Mathematical Modeling of Packed Bed Reactors: Numerical Solutions and Control Model Development

Abstract

This chapter presents an analysis of the development of dynamic models for packed bed reactors, with particular emphasis on models that can be used in control system design. The method of approach formulates a comprehensives, relatively detailed packed bed reactor model. The chapter also considers the techniques available for numerical solution of the model; and utilizes one such numerical solution to examine simplifications of the model based on its underlying physics. It then describes how the model may be reduced mathematically to one useful for control system design. Mathematical models of packed bed reactors are needed for the description of steady-state and dynamic behavior for process design, optimization, and control. Although insufficient detail can lead to a model incapable of accurately representing the reactor's response to changes in operating variables, excessive detail can lead to a model that is computationally impractical or contains parameters the values of which cannot accurately be determined from operating data. Thus, although the development is intended to be generally applicable to packed bed reactor modeling, all numerical results are obtained for the methanation system. As a result, some approximations that are found to apply in the methanation system may not in other reaction systems, and, where possible. The chapter discusses approaches to numerical solution of the model with a detailed exposition of one approach, orthogonal collocation. Common physical assumptions made in packed bed reactor modeling are evaluated.

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