Chemistry Reference
In-Depth Information
Wood 2000; Plyasunov, Shock, and O'Connell 2006). In recent years, extensions
have been made to ionic liquid systems and to solubilities of solids, such as phar-
maceuticals, in mixed solvents (Abildskov, Ellegaard, and O'Connell 2009, 2010a,
2010b; Ellegaard, Abildskov, and O'Connell 2009; Ellegaard 2011).
The purpose of this chapter is to review these applications of FST methodol-
ogy for correlating and predicting properties of a wide variety of systems and as
a basis for validating EOS models. Some of the material is already in the previous
review monograph (O'Connell 1990), though little of that discussion is repeated here.
Since that time, advances have been made in several directions; these are the present
focuses. Section 9.2 describes applications to pure component and mixture densities;
Section 9.3 treats phase equilibria with a focus on dilute solutions; and Section 9.4
describes the use of FST formulations to test EOS models and mixing rules against
data for binary total and direct correlation function integrals (TCFIs) and (DCFIs).
9.2
FLUCTUATION SOLUTION THEORY MODELING
OF PURE COMPONENT AND MIXTURE DENSITY
DEPENDENCES ON PRESSURE AND COMPOSITION
Relations between the TCFIs and derivatives of pressure with respect to molar density
can be written for any number of components, as in Section 1.1.6 in Chapter 1. Matrix
inversion techniques can provide expressions for all of the pair TCFIs of the system.
Section 1.2 in Chapter 1 gives the full relations for applications to pure, binary, and
ternary systems. As shown in Section 1.2.3 in Chapter 1, there is also a set of relations
for the derivatives in terms of the DCFI, which are somewhat simpler and more direct.
There are two modeling objectives with these relations. One is to obtain a solution den-
sity at elevated pressures; the other is to obtain the component partial molar volumes for
the solution density variations with composition. The next section describes approaches
that have been used for both objectives in a wide variety of pure and binary systems.
9.2.1 c
omPressiBiliTies
FST gives relations for the reduced bulk modulus and the partial molar volume of
component
i
to integrals of TCFIs and DCFIs (Section 1.2 in Chapter 1). The great-
est use of this relationship has been for compressed liquids where the TCFI and
DCFI show simple corresponding states dependence on density with weak tempera-
ture dependence (Brelvi and O'Connell 1972, 1975a, 1975b; Mathias and O'Connell
1979, 1981; Campanella, Mathias, and O'Connell 1987; Huang and O'Connell 1987;
Abildskov, Ellegaard, and O'Connell 2010a). In terms of DCFIs, the expression is
n
c
n
c
∂
∂
β
ρ
p
∑
1
∑
(
)
{}
=
x
x
1
−
CT
,
ρ
(9.1)
i
j
ij
{}
Tx
,
i
=
j
=
1
