Matrix Formulation of Unifac/Uniquac Models for the Construction of Residue Curve Maps

Using the matrix formulation of the UNIFAC/UNIQUAC equations, we were able to obtain explicit formulas for the evaluation of activity coefficients and their partial derivatives. These formulas lead to a direct and explicit reduction of residue curve map (RCM) models from a set of differential-algebraic equations (DAEs) of index-1 to an equivalent set of ordinary differential equation (ODEs). Thus this approach allows for a wider selection of solution methods than those limited to handling DAEs such as the mass-matrix formulations. More importantly, the standard tools can now be used for qualitative analysis of the RCM models, e.g. the explicit construction of Jacobian matrices for stability analysis. The paper also includes example applications of the methods discussed to ternary and quaternary systems that exhibit multiple azeotropes.