403.16 K and at pressures up to 7.31 MPa[J].International Journal of Thermophysics,2004,25(6):1695-1711
[25]Wei M S W,Brown T S,Kidnay A J,Sloan E D.Vapor+liquid equilibria for the ternary system methane+ethane+carbon dioxide at230 K and its constituent binaries at temperatures from 207 to 270 K[J].J.Chem.Eng.Data,1995,40(4):726-731
[26]Webster L A,Kidnay A J.Vapor-liquid equilibria for the methanepropane-carbon dioxide systems at 230 K and 270 K[J].J.Chem.Eng.Data,2001,46(3):759-764
[27]Laugier S,Richon D.Vapor-liquid equilibria for hydrogen sulfide+hexane,+cyclohexane,+benzene,+pentadecane,and+(hexane+pentadecane)[J].J.Chem.Eng.Data,1995,40(1):153-159
[28]Kalra H,Robinson D B,Krishnan T R.The equilibrium phase properties of the ethane-hydrogen sulfide system at subambient temperatures[J].Journal of Chemical and Engineering Data,1977,22(1):85-88
[29]Valtz A,Chapoy A,Coquelet C,Paricaud P,Richon D.Vapour–liquid equilibria in the carbon dioxide-water system,measurement and modelling from 278.2 to 318.2 K[J].Fluid Phase Equilibria,2004,226:333-344
[30]Soo C B,Ahmar E E,Coquelet C,Ramjugernath D,Richon D.Vapor-liquid equilibrium measurements and modeling of the n-butane+ethanol system from 323 to 423 K[J].Fluid Phase Equilibria,2009,286(1):79-87
[2]Michelsen M L.A modified Huron-Vidal mixing rule for cubic equations of state[J].Fluid Phase Equilibria,1990,60(1):213-219
[3]Boulouvalas C,Spiliotis N,Coutsikos P,Tzouvaras N,Tassios D.Prediction of vapor-liquid equilibrium with LCVM model.A linear combination of the Huron-Vidal and Michelsen mixing rules coupled with the original UNIFAC and the t-m PR equation of state[J].Fluid Phase Equilibria,1994,92:75-106
[4]Heidman J L,Tsonopoulos C,Brady C J,Wilson G M.High-temperature mutual solubilities of hydrocarbons and water(Ⅱ):Ethylbenzene,ethylcyclohexane,and n-octane[J].AICh E Journal,1985,31(3):376-384
[5]Wang Wenchuan,Zhong Chongli.Mixing rules for hydrogen-containing systems[J].Fluid Phase Equilibria,1989,47(1):103-114
[6]Coutinho J A P,Kontogeorgis G M,Stenby E H.Binary interaction parameters for nonpolar systems with cubic equations of state:a theoretical approach(Ⅰ).CO2/hydrocarbons using SRK equation of state[J].Fluid Phase Equilibria,1994,102(1):31-60
[7]Weber W,Petkov S,Brunner G.Vapour-liquid-equilibria and calculations using the Redlich-Kwong-Aspen-equation of state for tristearin,tripalmitin,and triolein in CO2 and propane[J].Fluid Phase Equilibria,1999,158-160:695-706
[8]Valderrama J O,Lopez C L,Arce P F.Mixing rules in equations of state applied to mixtures containing a supercritical fluid[J].Inf.Technol.,2000,11(2):59-64
[9]Chafer A,Fornari T,Berna A,Stateva R P.Solubility of quercetin in supercritical CO2+ethanol as a modifier:measurements and thermodynamic modelling[J].The Journal of Supercritical Fluids,2004,32(1):89-96
[10]Mc Farlane R A,Gray M R,Shaw J M.Evaluation of co-volume mixing rules for bitumen liquid density and bubble pressure estimation[J].Fluid Phase Equilibria,2010,293(1):87-100
[11]London F.The general theory of molecular forces[J].Trans.Faraday Soc.,1937,33:8-26
[12]Leach J W,Chappelear P S,Leland T W.Use of molecular shape factors in vapor-liquid equilibrium calculations with the corresponding states principle[J].AICh E Journal,1968,14(4):568-576
[13]Reid R C,Leland T W.Pseudocritical constants[J].AICh E Journal,1965,11(2):228-237
[14]Prausnitz J M,Gunn R D.Volumetric properties of nonpolar gaseous mixtures[J].AICh E Journal,1958,4(4):430-435
[15]Peng D Y,Robinson D B.A new two-constant equation of state[J].Industrial and Engineering Chemistry Fundamentals,1976,15(1):59-64
[16]Renon H,Prausnitz J M.Local compositions in thermodynamic excess functions for liquid mixtures[J].AICh E Journal,1968,14(1):135-144
[17]Li Xinru(李新如),Shen Yanshu(沈彦曙),Meng Xuelin(孟学林),Sheng Lei(圣磊),Zheng Danxing(郑丹星).Vapor-liquid equilibrium(VLE)for the system 1,1-difluoroethane-N,N-dimethylformamide[J].Journal of Engineering Thermophysics(工程热物理学报),2013,34(3):389-392
[18]Han X H,Xu Y J,Gao Z J,Wang Q,Chen G M.Vapor-liquid equilibrium study of an absorption heat transformer working fluid of(HFC-32+DMF)[J].J.Chem.Eng.Data,2011,56(4):1268-1272
[19]Han X H,Gao Z J,Xu Y J,Qiu Y,Min X W,Cui X L,Chen G M.Solubility of refrigerant 1,1,1,2-tetrafluoroethane in the N,N-dimethyl formamide in the temperature range from 263.15 to 363.15 K[J].J.Chem.Eng.Data,2011,56(5):1821-1826
[20]Wang Q,Xu Y J,Gao Z J,Qiu Y,Min X W,Han X H,Chen G M.Isothermal vapor-liquid equilibrium data for the binary mixture ethyl fluoride(HFC-161)+1,1,1,2,3,3,3-heptafluoroproane(HFC-227ea)over a temperature range from 253.15 K to 313.15 K[J].Fluid Phase Equilibria,2010,297(1):67-71
[21]Zhang Yu(张宇),Gong Maoqiong(公茂琼),Wu Jianfeng(吴剑峰).Vapor-liquid equilibrium measurement and correlation for R23+R116system[J].Journal of Chemical Industry and Engineering(China)(化工学报),2008,59(2):269-275
[22]Wang Q,Gao Z J,Xu Y J,Han X H,Chen G M.Isothermal vapor-liquid equilibrium data for the binary mixture trifluoroethane(HFC-143a)+ethyl fluoride(HFC-161)over the temperature range253.15 to 303.15 K[J].J.Chem.Eng.Data,2010,55(9):2990-2993
[23]Valtz A,Coquelet C,Richon D.Vapor-liquid equilibrium data for the sulfur dioxide(SO2)+1,1,1,2,3,3,3-heptafluoropropane(R227ea)system at temperatures from 288.07 to 403.19 K and pressures up to5.38 MPa:representation of the critical point and azeotrope temperature dependence[J].Fluid Phase Equilibria,2004,220(1):77-83
[24]Valtz A,Coquelet C,Richon D.Vapor–liquid equilibrium data for the sulfur dioxide(SO2)+difluoromethane(R32)system at temperatures from 288.07 to 403.16 K and at pressures up to 7.31 MPa[J].International Journal of Thermophysics,2004,25(6):1695-1711
[25]Wei M S W,Brown T S,Kidnay A J,Sloan E D.Vapor+liquid equilibria for the ternary system methane+ethane+carbon dioxide at230 K and its constituent binaries at temperatures from 207 to 270 K[J].J.Chem.Eng.Data,1995,40(4):726-731
[26]Webster L A,Kidnay A J.Vapor-liquid equilibria for the methanepropane-carbon dioxide systems at 230 K and 270 K[J].J.Chem.Eng.Data,2001,46(3):759-764
[27]Laugier S,Richon D.Vapor-liquid equilibria for hydrogen sulfide+hexane,+cyclohexane,+benzene,+pentadecane,and+(hexane+pentadecane)[J].J.Chem.Eng.Data,1995,40(1):153-159
[28]Kalra H,Robinson D B,Krishnan T R.The equilibrium phase properties of the ethane-hydrogen sulfide system at subambient temperatures[J].Journal of Chemical and Engineering Data,1977,22(1):85-88
[29]Valtz A,Chapoy A,Coquelet C,Paricaud P,Richon D.Vapour–liquid equilibria in the carbon dioxide-water system,measurement and modelling from 278.2 to 318.2 K[J].Fluid Phase Equilibria,2004,226:333-344
[30]Soo C B,Ahmar E E,Coquelet C,Ramjugernath D,Richon D.Vapor-liquid equilibrium measurements and modeling of the n-butane+ethanol system from 323 to 423 K[J].Fluid Phase Equilibria,2009,286(1):79-87