Perturbation analysis of gas—solid reactions—I. Solid of low initial permeability

A general model for gas—solid reactions considering both internal and external reaction, and accounting for the effect of local internal conversion at the shrinking core surface, is analyzed here by a perturbation procedure for low initial relative permeability. It is shown that the shrinking core model including both surface reaction and product layer diffusion can arise only in this limit. Prior approaches considering only internal reaction have yielded only the diffusional control limit of the shrinking core model. The perturbation procedure shows that the shrinking core surface is always accompanied by a narrow reaction zone in which internal reaction occurs even for low initial permeability. The effect of this reaction zone on the overall conversion is found to be significant, with errors in the shrinking core model predictions as large as 12%, even when the ratio of the effective diffusivity in the core to that in the completely converted solid is only 0.06. One-term perturbation corrections to the shrinking core model, valid for all internal pore structures, are developed analytically.