GLOBAL STABILITY ANALYSIS AND CALCULATION OF LIQUID-LIQUID EQUILIBRIUM IN MULTICOMPONENT MIXTURES

A global algorithm for implementing the Gibbs tangent plane stability test in multicomponent, multiphase liquid mixtures is described. The a lgorithm is self-starting and significantly improves the reliability a nd robustness of multiphase equilibrium calculations. The main improve ment is a result of a new approach for locating the stationary points of the tangent plane distance function. This relies on the geometric p roperties of the tangent plane distance function but is independent of the specific fluid model. For ternary mixtures, it is shown that stat ionary points in the tangent plane distance function satisfy a global topological constraint N-max + N-min - N-sad = 1 where N-max is the nu mber of maxima, N-min is the number of minima, and N-sad is the number of saddles. This provides a global consistency check on the numerical results that is independent of the specific model or parameters used to describe the mixture. The method has been implemented and tested on a variety of problems with three and four components and up to three liquid phases. Solutions can be found with sufficient speed for intera ctive design and modeling. In all of the examples, solutions for the e ntire phase diagram were found without fail, and certain problems that are difficult or impossible to solve using other methods were modeled successfully.