Journal of Fluid Mechanics

Papers

Fluid drainage from the edge of a porous reservoir

Zhong Zhenga1, Beatrice Soha2, Herbert E. Hupperta3a4a5 and Howard A. Stonea1 c1

a1 Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA

a2 Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA

a3 Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK

a4 School of Mathematics, University of New South Wales, Kensington, NSW 2052, Australia

a5 Faculty of Science, University of Bristol, Bristol BS2 6BB, UK

Abstract

We report theoretical and experimental studies to describe buoyancy-driven fluid drainage from a porous medium for configurations where the fluid drains from an edge. We first study homogeneous porous systems. To investigate the influence of heterogeneities, we consider the case where the permeability varies transverse to the flow direction, exemplified by a V-shaped Hele-Shaw cell. Finally, we analyse a model where both the permeability and the porosity vary transverse to the flow direction. In each case, a self-similar solution for the shape of these gravity currents is found and a power-law behaviour in time is derived for the mass remaining in the system. Laboratory experiments are conducted in homogeneous and V-shaped Hele-Shaw cells, and the measured profile shapes and the mass remaining in the cells agree well with our model predictions. Our study provides new insights into drainage processes such as may occur in a variety of natural and industrial activities, including the geological storage of carbon dioxide.

(Received August 07 2012)

(Revised November 15 2012)

(Accepted December 14 2012)

(Online publication February 08 2013)

Key words

  • geophysical and geological flows;
  • gravity currents

Correspondence

c1 Email address for correspondence: hastone@princeton.edu

Metrics