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High-speed Particle Image Velocimetry Near Surfaces
Published on: June 24, 2013
Anomalous transport in correlated velocity fields
Brian Berkowitz1, Harvey Scher
1Department of Environmental Sciences and Energy Research, Weizmann Institute of Science, 76100 Rehovot, Israel.
Summary
This study reveals that the power-law tail of local transition times, not correlation structures, primarily governs particle transport in heterogeneous hydraulic conductivity fields. This finding is crucial for understanding contaminant transport and water flow in complex subsurface environments.
Area of Science:
- Environmental science
- Geophysics
- Hydrology
Background:
- Understanding subsurface solute transport is critical for environmental management.
- Heterogeneous hydraulic conductivity fields significantly impact fluid and contaminant movement.
- Continuous Time Random Walk (CTRW) models offer a framework for analyzing anomalous transport phenomena.
Purpose of the Study:
- To identify key structural features of heterogeneous hydraulic conductivity fields that dominate particle transport behavior.
- To compare two distinct analytical approaches within the CTRW framework for particle transport simulations.
- To investigate the influence of correlated flow fields on transport dynamics.
Main Methods:
- Simulated particle transport in two correlated Darcy flow fields with heterogeneous hydraulic conductivity.
- Analysis using Lagrangian velocities to derive correlated space-time distributions for particle tracking.
- Application of a truncated power-law form of the probability density function (pdf) of local transit times within a CTRW partial differential equation.
- Fitting simulated breakthrough curve (BTC) data using both approaches.
Main Results:
- Both analytical approaches yielded excellent fits to simulated BTC data.
- A single parameter, beta, characterizing dispersive transport, was consistently obtained.
- The value of beta, derived from the Darcy field's pdf histogram, dictates the late-time tail behavior.
- Power-law tails in local transition times and the limits of non-Fickian behavior were identified as dominant transport features.
Conclusions:
- The presence of a power-law tail in local transition times and the extent of non-Fickian transport are the primary drivers of large-scale transport behavior.
- The specific correlation structures of hydraulic conductivity fields play a secondary role compared to rare, impactful events like low-velocity regions.
- These findings enhance the understanding of solute and contaminant transport in complex geological formations.
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