Solution to recycle problems in computer-aided design

Abstract

A method of numerical solution of process models in computer-aided design has been investigated. The steady - state model of a process is usually solved many times in the course of design, especially if the model is complicated by recycle. There is therefore a strong need for techniques which will allow the efficient and automatic solution of process models. Typical systems of non-linear equations are shown to be aparse in variables, a property which can be used to simplify the solution by partitioning. An ordered iterat ive solution of the partitioned blocks is usually necessary because of recycle streams. Algorithms for partitioning and ordering have been developed. The units are ordered into a sequence with a minimum number of recycle variables by a modified dynamic programming algorithm after partitioning of the flowsheet by a search algorithm. Three algorithms for convergence of the ordered iterative solution have been programmed. Of these, the quasi-Newton algorithm does not require computation of the matrix of partial differentials and appears ideal for use in computer-aided design programs. The algorithms for partitioning, ordering, and convergence of the iterative solution provide a means for the automatic solution of models of arbitrary processes. The algorithms have been tested by application to two design investigations; modification of multi-effect evaporator stations in the sugar industry and design of mineral flotation circuits. A flexible program which allows conventional tabular input has been written for these investigations. The combination of numerical techniques and flexible program has proved to be a useful system for the design of real processes.