The effect of bulk concentration gradient on fluid–solid reaction rate

Abstract

Considerable attention has been paid to the development of mathematical models to describe fluid–solid reaction systems as they play a significant role in many chemical, metallurgical, and other engineering areas. The present work is aimed at examining one of the assumptions generally made in the mathematical modeling of fluid–solid reaction systems; namely, that the bulk concentration of the fluid reactant is uniform around the solid surface. This is a reasonable assumption under well-mixed conditions of the fluid phase. However, under certain conditions, concentration gradients in the axial direction in the fluid near the surface may be present; a packed bed is an example of such a case. It is of interest to investigate how large the concentration gradient should be before the assumption of a uniform bulk concentration around a pellet to cause a significant error. The effect of a fluid concentration gradient has been studied for a catalytic reaction on the external surface of a nonporous sphere. Petersen et al. (1964) found that external concentration gradients do not significantly affect the overall reaction rate except for the case of a second-order reaction when the reactant concentration drops from its maximum value to zero over the distance of a particle diameter, which is a rather unlikely situation in practice. Similar results were obtained by Acrivos and Chambré (1957), who recommended the use of this approximation with caution when a series of consecutive reactions takes place. In many fluid–solid reactions, the reaction progresses towards the interior of the pellet as the solid reactant near the external surface is consumed, leaving behind either a porous solid product or inert solid matrix. Although it is generally believed that a bulk concentration gradient does not significantly affect the behavior of most noncatalytic fluid–solid reactions of industrial relevance, no formal verification of this statement has yet been provided in the literature. In this work, the validity of this hypothesis is tested for a simple fluid–solid reaction configuration.