# 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:

- 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. https://www.osti.gov/servlets/purl/1374351.
```

```
@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}

}

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