Decomposition of very large-scale Newton-Raphson based flowsheeting problems

Abstract

This paper presents an approach for decomposing and solving the very large set of linear equations forming the innermost loop of the Newton-Raphson method. In a straightforward manner the equation set is decomposed into smaller sets, one of each unit in the process and a small set for the overall process. Solution proceeds in three steps: forward elimination for each unit subset, solving completely the residual plus overall process flowsheet equations, and a backward substitution for the unit subsets. The decomposition permits effective use of mass memory when solving very large flowsheeting problems. It also enhances the performance of local pivot strategies used in existing sparse matrix codes.