Predicting first-passage times in sparse discrete fracture networks

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Graph-based methods identify sub-regions in fracture networks where the fastest transport occurs. (a) Full network, (b) subnetwork corresponding to the 10 shortest paths between flow boundaries, (c) graph representation of (a), (d) 10 shortest paths between flow boundaries in the graph, (e) comparison of first passage times in the full network and subnetwork based on the 10 shortest paths, (f) comparison of computational times.

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Predicting how long it takes for a chemical to be transported through sparse fracture networks is a common and critical challenge in many subsurface applications including the detection of clandestine low-level nuclear tests, hydrocarbon extraction, aquifer storage and management, environmental restoration of contaminated fractured media, and geological carbon dioxide (CO₂) sequestration. Modern subsurface flow and transport models can provide estimates for these transit times, commonly referred to as first passage times, but are hindered by the high computational expense associated with explicitly representing complex fracture networks and ensemble analysis required to quantify uncertainty.

Los Alamos researchers have designed a methodology to identify sub-regions in fracture networks where the fastest transport occurs. The method leverages two Laboratory-developed software suites, NetworkX and dfnWorks, to provide accurate estimates of first passage times with an order of magnitude reduction in computational cost. The cornerstone of the method is combining the topology discrete fracture network with boundary conditions of the simulation to derive a graph representation where nodes in the graph correspond to fractures in the network and nodes are connected if two fractures intersect. This graph is amenable to network analysis tools that allowed for efficient query of the network structure. The journal Physical Review E published the method.

The team demonstrated that identifying the subgraphs corresponding to the shortest paths between the inflow to outflow boundaries can be used to accurately predict where the fastest particles pass through the fracture networks. The Figure provides an overview of their new method. Subfigure (a) shows a discrete fracture network (DFN) generated using the dfnWorks software suite. Subfigure (c) is a graph representation of that network where fractures are represented as nodes and edges exists between nodes if the corresponding fracture intersect. Additional nodes are added to incorporate the inflow (red) and outflow (blue) boundary conditions. Subfigure (d) shows the subgraph corresponding to 10 shortest paths from inflow to outflow boundaries, identified using NetworkX, and (b) is the corresponding sub-network within the DFN. Subfigure (e) compares the first arrival times of particles in the full network and subnetworks corresponding to the 10 shortest paths in a set of 100 networks. The results are in good agreement demonstrating the accuracy of the method. The required CPU times are presented in subfigure (f) and highlight that simulating flow and transport in the sub-network is an order of magnitude less expensive that the full network demonstrating the method’s efficiency.

Graph-based methods identify sub-regions in fracture networks where the fastest transport occurs. (a) Full network, (b) subnetwork corresponding to the 10 shortest paths between flow boundaries, (c) graph representation of (a), (d) 10 shortest paths between flow boundaries in the graph, (e) comparison of first passage times in the full network and subnetwork based on the 10 shortest paths, (f) comparison of computational times.

Reference: “Predictions of First Passage Times in Sparse Discrete Fracture Networks using Graph-based Reductions,” Physical Review E 96, no. 1 (2017): 013304; doi: 10.1103/PhysRevE.96.013304. Authors: Jeffrey D. Hyman and Hari Viswanathan (Computational Earth Science EES-16), Aric Hagberg and Gowri Srinivasan (Applied Mathematics and Plasma Physics T-5), and Jamal Mohd-Yusof (Applied Computer Science, CCS-7).

The Laboratory Directed Research and Development (LDRD) program and a Laboratory Director’s Postdoctoral Fellowship supported this research through funding provided to “Advancing Predictive Capability for Brittle Failure Using Dynamic Graphs” (Principal Investigator, Hari Srinivasan). Hyman received partial support through a Laboratory Director’s Postdoctoral Fellowship. The work supports the Lab’s Global Security Nuclear Non-proliferation and Energy Security mission area areas, and the Information, Science, and Technology science pillar through prediction of transit times through sparse fracture networks. Technical contact: Jeffrey Hyman