A Novel Approach of Stress Dependent Permeability Modeling of Nanoporous Rocks

Darcy's law does not always govern flow in shale matrices. Rather, a considerable portion of the flow is dominated by non-Darcy flow regimes. Therefore, modeling permeability of shale matrices is a challenge because at each pressure different proportion of the rock are experiencing different flow regimes. In this study, a new apparent permeability model is presented to describe the combined Darcy and non-Darcy flow of gases at different pressures. This model is then, combined with pore size distribution data (PSD) of shale to establish different proportion of pore sizes of rock experiencing different flow regimes at different pressures. The combined approach of permeability model and pore size distribution data used to estimate the apparent permeability of the shale matrix at each pressure has been named as Permeagram approach in this paper. Finally, the Permeagram is coupled with constitutive equations applicable for shale rocks to formulate a coupled stress-dependent permeability model for shale. The coupled model was validated against permeability data of Marcellus shale with different stress variations. The modeled data was in close agreement with the experimental data and this validation step further solidifies the robustness of the proposed model.