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

Abstract

Here, we present a graph-based methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We also 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. We obtain accurate estimates of first passage times with an order of magnitude reduction of CPU time and mesh size using the proposed method.

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1374351
Alternate Identifier(s):
OSTI ID: 1369102
Report Number(s):
LA-UR-17-22022
Journal ID: ISSN 2470-0045; PLEEE8
Grant/Contract Number:
AC52-06NA25396; 20150763PRD4; 20170103DR
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 96; Journal Issue: 1; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 54 ENVIRONMENTAL SCIENCES; Earth Sciences; discrete fracture networks, graph theory, shortest paths, flow and transport

Citation Formats

Hyman, Jeffrey De'Haven, Hagberg, Aric Arild, Mohd-Yusof, Jamaludin, Srinivasan, Gowri, and Viswanathan, Hari S. Predictions of first passage times in sparse discrete fracture networks using graph-based reductions. United States: N. p., 2017. Web. doi:10.1103/PhysRevE.96.013304.
Hyman, Jeffrey De'Haven, Hagberg, Aric Arild, Mohd-Yusof, Jamaludin, Srinivasan, Gowri, & Viswanathan, Hari S. Predictions of first passage times in sparse discrete fracture networks using graph-based reductions. United States. doi:10.1103/PhysRevE.96.013304.
Hyman, Jeffrey De'Haven, Hagberg, Aric Arild, Mohd-Yusof, Jamaludin, Srinivasan, Gowri, and Viswanathan, Hari S. Mon . "Predictions of first passage times in sparse discrete fracture networks using graph-based reductions". United States. doi:10.1103/PhysRevE.96.013304.
@article{osti_1374351,
title = {Predictions of first passage times in sparse discrete fracture networks using graph-based reductions},
author = {Hyman, Jeffrey De'Haven and Hagberg, Aric Arild and Mohd-Yusof, Jamaludin and Srinivasan, Gowri and Viswanathan, Hari S.},
abstractNote = {Here, we present a graph-based methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We also 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. We obtain accurate estimates of first passage times with an order of magnitude reduction of CPU time and mesh size using the proposed method.},
doi = {10.1103/PhysRevE.96.013304},
journal = {Physical Review E},
number = 1,
volume = 96,
place = {United States},
year = {Mon Jul 10 00:00:00 EDT 2017},
month = {Mon Jul 10 00:00:00 EDT 2017}
}

Journal Article:
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  • We characterize how different fracture size-transmissivity relationships influence flow and transport simulations through sparse three-dimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semicorrelation, and noncorrelation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected somore » that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same. We observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used. While fracture network geometry plays the principal role in determining where transport occurs within the network, the relationship between size and transmissivity controls the flow speed. Lastly, these observations indicate DFN modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics.« less
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