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

Abstract

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 twoparameter 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.

Generalization Comparison Study of the Performance of Six Different Alpha Functions Coupled to a Peng–Robinson Equation of State

“…For example, for vapor pressure, Piña-Martinez et al show that for the original Soave alpha function coupled with PR EoS and the updated presents values of 2.7 and 1.8%, these deviations are in the same range provided by this work. Similar to the behavior shown in P sat is the same detailed in Δ vap H and C pl sat , where the AARD X are between the ranges provided by original and updated Soave PR EoS and other new alpha functions …”

“…Similar to the behavior shown in P sat is the same detailed in Δ vap H and C pl sat , where the AARDX are between the ranges provided original and updated Soave PR EoS 29 and other new alpha functions. 45 , f l , and Δ vap S during prediction in the saturation condition (the subscripts l, v and vap indicate liquid, vapor, and vaporization while the superscript s indicates residual property). On the other hand, Figure 1 illustrates the LSD Fisher results for the AARDX comparison alpha functions.…”

Principles and methods of liquid metal actuators

“…For the process of gas–liquid change, the Peng–Robinson equation of state can be introduced to describe the state of the fluid, 91 where p is the pressure, R is the gas constant, T is the temperature, v is the volume, and the remaining parameters are given below, a ( T ) = a c α ( T r ) k = 0.37464 + 1.5422 ω − 0.26992 ω 2 where T r = T / T c , T c is the thermodynamic critical temperature, p c is the critical pressure, and ω is the eccentricity factor.…”