Equations of State: From the Ideas of van der Waals to Association Theories

The ideas of van der Waals have resulted to cubic equations of state like Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR) which are widely used in the petroleum and chemical industries. It is often thought that the range of applicability of van der Waals-type models is limited to mixtures of compounds relatively similar in size.

We employ in this work an approach for investigating the various terms of cubic equations of state by looking at the excess Gibbs energy and activity coefficient expressions which are derived from these equations of state. We illustrate that the results of cubic equations of state are sensitive to the mixing and combining rules used.

Moreover, it is shown that previously reported deficiencies for size-asymmetric systems are more related to the van der Waals one fluid mixing rules used rather than the functionality of the cubic equation of state itself. Improved models for polar systems have been developed using the so-called EoS/GE mixing rules and we illustrate with the same methodology how these mixing rules should best be used for size-asymmetric systems.

Despite the significant capabilities of cubic equations of state, their limitations lie especially in the description of complex phase behavior, e.g. liquid–liquid equilibria for highly polar and/or hydrogen bonding containing molecules. In these cases, advanced equations of state based on statistical mechanics that incorporate ideas from perturbation (e.g.

SAFT and CPA), chemical (e.g. APACT) and lattice (e.g. NRHB) theories are preferred. Some of the most promising approaches are briefly outlined here. Their capabilities and limitations/challenges, pointing out to future research needs are also discussed.