Synthesis of a Non Dispersive Solvent Extraction Plant for Effluent Treatment and Metal Recovery

A Nonlinear Mixed Integer Programming approach is presented to select the number of membrane modules required in the extraction and stripping sectors of a Non Dispersive Solvent Extraction Plant for effluent treatment and metal recovery. The differential equations that model each membrane module are discretized using orthogonal collocation on finite elements leading to an algebraic system of equations. Binary variables are used to select the number of membrane modules in the extraction and stripping sectors. A superstructure with hollow fibre membrane modules in series in the extraction and stripping sectors is presented. A Mixed Integer Non Linear Programming problem is formulated in GAMS to optimise the superstructure. An initialisation strategy for the solution of the Mixed Integer Non Linear Programming problem is presented. The solution of the non linear programming problem, with the extraction and stripping areas rounded up to the nearest superior integer number of membrane modules for both sectors is used as the initial point. This initialisation reduces significantly the time required to solve the MINLP problem leading in most cases to the optimal solution.