Intermittent Properties of Flow in Porous Media

Abstract

From numerical simulations of pore-scale flow in porous media, we demonstrate the existence of an intermittent-like behaviour of Lagrangian velocities similar to the one observed in turbulent flows. This phenomenon, characterized by non-Gaussian distributions of Lagrangian velocity increments and long-range correlation of Lagrangian accelerations, is at the origin at the breakdown of the classical upscaled models. For transport in porous media this is manifested by anomalous scaling of the temporal evolution of the characteristic dispersion length, called anomalous dispersion. Long range correlation is related to the existence of stagnation zones and localized high velocity channels. While for turbulence, intermittency of Lagrangian velocities can be represented by multifractal random walk, for porous media we show that the dynamical picture is different and that this process is well captured by a correlated continuous time random walk.