Characterizing the Influence of Fracture Density on Network Scale Transport

The topology of natural fracture networks is inherently linked to the structure of the fluid velocity field and transport therein. Here we study the impact of network density on flow and transport behaviors. We stochastically generate fracture networks of varying density and simulate flow and transport with a discrete fracture network model, which fully resolves network topology at the fracture scale. We study conservative solute trajectories with Lagrangian particle tracking and find that as fracture density decreases, solute channelization to large local fractures increases, thereby reducing plume spreading. Furthermore, in sparse networks mean particle travel distance increases and local network features, such as velocity zones where flow is counter to the primary pressure gradient, become increasingly important for transport. As the network density increases, network statistics homogenize and such local features have a reduced impact. We quantify local topological influence on transport behavior with an effective tortuosity parameter, which measures the ratio of total advective distance to linear distance at the fracture scale; large tortuosity values are correlated to slow‐velocity regions. These large tortuosity, slow‐velocity regions delay downstream transport and enhance tailing on particle breakthrough curves. Finally, we predict transport with an upscaled, Bernoulli spatial Markov random walk model and parameterize local topological influences with a novel tortuosity parameter. Bernoulli model predictions improve when sampling from a tortuosity distribution, as opposed to a fixed value as has previously been done, suggesting that local network topological features must be carefully considered in upscaled modeling efforts of fracture network systems.T. S. is supported by the National Science Foundation Graduate Research Fellowship under Grant DGE‐1841556. D. B. was supported by the US Army Research Office under Contract/Grant W911NF‐18‐1‐0338 and by the National Science Foundation under award CBET‐1803989. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract 89233218CNA000001). J. D. H. acknowledges support from the LANL LDRD program office Grant 20180621ECR and DOE's Office of Science Basic Energy SciencesE3W1: LA‐UR‐19‐27671. M. D. acknowledges funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007‐2013)/ ERC Grant Agreement 617511 (MHetScale). DFNWORKS and and simulation data can be obtained at GitHub (https://github.com/lanl/dfnWorks and https://github.com/tjsherman24/FractureNetworkDensity, respectively).Peer reviewe