Fluid Flow through Porous Media: The Role of Stagnant Zones

Abstract

We investigate fluid flow through disordered porous media by direct simulation of the Navier-Stokes equations in a two-dimensional percolation structure. We find, in contrast to the log-normal distribution for the local currents found in the analog random resistor network, that over roughly 5 orders of magnitude the distribution $n(E)$ of local kinetic energy $E$ follows a power law, with $n(E)\ensuremath{\propto}{E}^{\ensuremath{-}\ensuremath{\alpha}}$, where $\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.90\ifmmode\pm\else\textpm\fi{}0.03$ for the entire cluster, while $\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.64\ifmmode\pm\else\textpm\fi{}0.05$ for fluid flow in the backbone only. Thus the ``stagnant'' zones play a significant role in transport through porous media, in contrast to the dangling ends for the analogous electrical problem.