Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

Hyman, Jeffrey D.; Rajaram, Harihar; Srinivasan, Shriram; Makedonska, Nataliia; Karra, Satish; Viswanathan, Hari; Srinivasan, Gowri

doi:10.1029/2019GL085454

Title: Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

Journal Article · 03 November 2019 · Geophysical Research Letters

DOI: https://doi.org/10.1029/2019GL085454 · OSTI ID:1581275

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Johns Hopkins Univ., Baltimore, MD (United States)

Here, we develop a theoretical model for power law tailing behavior of transport in fractured rock based on the relative dominance of the decay rate of the advective travel time distribution, modeled using a Pareto distribution (with tail decaying as ~ time^-(1+α)), versus matrix diffusion, modeled using a Lévy distribution. The theory predicts that when the advective travel time distribution decays sufficiently slowly (α<1), the late-time decay rate of the breakthrough curve is -(1+α/2) rather than the classical -3/2. Yet, if α>1, the -3/2 decay rate is recovered. For weak matrix diffusion or short advective first breakthrough times, we identify an early-time regime where the breakthrough curve follows the Pareto distribution, before transitioning to the late-time decay rate. The theoretical predictions are validated against particle tracking simulations in the three-dimensional discrete fracture network simulator dfnWorks, where matrix diffusion is incorporated using a time domain random walk.

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

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001; AC52-06NA25396

OSTI ID:: 1581275

Report Number(s):: LA-UR--19-23625

Journal Information:: Geophysical Research Letters, Journal Name: Geophysical Research Letters Journal Issue: 23 Vol. 46; ISSN 0094-8276

Publisher:: American Geophysical UnionCopyright Statement

Country of Publication:: United States

Language:: English

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