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

Modeling
HRT is a promising theory, its mathematical structure is too complex for typical
engineering applications.
3. Crossover approach based on a phase-space cell approximation: Based on
Wilson’s phase-space cell approximation (Wilson, 1971), White and co-workers derived a
recursion procedure for pure fluids (White, 1993 and White and Zhang, 1993). White’s
global RG theory consists of a set of recursion relations where the contribution of longer
and longer wavelength density fluctuations up to the correlation length is successively
taken into account in the free energy density. In this way, properties approach the
asymptotic behaviour in the critical region, and they exhibit a crossover between the
classical and the universal scaling behaviour in the near-critical region. Lue and Prausnitz,
(1998) extended the accuracy and range of White’s equations through an improved
Hamiltonian. The theory was applied to square-well fluids and results compared to
simulation and experimental results, using the square-well model. The approach was then
used by Jiang and Prausnitz (1999 and 2000) to describe the pure n-alkanes family and
some of their mixtures. Jiang and Prausnitz were the first who applied the theory to chain
molecules, modelled as square well chains. An advantage of this method versus Kiselev’s
is that it is an easy-computing numerical method based on recursive equations, and the two
additional parameters can be transferred within the same series. The main disadvantage is
its numerical character, versus the analytical nature of Kiselev’s method. However, the
resolution of the involved recursive equations is very fast in computers available
nowadays. Compared to HRT, it has a simpler mathematical structure that can be applied
to a classical equation-of-state. Thus, White’s theory is useful for engineering application
as shown previously (Jiang and Prausnitz, 1999).
Unfortunately, RG theory cannot easily be generalized to mixtures except for a
nearly pure system with a trace impurity (Wilson, 1975). Fisher and others have proposed
that a theory for critical phenomena of mixtures can be based on the assumption that a
universal property of a mixture near its critical point is isomorphic to that of a onecomponent
system, provided that certain appropriately chosen thermodynamic variables
are kept constant (Fischer, 1968; Anisimov et al., 1971). Under this assumption, RG theory
for a one-component system can be applied directly to mixtures. The results of some RG
theories based on the isomorphism approximation are in good agreement with
experimental data (Parola and Reatto, 1995; Jin and Sengers, 1993; Hager and Sengers,
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