Emergence of Stable Laws for First Passage Times in Three-Dimensional Random Fracture Networks

Hyman, Jeffrey De'Haven; Dentz, Marco; Hagberg, Aric Arild; Kang, Peter

doi:10.1103/physrevlett.123.248501

Title: Emergence of Stable Laws for First Passage Times in Three-Dimensional Random Fracture Networks

Journal Article · 09 December 2019 · Physical Review Letters

DOI: https://doi.org/10.1103/physrevlett.123.248501 · OSTI ID:1659184

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Spanish National Research Council (IDAEA-CSIC), Barcelona (Spain)
Univ. of Minnesota, Minneapolis, MN (United States)

Here, we study first passage behaviors in the flow through three-dimensional random fracture networks. Network and flow heterogeneity lead to the emergence of heavy-tailed first passage time distributions that evolve with increasing distance between the start and target planes, and transition toward stable laws. Analysis of the spatial memory of the first passage process shows that particle motion can be quantified stochastically by a time domain random walk conditioned on the initial velocity data. This approach identifies advective tortuosity, the velocity point distribution and the average fracture link length as key quantities for the prediction of first passage times. Using this approach, we develop a theory for the evolution of first passage times with increasing distance between the start and target planes and the convergence towards stable laws.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: Korea Ministry of Environment (MOE); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1659184

Report Number(s):: LA-UR-19-23405

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 24 Vol. 123; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Title: Emergence of Stable Laws for First Passage Times in Three-Dimensional Random Fracture Networks

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