Catalyst distribution, optimal, Dirac-delta

The optimal distribution of silver catalyst in a-Al203 pellets is investigated experimentally for the ethylene epoxidation reaction network, using a novel single-pellet reactor. Previous theoretical work suggests that a Dirac-delta type distribution of the catalyst is optimal. This distribution is approximated in practice by a step-distribution of narrow width. The effect of the location and width of the active layer on the conversion of ethylene and the selectivity to ethylene oxide, for various ethylene feed concentrations and reaction temperatures, is discussed. The results clearly demonstrate that for optimum selectivity, the silver catalyst should be placed in a thin layer at the external surface of the pellet. 

The effects of non-uniform distribution of the catalytic material within the support in the performance of catalyst pellets started receiving attention in the late 60 s (cf 1-4). These, as well as later studies, both theoretical and experimental, demonstrated that non-uniformly distributed catalysts can offer superior conversion, selectivity, durability, and thermal sensitivity characteristics over those wherein the activity is uniform. Work in this area has been reviewed by Gavriilidis et al. (5). Recently, Wu et al. (6) showed that for any catalyst performance index (i.e. conversion, selectivity or yield) and for the most general case of an arbitrary number of reactions, following arbitrary kinetics, occurring in a non-isothermal pellet, with finite external mass and heat transfer resistances, the optimal catalyst distribution remains a Dirac-delta function. 

Catalyst attached to membrane pore surface. The final distribution of the catalyst in the membrane pores can significantly impact the reactor performance. The optimal form of the catalyst distribution for maximizing conversion was studied mathematically by Keller et al. [1984]. They determined that the optimal distribution of the catalyst concentration is of the Dirac delta function. 

When the Dirac delta distribution is placed closer to the permeate side (i.e., a subsurface step distribution) of an CMR, the total conversion is actually lower than that with a uniform catalyst distribution (Figure 9.7). For a performance index other than the total conversion (such as product purity or product molar flow rate), the optimal distribution of the catalyst concentration can be rather complex even for reversible first-order reactions as displayed in Figure 9.8. 

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