n - PATh :.: Process and Product Applied Thermodynamics research ...

III.1. Introduction
Modeling
Most conventional engineering equations of state are variations of the van der
Waals equation. They are based on the idea of a hard-sphere reference term to represent the
repulsive interactions, and a mean-field term to account for the dispersion and any other
long-range forces. Commonly used EoS (e.g. Peng-Robinson, Soave-Redlich-Kwong,
modified Benedict-Webb-Rubin) involve improvements to either the treatment of the hardsphere
contribution or the mean-field terms. Such an approach is suitable for simple, nonpolar,
nearly spherical molecules such as hydrocarbons, simple inorganics as nitrogen and
carbon monoxide, etc. For these compounds, the most important intermolecular forces are
repulsion and dispersion, together with weak electrostatic forces due to dipoles,
quadrupoles, etc. Nevertheless, many fluids, and particularly mixtures, do not fall within
this simple classes as polar solvents, hydrogen-bonded fluids, polymers, electrolytes, liquid
crystals, plasmas, and so on which are highly polar, associating and often non-spherical.
Although it is possible, in practice, to use one of these classical equations for these
systems, their limitations rapidly become evident. The correlation of data requires complex
and unsound mixing rules and temperature dependent binary parameters, and the predictive
capability of this approach is usually poor. The reason for this is that, for such fluids,
important new intermolecular forces come into play such as Coulombic forces, strong
polar forces, complexing forces, forces associated with chain flexibility, induction forces,
etc. that are not taken into account explicitly. In such cases a more appropriate reference is
one that incorporates both the chain length (molecular shape) and molecular association,
since both effects have a dramatic effect on the fluid structure. Other interactions (e.g.
dispersion, long-range dipolar forces, etc) can then be treated via a perturbation or
approximate mean-field term.
The development of novel processes at extreme conditions (such as, for example,
processes where one or more of the components are supercritical) and the design of new
materials over the last two decades imposed the need for new models. At the same time,
significant developments in the area of applied statistical mechanics resulted in a number
of semi-empirical EoS, such as the lattice fluid theory (LFT), (Sanchez and Lacombe,
1976) the perturbed hard-chain theory (Donohue and Prausnitz, 1978), and their
modifications. These EoS are more complex than cubic EoS but significantly more
accurate for various complex fluids, such as hydrogen bonding fluids, supercritical fluids,
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