A NEW PROCEDURE FOR YIELDING A RAPID SOLUTION BY USE OF THE MULTI-THETA METHOD OF CONVERGENCE

The definition of a new multiplier and the modification of the multi-t heta method of convergence are developed for solving distillation prob lems. Furthermore, a procedure for stabilizing the numerical calculati ons and for yielding rapid solutions is proposed. It is found that an assumed value of a multiplier in each iterative computation can be ass igned to an arbitrary number, and that it is better to be set equal to unity. To demonstrate the advantage of the proposed damping method, s ome numerical examples for distillation with hydrolysis of methyl acet ate are presented. The reactive distillation problems are solved with the proposed procedure, and the results are compared with those by a c onventional method. The proposed method constricts the large excursion resulting from the Newton-Raphson method. Then the corrected values c an be confined within a region of convergence. The procedure proposed herein may be extended to other types of multistage separation process es.