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Transport behavior of coupled continuous-time random walks
Marco Dentz1, Harvey Scher, Devora Holder
1Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia (UPC), Barcelona, Spain.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2008
Summary
This study explores anomalous transport in disordered media using coupled continuous time random walk (CTRW) simulations. Findings reveal enhanced transport phenomena and broader applications in geological formations and fractured networks.
Area of Science:
- Geophysics and Environmental Science
- Complex Systems and Statistical Physics
Background:
- Anomalous, or non-Fickian, transport in disordered media like geological formations arises from a wide spectrum of transition rates.
- The continuous time random walk (CTRW) framework models these features using a joint probability density of space-time displacements, psi(s,t).
- Previous models often used a decoupled form, psi(s,t)=F(s)psi(t), simplifying analysis but potentially limiting scope.
Purpose of the Study:
- To investigate the expanded transport phenomena resulting from a fully coupled psi(s,t) in CTRW simulations.
- To explore the impact of power-law spatial distributions and various velocity distributions (Phi(xi)) on transport.
- To analyze the competition between displacement length and time-event scales in coupled transport.
Main Methods:
- Numerical simulations using the continuous time random walk (CTRW) framework.
- Introduction of power-law dependence in the spatial displacement (s) distribution.
- Coupling of time and velocity distributions (t=s(xi)) with various Phi(xi), including constant velocity.
- Analysis of spatial moments and plume shapes under coupled transport conditions.
Main Results:
- Unlike Lévy flights, coupled CTRW with these distributions yields well-defined spatial moments.
- Plume shapes are influenced by the entire velocity distribution, showing competition between short and long time/displacement scales.
- The study demonstrates an enhanced range of transport behaviors compared to decoupled models.
Conclusions:
- Coupled CTRW simulations reveal richer transport dynamics in disordered media than previously modeled.
- These findings have broader applications, including correlated migrations in random fracture networks and heterogeneous permeability fields.
- The study also assesses the validity of the decoupled approximation under different spatial distribution characteristics.
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