Activity coefficients in nearly athermal mixtures predicted from equations of state: Don't blame the cubic when it is the lack of a third parameter!

Abstract

The idea that cubic EoS's are very primitive and limited models, quite extended at present among researchers working on fluid properties and phase equilibria, has different roots, including some limitations observed specifically for classic and popular equations like Peng-Robinson (PR) or Soave-Redlich-Kwong (SRK). These are two-parameter models, i.e. they have only an attractive and a repulsive parameter to characterize each molecule, while other models like SAFT but also cubic –and still for non-associating molecules-introduce also a third parameter related somehow to the molecular structure or shape. One of the alluded limitations, actually a very clear one, is the complete failure in describing the non-ideality in nearly athermal mixtures, like those composed of n-alkanes with different chain lengths: SRK and PR predict positive deviations from ideality, which increase with the system asymmetry, while experimental measurements show exactly the opposite, i.e. increasing negative deviations from ideality. This provides an excellent opportunity to try to clarify whether such failure is due to the cubic nature of these classic models or to their two-parameter character and/or to the classic van der Waals one-fluid (vdW1f) mixing rules typically used. With that motivation, in this work we used models representing three different categories, in a completely predictive way: a two-parameter cubic EoS (PR), a three-parameter cubic EoS (RKPR) and a three-parameter SAFT EoS (PC-SAFT). Their predictions of infinite dilution activity coefficients were analyzed and compared, in contrast to available data for different mixtures of n-butane to n-octane as the lighter compound and paraffins ranging from C16 to C36 as the heavier, in both extremes of dilution. The obtained results, and their analysis, allowed us to extract very clear conclusions which were not present in the literature so far, regarding the importance of a third parameter in any type of EoS.