Application of a global optimization algorithm to phase stability and liquid–liquid equilibrium calculations

• A global optimization algorithm has been developed for finding all singular points of an objective function.
• The idea of following ridges and valleys has been significantly enhanced by applying arc length continuation method.
• The algorithm locates all stationary points of the Gibbs tangent plane distance function predicted by any LLE model.
• The combined phase equilibrium and stability algorithm significantly improves reliability of VLLE calculations.

A global optimization algorithm was developed for finding all singular points (minima, maxima and saddles) of an objective function by exploring the natural connectedness that exists between their singular points. The idea of following ridges and valleys using information gathered along the way was significantly enhanced by applying the arc length continuation method. The algorithm was applied to the Gibbs tangent plane stability test for multiphase liquid mixtures. The global optimization algorithm gives an efficient and robust scheme for locating all stationary points of the tangent plane distance function predicted by any thermodynamic model. Since it provides very good initial estimates for the liquid–liquid equilibrium calculations, it became an integral part of a combined phase equilibrium and stability algorithm. The combined algorithm is self-starting and significantly improves reliability and robustness of multiphase equilibrium calculations. It was successfully tested on a variety of problems and is applicable to any component's mixtures and any number of liquid phases. Solutions have been found for the entire phase diagram.

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