Optimization of the active component distribution through the catalyst bed for the case of adiabatic reactor

This article is the next one in the previous series of publications concerning the optimal active component distribution. The aim of the present work is to extend the optimization problem taking into account the energy balance. The variational problem on searching for the optimal active component distribution profile along the catalyst bed was formulated for the case of an adiabatic reactor at an arbitrary form of reaction rate expression. The Euler differential equation was derived and the existence conditions for the solution of variational problem were obtained. A numerical algorithm was suggested and the optimal profiles of the active component distribution were calculated for the first-order reaction. Under isothermal conditions with linear dependence of the reaction rate on reactant concentration at a constant mass transfer coefficient, the uniform distribution is optimal. As opposed to the case of an isothermal reactor with a first-order catalytic reaction, in an adiabatic reactor considerable economy in the active component loading might be achieved due to optimization of its distribution. It was shown that the optimal active component distribution profiles were axially decreasing for the first-order exothermic reactions and increasing for endothermic reactions. The optimal active component distribution profile was calculated for the case of methane combustion on catalytic monoliths.