A new fractal permeability model for the dual-porous medium with a bundle of rough tree-like fracture networks

Shale gas reservoirs are typical dual-porous media where complex pore structures and fracture networks significantly impact gas transport. However, accurately predicting permeability in such media, especially complex fracture networks, remains challenging. The complex fracture network is modeled as of a bundle of rough tree-like fracture networks. The proposed permeability model comprehensively describes the structural characteristics of pores and fractures in shale gas reservoirs, including the fractal distribution of pore diameters and fracture apertures, the rough surface, and branching characteristics of fracture networks. Then, the model's accuracy is validated using reliable experimental permeability data. This model accurately predicts gas permeability and effectively describes gas transport characteristics in shale gas reservoirs with rough tree-like fracture networks. Each parameter has a clear physical meaning and avoids the use of empirical constants. Finally, sensitivity analyses are conducted to explore the effects of structural parameters on the permeability of dual-porous media. The results show that the permeability K of dual-porous media decreases exponentially with the increase in tortuosity fractal dimension Dtp of pores and surface fractal dimension Df of fractures, while it increases as a power function with increasing pore diameter fractal dimension Dp and fracture aperture fractal dimension Dh. The structural parameters of rough tree-like fracture networks significantly impact the permeability of dual-porous media. Increasing the aperture ratio γ, reducing the length ratio β, branching levels m, and the branching angles θ can significantly reduce gas flow resistance, decrease fluid kinetic energy loss, and increase the permeability of dual-porous media. This theoretical model is significant for enhancing permeability models of dual-porous media in shale gas reservoirs, offering reliable theoretical support for understanding gas migration and optimizing shale gas extraction.