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.

(Combinatorial term omitted)

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 fromto : 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)

At infinite dilution, (2b)

Now, can be calculated from Eq. (3) by combining Eq (1) and (2b):

(3)

In Eq. (1) and (2),

(Correspond to D0JI, D1JI, D2JI) Equation (3) is equivalent to the equation:

, with

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.