Computation and thermodynamic interpretation of high-pressure vapour—liquid equilibrium—a review

Abstract

The thermodynamic interpretation and modelling of high-pressure vapour—liquid equilibrium (HPVLE) data is a much more difficult proposition than for the low-pressure case. At present two methods have been developed for thermodynamic interpretation of binary isothermal HPVLE data. Initially HPVLE modelling was by the combined method which was essentially a logical progression of the excellent low-pressure correlation techniques in use at the time. In the combined method activity and fugacity coefficients are used to describe the liquid and vapour non-idealities respectively. To determine the activity and fugacity coefficients a liquid-phase model and an equation of state (EOS) are required respectively. This method permits excellent representation of the liquid and vapour phases of complex systems in low to medium pressure ranges. To overcome the difficulties of describing supercritical components and therefore the high-pressure critical region in the combined method, the direct method was developed. (We have followed Wichterle in the designations “combined method” and “direct method”. Other descriptive terms are in use, e.g. “activity coefficient method”, “activity/fugacity method” for the former, and “EOS method” for the latter). The direct method has the further advantage that separate binary interaction coefficients for the liquid phase are not required, i.e. only for the EOS. The direct method uses fugacity coefficients to describe both phases. The application of the direct method to the liquid phase and to complex polar systems has produced many difficulties in modelling and prediction, largely due to the empirical nature of the EOS mixing rules, and much effort has been devoted to this area recently. The most recent developments for modelling complex mixtures in the direct method, such as those that incorporate the activity coefficient into the liquid- and vapour-phase fugacity coefficients via the EOS mixing rules, will also be discussed. The purpose of this review is to provide those entering the field with an insight into the theoretical basis and to summarise the main developments in the above two methods. The historical and the most recent developments in liquid-phase models and EOS required in the above methods are reviewed. It would be impossible to comprehensively cover all the liquid-phase models and EOS developed as literally referred to more specialist reviews if more detail on a certain topic is required. A brief overview of thermodynamic consistency testing of HPVLE data, a somewhat neglected area, is given as well.