(620e) 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.