Optimal use of mixed catalysts for two successive chemical reactions

Recently, Gunn and Thomas showed that—when the conversion of a feedstock to a product takes place in two chemically distinct steps, each of which is promoted by a different catalyst—there are advantages to be gained by mixing the catalysts in a single reactor rather than carrying out the two reaction steps separately. In this paper, the maximum principle is applied to the problem of determining the optimal variation in catalyst blend along the reactor and, for a simple first-order kinetic scheme, it is shown to lead to a complete solution in closed form.