The application of the substitute objective function minimization for solving multi-stage separation problems

A new algorithm is developed for steady-state simulation of stagewise counter-current separation processes. Model equations are decoupled by stages. Iterative variables are selected from stage variables of one stage of a separation column. The convergence of the method is ensured by means of an optimization procedure in which the objective function derived from departures of calculated and assumed values of tear variables is minimized. Inequality constraints for all state variables are taken into account and introduced into the minimization routine by means of the substitute objective function. Finally the new sum-of-squares function becomes unimodal in the whole range of tear variables. The method is illustrated by solving problems for the solvent extraction of metals.