An analysis of the pressure build-up inside a reacting pellet during gas solid reactions

A method has been outlined for the calculation of the pressure gradient that can exist within the reacted shell when a spherical pellet reacts with a gas and undergoes a transport controlled topochemical reaction. It is known that pressure gradients can arise because of Knudsen flow existing in the reacted shell with small pores and the reactant gas having a different diffusivity than that of the product gas. The phenomena can be represented by a boundary value problem involving a set of partial differential equations with a moving boundary, incorporating time and positional dependence of diffusivities of the reactant and product gases. In the present work, the resulting equations have been solved numerically. A study has been made of the influence of the relevant parameters like total and Knudsen diffusivity ratios of the reactant and product gases, the porosity to tortuosity ratio of the reacted shell, the Biot modulus, the equilibrium constant of the reaction and the viscous flow parameter on the pressure build up inside the reacted shell.