Handbook of Solvents - George Wypych - ChemTech - Ventech!

1430 Aydin K. Sunol and Sermin G. Sunol
their inadequacy in representing the critical point. The non-classical scaling approaches 29,30
fail when extended beyond the very narrow critical region and their combinations with
equations of state (crossover EOSs) are still far from having practical applicability. Therefore,
we will focus on the van der Waals family of Equation of States. 31
These equations of states have both a repulsive and an attractive term. The most popular
variants differ in how the attractive terms are modeled. The success of more recent
Peng-Robinson 32 (PR) and Soave-Redlich-Kwong 33 (SRK) equation of states in phase behavior
representation is due to the added parameter, accentric factor that incorporates vapor
pressure information into the model. The shortcomings around the critical point are mainly
due to the enhanced contribution of repulsive forces that can be modified through Perturbed
Hard Chain Theory (PHCT). 34 Naturally, one other inherent difficulty is due to the instability
of high molecular weight compounds at their critical point. This implies use of other parameters
or pseudo critical properties to model the compounds and their mixtures. These
equations of states are better in representing molar gas volume then the liquid. The accuracy
of molar liquid volume can be improved through volume translation. 35 The added terms and
parameters naturally complicate the equation of state since the order of the equation increases
above cubic.
Yet another essential dimension of the equation of states is their representation of mixture
properties, which is achieved through mixing rules (models) that often include adjustable
binary interaction parameters determined from multi-component, ideally binary, data.
Most classical approaches fail to model mixing behavior of systems with dissimilar size
components and hydrogen bonding, particularly if one expects to apply them throughout a
wide pressure and temperature range that extends from very low to high pressures. Some of
the empirical density dependent mixing rules such as Panagiotopoulos-Reid 36 can account
for the relative size of the solute and the solvent but have theoretical shortcomings violating
one fluid model. There are also approaches that combine equation of state with activity
models by forcing the mixture EOS to behave like the activity models (G E) at liquid densities.
31 EOS-G E models can be combined with group contribution models to make them predictive.
More recently, Wong-Sandler 37 mixing rules provide an avenue to incorporate more
readily available low-pressure information into the equation of states extrapolate throughout
the entire pressure range, as well as ensuring fundamentally correct boundary conditions.
38
Considering the difficulty associated with representing fugacity coefficients that may
vary over ten orders of magnitude by mere change in temperature, pressure and composition;
a simple equation of state such as Peng-Robinson, which is given below, do very well
in correlating the experimental data and representing the phase behavior well.
where:
RT
a
p = −
V −b
V V b b V b
( + ) + ( − )
m m m m
repulsive attractive term
term
=∑
b x b
i
i i
∑∑
0.5
( ) ( ij)
a = x x a a 1− k
i
j
i j i j
b i= 0.07780 (RT ci/p ci)