Dirac-delta function, optimal catalyst

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. 

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