The Emergence of Stable Laws for Breakthrough Curves in Three-Dimensional Discrete Fracture Networks
Abstract
We investigate particle motion and particle arrival times in three-dimensional discrete fracture networks. The distributions of arrival times are heavy tailed and evolve with distance between start and target planes toward stable laws. We analyze particle transitions between fractures. Rapid loss of spatial memory in particle velocities over distances of the order of the mean fracture length indicates that particle motion can be modeled stochastically through a Markov model for the particle velocity transitions between fractures. Using this approach, we find that the advective tortuosity, the average fracture link length and the velocity point distribution parameterize a predictive time-domain random walk model that is conditioned on the initial velocity data. Based on this approach, we derive a theory for the evolution of particle arrival times with increasing distance between start and target planes including the convergence toward stable laws.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFM.H33C..01D
- Keywords:
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- 1805 Computational hydrology;
- HYDROLOGY;
- 1822 Geomechanics;
- HYDROLOGY;
- 1829 Groundwater hydrology;
- HYDROLOGY;
- 1832 Groundwater transport;
- HYDROLOGY