Convergence Characteristics of Augmented Hessian Models for Separations

Abstract

Previous research has shown that the form and number of MESH equations used to describe distillation/extraction systems can change both the linearity and convergence characteristics. In this paper, the structures of the equation sets for distillation and extraction models are analyzed in terms of the form of the three dimensional Hessian associated with them. It is known that for highly nonlinear equilibrium stage problems the N(2C+1), N(2C+3) variable forms used in the Naphthali-Sandholm model are more difficult to converge than newer models of Ricker-Nakashio-King and Krishnamurthy-Taylor that have N(4C) and N(5C+1) variables respectively. The convergence behavior of specific equation sets that augment the size of the Hessian are compared with the standard forms.