Decomposition based and branch and bound global optimization approaches for the phase equilibrium problem

An increasingly popular approach when solving the phase and chemical equilibrium problem is to pose it as an optimization problem. However, diiculties are encountered due to the highly nonlinear nature of the models used to represent the behavior of the uids, and because of the existence of multiple local solutions. This work shows how it is possible to guarantee-global solutions for a certain important class of the phase and chemical equilibrium problem, namely when the liquid phase can be modeled using either the Non-Random Two-Liquid (NRTL) equation, or the UNIversal QUAsi Chemical (UNIQUAC) equation. Ideal vapor phases are easily incorporated into the global optimization framework. A number of interesting properties are described which drastically alter the structure of the respective problems. For the NRTL equation, it is shown that the formulation can be converted into a biconvex optimization problem. The GOP algorithm of Floudas and Visweswaran 8, 9] can then be used to obtain-global solutions in this case. For the UNIQUAC equation, the new properties show how the objective function can be transformed into the diierence of two convex functions (i.e. a D.C. programming problem is obtained), where the concave portion is separable. A branch and bound algorithm based on that of Falk and Soland 6] is used to guarantee convergence to an-global solution. Examples are presented which demonstrate the performance of both algorithms.