Upscaling poromechanical models of coalbed methane reservoir incorporating the interplay between non-linear cleat deformation and solvation forces

We construct herein a three-scale coupled mechanical model for naturally fractured coalbed methane reservoir with the ability of describing the stress balance between the solvation force, arising from the gas adsorption in nanopores, and the restoration stress stemming from the elastic response of the cleats. To determine the cleat porosity, the non-linear hyperbolic Barton-Bandis (BB) law, which captures increase in joint stiffness induced by the cleat closure due to matrix swelling, is postulated for the fracture mechanical response. At the microscale, the theory incorporates the coupling between the effects of the solvation force and the elastic response of the matrix. Such system of governing equations is coupled with the fluid pressure in the discrete cleat system with dependency of aperture with the normal stress dictated by the aforementioned BB-model. A reiterated homogenized procedure is pursued and capable of providing the constitutive response of the homogenized poromechanical parameters on gas pressure. Numerical simulations illustrate the performance of the proposed model.