Fracture Networks: Analysis with Graph Theory, LBM and FEM

Embedded fracture networks in rock masses are studied. The fluid flow in fracture networks with respect to variation of connectivity patterns is analyzed. Lattice Boltzmann method is used to show sensitivity of the permeability and fluid velocity distribution to connectivity patterns of generated fracture networks. Furthermore, fracture networks are mapped into the graphs and the characteristics of theses graphs are compared to the main spatial fracture networks. Among these characteristics, node’s degrees, clustering of edges and sub-graphs distribution are investigated. Implemented power law distributions of fracture length -in spatial fracture networksyield the same node’s degree distribution in transformed networks. Two general spatial networks are considered: random networks and networks with “hubness” properties (both with power law distribution of fracture length). In the first case, the fractures are embedded in a uniformly distributed fracture sets while the second case covers spatial fracture zones. The abnormal change (transition) in permeability is controlled by hub growth rate. Also, comparing LBM results with characteristic mean length of links of transformed networks shows a reverse relationship between the mentioned parameters. In addition, the abnormalities in advection through nodes are presented. As the last part of our research, the cubic law of transmitivity of each fracture is implemented in COMSOL software. The results of the later analysis are compared to LBM and advective flow–based networks equation.