Relationship between the binary interaction parameters (kij) of the Peng–Robinson and those of the Soave–Redlich–Kwong equations of state: Application to the definition of the PR2SRK model

The purpose of this paper is to establish a relationship between the binary interaction parameters of the Peng–Robinson (PR) and those of the Soave–Redlich–Kwong (SRK) equations of state (EoS). This objective could be reached thanks to the rigorous equivalence between the classical mixing rules with temperature-dependent kij and the combination at constant packing fraction of a Van Laar-type excess Gibbs energy model with a cubic EoS. This equivalence makes it possible to find out a relationship between the Eij(T) parameters issued from the Van Laar function and the kij(T) of the classical mixing rules. Our key idea was to make the hypothesis that the infinite pressure residual molar excess Gibbs energy ( g res E , ∞ ) was independent of the used EoS. Doing so, a simple relationship between the Eij suitable for the PR-EoS ( E i j PR ) and those suitable for the SRK EoS ( E i j SRK ) can be obtained. Using this relationship and the one linking the kij and the Eij, it was possible to find out a simple and general equation connecting the kij of a given EoS to the kij of any other EoS. This approach was then used to deduce k i j SRK from a known k i j PR . In a second step, using the previously mentioned mathematical equation relating k i j PR to k i j SRK , the PPR78 model which is a group contribution method for the estimation of the temperature-dependent BIPs of the PR-EoS was used to generate kij(T) for the SRK EoS. It is shown how the group interaction parameters initially determined for the PR-EoS can be simply used to predict the temperature-dependent BIPs of the SRK EoS. This new predictive model has been called PR2SRK. As discussed in this paper, the accuracy of this model is similar to the accuracy of the PPR78 approach.