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# A Mathematical Study of the Transient Behavior of a Fixed-Bed Catalytic Reactor

## Citation

Hwang, Kwang-chou (1965) A Mathematical Study of the Transient Behavior of a Fixed-Bed Catalytic Reactor. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/s4x7-2k68. https://resolver.caltech.edu/CaltechETD:etd-09202002-143911

## Abstract

Partial differential equations describing the transient behavior of a non-adiabatic fixed-bed catalytic reactor are derived with a minimum of simplifying assumptions. These equations axe applied to predict the transient behavior of a reactor for the oxidation of SO2 taking into account the behavior of both the fluid stream and the associated catalyst pellets.

Stability analyses of the numerical methods of solving the equations are presented in great detail, as the methods of analyses available in the literature are inadequate for the complicated system of equations encountered. A special study is made of the effects on stability of various methods of handling the nonlinear source terms in the equations. Some of the schemes proposed in the literature are found to be subject to severe stability criteria.

A method of obtaining a rigorous solution is devised. The method is always stable, and the use of varying time increment size is allowable. A rigorous solution takes only a few minutes of computer time with an IBM-7094 computer.

To investigate the effects of various limiting assumptions, three problems are studied using the rigorous method and also with methods employing various assumptions. These problems are the start-up, the loss of cooling with subsequent restoration, and the response of the exit concentration to a sinusoidal concentration forcing function at the entrance. For the system investigated, the effects of using an "effectiveness factor" model, neglecting radial changes, and neglecting the axial diffusion and axial velocity variations are found to be not large. The neglecting of reverse reactions, or the use of an average effectiveness factor throughout the whole reactor causes significant errors.

A simplified method, which for the system studied, gives a reasonably good approximation to the true solution, is used to investigate problems in the optimization and control of the reactor. The frequency response of the exit temperature to a sinusoidal forcing upon the optimum wall temperature is found to be equivalent to that of a phase lag network frequently used in regulating systems.

Limitations to the applicability of the simplified method are discussed.

Item Type: Thesis (Dissertation (Ph.D.)) (Chemical Engineering) California Institute of Technology Chemistry and Chemical Engineering Chemical Engineering Public (worldwide access) Longwell, Paul A. (advisor)Seagrave, Richard C. (advisor) Unknown, Unknown 4 November 1964 CaltechETD:etd-09202002-143911 https://resolver.caltech.edu/CaltechETD:etd-09202002-143911 10.7907/s4x7-2k68 No commercial reproduction, distribution, display or performance rights in this work are provided. 3654 CaltechTHESIS Imported from ETD-db 20 Sep 2002 08 Feb 2024 22:21

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