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

Jeffrey D. Hyman, Marco Dentz, Aric Hagberg, and Peter K. Kang
Phys. Rev. Lett. 123, 248501 – Published 9 December 2019
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Abstract

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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  • Received 16 April 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.248501

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary PhysicsNetworks

Authors & Affiliations

Jeffrey D. Hyman1,*, Marco Dentz2, Aric Hagberg3, and Peter K. Kang4

  • 1Computational Earth Science Group(EES-16), Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
  • 2Spanish National Research Council (IDAEA-CSIC), Barcelona 08034, Spain
  • 3Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos New Mexico 87545, USA
  • 4Department of Earth and Environmental Sciences, University of Minnesota—Twin Cities, Minneapolis, Minnesota 55455, USA

  • *Corresponding author. jhyman@lanl.gov

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Issue

Vol. 123, Iss. 24 — 13 December 2019

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