Fractal analysis of directional permeability of gas shale fracture networks: A numerical study

Since the directional permeability of gas shale fracture networks is significantly dependent on the geometric properties of fractures, in this work, a numerical study was performed to analyze the relationships of them, in which fracture length followed a fractal distribution and fracture orientation followed a normal distribution. Assumptions were made that fractures are more permeable than shale matrix and gas shale fracture networks are consisted of two sets of fractures with different distributions of length, aperture and orientation. The results show that with increasing the ratio of fractal dimensions or apertures of the two fracture sets, the direction of the maximum permeability moves towards the orientation of fractures with a larger fractal dimension or aperture. The ratio of the maximum and the minimum permeability decreases with the increment of intersecting angle of the two fracture sets, following exponential functions. For the ratio of apertures of the two sets of fractures varying from 1 to 5, the ratio of the maximum and the minimum permeability would decrease from 9.93 to 4.55 and increase from 2.79 to 5.35 for intersecting angle having the values of 30° and 60°, respectively. The larger orientation variance results in the smaller difference between the maximum and the minimum permeability. The reduction/increase rate of permeability decreases and increases for the models with orientation normally and uniformly distributed, respectively