Title

SOLUTION OF EQUATION SYSTEMS FOR PROCESS SIMULATION

Date of Completion

January 1982

Keywords

Engineering, Chemical

Degree

Ph.D.

Abstract

This work addresses a number of fundamental problems relevant to the solution of equation systems encountered in steady-state and dynamic simulation of chemical engineering processes. Particular consideration is given to the treatment of thermodynamic and physical property functions. Those functions are typically highly nonlinear, expensive to evaluate and difficult to differentiate.^ A new Hybrid algorithm is proposed for solving systems of nonlinear algebraic equations. It combines the best aspects of the Newton and Quasi-Newton approaches. Like Newton method, it utilizes computed values of partial derivatives, when they are easily obtained. Those terms for which differentiation is unfeasible or not economical are approximated, using a Quasi-Newton method. Thermodynamic functions are further divided into their ideal and nonideal components; the first one is also computed, the second one is efficiently approximated by the Hybrid method. The method is superlinearly convergent, insensitive to scaling, and applicable to large, sparse equation systems.^ For dynamic simulation, the idea of local approximations to the rigorous thermodynamic models is used. A key ingredient to this idea is a method for computing the adjustable parameters present in the local models, so that good approximations are maintained at all times. A novel updating procedure is presented, that performs this task. It makes only occasional use of rigorous thermodynamic information in order to "tune" the local models about the current process conditions.^ In addition, a method is developed for determining when the local models should be updated. The interval between successive updates is adjusted automatically, depending on the measured error between rigorous evaluations and local model predictions. This procedure greatly reduces the requirements for rigorous evaluations.^ The methods developed for both steady-state and dynamic simulation permit constructing an easy interface between solution procedures and existing thermodynamic packages. At the same time they achieve a very significant reduction of rigorous property evaluations and of associated simulation cost.^