Stochastic dynamics of intermittent pore-scale particle motion in three-dimensional porous media
Abstract
A proper understanding of velocity dynamics is key for making transport predictions through porous media at any scale. We study the velocity evolution process from particle dynamics at the pore-scale with particular interest in preasymptotic (non-Fickian) behavior. Experimental measurements from 3-dimensional particle tracking velocimetry are used to obtain Lagrangian velocity statistics for three different types of media heterogeneity. Particle velocities are found to be intermittent in nature, log-normally distributed and non-stationary. We show that these velocity characteristics can be captured with a correlated Ornstein-Uhlenbeck process for a random walk in space that is parameterized from velocity distributions. Our simple model is rigorously tested for accurate reproduction of velocity variability in magnitude and frequency. We further show that it captures exceptionally well the preasymptotic mean and mean squared displacement in the ballistic and superdiffusive regimes, and can be extended to determine if and when Fickian behavior will be reached. Our approach reproduces both preasymptotic and asymptotic transport behavior with a single transport model, demonstrating correct description of the fundamental controls of anomalous transport.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2017
- Bibcode:
- 2017AGUFM.H31M..04M
- Keywords:
-
- 0414 Biogeochemical cycles;
- processes;
- and modeling;
- BIOGEOSCIENCES;
- 1009 Geochemical modeling;
- GEOCHEMISTRY;
- 1830 Groundwater/surface water interaction;
- HYDROLOGY;
- 1831 Groundwater quality;
- HYDROLOGY