We evaluate the use of graphs as a fast and relevant substitute to DFNs. Graphs reduce the DFNs’ complexity to their connectivity structure by forming an assembly of nodes connected by edges, to which physical properties, like a conductance, can be assigned. Both the graph architecture (either fracture- or intersection- based) and the edge conductance definition, have an impact on the estimation of flow and transport parameters. The intersection graph brings a reliable description of the flow connectivity but with edge redundancy in fractures with a large number of intersections. As a consequence, the expression of the edge conductances should depend on the number of intersections in the fracture plane. We first introduce some of our previous work which propose a reliable expression of the edge conductance in the case of a pair of intersections. For the intersection graph, a correction on the conductance expression is proposed for fractures with a large number of intersections. Both graphs provide very good estimate of the bulk permeability although they tend to slightly overestimate it when the DFN connectivity increases (~×2) certainly due to fractures with large intersection numbers. We address this issue by analyzing flow simulations on a fracture with multiple intersections. We also propose another way to correct the intersection graph, which consists in removing redundant edges. The method drastically simplifies the intersection graph, which is promising in term of computational time. The bulk permeability is overestimated by a factor of 2.3 but independently of the DFN density and connectivity.
Fracture networks constitute the basic support for flow and transport in rock matrices, mostly in crystalline rocks. They are multi-scale systems with a broad distribution of the fracture sizes, commonly represented by a decreasing power-law (Bonnet et al., 2001; Bour et al., 2002). They are characterized by a complex topology (the way fractures connect to each other), which is the very first property to characterize the network flow and transport.