Maximal and minimal solutions, effectiveness factors for chemical reaction in porous catalysts

Abstract

A chemical reaction in a porous catalyst particle is considered. It is shown that in both the isothermal and non-isothermal cases, with either Dirichlet or third kind boundary conditions, two sequences of functions can be obtained, one of which converges to the maximal solution and the other to the minimal solution. Corresponding to these two sequences of functions, two sequences of numbers, which converge to the maximal and the minimal effectiveness factors, can be obtained. It is shown that in the isothermal case, the maximal (minimal) solution has the minimal (maximal) effectiveness factor while in the non-isothermal case, the maximal (minimal) temperature solution has the maximal (minimal) effectiveness factor. Two numerical examples are given to illustrate the results.