On the temperature dependence of the α function in the cubic equation of state

New Alpha Functions for the Peng-Robinson Cubic Equation of State

The alpha function is an important part of the attractive term of cubic equation of state (EoS), which affected the predictive accuracy of thermodynamic properties. In this paper, four new alpha functions (Alpha Function-1 to Alpha Function-4) were proposed for the Peng-Robinson (PR) EoS. The proposed alpha functions and their derivatives satisfied the requirements of the thermodynamic consistency test. The four alpha functions with PR EoS were used to predict the thermodynamic properties of 11 kinds of compounds, the average relative deviation (ARD) of Alpha Function-1 and Alpha Function-2 for the prediction of vapor pressures was 0.57%, and the ARDs of Alpha Function-3 and Alpha Function-4 were 0.44 and 0.38%, respectively. The ARDs of Alpha Function-4 for the estimation of enthalpy of vaporization, liquid volume, and liquid isobaric heat capacity of seven kinds of compounds were 1.46, 7.54, and 7.59%, respectively. The proposed three-parameter alpha functions were more accurate than the two-parameter function for the prediction the vapor pressure and enthalpy of vaporization of pure compounds. However, any alpha function used in the attractive term of PR EoS had great deviations for the estimation of liquid volume and isobaric heat capacity.