Are safe results obtained when the PC-SAFT equation of state is applied to ordinary pure chemicals?

摘要

The PC-SAFT equation of state is a very popular and promising model for fluids thatemploys a complicated pressure-explicit mathematical function (and can therefore not besolved analytically at a specified pressure and temperature, contrary to classical cubicequations). In this work, we demonstrate that in case of pure fluids, the PC-SAFT equationmay exhibit up to five different volume-roots whereas cubic equations give at themost three volume-roots (and yet, only one or two volume roots have real significance).The consequence of this strongly atypical behaviour is the existence of two different fluidfluidcoexistence lines (the vapour pressure-curve and an additional liquid-liquid equilibrium curve) and two critical points for a same pure component, which is obviously physically inconsistent.In addition to n-alkanes, nearly sixty very common pure components (branchedalkanes, cycloalkanes, aromatics, esters, gases, and so on) were tested out and withoutany exception, we can claim that all of them exhibit this undesired behaviour. In addition,such similar phenomena (i.e. existence of more than three volume-roots) may also arisewith mixtures. From a computational point of view, most of the algorithms used for solvingequations of state only search for three roots at the most and are thus likely to beinefficient when an equation of state gives more than three volume-roots. To overcomethis limitation, a simple procedure allowing to identify all the possible volume-roots of anequation of state is proposed.