A global optimization technique for solid-liquid equilibrium calculations : application to calcium phosphate precipitation

Phase equilibrium calculations constitute an important problem for designing and optimizing crystallization processes. The Gibbs free energy is generally used as an objective function to find the quantities and the composition of phases at equilibrium. In such problems, the Gibbs free energy is not only complex but can have several local minima. This paper presents a contribution to handle this kind of problems by implementation of a hybrid optimization technique based on the successive use of a Genetic Algorithm (GA) and of a classical Sequential Quadratic Programming (SQP) method: the GA is used to perform a first search in the solution space and to locate the neighborhood of the solution. Then, the SQP method is employed to refine the solution. The basic operations involved in the design of the GA developed in this study (encoding with binary representation of real values, evaluation function, adaptive plan) are presented. Calcium phosphate precipitation which is of major interest for P-recovery from wastewater has been adopted as an illustration of the implemented algorithm