The paper considers a theoretical model to study sulfate ion diffusion in saturated porous media - cement based mineral composites, accounting for simultaneous effects, such as filling micro-capillaries (pores) with ions and chemical products and liquid push out of them. Pore volume change and its effect on the distribution of ion concentration within the specimen are investigated. Relations for the distribution of the capillary relative radius and volume within the composite under consideration are found. The numerical algorithm used is further completed to consider capillary size change and the effects accompanying sulfate ion diffusion. Ion distribution within the cross section and volume of specimens fabricated from mineral composites is numerically studied, accounting for the change of material capillary size and volume. Characteristic cases of 2D and 3D diffusion are analyzed. The results found can be used to both assess the sulfate corrosion in saturated systems and predict changes occurring in the pore structure of the composite as a result of sulfate ion diffusion.