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

Modeling
and polymers. Furthermore, the tremendous increase of computing power at reasonable
prices made these new complex models attractive for process simulation calculations.
Statistical mechanics is a reliable tool for calculating the structure and
thermodynamics of a fluid given its intermolecular potential function. However, for most
systems of interest, this solution requires the use of one or more approximations, which
determine the accuracy of the theory. Two methods can be used for the modeling of
complex homogeneous fluids, namely, integral-equation theories and perturbation theories.
Both have been successful in solving the thermodynamic properties of some moderately
complex fluids (nonspherical molecules, polar and polarizable fluids) (Hansen and
McDonald, 1986; Gray and Gubbins, 1984). The possibility of molecular association can
be introduced into integral-equation theories by considering a strong, spherically
symmetric attraction, such as would be observed in the case of ionic systems. Although
initial attempts failed to reproduce the low density limit for associating fluids, this
difficulty has since been overcome. In perturbation approaches, one considers a reference
fluid with well-known properties (e.g., a homomorphic, nonassociating fluid) and obtains
the properties due to association through a perturbation expansion. This however, is not
straightforward, as the association forces involved are strong and highly directional and the
typical expansions used for weakly attractive fluids fail to converge (Muller and Gubbins,
2000).
In a series of four papers, Wertheim developed a statistical thermodynamic theory
for fluids with a repulsive core and one or more highly directional short range attractive
sites, known as TPT (Wertheim, 1984, 1986 and 1987). In TPT, the Helmholtz free energy,
A, is calculated from a graphical summation of interactions between different species.
Based on the first-order TPT, usually referred as TPT-1, Chapman, Gubbins, and coworkers
developed an EoS for spherical and chain molecules with one or more hydrogenbonding
sites (Jackson et al., 1988 and Chapman et al., 1988). The essence of their
approach was the use of Wertheim's theory to describe a reference fluid which includes
both the molecular shape and molecular association, instead of the much simpler hardsphere
model employed in most engineering equations of state. The effect of weaker
intermolecular forces, like dispersion and induction, were included through a mean-field
perturbation term. They called this approach the Statistical Associating Fluid Theory
(SAFT).
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