A fractal relative permeability model based on tortuous capillary network of unsaturated porous rock media

Accurate prediction of relative permeability in porous rock media remains a persistent challenge, primarily due to the oversimplified representation of fluid distribution and the neglected residual phase effects in conventional models. To address these limitations, we propose a fractal-based model integrated with capillary network theory. The model introduces three distinct flow regimes—single flow zone of wetting phase fluid, two-phase displacement mixed flow zone, and single flow zone of non-wetting phase fluid—regulated by critical radii ( , ) and residual non-wetting phase coefficient ( ). Fractal dimensions ( , ) quantify pore geometric characteristics and tortuosity, while a generalized capillary pressure equation captures dynamic interfacial behavior. Validation against gas-water and gas-oil experimental data demonstrates exceptional accuracy ( ), with mean absolute errors (MAE) reduced by 60–70% compared to the Li model (MAE=0.098) and Brooks-Corey model (MAE = 0.075). Sensitivity analyses reveal the following: and suppress wetting-phase permeability ( ) by enhancing small-pore tortuosity but slightly improve non-wetting-phase permeability ( ); the mixed-flow boundary parameter ( ) and exert nonlinear impacts, particularly in heterogeneous media. This mechanistically rigorous model enables robust predictions for hydrocarbon recovery, CO 2 sequestration, and geothermal energy extraction in complex porous systems. • Novel Model Development: A novel relative permeability model is proposed, integrating fractal theory and capillary tube model. It comprehensively considers the distribution of wetting and non-wetting phases in seepage channels, including single-flow zones of wetting and non-wetting phases and the two-phase displacement mixed-flow zone. • Model Verification: The model's accuracy and feasibility are validated by comparing its results with experimental data from different types of porous rock media and theoretical results from references. The new model shows excellent agreement with the experimental data, with correlation coefficients R 2 greater than 0.98 in most cases, and lower errors (MAE = 0.032, RMSE = 0.041 at low wetting phase saturation S w