GLOBAL OPTIMIZATION FOR THE PHASE AND CHEMICAL-EQUILIBRIUM PROBLEM - APPLICATION TO THE NRTL EQUATION

Several approaches have been proposed for the computation of solutions to the phase and chemical equilibrium problem when the problem is pos ed as the minimization of the Gibbs free energy function. None of them can guarantee convergence to the true optimal solution, and are highl y dependent on the supplied initial point. Convergence to local soluti ons often occurs, yielding incorrect phase and component distributions . This work examines the problems when the liquid phase is adequately modeled by the Non-Random Two Liquid (NRTL) activity coefficient expre ssion and the vapor phase is assumed to be ideal. The contribution of the proposed approach is two-fold. Firstly, a novel and important prop erty of the Gibbs free energy expression involving the NRTL equation i s provided. It is subsequently shown that by introducing new variables , the problem can then be transformed into one where a biconvex object ive function is minimized over a set of bilinear constraints. Secondly , the Global OPtimization (GOP) algorithm is used to exploit these ind uced properties of the formulation to guarantee convergence to an epsi lon-global solution, regardless of the starting point. A geometrical i nterpretation is provided for a selected smaller, but challenging, exa mple. Numerous examples are presented which demonstrate the broad appl icability of the proposed approach.