Are Safe Results Obtained When the PC-SAFT Equation of State Is Applied to Ordinary Pure Chemicals?

Actual representation of fluid phase behaviour is an important issue in chemical engineering. Since the pioneering work of Van der Waals, many equations of state (EoS) for fluids have emerged. They are capable of accounting for both liquid and vapour phases and allow to represent the thermodynamic behaviour of pure components and mixtures. The quality of such models is generally assessed through their ability to describe physical phenomena (changes of state, criticality, azeotropy and so on) as well as their capacity to accurately calculate PVT properties and phase equilibria. However, beyond qualitative and quantitative efficiency, the knowledge of the limitations of the models is of major importance and must be necessarily taken into account to avoid erroneous calculations.

 

In this study, we essentially focus on the drawbacks of the very popular and promising PC-SAFT EoS which lead to inconsistent predictions of phase behaviour. We demonstrate that in case of pure fluids, the PC-SAFT equation may exhibit up to five different volume-roots whereas cubic equations give at the most 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 fluid-fluid coexistence 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. The two fluid-fluid coexistence lines intersect at a point T very similar to a pure component triple point, since it is a point where three phases are coexisting: two liquid phases and one vapour phase.

In addition to n-alkanes, nearly sixty very common pure components (branched alkanes, cycloalkanes, aromatics, esters, gases, and so on) were tested out and without any 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 arise with mixtures. From a computational point of view, most of the algorithms used for solving equations of state only search for three roots at the most and are thus likely to be inefficient when an equation of state gives more than three volume-roots. To overcome this limitation, a simple procedure allowing to identify all the possible volume-roots of an equation of state is proposed.