Extension of poromechanics to surface effects
Résumé
In their celebrated works, Young [1] and Laplace [2] explained why the pressure in a soap bubble is greater than the pressure out of it: this is a direct consequence of the fact that the film of soap wants to make its area as small as possible. The same happens in porous solids: a surface stress acts on the surface of the pores, which consequently deform, thus leading to a macroscopic strain of the porous material. Surface effects explain for instance why metal hydride reservoirs swell when used for hydrogen storage. They also explain why, during an injection of carbon dioxide in a coal bed reservoir, the injectivity is first decreasing but then increasing over time, a phenomenon known as the ‘permeability rebound'. Usual poromechanics equations do not take into account surface effects. Based on a thermodynamic approach, we present in this work an extension of the poroelastic equations to surface effects. The fact that energy can be stored at the solid-pore interface is explicitly taken into account. We thus provide a framework in which to calculate the macroscopic strain caused by the surface stress that prevails at the surface of the pores. We show that the microstructure (i.e., how the solid and the pores are organized in space) plays a significant role in how the porous material will deform under the action of surface stresses. The relevant microstructural parameters and their physical significance are identified. We finally show that the extended poromechanics here derived, combined with the use of molecular simulations, enable to capture the changes of injectivity observed over time during an injection of carbon dioxide in a coal bed reservoir. The late Pr. Olivier Coussy is gratefully acknowledged for the key role he played in this research. [1] T. Young, “An Essay on the Cohesion of Fluids”, Philosophical Transactions of the Royal Society of London, v. 95, p. 65-87, 1805. [2] P.-S. de Laplace, Traité de mécanique céleste, Gauthier-Villars, Paris, 1806.