Abstract
In a low permeability formation, connectivity of natural and induced fractures determines overall hydraulic diffusivity in fluid flow through this formation and defines effective rock permeability. Efficient evaluation of fracture connectivity is a nontrivial task. Here, we utilize a topological concept of global efficiency to evaluate this connectivity. We address the impact of key geometrical properties of stochastic fracture networks (fracture lengths, orientations, apertures, and positions of fracture centers) on the macro-scale flow properties of a shale-like formation. Six thousand different realizations have been generated to characterize these properties for each fracture network. We find that a reduced graph of a fracture network, which consists of the shortest paths from the inlet nodes (fractures) to all outlet nodes, contributes most to fluid flow. Three-dimensional (3D) fracture networks usually have higher global efficiency than two-dimensional (2D) ones, because they have better connectivity. All geometrical properties of fractures influence quality of their connectivity. Aperture distribution impacts strongly global efficiency of a fracture network and its influence is more significant when the system is dominated by large fractures. Fracture clustering lowers global efficiency in both 2D and 3D fracture networks. Global efficiency of 2D and 3D fracture networks also decreases with the increasing exponent of the power-law distribution of fracture lengths, which means that the connectivity of the system decreases with an increasing number of small fractures. Realistic fracture networks, composed of several sets of fractures with constrained preferred orientations, share all the characteristics of the stochastic fracture networks we have investigated.