Activity Coefficient Models Part 2: Local Composition Models, from Wilson and NRTL to UNIQUAC and UNIFAC

Abstract

Traditional cubic EoS using the classical vdW1f mixing rules and activity coefficient models like the Margules and van Laar equations use 'average' or 'overall' compositions. They are models based on 'random mixing'. However, due to intermolecular forces, the mixing of molecules is never entirely random and a way to account for the non-randomness can lead to improved models and better descriptions of phase behavior. Since their advent with the Wilson equation in 1964, 1 local composition (LC) activity coefficient models have drastically changed the range of applicability of liquid phase models.There exist several models which employ the LC concept, which is illustrated in Figure 5.1. All of these models are based on the physical picture that the mixing of molecules is 'non-random' and this is accomplished by using the so-called 'local compositions' which are, in the general case, different from the average concentrations due to the short-range nature of intermolecular forces. Due to their basis in this different principle, LC models differ drastically from random-mixing-based models (Chapter 4). LC models allow for a certain degree of non-randomness and they can thus be expected to represent more realistically the phase behavior of complex mixtures. Of course, we need to know the distribution of the local fractions, which is given by a Boltzmann factor expression, and different functions are employed in the various LC models, see Table 5.1.As we will see, in most cases two interaction parameters per binary mixture in LC models are sufficient for obtaining good VLE results. The interaction parameters in LC models have, as seen from their derivation (see Appendix 5.A), an in-built temperature dependency and some theoretical significance. Moreover, LC models can be readily extended to multicomponent systems, easier than, for example, the van Laar and Margules equations. Two of the LC models, namely Wilson and UNIQUAC, have been further developed into predictive group contribution (GC) versions (ASOG and UNIFAC), suitable for preliminary design in the absence of

A Geometric Approach for the Calculation of the Nonrandomness Factor Using Computational Chemistry

“…Prausnitz in 1975 . It is a local composition model based on the two-fluid theory and is capable of representing vapor–liquid equilibria (VLE) − and liquid–liquid equilibria (LLE) ,,− of mixtures. , UNIQUAC was deduced from a statistical mechanics basis, extending Guggenheim’s quasi-chemical theory, , and building on the work of Wilson …”

“…14 It is a local composition model based on the two-fluid theory and is capable of representing vapor−liquid equilibria (VLE) 15−18 and liquid−liquid equilibria (LLE) 4,5,19−21 of mixtures. 14,22 UNIQUAC was deduced from a statistical mechanics basis, extending Guggenheim's quasichemical theory, 14,23 and building on the work of Wilson. 24 According to UNIQUAC, the excess Gibbs free energy (G E ) is the sum of combinatorial (G C E ) and residual (G R E ) contributions, as can be seen in eq 3.…”