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Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves
Abstract
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.
- Authors:
-
[1];
[2];
[1];
[1];
[1];
[1];
[1]
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Johns Hopkins Univ., Baltimore, MD (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1581275
- Alternate Identifier(s):
- OSTI ID: 1576828
- Report Number(s):
- LA-UR-19-23625
Journal ID: ISSN 0094-8276
- Grant/Contract Number:
- 89233218CNA000001; AC52-06NA25396; 20180621ECR; 20170103DR; 20170508DR
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Geophysical Research Letters
- Additional Journal Information:
- Journal Volume: 46; Journal Issue: 23; Journal ID: ISSN 0094-8276
- Publisher:
- American Geophysical Union
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 58 GEOSCIENCES; Earth Sciences; Energy Sciences
Citation Formats
Hyman, Jeffrey D., Rajaram, Harihar, Srinivasan, Shriram, Makedonska, Nataliia, Karra, Satish, Viswanathan, Hari, and Srinivasan, Gowri. Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves. United States: N. p., 2019.
Web. doi:10.1029/2019GL085454.
Hyman, Jeffrey D., Rajaram, Harihar, Srinivasan, Shriram, Makedonska, Nataliia, Karra, Satish, Viswanathan, Hari, & Srinivasan, Gowri. Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves. United States. doi:10.1029/2019GL085454.
Hyman, Jeffrey D., Rajaram, Harihar, Srinivasan, Shriram, Makedonska, Nataliia, Karra, Satish, Viswanathan, Hari, and Srinivasan, Gowri. Sun .
"Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves". United States. doi:10.1029/2019GL085454.
@article{osti_1581275,
title = {Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves},
author = {Hyman, Jeffrey D. and Rajaram, Harihar and Srinivasan, Shriram and Makedonska, Nataliia and Karra, Satish and Viswanathan, Hari and Srinivasan, Gowri},
abstractNote = {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.},
doi = {10.1029/2019GL085454},
journal = {Geophysical Research Letters},
number = 23,
volume = 46,
place = {United States},
year = {2019},
month = {11}
}
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DOI: 10.1029/2019GL085454
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