Gradient Effects 4 Catalyst Internal Structure

When diffusion and reaction occur simultaneously within a porous solid structure, concentration gradients of reactant and product species are established. If the various diffusional processes discussed in Section 12.2 are rapid compared with the chemical reaction rate, the entire accessible internal surface of the catalyst will be effective in promoting reaction because the reactant molecules will spread essentially uniformly throughout the pore structure, before they have time to react. Here only a small concentration gradient will exist between the exterior and interior of the particle, and there will be diffusive fluxes of reactant molecules in and product molecules out that suffice to balance the reaction rate within the particle. In... 

Interaction ofthe external and internal masstransferwith the chemical reaction may lead to a concentration gradient ofthe reactant in the boundary layer surrounding a solid catalyst and within the porous structure. For a first-order reaction, this leads to the following equation for the effective reaction rate ... 

When internal catalyst pellet concentration gradients have to be accounted for, the right-hand side of (14.2.4-3) would have to be multiplied by rj, the effectiveness factor, computed as described in Chapters 3 and 11. Accounting for temperature gradients in the axial direction would require an additional differential heat balance, analogous in structure to (14.2.4-2). 

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