Low dimensional modeling of flow reactors

A new method is devised to obtain a low dimensional dynamic model of flow reactors governed by nonlinear partial differential equations. This is based on the Karhunen-Loeve decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system. These empirical eigenfunctions are then employed as a basis set of a Galerkin procedure tb reduce the distributed parameter system to a lumped parameter system in the optimal way in the sense that the degree of freedom of the resulting lumped parameter system is minimum. Flow reactors such as combustors, incinerators and CVD reactors cannot be described appropriately by conventional assumptions such as well-mixed flow or plug flow, and we need accurate flow patterns and convection-conduction/diffusion rates before characterizing or predicting their performance. Because the governing equations of these processes are nonlinear partial differential equations and, moreover, most practical how reactors are of irregular shapes, the traditional Galerkin methods or orthogonal collocation are never feasible to lump these systems for the purpose of control or parameter estimation. But the Karhunen-Loeve Galerkin procedure suggested in the present paper can easily reduce these nonlinear partial differential equations defined on irregular domains into reliable dynamic models with a few degrees of freedom, which may later be employed in the parameter estimation or reactor control. Copyright (C) 1996 Elsevier Science Ltd.