A novel method for investigating the repulsive and attractive parts of cubic equations of state and the combining rules used with the vdW-1f theory

A novel method for investigating the performance of the repulsive and attractive terms of a cubic equation of state (EoS) along with different combining rules for the cross covolume (b(12)) and cross-energy (a(12)) parameters used with the van der Waals one-fluid theory is presented. The method utilizes the EoS-derived liquid-phase activity coefficient which is separated into a combinatorial-free volume part (gamma(c-fv)), obtained from the repulsive term of the EoS, and a residual one (gamma(res)) obtained from the attractive term.

Athermal systems (alkane solutions) are used where we can reasonably expect that the residual part will be close to one and, consequently, the combinatorial-free volume part will be close to the experimental value. For these solutions the main effect of nonideality comes from size/shape differences rather than energetic ones.

Thus, it is reasonable to assume that gamma(res) is approximately unity. It is demonstrated that the empirically used combining rules, the arithmetic mean (AM) for b(12) and the geometric mean (GM) for a(12), while not giving completely satisfactory results, are the best choices by far. Moreover, the qualitative agreement between the gamma(c-fv) values with the experimental ones suggest that the van der Waals (vdW) repulsive term is applicable not only to mixtures with spherical molecules, as originally suggested by van der Waals, but also to very asymmetric ones.

On the other hand, the attractive term leads to gamma(res) values that can be substantially different from unity for asymmetric athermal systems. Furthermore, we show that the l(ij) interaction parameter (correction to the covolume term) is, for athermal systems, more important than the commonly employed k(ij) parameter (correction to the cross-energy term).

What is particularly interesting is that a single (per system) l(ij) value yields, simultaneously, physically meaningful activity coefficient values and excellent vapor-liquid equilibria correlation. Thus, the whole ethane/n-alkane series (up to n-C-44) can be described with a unique l(ij) value. (C) 1997 Published by Elsevier Science Ltd.