Dynamic Effectiveness Factor for Catalyst Particles

Dynamic Effectiveness Factor for Catalyst Particles - 11058...

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Dynamic Effectiveness Factor for Catalyst Particles Jose ´ A Ä lvarez-Ramı ´ rez,* J. Alberto Ochoa-Tapia, and Francisco J. Valde ´ s-Parada Di V isio ´ n de Ciencias Ba ´ sicas e Ingenierı ´ a, Uni V ersidad Auto ´ noma Metropolitana - Iztapalapa, Apartado Postal 55-534, Mexico D.F. 09340, Mexico Recei V ed: January 17, 2005; In Final Form: March 31, 2005 The effectiveness factor (EF) is a nondynamic concept that has been demonstrated to be useful for the analysis and design of reaction - diffusion systems (e.g., catalyst particles). The aim of this paper is to introduce a dynamic EF factor (DEF) concept that extends the existing nondynamic one. In the first step, the standard EF is interpreted as a scaling factor that transforms total reaction rates from surface/bulk to catalyst particle conditions. Through the use of Fourier transform (i.e., frequency domain) to deal with time variations, the above interpretation is extended to dynamic conditions by defining the DEF as a linear operator transforming total reaction rate signals from surface/bulk to catalyst particle conditions. It is shown that the classical nondynamic EF concept is recovered in the steady-state limit of the DEF definition. Interestingly, the DEF can be easily computed from the nondynamic EF expressions by introducing a complex Thiele modulus. Results show that for reaction - diffusion processes where the diffusion mechanism is governed by Fick’s law the magnitude of the DEF decreases with the frequency. This means that the best reaction rate performance is obtained when the process operates at steady-state (i.e., nondynamic) conditions. However, when a diffusion model with relaxation time is assumed to hold, resonant peaks at nontrivial frequencies can be displayed. Physically, this behavior implies that dynamic (e.g., periodic) operation of the reaction - diffusion process can yield better performance when compared with its nondynamic counterpart. 1. Introduction In most practical heterogeneous reaction systems involving catalyzed chemical reactions, catalyst particles are made large enough to minimize the pressure drop in the packed bed such that intraparticle resistance to mass transfer becomes significant. By departure from mass and energy balances, the description of reaction - diffusion phenomena in a heterogeneous reaction system commonly involves distributed parameter models (e.g., partial differential equations (PDEs)) for both a fluid and catalyst particles. Despite its quite good accuracy, this type of model is rarely used for design and/or simulation purposes because of the difficulty to find a computationally nonexpensive solution. For instance, excessive computational burden can occur within an optimization framework where the distributed parameter model of the catalyst particle should be solved at each optimization trial. A commonly used approach to avoid the drawback of solving the catalyst particle model is the use of an effectiveness factor (EF) concept. 1
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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.

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Dynamic Effectiveness Factor for Catalyst Particles - 11058...

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