A fractal-like formulation of the random pore model (RPM) is proposed for the reaction of a gas with a solid, with the rate controlled by both diffusion in the layer of solid product and the kinetics of reaction. This approach gives a time-dependent diffusivity in the product. The model's predictions are compared with measurements of the removal of SO2 with limestone, carried out in a lab-scale fluidized bed reactor. The fractal-like RPM described the production of CaSO4 better than the standard RPM, which overestimated the uptake of SO2 in the first 40 min. The decrease of diffusivity in the product layer with time was ascribed to the degree of crystallization of the product, CaSO4, increasing with time and resulting in a lower ionic mobility in its lattice. The equation proposed is a simple and general one for a gas reacting with a solid (alternative example: the carbonation of lime), whose microstructural properties change significantly with the extent of reaction. (C) 2016 Elsevier Ltd. All rights reserved.