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Continuous time random walks for the evolution of Lagrangian particle velocities in heterogeneous porous and fractured media flows

Abstract : We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous porous and fractured media flows based on a stochastic relaxation process. This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model persistence over a characteristic time scale. We first establish the relations between Eulerian and Lagrangian velocities for both equidistant and isochronal sampling along streamlines, under transient and stationary conditions. Based on this, we develop the CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. Unlike classical CTRW formulations, the proposed approach quantifies both stationary and non-stationary Lagrangian velocity statistics, and their evolution from arbitrary initial velocity distributions. We provide explicit expressions for the Lagrangian velocity distributions, and determine the behaviors of the mean particle velocity, velocity covariance and particle dispersion. We find strong correlation and anomalous dispersion for velocity distributions which are tailed toward low velocities. The developed CTRW approach and thus the Lagrangian particle dynamics are fully determined by the Eulerian velocity distribution and the characteristic correlation scale. The developed framework is applied to particle transport in two-dimensional random fracture networks.
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Conference papers
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https://hal-insu.archives-ouvertes.fr/insu-01416941
Contributor : Isabelle Dubigeon <>
Submitted on : Thursday, December 15, 2016 - 10:08:38 AM
Last modification on : Tuesday, December 10, 2019 - 1:44:03 PM

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  • HAL Id : insu-01416941, version 1

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Marco Dentz, Peter Kang, Alessandro Comolli, Tanguy Le Borgne, Daniel Lester. Continuous time random walks for the evolution of Lagrangian particle velocities in heterogeneous porous and fractured media flows . American Geophysical Union Fall Meeting 2016, American Geophysical Union, Dec 2016, San Francisco, United States. pp.H34D-05. ⟨insu-01416941⟩

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