Estimation of rough fracture network permeability using fractal and topology theories

Accurate characterization of the rough fracture network in real rocks is an essential prerequisite for precise estimation of fracture network permeability. The characterization of a fracture network in previous theoretical models is usually based on statistical theory, ignoring the topological characteristics of the real fracture network. In this paper, based on fractal and topological theories, the rough characteristics of real rock fractures are considered, and fracture network branch lengths and connectivity are introduced. A new theoretical prediction equation of fractal permeability for rough fracture networks is derived. Subsequently, the reliability of the proposed theoretical model is verified based on discrete fracture network (DFN) modeling and numerical simulation, and the main influencing factors of the rough fracture network permeability are analyzed. The results show that the rough fracture network permeability theoretical model proposed in this paper can effectively evaluate fractured rock permeability. Connectivity is linearly related to permeability. The better the connectivity of the rough fracture network, the denser the streamlines within the fractured rock and the higher the flow rate. The rough fracture network permeability increases with the increase of connectivity, minimum branch length, maximum branch length, tortuosity, and aperture proportionality coefficient, and decreases with the increase of tortuosity fractal dimension and fracture dip angle. When the branch length ratio lbmin/lbmax is less than 0.2, the larger the fractal dimension of the rough fracture network, the lower the permeability. When the ratio is greater than 0.2, the opposite is true. The sensitivity of the rough fracture network permeability to the fracture dip angle θ and the aperture proportionality coefficient β is higher, while the sensitivity to the fractal dimension Df of the rough fracture network is lower.