Dispersion and Mixing in Three‐Dimensional Discrete Fracture Networks: Nonlinear Interplay Between Structural and Hydraulic Heterogeneity

We investigate the relative impact of topological, geometric, and hydraulic heterogeneity on transport processes in three-dimensional fracture networks. Focusing on the two largest scales of heterogeneity in these systems, individual fracture and network structure, we compare transport through analogous structured and disordered three-dimensional fracture networks with varying degrees of hydraulic heterogeneity. For the moderate levels of hydraulic heterogeneity we consider, network structure is the dominant control of transport through the networks. Less dispersion, both longitudinal and transverse, is observed in structured networks than in disordered networks, due in part to the higher connectivity in the former, independent of the level of hydraulic heterogeneity. However, increases in dispersion with higher hydraulic heterogeneity are larger in the disordered networks than in the structured networks, thereby indicating that the interplay between structural and hydraulic heterogeneity is nonlinear. We propose a measure of disorder in fracture networks by computing the Shannon entropy of the spectrum of the Laplacian of a weighted graph representation of the networks, where the weights are given by a combination of topological, geometric, and hydraulic properties. This metric, as a relative indicator by comparison between two networks, is a first approach to the dispersion potential and ‘‘mixing capacity’’ of a fracture network.