Homogeneous model, catalytic pellets

The pseudo-homogeneous assumption means that both the solid and fluid phases are are considered a single phase. Therefore, we avoid considering mass and heat transfer from and to the catalytic pellets. This model assumes that the conqionent concentrations and the temperature in the pellets are the same as those in the fluid phase. This assumption is approximated when the catalyst pellet is small and mass and heat transfer between the pellets and the fluid phase are rapid. The reaction rate for this model, called the global reaction rate, includes heat and mass transfer. If heat and mass transfer are made insignificant, then the reaction rate is called the intrinsic reaction rate. 

This allows us to make a homogeneous model of the porous catalyst pellet in which we now have a diffusive flux given as the product of an effective diffusion coefficient and a concentration gradient, and a rate of reaction given by the product of the catalytic area and the reaction rate per unit area. 

As indicated by equation (15-12), the simplified homogeneous mass transfer model for diffusion and one chemical reaction within the internal pores of an isolated catalytic pellet is written in dimensionless form for reactant A as... 

In this chapter we present a pseudo-homogeneous model of diffusion and heterogeneous surface-catalyzed chemical reaction within the internal pores of catalytic pellets with rectangular symmetry. 

Under steady-state conditions in a plug-flow tubular reactor, the onedimensional mass transfer equation for reactant A can be integrated rather easily to predict reactor performance. Equation (22-1) was derived for a control volume that is differentially thick in all coordinate directions. Consequently, mass transfer rate processes due to convection and diffusion occur, at most, in three coordinate directions and the mass balance is described by a partial differential equation. Current research in computational fluid dynamics applied to fixed-bed reactors seeks a better understanding of the flow phenomena by modeling the catalytic pellets where they are, instead of averaging or homogenizing... 

It has to be pointed out that the model in the presented form is strictly speaking only correct for a homogeneous distribution of the catalytic activity and a constant diffusion coefficient within the particle, that is, for the ideal case of a material with one size of pore. For pellets with a pore size distribution the selectivities are not calculated accurately. Such a situation is quite common, for example, a pellet may contain macro-and micropores if it has been shaped from microparticles (with micropores) by compression (see Example 4.5.11 in Section 4.S.6.3). 

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