Conversion estimates for gas-solid reactions

Abstract

Many chemical engineering processes involve a reaction between a diffusing substance and an immobile solid phase. The usual treatments are based on the assumptions that either diffusion or reaction dominates. Instead, we shall model an isothermal process in which reaction and diffusion are of the same order as would occur, for instance, in low temperature coke burning. Mass balances then lead to a parabolic system for the concentrations of the two phases. The system can be reduced to a scalar parabolic problem for the cumulative gas concentration. The popular pseudo-steady-state approximation is then obtained by setting the porosity ∈ equal to zero. This pseudo-steady-state problem is an elliptic problem in which time appears only as a parameter in the boundary condition. In previous work, we have shown that the pseudo-steady-state solution provides an O(∈) approximation to the exact concentration, uniformly in space and time. The present paper is concerned with estimates for the conversion, that is, the fraction of solid that has been converted to products by time t. We obtain bounds for the conversion in terms of a similar quantity (explicity calculable in some cases) for the pseudo-steady-state problem.