Research On The Modification Of Alpha Functions For Cubic Equation Of State

Cubic equations of state play an important role in the chemical process simulation and design.The cubic equation of state is suitable for the prediction of thermodynamic properties of pure and mixture fluids at the middle and high pressures.The alpha function of the attractive term of cubic equation of state can improve the predictive accuracy of thermodynamic properties.In this paper,the polynomical and exponential alpha functions were systematically evaluated,and new alpha functions based on PR Eo S were proposed.The generalized alpha functions were also studied.The polynomial alpha functions were evaluated with 4400 saturated vapor pressure data of 11 kinds of compounds.Mathias-Copeman(1983),Androulakis-Kalospiros-Tassions(1989),and Schwartzentruber-Renon-Watanasiri(1990)alpha functions with three or four parameters can accurately predict the vapor pressures of non-polar and polar compounds,with the average relative deviations(ARD)being less than 0.34%.The ARDs of two-parameter alpha functions,such as Stryjek-Vera(1986),are between 0.5% and 0.8% for the prediction of saturated vapor pressures of 11 kinds of compounds.POLY alpha function was modified on the base of Stryjek-Vera(1986)to improve the prediction of vapor pressure in the low reduced temperature range.The ARDs of vapor pressures for 11 kinds of compounds in the reduced temperature range less than 0.7 or between 0.7 and 1.0 are 0.31% and 0.38%,respectively.The ARDs of enthalpy of vaporization,liquid volume and isobar heat capacity for 7 kinds of compounds are 1.37%,7.54% and 6.90%,respectively.The Almeida-Aznar-Telles(1991)and Mahmoodi-Sedigh(2017)alpha functions with three parameters can accurately predict the vapor pressures,and the ARDs are 0.33% and 0.38%,respectively.The ARDs of Heyen(1980)and Melhem-SainiGoodwin(1989)alpha functions for the vapor pressure are all 0.60%.The ARD of Trebble-Bishnoi(1987)alpha function with one parameter for the vapor pressure is almost ten times of that of the three-parameter alpha functions.The EXP-1,EXP-2,EXP-3 and EXP-4 alpha functions were proposed on the base of MelhemSaini-Goodwin(1989)and Almeida-Aznar-Telles(1991)alpha functions,which can satisfy the requirement of consistency test.The ARDs of EXP-1 and EXP-2 two-parameter alpha functions for the vapor pressure are 0.57%,and the ARDs of EXP-3 and EXP-4 are 0.44% and 0.38%.The ARDs of EXP-4 alpha function for enthalpy of vaporization,liquids volume and isobar heat capacity of 7 kinds of compounds are 1.46%,7.54%,and 7.59%,which is superior to that of Mahmoodi-Sedigh(2017)and slightly less than that of Almeida-Aznar-Telles(1991)alpha function.The generalized alpha function is imporatant way for improving the application of cubic equation of state.The ARDs of vapor pressures predicted with polynomial and exponential alpha functions that were generalized with the acentric factor for the prediction of vapor pressures,are between 3.7%-4.2%.PR-Heyen-Forero(2016)alpha function generalized with polarity factor and acentric factor can accurately predict vapor pressures of polar comounds,with ARD being 3.09%.The generalized EXP-1 alpha function with reduced dipole moment and acentric factor can meet the requirement of consistency test.The ARD of the vapor pressure for the compounds involving or not involving in the parameter fitting is 2.60% and 2.61%.The prediction of vapor pressures for alcohols with generalized EXP-1 alpha function is better than that with the alpha function generalized with acentric factor.The ARDs of enthalpy of vaporization,liquid volume,and isobar heat capacity for 7 kinds of compounds that were involved in the parameter fitting are 2.04%,7.42%,and 10.01%,respectively,which is slightly higher than that of the ungeneralized EXP-1 alpha function.The ARDs of enthalpy of vaporization,liquid volume,and isobar heat capacity for 7 kinds of compounds that were not involved in the parameter fitting are 1.62%,4.15%,and 11.52%,respectively.The generalized EXP-1 alpha function improved the predictions of enthalpy of vaporization,liquid volume,and isobar heat capacity.In general,the three-parameter alpha functions are more accurate than the two-parameter and one-parameter alpha functions for the prediction of vapor pressures below the critical point.The proposed POLY and EXP-4 alpha function can accurately predict the vapor pressure and enthalpy of vaporization of pure compounds below the critical point.The POLY alpha function is slightly more accurate than EXP-4 alpha function for the prediction of thermodynamic properties.The alpha function generalized with the reduced dipole moment and acentric factor is more accurate than that generalized with the acentric factor for the prediction of the vapor pressure,enthalpy of vaporization,liquid volume,and isobar heat capacity of alcohols.Both the generalized and ungeneralized alpha functions in combination with PR Eo S are not suitable for the prediction of the thermodynamic properties of associative compounds,such as acids and water,which attribute to the function forms of cubic EoS.