A four parameter cubic equation of state with temperature dependent covolume parameter
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摘要
A four-parameter, Ghoderao–Dalvi–Narayan 2 cubic equation of state(GDN2 CEOS), is presented which incorporates the following: 1. The experimental value of the critical compressibility factor has been used as a fixed input parameter for calculations; 2. All the parameters(a, b, c, d) of CEOS are temperature dependent functions in the subcritical region and are temperature independent functions in the supercritical region and; 3. A new α function is introduced with two compound specific parameters which are estimated by matching saturated vapor pressure at two fixed temperature points T_r= 0.5, 0.7. Our formalism enables us to cast three of the four parameters of the CEOS as a function of the remaining parameter. The proposed CEOS is used to predict properties of 334 pure compounds, including saturated vapor pressure and liquid density, compressed liquid density, heat capacities at the constant pressure and volume, enthalpy of vaporization, sound velocity. To calculate thermodynamic properties of a pure compound, the present CEOS require the critical temperature, the critical pressure, the Pitzer's acentric factor, the critical compressibility factor, and two parameters of the alpha function. The saturated liquid density predictions for pure fluids are very accurate when compared with GDN1(Ghoderao–Dalvi–Narayan 1),MPR(Modified Peng–Robinson), and PT(Patel–Teja) equations of state. Unlike MPR EOS, the proposed temperature dependent covolume parameter b in the present work satisfies all the constraints mentioned in the literature to avoid thermodynamic inconsistencies at the extreme temperature and pressure. Using van der Waals one-fluid mixing rule, the present CEOS is further used to predict bubble pressure and the vapor mole fraction of binary mixtures.
A four-parameter, Ghoderao–Dalvi–Narayan 2 cubic equation of state(GDN2 CEOS), is presented which incorporates the following: 1. The experimental value of the critical compressibility factor has been used as a fixed input parameter for calculations; 2. All the parameters(a, b, c, d) of CEOS are temperature dependent functions in the subcritical region and are temperature independent functions in the supercritical region and; 3. A new α function is introduced with two compound specific parameters which are estimated by matching saturated vapor pressure at two fixed temperature points T_r= 0.5, 0.7. Our formalism enables us to cast three of the four parameters of the CEOS as a function of the remaining parameter. The proposed CEOS is used to predict properties of 334 pure compounds, including saturated vapor pressure and liquid density, compressed liquid density, heat capacities at the constant pressure and volume, enthalpy of vaporization, sound velocity. To calculate thermodynamic properties of a pure compound, the present CEOS require the critical temperature, the critical pressure, the Pitzer's acentric factor, the critical compressibility factor, and two parameters of the alpha function. The saturated liquid density predictions for pure fluids are very accurate when compared with GDN1(Ghoderao–Dalvi–Narayan 1),MPR(Modified Peng–Robinson), and PT(Patel–Teja) equations of state. Unlike MPR EOS, the proposed temperature dependent covolume parameter b in the present work satisfies all the constraints mentioned in the literature to avoid thermodynamic inconsistencies at the extreme temperature and pressure. Using van der Waals one-fluid mixing rule, the present CEOS is further used to predict bubble pressure and the vapor mole fraction of binary mixtures.
A four-parameter, Ghoderao–Dalvi–Narayan 2 cubic equation of state(GDN2 CEOS), is presented which incorporates the following: 1. The experimental value of the critical compressibility factor has been used as a fixed input parameter for calculations; 2. All the parameters(a, b, c, d) of CEOS are temperature dependent functions in the subcritical region and are temperature independent functions in the supercritical region and; 3. A new α function is introduced with two compound specific parameters which are estimated by matching saturated vapor pressure at two fixed temperature points T_r= 0.5, 0.7. Our formalism enables us to cast three of the four parameters of the CEOS as a function of the remaining parameter. The proposed CEOS is used to predict properties of 334 pure compounds, including saturated vapor pressure and liquid density, compressed liquid density, heat capacities at the constant pressure and volume, enthalpy of vaporization, sound velocity. To calculate thermodynamic properties of a pure compound, the present CEOS require the critical temperature, the critical pressure, the Pitzer's acentric factor, the critical compressibility factor, and two parameters of the alpha function. The saturated liquid density predictions for pure fluids are very accurate when compared with GDN1(Ghoderao–Dalvi–Narayan 1),MPR(Modified Peng–Robinson), and PT(Patel–Teja) equations of state. Unlike MPR EOS, the proposed temperature dependent covolume parameter b in the present work satisfies all the constraints mentioned in the literature to avoid thermodynamic inconsistencies at the extreme temperature and pressure. Using van der Waals one-fluid mixing rule, the present CEOS is further used to predict bubble pressure and the vapor mole fraction of binary mixtures.
引文
[1]A.Maghari,L.Hosseinzadeh-Shahri,Evaluation of the performance of cubic equations of state in predicting the regularities in dense fluids,Fluid Phase Equilib.206(2003)287-311.
[2]G.Wilczek-Vera,J.H.Vera,Understanding cubic equations of state:A search for the hidden clues of their success,AIChE J.61(2015)2824-2831.
[3]J.O.Valderrama,The legacy of Johannes Diderik van der Waals,a hundred years after his nobel prize for physics,J.Supercrit.Fluids 55(2010)415-420.
[4]G.Schmidt,H.Wenzel,A modified van der Waals type equation of state,Chem.Eng.Sci.35(1980)1503-1512.
[5]Y.Adachi,B.C.Y.Lu,H.Sugie,A new four parameter equation of state,Fluid Phase Equilib.11(1983)29-48.
[6]H.Hinojosa-Gomez,J.F.Barragan-Aroche,E.R.Bazua-Rueda,A modification to the Peng-Robinson-fitted equation of state for pure substances,Fluid Phase Equilib.298(2010)12-23.
[7]P.Hosseinifar,S.Jamshidi,An evolved cubic equation of state with a new attractive term,Fluid Phase Equilib.408(2016)58-71.
[8]J.S.Lopez-Echeverry,S.Reif-Acherman,E.Araujo-Lopez,Peng-Robinson equation of state:40 years through cubics,Fluid Phase Equilib.447(2017)39-71.
[9]G.Soave,Equilibrium constants from a modified Redlich-Kwong equation of state,Chem.Eng.Sci.27(1972)1197-1203.
[10]D.Y.Peng,D.B.Robinson,A new two-constant equation of state,Ind.Eng.Chem.Fundam.15(1976)59-64.
[11]A.Peneloux,R.E.Rauzy,R.Freze,A consistent correction for Redlich-Kwong-Soave volumes,Fluid Phase Equilib.8(1982)7-23.
[12]P.Watson,M.Casella,S.Salerno,D.Tassios,Prediction of vapor pressures and saturated molar volumes with a simple cubic equation of state:part II:The van der Waals-711 EOS,Fluid Phase Equilib.27(1986)35-52.
[13]J.C.Tsai,Y.P.Chen,Application of a volume-translated Peng-Robinson equation of state on vapor-liquid equilibrium calculations,Fluid Phase Equilib.145(1998)193-215.
[14]H.B.de Sant'Ana,P.Ungerer,J.C.De Hemptinne,Evaluation of an improved volume translation for the prediction of hydrocarbon volumetric properties,Fluid Phase Equilib.154(1999)193-204.
[15]J.N.Jaubert,R.Privat,Y.Le Guennec,L.Coniglio,Note on the properties altered by application of a Peneloux-type volume translation to an equation of state,Fluid Phase Equilib.419(2016)88-95.
[16]R.Privat,M.Visconte,A.Zazoua-Khames,J.N.Jaubert,Analysis and prediction of the alpha-function parameters used in cubic equations of state,Chem.Eng.Sci.126(2015)584-603.
[17]Y.Le Guennec,R.Privat,J.N.Jaubert,Development of the translated-consistent tc-PRand tc-RK cubic equations of state for a safe and accurate prediction of volumetric,energetic and saturation properties of pure compounds in the sub and super-critical domains,Fluid Phase Equilib.429(2016)301-312.
[18]N.C.Patel,A.S.Teja,A new cubic equation of state for fluids and fluid mixtures,Chem.Eng.Sci.37(1982)463-473.
[19]C.H.Twu,J.E.Coon,J.R.Cunningham,A new cubic equation of state,Fluid Phase Equilib.75(1992)65-79.
[20]R.Schmidt,W.Wanger,A new form of the equation of state for pure substances and its application to oxygen,Fluid Phase Equilib.19(1985)175-200.
[21]A.M.Abudour,S.A.Mohammad,R.L.Robinson Jr.,K.A.M.Gasem,Volume-translated Peng-Robinson equation of state for saturated and single-phase liquid densities,Fluid Phase Equilib.335(2012)74-87.
[22]M.A.Trebble,P.R.Bishnoi,Development of a new four parameter cubic equation of state,Fluid Phase Equilib.35(1987)1-18.
[23]D.S.Jan,F.N.Tsai,A new four-parameter cubic equation of state for fluids,Can.J.Chem.Eng.69(1991)992-996.
[24]P.H.Salim,M.A.Trebble,A modified Trebble-Bishnoi equation of state:Thermodynamic consistency revisited,Fluid Phase Equilib.65(1991)59-71.
[25]P.N.P.Ghoderao,V.H.Dalvi,M.Narayan,A four-parameter cubic equation of state for pure compounds and mixtures,Chem.Eng.Sci.190(2018)173-189.
[26]L.B.Loeb,The Kinetic Theory of Gases,3rd Dover publications,New York,2004.
[27]A.Dashtizadeh,G.R.Pazuki,V.Taghikhani,C.Ghotbi,A new two-parameter cubic equation of state for predicting phase behavior of pure compounds and mixtures,Fluid Phase Equilib.242(2006)19-28.
[28]A.Haghtalab,P.Mahmoodi,S.H.Mazloumi,A modified Peng-Robinson equation of state for phase equilibrium calculation of liquefied,synthetic natural gas,and gas condensate mixtures,Can.J.Chem.Eng.89(2011)1376-1387.
[29]A.H.Farrokh-Niae,H.Moddarress,M.Mohsen-Nia,A three-parameter cubic equation of state for prediction of thermodynamic properties of fluids,J.Chem.Thermodyn.40(2008)84-95.
[30]Z.Duan,J.Hu,A new cubic equation of state and its applications to the modeling of vapor-liquid equilibria and volumetric properties of natural fluids,Geochim.Cosmochim.Acta 68(2004)2997-3009.
[31]L.A.Forero G.,J.A.Velasquez J.,A modified Patel-Teja cubic equation of state.Part II:Parameters for polar substances and its mixtures,Fluid Phase Equilib.364(2015)75-87.
[32]R.S.Kamath,L.T.Biegler,I.E.Grossmann,An equation-oriented approach for handling thermodynamics based on cubic equation of state in process optimization,Comput.Chem.Eng.34(2010)2085-2096.
[33]R.Monroy-Loperena,A note on the analytical solution of cubic equations of state in process simulation,Ind.Eng.Chem.Res.51(2012)6972-6976.
[34]M.M.Abbot,Cubic equations of state,AIChE J.19(1973)596-601.
[35]Y.Le Guennec,R.Privat,S.Lasala,J.N.Jaubert,On the imperative need to use a consistentα-function for the prediction of pure-compound supercritical properties with a cubic equation of state,Fluid Phase Equilib.445(2014)45-53.
[36]Y.Le Guennec,S.Lasala,R.Privat,J.N.Jaubert,A consistency test forα-functions of cubic equations of state,Fluid Phase Equilib.427(2016)513-538.
[37]S.I.Sandler,Chemical,Biochemical and Engineering Thermodynamics,4th ed.John Wiley&Sons,Inc.,USA,2006.
[38]V.Kalikhman,D.Kost,I.Polishuk,About the physical validity of attaching the repulsive terms of analytical EOS models by temperature dependencies,Fluid Phase Equilib.293(2010)164-167.
[39]M.A.Trebble,P.R.Bishnoi,Accuracy and consistency comparision of ten cubic equations of state for polar and non-polar compounds,Fluid Phase Equilib.29(1986)465-474.
[40]G.G.Fuller,A modified Redlich-Kwong-Soave equation of state capable of representing the liquid state,Ind.Eng.Chem.Fundam.15(1976)254-257.
[41]P.J.Linstrom,National institute of standard and technology,Standard Reference Database Number 69,http://webbook.nist.gov/chemistry/fluid/2005,Accessed date:3August 2017.
[42]D.W.Green,R.H.Perry,Perry's Chemical Engineer's Handbook,8th ed.McGraw-Hill,New-York,2007.
[43]T.Y.Kwak,G.A.Mansoori,Van der Waals mixing rules for cubic equations of state.Applications for supercritical fluid extraction modelling,Chem.Eng.Sci.41(1986)1303-1309.
[44]I.Wichterle,R.Kobayashi,Vapor-liquid equilibrium of methane-ethane system at low temperatures and high pressures,J.Chem.Eng.Data 17(1972)9-12.
[45]I.Wichterle,R.Kobayashi,Vapor-liquid equilibrium of methane-propane system at low temperatures and high pressures,J.Chem.Eng.Data 17(1972)4-9.
[46]L.C.Kahre,Low-temperature K data for methane-n-butane,J.Chem.Eng.Data 19(1974)67-71.
[47]H.M.Lin,H.M.Sebastian,J.J.Simnick,K.C.Chao,Gas-liquid equilibrium in binary mixtures of methane with n-decane,benzene,and toluene,J.Chem.Eng.Data 24(1979)146-149.
[48]S.Srivastan,N.A.Darwish,K.A.M.Gasem,R.L.Robinson Jr.,Solubility of methane in hexane,decane,and dodecane at temperatures from 311 to 423 K and pressures to 10.4 MPa,J.Chem.Eng.Data 37(1992)516-520.
[49]N.A.Darwish,J.Fathikalajahi,K.A.M.Gasem,R.L.Robinson Jr.,Solubility of methane in heavy normal paraffins at temperatures from 323 to 423 K and pressures to 10.7MPa,J.Chem.Eng.Data 38(1993)44-48.
[50]C.J.Blanc,J.C.B.Setler,Vapor-liquid equilibria for the ethane-propane system at low temperature,J.Chem.Eng.Data 33(1988)111-115.
[51]V.Lhotak,I.Wichterle,Vapor-liquid equilibria in the ethane-n butane system at high pressures,Fluid Phase Equilib.6(1981)229-235.
[52]K.A.M.Gasem,A.M.Raff,N.Darwish,R.L.Robinson Jr.,Solubility of ethane in n-hexane at pressures to 5.4 MPa and temperatures from 311 to 394 K,J.Chem.Eng.Data34(1989)397-398.
[53]H.Gardeler,K.Fischer,J.Gmehling,Experimental determination of vapor-liquid equilibrium data for asymmetric systems,Ind.Eng.Chem.Res.41(2002)1051-1056.
[54]Y.Kayukawa,K.Fujii,Y.Higashi,Vapor-liquid equilibrium(VLE)properties for the binary systems propane(1)+n-butane(2)and propane(1)+isobutane(3),J.Chem.Eng.Data 50(2005)579-582.
[55]J.L.Guillevic,D.Richon,H.Renon,Vapor-liquid equilibrium measurements up to558 K and 7 MPa:A new apparatus,Ind.Eng.Chem.Fundam.22(1983)495-499.
[56]K.J.Lee,W.K.Chen,J.W.Ko,L.S.Lee,C.M.J.Chang,Isothermal vapor-liquid equilibria for binary mixtures of hexane,heptane,octane,nonane and cyclohexane at 333.15K,343.15 K and 353.15 K,J.Taiwan Inst.Chem.Eng.40(2009)573-579.
[57]A.Dejoz,V.Gonza′Lez-Alfaro,P.J.Miguel,M.I.Va'zquez,Isobaric vapor-liquid equilibria for binary systems composed of octane,decane,and dodecane at 20 k Pa,J.Chem.Eng.Data 41(1996)93-96.
[58]Q.N.Ho,K.S.Yoo,B.G.Lee,J.S.Lim,Measurement of vapor-liquid equilibria for the binary mixture of propylene(R-1270)+propane(R-290),Fluid Phase Equilib.245(2006)63-70.
[59]S.Laugier,D.Richon,High-pressure vapor-liquid equilibria for ethylene+4-methyl-1-pentene and 1-butene+1-hexene,J.Chem.Eng.Data 41(1996)282-284.
[60]M.K.F.Malewsklt,S.I.Sandler,High-pressure vapor-liquid equilibria of the binary mixtures nitrogen 4-n-butane and argon+n-butane,J.Chem.Eng.Data 34(1989)424-426.
[61]L.A.Webster,A.J.Kidnay,Vapor-liquid equilibria for the methane-propane-carbon dioxide systems at 230 K and 270 K,J.Chem.Eng.Data 46(2001)759-764.
[62]J.H.Kim,M.S.Kim,Vapor-liquid equilibria for the carbon dioxide+propane system over a temperature range from 253.15 to 323.15 K,Fluid Phase Equilib.238(2005)13-19.
[63]M.E.Pozo De Fernindez,J.A.Zollweg,W.B.Streett,Vapor-liquid EquiWrium in the binary system carbon dioxide 4-n-butane,J.Chem.Eng.Data 34(1989)324-328.
[64]Y.H.Li,K.H.Diilard,R.L.Robinson,,Vapor-liquid phase equilibrium for carbon dioxide-n-hexane at 40,80,and 120°C J.Chem.Eng.Data 26(1981)53-55.
[65]H.Kalra,H.Kubota,D.B.Robinson,H.J.Ng,Equilibrium phase properties of the carbon dioxide-n-heptane system,J.Chem.Eng.Data 23(1978)317-321.
[66]M.K.Gupta,Y.H.Li,B.J.Hulsey,R.L.Robinson Jr.,Phase equilibrium for carbon dioxide-benzene at 313.2,353.2,and 393.2 K,J.Chem.Eng.Data 27(1982)55-57.
[67]B.Yucelen,A.J.Kidnay,Vapor-liquid equilibria in the nitrogen+carbon dioxide+propane system from 240 to 330 K at pressures to 15 MPa,J.Chem.Eng.Data 44(1999)926-931.
[68]G.Silva-Oliver,G.Eliosa-Jimenez,F.Garc?a-Sanchez,J.R.Avendano-Gomezb,Highpressure vapor-liquid equilibria in the nitrogen-n-pentane system,Fluid Phase Equilib.250(2006)37-48.
[69]G.Eliosa-Jimeneza,F.Garcia-Sancheza,G.Silva-Oliver,Vapor-liquid equilibrium data for the nitrogen+n-octane system from(344.5 to 543.5)K and at pressures up to 50 MPa,Fluid Phase Equilib.282(2009)3-10.
[70]B.S.Gupta,M.J.Lee,Isobaric vapor-liquid equilibrium for the binary mixtures of nonane with cyclohexane,toluene,m-xylene,or p-xylene at 101.3 kPa,Fluid Phase Equilib.313(2012)190-195.
[71]C.Diaz,J.Tojo,Phase equilibria behaviour of n-heptane with o-xylene,m-xylene,pxylene and ethylbenzene at 101.3 kPa,J.Chem.Thermodyn.34(2002)1975-1984.
[72]K.J.Lee,W.K.Chen,L.S.Lee,C.M.J.Chang,J.W.Ko,Isothermal vapor-liquid equilibria for binary mixtures of benzene,toluene,m-xylene,and N-methylformamide at333.15 K and 353.15 K,Fluid Phase Equilib.280(2009)42-48.
[73]W.K.Chen,K.J.Lee,J.W.Ko,C.M.J.Chang,D.Hsiang,L.S.Lee,Vapor-liquid equilibria and density measurement for binary mixtures of toluene,benzene,o-xylene,m-xylene,sulfolane and nonane at 333.15 K and 353.15 K,Fluid Phase Equilib.287(2010)126-133.
[2]G.Wilczek-Vera,J.H.Vera,Understanding cubic equations of state:A search for the hidden clues of their success,AIChE J.61(2015)2824-2831.
[3]J.O.Valderrama,The legacy of Johannes Diderik van der Waals,a hundred years after his nobel prize for physics,J.Supercrit.Fluids 55(2010)415-420.
[4]G.Schmidt,H.Wenzel,A modified van der Waals type equation of state,Chem.Eng.Sci.35(1980)1503-1512.
[5]Y.Adachi,B.C.Y.Lu,H.Sugie,A new four parameter equation of state,Fluid Phase Equilib.11(1983)29-48.
[6]H.Hinojosa-Gomez,J.F.Barragan-Aroche,E.R.Bazua-Rueda,A modification to the Peng-Robinson-fitted equation of state for pure substances,Fluid Phase Equilib.298(2010)12-23.
[7]P.Hosseinifar,S.Jamshidi,An evolved cubic equation of state with a new attractive term,Fluid Phase Equilib.408(2016)58-71.
[8]J.S.Lopez-Echeverry,S.Reif-Acherman,E.Araujo-Lopez,Peng-Robinson equation of state:40 years through cubics,Fluid Phase Equilib.447(2017)39-71.
[9]G.Soave,Equilibrium constants from a modified Redlich-Kwong equation of state,Chem.Eng.Sci.27(1972)1197-1203.
[10]D.Y.Peng,D.B.Robinson,A new two-constant equation of state,Ind.Eng.Chem.Fundam.15(1976)59-64.
[11]A.Peneloux,R.E.Rauzy,R.Freze,A consistent correction for Redlich-Kwong-Soave volumes,Fluid Phase Equilib.8(1982)7-23.
[12]P.Watson,M.Casella,S.Salerno,D.Tassios,Prediction of vapor pressures and saturated molar volumes with a simple cubic equation of state:part II:The van der Waals-711 EOS,Fluid Phase Equilib.27(1986)35-52.
[13]J.C.Tsai,Y.P.Chen,Application of a volume-translated Peng-Robinson equation of state on vapor-liquid equilibrium calculations,Fluid Phase Equilib.145(1998)193-215.
[14]H.B.de Sant'Ana,P.Ungerer,J.C.De Hemptinne,Evaluation of an improved volume translation for the prediction of hydrocarbon volumetric properties,Fluid Phase Equilib.154(1999)193-204.
[15]J.N.Jaubert,R.Privat,Y.Le Guennec,L.Coniglio,Note on the properties altered by application of a Peneloux-type volume translation to an equation of state,Fluid Phase Equilib.419(2016)88-95.
[16]R.Privat,M.Visconte,A.Zazoua-Khames,J.N.Jaubert,Analysis and prediction of the alpha-function parameters used in cubic equations of state,Chem.Eng.Sci.126(2015)584-603.
[17]Y.Le Guennec,R.Privat,J.N.Jaubert,Development of the translated-consistent tc-PRand tc-RK cubic equations of state for a safe and accurate prediction of volumetric,energetic and saturation properties of pure compounds in the sub and super-critical domains,Fluid Phase Equilib.429(2016)301-312.
[18]N.C.Patel,A.S.Teja,A new cubic equation of state for fluids and fluid mixtures,Chem.Eng.Sci.37(1982)463-473.
[19]C.H.Twu,J.E.Coon,J.R.Cunningham,A new cubic equation of state,Fluid Phase Equilib.75(1992)65-79.
[20]R.Schmidt,W.Wanger,A new form of the equation of state for pure substances and its application to oxygen,Fluid Phase Equilib.19(1985)175-200.
[21]A.M.Abudour,S.A.Mohammad,R.L.Robinson Jr.,K.A.M.Gasem,Volume-translated Peng-Robinson equation of state for saturated and single-phase liquid densities,Fluid Phase Equilib.335(2012)74-87.
[22]M.A.Trebble,P.R.Bishnoi,Development of a new four parameter cubic equation of state,Fluid Phase Equilib.35(1987)1-18.
[23]D.S.Jan,F.N.Tsai,A new four-parameter cubic equation of state for fluids,Can.J.Chem.Eng.69(1991)992-996.
[24]P.H.Salim,M.A.Trebble,A modified Trebble-Bishnoi equation of state:Thermodynamic consistency revisited,Fluid Phase Equilib.65(1991)59-71.
[25]P.N.P.Ghoderao,V.H.Dalvi,M.Narayan,A four-parameter cubic equation of state for pure compounds and mixtures,Chem.Eng.Sci.190(2018)173-189.
[26]L.B.Loeb,The Kinetic Theory of Gases,3rd Dover publications,New York,2004.
[27]A.Dashtizadeh,G.R.Pazuki,V.Taghikhani,C.Ghotbi,A new two-parameter cubic equation of state for predicting phase behavior of pure compounds and mixtures,Fluid Phase Equilib.242(2006)19-28.
[28]A.Haghtalab,P.Mahmoodi,S.H.Mazloumi,A modified Peng-Robinson equation of state for phase equilibrium calculation of liquefied,synthetic natural gas,and gas condensate mixtures,Can.J.Chem.Eng.89(2011)1376-1387.
[29]A.H.Farrokh-Niae,H.Moddarress,M.Mohsen-Nia,A three-parameter cubic equation of state for prediction of thermodynamic properties of fluids,J.Chem.Thermodyn.40(2008)84-95.
[30]Z.Duan,J.Hu,A new cubic equation of state and its applications to the modeling of vapor-liquid equilibria and volumetric properties of natural fluids,Geochim.Cosmochim.Acta 68(2004)2997-3009.
[31]L.A.Forero G.,J.A.Velasquez J.,A modified Patel-Teja cubic equation of state.Part II:Parameters for polar substances and its mixtures,Fluid Phase Equilib.364(2015)75-87.
[32]R.S.Kamath,L.T.Biegler,I.E.Grossmann,An equation-oriented approach for handling thermodynamics based on cubic equation of state in process optimization,Comput.Chem.Eng.34(2010)2085-2096.
[33]R.Monroy-Loperena,A note on the analytical solution of cubic equations of state in process simulation,Ind.Eng.Chem.Res.51(2012)6972-6976.
[34]M.M.Abbot,Cubic equations of state,AIChE J.19(1973)596-601.
[35]Y.Le Guennec,R.Privat,S.Lasala,J.N.Jaubert,On the imperative need to use a consistentα-function for the prediction of pure-compound supercritical properties with a cubic equation of state,Fluid Phase Equilib.445(2014)45-53.
[36]Y.Le Guennec,S.Lasala,R.Privat,J.N.Jaubert,A consistency test forα-functions of cubic equations of state,Fluid Phase Equilib.427(2016)513-538.
[37]S.I.Sandler,Chemical,Biochemical and Engineering Thermodynamics,4th ed.John Wiley&Sons,Inc.,USA,2006.
[38]V.Kalikhman,D.Kost,I.Polishuk,About the physical validity of attaching the repulsive terms of analytical EOS models by temperature dependencies,Fluid Phase Equilib.293(2010)164-167.
[39]M.A.Trebble,P.R.Bishnoi,Accuracy and consistency comparision of ten cubic equations of state for polar and non-polar compounds,Fluid Phase Equilib.29(1986)465-474.
[40]G.G.Fuller,A modified Redlich-Kwong-Soave equation of state capable of representing the liquid state,Ind.Eng.Chem.Fundam.15(1976)254-257.
[41]P.J.Linstrom,National institute of standard and technology,Standard Reference Database Number 69,http://webbook.nist.gov/chemistry/fluid/2005,Accessed date:3August 2017.
[42]D.W.Green,R.H.Perry,Perry's Chemical Engineer's Handbook,8th ed.McGraw-Hill,New-York,2007.
[43]T.Y.Kwak,G.A.Mansoori,Van der Waals mixing rules for cubic equations of state.Applications for supercritical fluid extraction modelling,Chem.Eng.Sci.41(1986)1303-1309.
[44]I.Wichterle,R.Kobayashi,Vapor-liquid equilibrium of methane-ethane system at low temperatures and high pressures,J.Chem.Eng.Data 17(1972)9-12.
[45]I.Wichterle,R.Kobayashi,Vapor-liquid equilibrium of methane-propane system at low temperatures and high pressures,J.Chem.Eng.Data 17(1972)4-9.
[46]L.C.Kahre,Low-temperature K data for methane-n-butane,J.Chem.Eng.Data 19(1974)67-71.
[47]H.M.Lin,H.M.Sebastian,J.J.Simnick,K.C.Chao,Gas-liquid equilibrium in binary mixtures of methane with n-decane,benzene,and toluene,J.Chem.Eng.Data 24(1979)146-149.
[48]S.Srivastan,N.A.Darwish,K.A.M.Gasem,R.L.Robinson Jr.,Solubility of methane in hexane,decane,and dodecane at temperatures from 311 to 423 K and pressures to 10.4 MPa,J.Chem.Eng.Data 37(1992)516-520.
[49]N.A.Darwish,J.Fathikalajahi,K.A.M.Gasem,R.L.Robinson Jr.,Solubility of methane in heavy normal paraffins at temperatures from 323 to 423 K and pressures to 10.7MPa,J.Chem.Eng.Data 38(1993)44-48.
[50]C.J.Blanc,J.C.B.Setler,Vapor-liquid equilibria for the ethane-propane system at low temperature,J.Chem.Eng.Data 33(1988)111-115.
[51]V.Lhotak,I.Wichterle,Vapor-liquid equilibria in the ethane-n butane system at high pressures,Fluid Phase Equilib.6(1981)229-235.
[52]K.A.M.Gasem,A.M.Raff,N.Darwish,R.L.Robinson Jr.,Solubility of ethane in n-hexane at pressures to 5.4 MPa and temperatures from 311 to 394 K,J.Chem.Eng.Data34(1989)397-398.
[53]H.Gardeler,K.Fischer,J.Gmehling,Experimental determination of vapor-liquid equilibrium data for asymmetric systems,Ind.Eng.Chem.Res.41(2002)1051-1056.
[54]Y.Kayukawa,K.Fujii,Y.Higashi,Vapor-liquid equilibrium(VLE)properties for the binary systems propane(1)+n-butane(2)and propane(1)+isobutane(3),J.Chem.Eng.Data 50(2005)579-582.
[55]J.L.Guillevic,D.Richon,H.Renon,Vapor-liquid equilibrium measurements up to558 K and 7 MPa:A new apparatus,Ind.Eng.Chem.Fundam.22(1983)495-499.
[56]K.J.Lee,W.K.Chen,J.W.Ko,L.S.Lee,C.M.J.Chang,Isothermal vapor-liquid equilibria for binary mixtures of hexane,heptane,octane,nonane and cyclohexane at 333.15K,343.15 K and 353.15 K,J.Taiwan Inst.Chem.Eng.40(2009)573-579.
[57]A.Dejoz,V.Gonza′Lez-Alfaro,P.J.Miguel,M.I.Va'zquez,Isobaric vapor-liquid equilibria for binary systems composed of octane,decane,and dodecane at 20 k Pa,J.Chem.Eng.Data 41(1996)93-96.
[58]Q.N.Ho,K.S.Yoo,B.G.Lee,J.S.Lim,Measurement of vapor-liquid equilibria for the binary mixture of propylene(R-1270)+propane(R-290),Fluid Phase Equilib.245(2006)63-70.
[59]S.Laugier,D.Richon,High-pressure vapor-liquid equilibria for ethylene+4-methyl-1-pentene and 1-butene+1-hexene,J.Chem.Eng.Data 41(1996)282-284.
[60]M.K.F.Malewsklt,S.I.Sandler,High-pressure vapor-liquid equilibria of the binary mixtures nitrogen 4-n-butane and argon+n-butane,J.Chem.Eng.Data 34(1989)424-426.
[61]L.A.Webster,A.J.Kidnay,Vapor-liquid equilibria for the methane-propane-carbon dioxide systems at 230 K and 270 K,J.Chem.Eng.Data 46(2001)759-764.
[62]J.H.Kim,M.S.Kim,Vapor-liquid equilibria for the carbon dioxide+propane system over a temperature range from 253.15 to 323.15 K,Fluid Phase Equilib.238(2005)13-19.
[63]M.E.Pozo De Fernindez,J.A.Zollweg,W.B.Streett,Vapor-liquid EquiWrium in the binary system carbon dioxide 4-n-butane,J.Chem.Eng.Data 34(1989)324-328.
[64]Y.H.Li,K.H.Diilard,R.L.Robinson,,Vapor-liquid phase equilibrium for carbon dioxide-n-hexane at 40,80,and 120°C J.Chem.Eng.Data 26(1981)53-55.
[65]H.Kalra,H.Kubota,D.B.Robinson,H.J.Ng,Equilibrium phase properties of the carbon dioxide-n-heptane system,J.Chem.Eng.Data 23(1978)317-321.
[66]M.K.Gupta,Y.H.Li,B.J.Hulsey,R.L.Robinson Jr.,Phase equilibrium for carbon dioxide-benzene at 313.2,353.2,and 393.2 K,J.Chem.Eng.Data 27(1982)55-57.
[67]B.Yucelen,A.J.Kidnay,Vapor-liquid equilibria in the nitrogen+carbon dioxide+propane system from 240 to 330 K at pressures to 15 MPa,J.Chem.Eng.Data 44(1999)926-931.
[68]G.Silva-Oliver,G.Eliosa-Jimenez,F.Garc?a-Sanchez,J.R.Avendano-Gomezb,Highpressure vapor-liquid equilibria in the nitrogen-n-pentane system,Fluid Phase Equilib.250(2006)37-48.
[69]G.Eliosa-Jimeneza,F.Garcia-Sancheza,G.Silva-Oliver,Vapor-liquid equilibrium data for the nitrogen+n-octane system from(344.5 to 543.5)K and at pressures up to 50 MPa,Fluid Phase Equilib.282(2009)3-10.
[70]B.S.Gupta,M.J.Lee,Isobaric vapor-liquid equilibrium for the binary mixtures of nonane with cyclohexane,toluene,m-xylene,or p-xylene at 101.3 kPa,Fluid Phase Equilib.313(2012)190-195.
[71]C.Diaz,J.Tojo,Phase equilibria behaviour of n-heptane with o-xylene,m-xylene,pxylene and ethylbenzene at 101.3 kPa,J.Chem.Thermodyn.34(2002)1975-1984.
[72]K.J.Lee,W.K.Chen,L.S.Lee,C.M.J.Chang,J.W.Ko,Isothermal vapor-liquid equilibria for binary mixtures of benzene,toluene,m-xylene,and N-methylformamide at333.15 K and 353.15 K,Fluid Phase Equilib.280(2009)42-48.
[73]W.K.Chen,K.J.Lee,J.W.Ko,C.M.J.Chang,D.Hsiang,L.S.Lee,Vapor-liquid equilibria and density measurement for binary mixtures of toluene,benzene,o-xylene,m-xylene,sulfolane and nonane at 333.15 K and 353.15 K,Fluid Phase Equilib.287(2010)126-133.