Poromechanics of Saturated Isotropic Nanoporous Materials

Abstract

Poromechanics offers a consistent theoretical framework for describing the mechanical response of porous solids. When dealing with fully saturated nanoporous materials, which exhibit pores of the nanometer size, additional 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, and into a change of the apparent permeability. The present work investigates how poromechanics may be refined in order to capture adsorption and molecular packing induced effects in nanoporous solids. The revisited formulation introduces an effective pore pressure, defined as a thermodynamic variable at the representative volume element scale (mesoscale), which is related to the mechanical work of the fluid at the pore scale (nanoscale). Accounting for the thermodynamic equilibrium of the system, this effective pore pressure is obtained as a function of the bulk fluid pressure, the temperature and the total and excess adsorbed masses of fluid. We derive the analytical swelling strains due to sorption and molecular packing. A good agreement in the comparison with experimental data dealing with the swelling of coal due to methane and carbon dioxyde sorption is observed, as a preliminary stage towards modelling partially saturated solids and applications to cement paste.

A transverse isotropic model for microporous solids: Application to coal matrix adsorption and swelling

“…Anisotropy modeling is not included by Hol and Spiers [], although it has been considered by the same authors elsewhere [ Hol et al , ]. Second, Vermorel et al [] developed a poromechanical formulation based on properties defined at the molecular scale, such as microporosity or microporous skeleton stiffness K s . This formulation proposes an adsorption‐mechanical coupling based on the definition of an apparent microporosity which depends on excess n ex and total n t adsorbed amounts.…”

“…However, correctly interpreting gravimetric adsorption data by taking into account the full coupling between adsorption and strain still remains a challenging issue. While this issue is not fully solved, in addition to the interpretation proposed here, as alternatives, one can aim at using models which also utilize excess adsorption data [e.g., Vermorel et al , ; Vermorel and Pijaudier‐Cabot , ] or instead at measuring total adsorbed amounts directly (e.g., as proposed by Hol et al []).…”