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Modeling
The pioneering work of Wertheim in the mid-1980s resulted in a family of
engineering EoS developed in the 1990s that includes SAFT (Jackson et al., 1988 and
Chapman et al., 1988), polar-SAFT (Walsh et al., 1992) SAFT-HS (Green and Jackson,
1992), simplified SAFT (Fu and Sandler, 1995) SAFT-LJ (Muller and Gubbins, 1995a;
Kraska and Gubbins, 1996) copolymer SAFT (Banaszak et al., 1996), soft-SAFT (Blas and
Vega, 1997, 1998a, 1998b; Pàmies and Vega, 2001), SAFT-VR (Gil-Villegas et al., 1997)
SAFT1 (Adidharma and Radosz, 1998), SAFT-BACK (Pfohl and Brunner, 1998),
crossover SAFT (Kiselev and Ely, 1999a, 1999b and 2000), PC-SAFT (Gross and
Sadowski, 2001), crossover soft-SAFT (Llovell et al., 2004) and SAFT-VRX (McCabe and
Kiselev, 2004). The different versions differ mainly on the intermolecular potential chosen
to describe the reference fluid. The original SAFT EoS uses a perturbation expansion with
a hard-sphere fluid as a reference and a dispersion term as a perturbation. The hard-sphere
Helmholtz free energy is calculated through the expression of Carnahan and Starling and
the dispersion term through correlations of molecular simulation data for the LJ fluid,
which are functions of the reduced temperature and density (Jackson et al., 1988 and
Chapman et al., 1988). Other intermolecular potentials, such as the square-well (Banaszak
et al., 1993 and Tavares et al, 1997) and the Yukawa potential (Davies et al. 1999) have
been used as the model for the segment interactions. Jackson et al. proposed a generalized
potential function with an attractive part of variable range in the so-called SAFT-VR
approach (Gil-Villegas et al., 1997). The availability of an analytical EoS for the LJ fluid
(Johnson et al., 1993 and Kolafa and Nezbeda, 1994) led to other versions of the SAFT
equation (Muller and Gubbins, 1995a; Kraska and Gubbins, 1996), like the soft-SAFT EoS
that will be described in the next section. Two excellent reviews on the development,
applications and different versions of SAFT-type equations were provided by Müller and
Gubbins (2001) and also by Economou (2002).
Due to its robustness, versatility and elegance the SAFT model and its different
versions have received an impressive acceptance in academia and in industry for phase
equilibrium calculations of VLE of hydrocarbons, alcohols, fluorohydrocarbons, LLE for
hydrocarbons, alcohols, solvating mixture, fluid phase equilibria of aqueous mixtures,
phase equilibria of reservoir fluids, phase behaviour and solubility of polymer and
copoymer solutions, supercritical extraction, among others (Muller and Gubbins, 2000).
The theory is now finding application to a range of complex fluid problems, including
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