Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-25T16:02:38.357Z Has data issue: false hasContentIssue false
  • English
  • Français

Topographic controls on gravity currents in porous media

Published online by Cambridge University Press:  09 October 2013

Samuel S. Pegler ,
Herbert E. Huppert  and
Jerome A. Neufeld
Samuel S. Pegler*
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Herbert E. Huppert
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK Faculty of Science, University of Bristol, Bristol BS8 1UH, UK School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia
Jerome A. Neufeld
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK BP Institute and Department of Earth Sciences, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: ssp23@cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a theoretical and experimental study of the propagation of gravity currents in porous media with variations in the topography over which they flow, motivated in part by the sequestration of carbon dioxide in saline aquifers. We consider cases where the height of the topography slopes upwards in the direction of the flow and is proportional to the $n\text{th} $ power of the horizontal distance from a line or point source of a constant volumetric flux. In two-dimensional cases with $n\gt 1/ 2$, the current evolves from a self-similar form at early times, when the effects of variations in topography are negligible, towards a late-time regime that has an approximately horizontal upper surface and whose evolution is dictated entirely by the geometry of the topography. For $n\lt 1/ 2$, the transition between these flow regimes is reversed. We compare our theoretical results in the case $n= 1$ with data from a series of laboratory experiments in which viscous glycerine is injected into an inclined Hele-Shaw cell, obtaining good agreement between the theoretical results and the experimental data. In the case of axisymmetric topography, all topographic exponents $n\gt 0$ result in a transition from an early-time similarity solution towards a topographically controlled regime that has an approximately horizontal free surface. We also analyse the evolution over topography that can vary with different curvatures and topographic exponents between the two horizontal dimensions, finding that the flow transitions towards a horizontally topped regime at a rate which depends strongly on the ratio of the curvatures along the principle axes. Finally, we apply our mathematical solutions to the geophysical setting at the Sleipner field, concluding that topographic influence is unlikely to explain the observed non-axisymmetric flow.

JFM classification

Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Porous media Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 734 , 10 November 2013 , pp. 317 - 337
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arts, R., Chadwick, A., Eiken, O., Thibeau, S. & Nooner, S. 2008 Ten years’ experience of monitoring ${\mathrm{CO} }_{2} $ injection in the Utsira Sand at Sleipner, offshore Norway. First Break 26, 65–72.Google Scholar
Barenblatt, G. I. 1996 Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press.CrossRefGoogle Scholar
Bear, J. 1988 Dynamics of Fluids in Porous Media. Dover.Google Scholar
Bickle, M. J., Chadwick, R. A., Huppert, H. E., Hallworth, M. A. & Lyle, S. 2007 Modelling carbon dioxide accumulation at Sleipner: implications for underground carbon storage. Earth Planet. Sci. Lett. 255, 164–176.CrossRefGoogle Scholar
Boait, F. C., White, N. J., Bickle, M. J., Chadwick, R. A., Neufeld, J. A. & Huppert, H. E. 2012 Spatial and temporal evolution of injected ${\mathrm{CO} }_{2} $ at the sleipner field, north sea. J. Geophys. Res. 117, B03309.Google Scholar
Golding, M. J. & Huppert, H. E. 2010 The effect of confining impermeable boundaries on gravity currents in a porous medium. J. Fluid Mech. 649, 1–17.Google Scholar
Gunn, I. & Woods, A. W. 2011 On the flow of buoyant fluid injected into a confined, inclined aquifer. J. Fluid Mech. 672, 109–129.Google Scholar
Hesse, M. A., Tchelepi, H. A., Cantwell, B. J. & Orr, F. M. Jr 2007 Gravity currents in horizontal porous layers: transition from early to late self-similarity. J. Fluid Mech. 577, 363–383.Google Scholar
Huppert, H. E. 1986 The intrusion of fluid mechanics into geology. J. Fluid Mech. 173, 557–594.Google Scholar
Huppert, H. E. & Woods, A. W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292, 55–69.Google Scholar
de Loubens, R. & Ramakrishnan, T. S. 2011 Analysis and computation of gravity induced migration in porous media. J. Fluid Mech. 675, 60–86.CrossRefGoogle 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
Mitchell, V. & Woods, A. W. 2006 Gravity driven flow in confined aquifers. J. Fluid Mech. 566, 345–355.CrossRefGoogle Scholar
Neufeld, J. A., Vella, D. & Huppert, H. E. 2009 The effect of a fissure on storage in a porous medium. J. Fluid Mech. 639, 239–259.Google Scholar
Nordbotten, J. M. & Celia, M. A. 2006 Similarity solutions for fluid injection into confined aquifers. J. Fluid Mech. 561, 307–327.Google Scholar
Orr, F. M. Jr 2009 Onshore geological storage of ${\mathrm{CO} }_{2} $ . Science 325, 1656–1658.CrossRefGoogle Scholar
Pegler, S. S., Kowal, K. N., Hasenclever, L. Q. & Worster, M. G. 2013 Lateral controls on grounding-line dynamics. J. Fluid Mech. 722, R1.Google Scholar
Vella, D. & Huppert, H. E. 2006 Gravity currents in a porous medium at an inclined plane. J. Fluid Mech. 555, 353–362.Google Scholar