MSE Density Parameter Update
In UNIQUAC term, the excess molar volume, , is assumed to be analogous to that of the excess Gibbs energy, i.e.
where is a different interaction parameter from that of
in the
model.
The symmetrically normalized
(subscript UNIQ is omitted in the following text) needs to be converted to the unsymmetrically normalized value (
) for density calculations in MSE.
Conversion from
to
:
Standard state chemical potentials in the two normalizations are related by
(or
)
which is derived from equality of chemical potentials in two normalizations, and using
1 in the infinite dilution limit. Derivatives of ’s with respect to pressure give volumes, i.e.
->
Here is how to calculate
Analogous to
,
can be defined as
and derived from Eq. (1) as:
(2a)
Now, can be calculated from Eq. (3) by combining Eq (1) and (2b):
In Eq. (1) and (2),
(Correspond to D0JI, D1JI, D2JI)
Equation (3) is equivalent to the equation:
Solution volume is then calculated by
Here is calculated from contributions of UNIQUAC and “middle-range” terms, if applicable, and
is from either HKF or as described in 2002 paper for organic component.