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

We examine the prediction of high pressure (liquid + liquid) equilibrium (LLE) from the Peng–Robinson equation with three excess Gibbs free energy (Gex)-based mixing rules (MR): the first order modified Huron–Vidal (MHV1), the Wong–Sandler (WS), and a hybrid of these two (referred to as GexB2). 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 Gex model, used in MHV1 and GexB2 MR, leads to a similar miscibility gap from PR EOS and the Gex model used. On the other hand, the condition of matching excess Helmholtz energy from the EOS at infinite pressure to that from the Gex model, used in the WS MR, shows remarkable deviations. The condition of quadratic composition dependence in the second virial coefficient (B2), used in WS and GexB2 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 GexB2 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 GexB2 mixing rule provides the best predictive power for the LLE over a wide range of temperature and pressure.

► Prediction of LLE from the combined use of EOS and liquid model are examined.
► The mixing rule used affects the predicted pressure dependence of LLE.
► MHV1 mixing rule predicts decent LLE at low pressures.
► WS mixing rule predicts more accurate excess volume and LLE at high pressures.
► The hybrid of MHV1 and WS mixing rule gives overall the best predictions.