Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-30T20:14:22.577Z Has data issue: false hasContentIssue false
  • English
  • Français

Buoyancy-driven plumes in a layered porous medium

Published online by Cambridge University Press:  26 November 2019

Duncan R. Hewitt Open the ORCID record for Duncan R. Hewitt [Opens in a new window] ,
Gunnar G. Peng Open the ORCID record for Gunnar G. Peng [Opens in a new window]  and
John R. Lister Open the ORCID record for John R. Lister [Opens in a new window]
Duncan R. Hewitt*
Affiliation:
Department of Mathematics, University College London, 25 Gordon Street, LondonWC1H 0AY, UK
Gunnar G. Peng
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CambridgeCB3 0WA, UK
John R. Lister
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CambridgeCB3 0WA, UK
*
†Email address for correspondence: d.hewitt@ucl.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Thin, roughly horizontal low-permeability layers are a common form of large-scale heterogeneity in geological porous formations. In this paper, the dynamics of a buoyancy-driven plume in a two-dimensional layered porous medium is studied theoretically, with the aid of high-resolution numerical simulations. The medium is uniform apart from a thin, horizontal layer of a much lower permeability, located a dimensionless distance $L\gg 1$ below the dense plume source. If the dimensionless thickness $2\unicode[STIX]{x1D700}L$ and permeability $\unicode[STIX]{x1D6F1}$ of the low-permeability layer are small, the effect of the layer is found to be well parameterized by its impedance $\unicode[STIX]{x1D6FA}=2\unicode[STIX]{x1D700}L/\unicode[STIX]{x1D6F1}$. Five different regimes of flow are identified and characterized. For $\unicode[STIX]{x1D6FA}\ll L^{1/3}$, the layer has no effect on the plume, but as $\unicode[STIX]{x1D6FA}$ is increased the plume widens and spreads over the layer as a gravity current. For still larger $\unicode[STIX]{x1D6FA}$, the flow becomes destabilized by convective instabilities both below and above the layer, until, for $\unicode[STIX]{x1D6FA}\gg L$, the spread of the plume is dominated by convective mixing and buoyancy is transported across the layer by diffusion alone. Analytical models for the spread of the plume over the layer in the various different regimes are presented.

JFM classification

Convection: Plumes/thermals Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A37
Copyright
© 2019 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

Bauer-Gottwein, P., Langer, T., Prommer, H., Wolski, P. & Kinzelbach, W. 2007 Okavango delta islands: interaction between density-driven flow and geochemical reactions under evapo-concentration. J. Hydrol. 335, 389–405.CrossRefGoogle Scholar
Farcas, A. & Woods, A. W. 2013 Three-dimensional buoyancy-driven flow along a fractured boundary. J. Fluid Mech. 728, 279–305.CrossRefGoogle Scholar
Hesse, M. A. & Woods, A. W. 2010 Buoyant dispersal of CO2 during geological storage. Geophys. Res. Lett. 37, 01403.CrossRefGoogle Scholar
Hewitt, D. R., Neufeld, J. A. & Lister, J. R. 2012 Ultimate regime of high Rayleigh number convection in a porous medium. Phys. Rev. Lett. 108, 224503.CrossRefGoogle Scholar
Hewitt, D. R., Neufeld, J. A. & Lister, J. R. 2013 Convective shutdown in a porous medium at high Rayleigh number. J. Fluid Mech. 719, 551–586.CrossRefGoogle Scholar
Hewitt, D. R., Neufeld, J. A. & Lister, J. R. 2014 High Rayleigh number convection in a porous medium containing a thin low-permeability layer. J. Fluid Mech. 756, 844–869.CrossRefGoogle Scholar
Howard, L. N. 1964 Convection at high Rayleigh number. In Applied Mechanics, Proceedings of the 11th International Congress of Applied Mathematics (ed. Görtler, H.), pp. 1109–1115.Google Scholar
Huppert, H. E. & Neufeld, J. A. 2014 The fluid mechanics of carbon dioxide sequestration. Annu. Rev. Fluid Mech. 46, 255–272.CrossRefGoogle Scholar
Kissling, W. M. & Weir, G. J. 2005 The spatial distribution of the geothermal fields in the Taupo Volcanic Zone, New Zealand. J. Volcanol. Geotherm. Res. 125, 136–150.CrossRefGoogle Scholar
MacFarlane, D. S., Cherry, J. A., Gillham, R. W. & Sudicky, E. A. 1983 Migration of contaminants in groundwater at a landfill: a case study. J. Hydrol. 63, 1–29.CrossRefGoogle Scholar
Neufeld, J. A., Vella, D., Huppert, H. E. & Lister, J. R. 2011 Leakage from gravity currents in a porous medium. Part 1. A localized sink. J. Fluid Mech. 666, 391–413.CrossRefGoogle Scholar
Neufeld, J. A. & Huppert, H. E. 2009 Modelling carbon dioxide sequestration in layered strata. J. Fluid Mech. 625, 353–370.CrossRefGoogle Scholar
Pegler, S. S., Huppert, H. E. & Neufeld, J. A. 2014 Fluid migration between confined aquifers. J. Fluid Mech. 757, 330–353.CrossRefGoogle Scholar
Phillips, O. M. 2009 Geological Fluid Dynamics: Sub-surface Flow and Reactions. CUP.CrossRefGoogle Scholar
Pritchard, D. 2007 Gravity currents over fractured substrates in a porous medium. J. Fluid Mech. 584, 415–431.CrossRefGoogle Scholar
Pritchard, D. & Hogg, A. J. 2002 Draining viscous gravity currents in a vertical fracture. J. Fluid Mech. 459, 207–216.CrossRefGoogle Scholar
Pritchard, D., Woods, A. W. & Hogg, A. J. 2001 On the slow draining of a gravity current moving through a layered permeable medium. J. Fluid Mech. 444, 23–47.CrossRefGoogle Scholar
Rayward-Smith, W. J. & Woods, A. W. 2011 Dispersal of buoyancy-driven flow in porous media with inclinded baffles. J. Fluid Mech. 689, 517–528.CrossRefGoogle Scholar
Roes, M. A., Bolster, D. T. & Flynn, M. R. 2014 Buoyant convection from a discrete source in a leaky porous medium. J. Fluid Mech. 755, 204–229.CrossRefGoogle Scholar
Sahu, C. K. & Flynn, M. R. 2015 Filling box flows in porous media. J. Fluid Mech. 782, 455–478.CrossRefGoogle Scholar
Sahu, C. K. & Flynn, M. R. 2016 Filling box flows in an axisymmetric porous medium. Trans. Porous Med. 112, 619–635.CrossRefGoogle Scholar
Sahu, C. K. & Flynn, M. R. 2017 The effect of sudden permeability changes in porous media filling box flows. Trans. Porous Med. 119, 95–118.CrossRefGoogle Scholar
Slim, A. C. 2014 Solutal-convection regimes in a two-dimensional porous medium. J. Fluid Mech. 741, 461–491.CrossRefGoogle Scholar
Slim, A. C., Bandi, M. M., Miller, J. C. & Mahadevan, L. 2013 Dissolution-driven convection in a Hele–Shaw cell. Phys. Fluids 25, 024101.CrossRefGoogle Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. CUP.CrossRefGoogle Scholar
Wooding, R. A. 1963 Convection in a saturated porous medium at large Rayleigh number or Peclét number. J. Fluid Mech. 15, 527–544.CrossRefGoogle Scholar
Wooding, R. A., Tyler, S. W., White, I. & Anderson, P. A. 1997 Convection in groundwater below an evaporating salt lake: 2. Evolution of fingers or plumes. Water Resour. Res. 33, 1219–1228.CrossRefGoogle Scholar
Zheng, Z., Soh, B., Huppert, H. E. & Stone, H. A. 2013 Fluid drainage from the edge of a porous reservoir. J. Fluid Mech. 718, 558–568.CrossRefGoogle Scholar