Conversion estimates for gas-solid reactions: reversible kinetics independent of solid concentrations

Abstract

The mathematical formulation of gas-solid reactions are usually described by a system of nonlinear reaction-diffusion equations and closed-form solutions are not readily available for most cases. Back reactions are usually neglected in the analysis of solid conversion estimates for these systems. When reversible reactions are considered, the kinetics are assumed to be of first order in both the reactant and product gas concentrations, independent of the solid concentrations. In such a situation, a number of authors have investigated the two-stage model. This model uses the pseudo-steady-state assumption in conjunction with a special restriction that will allow the nonlinear problem to be mathematically tractable. In this work, we consider in detail the case where the form of kinetics is independent of both the reactant and product solid concentrations. First, we apply the pseudo-steady-state assumption and investigate the conditions under which the two-stage model need not be assumed. An extension, by means of the cumulative gas concentration method, is then made to allow for arbitrary values for all parameters and reaction orders in both the reactant and product gas concentrations. Expressions for the estimates of full conversion time for a range of kinetic models have been established.