Phenomenological understanding of poroelasticity via the micromechanics of a simple digital-rock model

Abstract

Poroelasticity is a material concept that expresses the reversible, macroscale process interactions that occur in a porous material, such as rocks. These process interactions take place between the pore fluids and the rock framework (or “skeleton”) that contains the pores. The phenomenological basis of poro-elasticity is examined via a micromechanics analysis, using a simplified digital-rock model that consists of solid elements in a lattice arrangement, and which hosts a well-connected, lattice-like network of simply shaped pore elements. The quasistatic poromechanical bulk response of this model is defined fully by closed-form equations that provide a clear understanding of the process interactions and that allow key effects to be identified. Several external boundary conditions (nonisotropic strain and stress) are analyzed, with drained and undrained pore-fluid conditions, along with arbitrary pore pressure states. The calculated responses of the pore-scale model, when translated into continuum-scale equivalent behaviors, indicate significant problems with the existing theories of poroelasticity that are rooted in an enriched-continuum perspective. Specifically, the results indicate that the principle of effective stress (and the Biot coefficient alpha) is wrongly attributed to a deficiency in the role of pore pressure. Instead, the micromechanics-based phenomenological understanding identifies the change of effective stress, in a characteristically confined setting, as being the result of changes in the stress components, with a key dependency on the specifics of the far-field constraints. Thus, poroelasticity is not a material characteristic; instead, it is a description of a nonlinear system operating at the pore scale. The analysis reveals a discrepancy between the stress states within the model domain and the external stress state. This yet remains to be addressed, to translate the microscale behavior into an equivalent material law.