Optimization of Catalytic Processes and Reactors

Abstract

Efficient methods and algorithms have been developed for the optimization of catalytic processes and reactors. In mathematical terms, these problems reduce to finding the extremum of a functional of a large number of variables whose domain of variation is subject to various constraints as sets of partial differential equations and algebraic inequalities. This implies solving problems in which the domain of extremals is closed. Applying Pontryagin's maximum principle to catalytic processes described by sets of differential equations with constrained phase and control variables allows the necessary set of optimal conditions to be found. A numerical algorithm has been developed for solving nonlinear boundary-value problems that arise when the maximum principle is employed. The efficiency of this algorithm is demonstrated by the example of the catalytic oligomerization of α-methylstyrene, a typical process requiring various kinds of optimization problems to be solved. The theoretical optimization of the process has served as the basis for the engineering optimization of an industrial reactor. Optimal controls were determined in both the theoretical and engineering optimization steps.