Apparent gas-water two phase permeability in inorganic shale considering multiple transport mechanisms and water occurrence state

The gas–water apparent permeability of inorganic shale is a critical parameter governing fluid transport efficiency in reservoir systems and serves as a fundamental basis for modeling shale gas recovery. This study develops a novel fractal-based model for capturing gas–water apparent permeability in inorganic shale. For the first time, the model can simultaneously characterize the apparent permeability of gas and water phases under varying water saturation, incorporating multiple fluid transport mechanisms and water occurrence states. Specifically, gas transport mechanisms include Darcy flow, slip effect, Fick diffusion and Knudsen diffusion, while water transport mechanisms involve Darcy flow and slip effect. Comprehensive validation against experimental and numerical data demonstrates the model's accuracy and versatility in calculating both two-phase and single-phase flow regimes. The model comparisons reveal that the presence of irreducible water reduces the apparent permeability of both gas and water phases. Subsequently, the model is applied to evaluate the effects of key parameters on gas–water apparent permeability. Results indicate that gas apparent permeability is positively correlated with the fractal dimension of the pore size distribution but is negatively correlated with reservoir pressure and the fractal dimension of pore tortuosity. For the water phase, apparent permeability is positively correlated with the fractal dimension of pore size distribution but is negatively correlated with the fractal dimension of pore tortuosity and critical pore sizes that determine water occurrence states. Furthermore, this study provides a detailed analysis of how these factors influence permeability induced by individual transport mechanisms and their contributions to overall apparent permeability.