Reaction and Diffusion in a Catalyst Particle

There is a second important reason for introducing the concept of an effectiveness factor. In the ordinary course of events, concentrations within a catalytic reactor packed with catalyst particles will vary both axially in the direction of flow and radially within the catalyst pellets. The model mass balance for such a system would consequently lead to a PDE. By using an effectiveness factor we reduce the PDE to an equivalent set of two ODEs, one the pellet mass balance in the radial direction, and the other the reactor mass balance in the direction of flow. The reaction rate, which previously varied in two directions rjr, z), is now a function of the axial distance only. We replace rffz, r) by Er, (z) is the so-called intrinsic reaction rate, which is measured experimentally on a fine powder and excludes diffusional 

The state variables in these processes, such as temperature or concentration, are in principle functions of bofh distance and time, leading to PDEs that are usually coupled and nonlinear. To reduce the model to a manageable set of ordinary differential and algebraic equations, the following assumptions are made  

The core contained by the moving front, such as a burning fuel particle, has uniform properties and can be treated as an unsteady compartment. 

The movement of the front itself is sufficiently slow that the transport gradients outside the core attain a quasi-steady state. This condition, which we have encountered before in Illustration 2.4, has the effect of eliminating time as a variable, with a consequent simplification of the model equation. 

The processes involved — transport and reaction — are dominated by a rate-controlling slow step. 

The topic addressed in this example is that of a solid particle that undergoes a continuous reaction with a gas, building up in the process a layer of porous solid product, which we denote by the general term ash. Reactant diffuses through a growing layer of ash to e surface of the shrinking particle where 

Mass Tranter and Separation Processes Principles and Applications 

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According to the above definitions, the effectiveness factor for any of the above shapes can adequately describe simultaneous reaction and diffusion in a catalyst particle. The equation for the effectiveness factor in a slab is the simplest in Table 6.3.1 and will be used for all pellet shapes with the appropriate Thiele modulus ... 

Illustration 4.9 Reaction and Diffusion in a Catalyst Particle. The Effectiveness Factor and the Design of Catalyst Pellets... 

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