Permeability model of fracture network based on branch length distribution and topological connectivity

Fracture networks are of significance in the production of coalbed methane from unconventional reservoirs. However, the complex distribution and geometry of fracture networks make effective predictions of their permeability difficult. This study obtains the shape of a natural fracture network in coal based on a stereomicroscopy experiment and analyzes the structural characteristics of the fracture network using graph theory. The fractal scaling law for the branch length distribution of the fractures and the relationships among the fractal dimensions of the branch length distribution, fracture area, porosity, connectivity, and ratio of maximum to minimum branch length are established. A new permeability model for a complex fracture network is developed based on fractal theory, and two important fracture characteristics, namely, tortuosity and connectivity, are considered. The model is verified using the results of previous studies and seepage tests, and the influence of the fracture network characteristic parameters on the permeability is analyzed. The results show that the permeability increases with increasing porosity, fractal dimension, proportionality coefficient, maximum fracture branch length, and connectivity and decreases with increasing tortuosity fractal dimension and dip angle.