Predictions of first passage times in sparse discrete fracture networks using graph-based reductions

Jeffrey D. Hyman, Aric Hagberg, Gowri Srinivasan, Jamaludin Mohd-Yusof, and Hari Viswanathan
Phys. Rev. E 96, 013304 – Published 10 July 2017

Abstract

We present a graph-based methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We derive graph representations of generic three-dimensional discrete fracture networks (DFNs) using the DFN topology and flow boundary conditions. Subgraphs corresponding to the union of the k shortest paths between the inflow and outflow boundaries are identified and transport on their equivalent subnetworks is compared to transport through the full network. The number of paths included in the subgraphs is based on the scaling behavior of the number of edges in the graph with the number of shortest paths. First passage times through the subnetworks are in good agreement with those obtained in the full network, both for individual realizations and in distribution. Accurate estimates of first passage times are obtained with an order of magnitude reduction of CPU time and mesh size using the proposed method.

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  • Received 20 March 2017

DOI:https://doi.org/10.1103/PhysRevE.96.013304

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsGeneral PhysicsNetworks

Authors & Affiliations

Jeffrey D. Hyman*

  • Computational Earth Science (EES-16), Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

Aric Hagberg and Gowri Srinivasan

  • Applied Mathematics and Plasma Physics (T-5), Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

Jamaludin Mohd-Yusof

  • Applied Computer Science (CCS-7), Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

Hari Viswanathan

  • Computational Earth Science (EES-16), Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

  • *Corresponding author: jhyman@lanl.gov

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Issue

Vol. 96, Iss. 1 — July 2017

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