Flow Intermittency, Dispersion, and Correlated Continuous Time Random Walks in Porous Media

Pietro de Anna, Tanguy Le Borgne, Marco Dentz, Alexandre M. Tartakovsky, Diogo Bolster, and Philippe Davy

Phys. Rev. Lett. 110, 184502 – Published 1 May 2013

Abstract

We study the intermittency of fluid velocities in porous media and its relation to anomalous dispersion. Lagrangian velocities measured at equidistant points along streamlines are shown to form a spatial Markov process. As a consequence of this remarkable property, the dispersion of fluid particles can be described by a continuous time random walk with correlated temporal increments. This new dynamical picture of intermittency provides a direct link between the microscale flow, its intermittent properties, and non-Fickian dispersion.

Received 19 October 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.184502

Authors & Affiliations

Pietro de Anna^1,5,*, Tanguy Le Borgne¹, Marco Dentz², Alexandre M. Tartakovsky³, Diogo Bolster⁴, and Philippe Davy¹

¹Géosciences Rennes, UMR 6118, CNRS, Université de Rennes 1, Rennes Cedex 35042, France
²Spanish National Research Council (IDAEA-CSIC), Barcelona 08034, Spain
³Pacific Northwest National Laboratory, Richland, Washington 99354, USA
⁴University of Notre Dame, South Bend, Indiana 46556, USA
⁵Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA