A fractal model for rough fractures and irregular pores in multi-field shale gas projects

Shale gas permeability is jointly controlled by fracture and pore characteristics, yet their coupled effects under multifactor conditions remain insufficiently quantified. This study proposes a fractal flow model integrating gas transport, shale deformation, and fracture–matrix interaction, introducing four fractal parameters (tortuosity, roughness, fracture quantity, and length) to quantify structural effects. The study results show that: (1) Fracture geometry controls pore structure evolution—as the roughness increases from 0.04 to 0.08, and both the tortuosity and fracture fractal dimensions increase from 1.2 to 1.6, the pore fractal dimension rises by 0.0019, 0.0028, and 0.0007, respectively. (2) Fracture complexity enhances gas flow—these structural changes reduce fracture gas pressure by 23%, 40%, and 32%, expanding diffusion pathways and improving connectivity, thereby enhancing permeability and gas transport efficiency. (3) Pore complexity promotes adsorption and impedes discharge—in contrast, higher pore fractal dimension (from 1.2 to 1.6) increases gas pressure by 20%, reflecting higher adsorption capacity and more tortuous flow paths. The findings quantitatively elucidate fracture–pore coupling mechanisms and their combined impacts on shale gas extraction, offering a predictive framework for optimizing shale gas recovery.