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The competition between gravity and flow focusing in two-layered porous media

Published online by Cambridge University Press:  27 February 2013

Herbert E. Huppert ,
Jerome A. Neufeld  and
Charlotte Strandkvist
Herbert E. Huppert*
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CMS Wilberforce Road, Cambridge CB3 0WA, UK Department of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia
Jerome A. Neufeld
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CMS Wilberforce Road, Cambridge CB3 0WA, UK BP Institute, University of Cambridge, Bullard Laboratories, Madingley Road, Cambridge CB3 0EZ, UK Department of Earth Sciences, University of Cambridge, Bullard Laboratories, Madingley Road, Cambridge CB3 0EZ, UK
Charlotte Strandkvist
Affiliation:
Centre for Mathematics and Physics in the Life Sciences and Experimental Biology, University College London, Gower Street, London WC1E 6BT, UK
*
†Email address for correspondence: [email protected]
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Abstract

The gravitationally driven flow of a dense fluid within a two-layered porous media is examined experimentally and theoretically. We find that in systems with two horizontal layers of differing permeability a competition between gravity driven flow and flow focusing along high-permeability routes can lead to two distinct flow regimes. When the lower layer is more permeable than the upper layer, gravity acts along high-permeability pathways and the flow is enhanced in the lower layer. Alternatively, when the upper layer is more permeable than the lower layer, we find that for a sufficiently small input flux the flow is confined to the lower layer. However, above a critical flux fluid preferentially spreads horizontally within the upper layer before ultimately draining back down into the lower layer. This later regime, in which the fluid overrides the low-permeability lower layer, is important because it enhances the mixing of the two fluids. We show that the critical flux which separates these two regimes can be characterized by a simple power law. Finally, we briefly discuss the relevance of this work to the geological sequestration of carbon dioxide and other industrial and natural flows in porous media.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 720 , 10 April 2013 , pp. 5 - 14
Copyright
©2013 Cambridge University Press

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References

Acton, J. M., Huppert, H. E. & Worster, M. G. 2001 Two-dimensional viscous gravity currents flower over a deep porous medium. J. Fluid Mech. 440, 359–380.Google Scholar
Anderson, D. M., McLaughlin, R. M. & Miller, C. T. 2003 The averaging of gravity currents in porous media. Phys. Fluids 10, 2810–2829.Google Scholar
Barenblatt, G. I. 1996 Scaling, Self-similarity, and Intermediate Asymptotics. Cambridge University Press.Google Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Dover.Google Scholar
Cinar, Y., Jessen, K., Berenblyum, R., Juanes, R. & Orr, F. M. Jr. 2006 An experimental and numerical investigation of crossflow effects in two-phase displacements. Soc. Petrol. Engng J. 90568, 216–226.Google Scholar
Huppert, H. E. 2006 Gravity currents: a personal perspective. J. Fluid Mech. 554, 299–322.Google Scholar
Huppert, H. E. & Woods, A. W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292, 55–69.Google Scholar
Lyle, S., Huppert, H. E., Hallworth, M., Bickle, M. & Chadwick, A. 2005 Axisymmetric gravity currents in a porous medium. J. Fluid Mech. 543, 293–302.Google Scholar
Phillips, O. M. 2009 Geological Fluid Dynamics: Sub-surface Flow and Reactions. Cambridge University Press.Google Scholar