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Unformatted text preview: Low-Order Models for Catalyst Particles: A Dynamic Effectiveness Factor Approach Jose ´ A ´ lvarez-Ramı´rez, Francisco J. Valde ´s-Parada, and J. Alberto Ochoa-Tapia Divisio ´n de Ciencias Ba ´sicas e Ingenierı´a, Universidad Auto ´noma Metropolitana–Iztapalapa, Mexico, D.F., Mexico DOI 10.1002/aic.10593 Published online August 31, 2005 in Wiley InterScience (www.interscience.wiley.com). Models for heterogeneous reactors are composed of distributed parameter ordinary and partial differential equations to describe balances both for a ﬂuid and a catalyst particle. For steady-state conditions, the effectiveness factor (EF) approach has been primarily used to reduce the model dimensionality, which yields an important computa- tional effort during reactor design stages. The idea behind EF is to express the reaction rate in a catalyst particle by its rate under surface/bulk conditions multiplied by the EF. As a consequence, only few arithmetic operations to obtain the catalyst particle total reaction rate have to be made, avoiding in this form repeated solutions of the more sophisticated distributed parameter model. The aim of this paper is to extend the EF approach to obtain a simple model for the dynamics of the catalyst particle total reaction rate. As a preliminary step, a Laplace domain approach is used to introduce a dynamic EF (DEF) concept as a linear operator that transforms reaction rate signals from surface/bulk to catalyst particle conditions. It is shown that the DEF becomes the transfer function of a model governing the dynamics of the catalyst particle reaction rate. However, the resulting transfer function is infinite-dimensional. This implies that, con- trary to the steady-state case, an exact simple modeling of the reaction rate dynamics is not possible. An approach to obtain low-order models, based on an approximate model matching, is proposed. For a first-order model, the time constant is computed for common particle geometries showing its dependency with the Thiele modulus. In fact, the results show that the (dominant) time constant is a decreasing function of the Thiele modulus. In this form, the faster the chemical reaction dynamics, the faster the reaction– diffusion catalyst particle dynamics. © 2005 American Institute of Chemical Engineers AIChE J, 51: 3219–3230, 2005 Keywords: catalyst particle, reaction– diffusion, low-order model, approximate model matching Introduction Dynamic models for heterogeneous reactors are composed of distributed parameter, ordinary, and partial differential equa- tions to describe balances both for a ﬂuid and a disperse phase composed by catalyst particles. Simple models for the ﬂuid can correspond to continuous stirred tank assumptions, which yield coupled ordinary differential and algebraic equations. Given that intraparticle resistance to mass transfer becomes significant for catalyst particles, mass and energy balances can lead to distributed parameter differential equations to describe the concentration dis-...
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This note was uploaded on 03/10/2011 for the course CBI 101 taught by Professor O.tapia during the Spring '11 term at UNAM MX.
- Spring '11