Microporous media, i.e., porous media made of pores with a nanometer size, are important for a variety of applications, for instance for sequestration of carbon dioxide in coal, or for storage of hydrogen in metal-organic frameworks. In a pore of nanometer size, fluid molecules are not in their bulk state anymore since they interact with the atoms of the solid: they are said to be in an adsorbed state. For such microporous media, conventional poromechanics breaks down.

In this work we derive poroelastic constitutive equations which are valid for a generic porous medium, i.e., even for a porous medium with pores of nanometer size. The complete determination of the poromechanical behavior of a microporous medium requires knowing how the amount of fluid adsorbed depends on both the fluid bulk pressure and the strain of the medium. The derived constitutive equations are validated with the help of molecular simulations on one-dimensional microporous media. Even when a microporous medium behaves linearly in the absence of any fluid (i.e., its bulk modulus does not depend on strain), we show that fluid adsorption can induce non-linear behavior (i.e., its drained bulk modulus can then depend significantly on strain). We also show that adsorption can lead to an apparent Biot coefficient of the microporous medium greater than unity or smaller than zero.

The poromechanical response of a microporous medium to adsorption significantly depends on the pore size distribution. Indeed, the commensurability (i.e., the ratio of the size of the pores to that of the fluid molecules) proves to play a major role. For a one-dimensional model of micropores with a variety of pore sizes, molecular simulations show that the amount of adsorbed fluid depends linearly on the strain of the medium. We derive linearized constitutive equations which are valid when such a linear dependence of the adsorbed amount of fluid on the strain is observed.

As an application, the case of methane and coal is considered. Molecular simulations of an adsorption of methane on a microporous realistic model for coal are performed with a flexible solid skeleton. The applicability of the set of linearized constitutive equations to this case is discussed and the results are shown to be consistent with swelling data measured during a classical adsorption experiment.