Enhanced continuum poromechanics to account for adsorption induced swelling of saturated isotropic microporous materials
Résumé
Poromechanics offers a consistent theoretical framework for describing the mechanical response of porous solids fully or partially saturated with a fluid phase. When dealing with fully saturated microporous materials, which exhibit pores of the nanometer size, effects due to adsorption and confinement of the fluid molecules in the smallest pores must be accounted for. From the mechanical point of view, these phenomena result into volumetric deformations of the porous solid, the so-called "swelling" phenomenon. The present work investigates how the poromechanical theory may be refined in order to describe such adsorption and confinement induced effects in microporous solids. Poromechanics is revisited in the context of isotropic microporous materials with generic pore size distributions. The new formulation introduces an effective pore pressure, defined as a thermodynamic variable at the representative volume element scale (mesoscale), which is related to the overall mechanical work of the confined fluid. Accounting for the thermodynamic equilibrium of the system, we demonstrate that the effective pore pressure depends on macroscopic variables, such as the bulk fluid pressure, the temperature and the total and excess adsorbed quantity of fluid. As an illustrating example, we apply the model to compute strains and variations of porosity in the case of the methane and carbon dioxide sorption on coal. Agreement with experimental data found in the literature is observed.