Dependence of connectivity dominance on fracture permeability and influence of topological centrality on the flow capacity of fractured porous media

Abstract

The influence of fracture permeability and fracture network connectivity on the equivalent permeability tensor of the fractured rock mass is investigated and compared. 70 discrete three-dimensional fracture networks with various connectivity are generated. By constructing a graph of each fracture network based on intersection judgment between fractures, two types of connected subnetworks (subgraphs) are extracted according to their potential contribution to flow. The equivalent permeability tensors of the fractured porous media containing the full fracture network and its subnetworks under eight fracture permeability are calculated, respectively. Results demonstrate: (1) the fracture permeability determines the upper and lower bounds of the magnitude of the equivalent permeability tensor of the fractured rock mass. (2) The dominance of the connectivity of a percolating fracture network on the equivalent permeability tensor is dependent on the ratio of matrix permeability to fracture permeability. When the ratio of fracture permeability to matrix permeability is less than 1 × 105, even high fracture network connectivity cannot exert control over the ensemble flow response and the equivalent permeability of the fractured rock mass is limited by the fracture permeability and intensity. (3) As the ratio exceeds 1 × 105, the number of percolating dimensions of the connected subnetworks plays a critical role in the shape of the equivalent permeability ellipsoid of the fractured porous media. Moreover, the average of the three principal values of the equivalent permeability tensor has a negative exponent relationship with the mean of nodes’ normalized betweenness centrality of the connected subnetwork and increases exponentially as the mean of nodes’ degree centrality of the connected subnetwork increases.