A new model of gas-water two-phase seepage based on the fractal structure of coal fracture-pore

Gas-water relative permeability significantly affects the efficiency of fluid transport. However, due to the complex fracture-pore structures in coal, accurately predicting this property remains a challenge. This study presents a novel gas-water relative permeability model developed based on the fractal characteristics of coal fracture-pore structures. The model utilizes a tree-like bifurcation network and a curved capillary bundle approach to characterize the roughness of the fracture-pore system. By incorporating the distribution theory of gas-water phases in annular flow and integrating the cubic law with the momentum balance equation, two permeability solution methods were established, grounded in two-phase flow regimes and multi-scale structural features. Moreover, the structural clogging mechanism is incorporated into the model to further improve its applicability and accuracy. To validate the model, theoretical results were compared with experimental data obtained using a self-developed experimental system. Additionally, a sensitivity analysis was conducted to evaluate the influence of various parameters. Several key factors were found to affect coal permeability: permeability K g was positively correlated with maximum fracture opening (e smax ), maximum pore diameter (r max ), fracture opening fractal dimension (D e ), pore distribution fractal dimension (D r ), and length ratio (χ); and negatively correlated with fracture tortuosity fractal dimension (D T ), pore tortuosity fractal dimension (D t ), characteristic length (L), bifurcation angle (α), and residual water saturation (S w ). Notably, fracture structure parameters exert a much greater influence on permeability than pore structure parameters, highlighting the critical role of fracture networks in controlling permeability in fracture-pore such as coal rock. This model provides parameter support for developing CO 2 storage efficiency prediction models and offers scientific guidance for designing fracture network regulation strategies in CO 2 storage schemes.