Effect of mixing rule boundary conditions on high pressure (liquid + liquid) equilibrium prediction

Abstract We examine the prediction of high pressure (liquid + liquid) equilibrium (LLE) from the Peng–Robinson equation with three excess Gibbs free energy ( G ex )-based mixing rules (MR): the first order modified Huron–Vidal (MHV1), the Wong–Sandler (WS), and a hybrid of these two (referred to as G ex B 2 ). These mixing rules differ by the boundary conditions used for determination of the temperature and composition dependence of parameters a and b in the PR EOS. The condition of matching the excess Gibbs free energy from the EOS at zero pressure to that from the G ex model, used in MHV1 and G ex B 2 MR, leads to a similar miscibility gap from PR EOS and the G ex model used. On the other hand, the condition of matching excess Helmholtz energy from the EOS at infinite pressure to that from the G ex model, used in the WS MR, shows remarkable deviations. The condition of quadratic composition dependence in the second virial coefficient ( B 2 ), used in WS and G ex B 2 MR, allows for both positive and negative values in the molar excess volume. Depending on the mixture, either the increase or decrease of the miscibility gap with pressure can be observed when the WS or the G ex B 2 MR is used. The condition of linear combination of molecular sizes of each component used in the MHV1 MR, however, often leads to small, positive molar excess volumes. As a consequence, the predicted LLE from using the MHV1 MR are insensitive to pressure. Therefore, we find that the G ex B 2 mixing rule provides the best predictive power for the LLE over a wide range of temperature and pressure.