A Complex Network Model for Analysis of Fractured Rock Permeability

Fractured rocks exist widely in nature. The fracture network is an effective storage space and main seepage channel of low-permeability oil and gas reservoirs, which controls the seepage system of low-permeability oil and gas reservoirs. The connection characteristics of fracture networks are complex and evolve dynamically with time. The rise of complex network research can provide reliable analysis for the relationship between network structures and network behaviors. In this work, the fracture network is considered as a hierarchical network with self-similarity, and complex network theory is applied to analyze the permeability of fractured rocks. According to the power-law relationship of degree distribution of network nodes, the number of nodes is corresponding to the number of network edges and a new power-law distribution relationship of edges with degree of nodes is proposed. Eventually, the permeability model of fractured rocks is derived and it is found that permeability of fractured rocks is a function of degree of maximum node< xmlns="http://www.w3.org/1998/Math/MathML">_kmax, self-similarity index< id="M2" xmlns="http://www.w3.org/1998/Math/MathML">γ, power index< id="M3" xmlns="http://www.w3.org/1998/Math/MathML">_dk, and other structural parameters. Compared with the existing numerical simulations, the validity of the model is verified. By calculating the influence of model parameters on the permeability, the following results are obtained: (1) fracture porosity is directly proportional to permeability; (2) fracture surface density is linearly increasing with permeability; (3) power index is inversely proportional to permeability; and (4) permeability is exponentially increasing with the maximum degree of a node.

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