Preferential flow in three-dimensional stochastic fracture networks: The effect of topological structure

Abstract

This study explores how the topology-based measure of connectivity of a three-dimensional discrete fracture network (DFN) can be used to predict flow channelization, a commonly observed phenomenon from the individual fracture scale to the system scale. First, four-intersection types in fracture intersection classification: I, L, T, and X-intersections, in the DFN topological graph were examined to determine the ones most strongly correlated with preferential flow. T- and X-intersections boosted the formation of preferential flow, and thus, a method of combining their densities to obtain topological connectivity measures was designed. This parameter was tested on the flow behavior of numerous DFNs whose fracture lengths followed a power-law distribution. A method to measure flow channeling was adopted to identify the direct links between the flow channeling and connectivity parameters. The results showed that the network-scale degree of flow channeling decreased as network density increased. However, a strong preferential flow was found at a low DFN density, which was controlled by the network density. More homogenous flow fields were observed in high-density networks, where the main flow paths were determined by the T-intersection and X-intersection densities. Finally, an explicit formula (R-M model) for predicting the flow channeling related to the proposed connectivity parameter was developed. Comparing with published data, the proposed flow channeling estimation model was more reliable than the density-based prediction model.