Evolution of shale apparent permeability under variable boundary conditions

In this study, a general shale apparent permeability model under the influence of gas sorption was derived based on the theory of poroelasticity. Unlike previous models, the impact of gas adsorption-induced swelling strain was treated as a local phenomenon. This was achieved through the introduction of an internal strain. The internal strain is directionally proportional to the swelling strain. The proportional coefficient has a clear physical meaning and is defined as the ratio of the Langmuir strain constant for shale matrix to the product of the Langmuir strain constant for shale bulk and the shale porosity. The general permeability model was degenerated into a set of specific shale permeability models under common experimental conditions: (1) constant effective stress; (2) constant pore pressure; and (3) constant confining stress. Nineteen groups of experimental data in the literature were used to verify the validity of those models: three for the boundary condition of constant effective stress; five for the condition of constant pore pressure; and eleven for the boundary condition of constant confining stress. The successful matches of these nineteen groups of experimental data with our model results demonstrate the validity of our general shale permeability. These models can be used to analyze the experimental observations of shale permeability under a spectrum of boundary conditions from constant confining stress to constant pore pressure.