A two-scale modelling approach to reaction–diffusion processes in porous materials

A two-scale model for a reaction–diffusion process in a porous material is developed and applied to a simplified problem related to concrete carbonation. The material is exposed to a gas which enters from the outside, diffuses through the air-filled pore space, and dissolves into the pore water where it reacts with a second solute. The problem exhibits two different spatial scales due to the great difference in diffusivities of the gas in air and water and the fine pore geometry. In contrast to common purely macroscopic models, the proposed two-scale model is capable of resolving both scales. It is shown by numerical simulations that different pore geometries lead to different macroscopic output. Results of a comparable purely macroscopic model can be recovered as a special case.