Fractal permeability model for a complex tortuous fracture network

The complex fracture network in unconventional oil and gas reservoirs is the main channel for the fluid flow, and effective prediction of fracture network permeability is the basis for further accurate assessment of oil and gas productivity. On the basis of the traditional parallel-plate cube law, we introduce the tortuosity fractal dimension DTf to characterize the tortuosity of fractures. Then, combined with fractal theory, a permeability model is derived for a complex tortuous discrete fracture network (DFN). A pixel probability decomposition algorithm is used to generate ten random DFNs that conform to the fractal scale relationship, and the effectiveness of the proposed model is verified by numerical simulation. The fracture geometry parameters are further analyzed and their effect on permeability discussed. The results show that the permeability K of a fracture network increases with an increase in porosity ϕ (0.117–0.292), fractal dimension Df (1.635–1.824), maximum fracture length lmax (3.337–7.472 m), and proportionality coefficient β (0.00108–0.0164), but decreases with the increasing tortuosity fractal dimension DTf (1.0018–1.0196) and fracture dip angle θ (10°–80°). Among these parameters, Df, DTf, and β have the greatest influence on the permeability of the fracture network, followed by θ, lmax, and ϕ.