Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-21T03:28:25.520Z Has data issue: false hasContentIssue false
  • English
  • Français

The fate of continuous input of relatively heavy fluid at the base of a porous medium

Published online by Cambridge University Press:  02 December 2021

Herbert E. Huppert  and
Samuel S. Pegler Open the ORCID record for Samuel S. Pegler [Opens in a new window]
Herbert E. Huppert*
Affiliation:
Institute of Theoretical Geophysics, King's College, CambridgeCB2 1ST, UK
Samuel S. Pegler
Affiliation:
School of Mathematics, University of Leeds, LeedsLS2 9JT, UK
*
†Email address for correspondence: heh1@cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We evaluate theoretically and confirm experimentally the shape of the fluid envelope resulting from the input of relatively heavy fluid at a constant rate from a point source at the base of a homogeneous porous medium. In three dimensions an initially expanding hemisphere transitions into a gravity current flowing over the assumed rigid, horizontal and impermeable bottom of the porous medium. A range of increasing transition times occurs if defined by extrapolation of the relationships in the two extreme regimes (hemispherical shape and thin-layer gravity current) so that they intersect, for: the ratio of buoyancy to fluid resistance; the horizontal extent of the fluid; the ratio of height at the centre to the radius; and just the height at the centre. Corresponding results are derived for two-dimensional geometries. In this case, we conduct a series of laboratory experiments demonstrating the transition between the radial and gravity current regimes both in terms of form and propagation rate. The results are extrapolated briefly to two-layer systems, in order to begin to understand effects due to vertically heterogeneous pore structures. We sketch, and verify by experiment, that an expanding hemisphere in a lower layer can reach a much more permeable upper layer and flow through it as a gravity current, thereby uniting the two regimes.

JFM classification

Low-Reynolds-number flows: Porous media Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Hele-Shaw flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A5
Check for updates
Copyright
© The Author(s), 2021. Published by 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

REFERENCES

Acton, J.M., Huppert, H.E. & Worster, M.G. 2001 Two-dimensional viscous gravity currents flowing over a deep porous medium. J. Fluid Mech. 440, 359–380.CrossRefGoogle Scholar
Afanasyev, A., Blundy, J., Melnik, O. & Sparks, S. 2018 Formation of magmatic brine lenses via focussed fluid-flow beneath volcanoes. Earth Planet. Sci. Lett. 486, 119–128.CrossRefGoogle Scholar
Barenblatt, G.I. 1996 Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics. Cambridge University Press.CrossRefGoogle Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Dover.Google Scholar
Bharath, K. & Flynn, M. 2021 Buoyant convection in heterogeneous porous media with an inclined permeability jump: an experimental investigation of filling box-type flows. J. Fluid Mech. 924, A35.CrossRefGoogle Scholar
Bickle, M.J. 2009 Geological carbon storage. Nat. Geosci. 2, 815–818.CrossRefGoogle Scholar
Guo, B., Zheng, Z., Celia, M.A. & Stone, H.A. 2016 Axisymmetric flows from fluid injection into a confined porous medium. Phys. Fluids 28 (2), 022107.CrossRefGoogle Scholar
Hinton, E.M. & Woods, A.W. 2018 Buoyancy-driven flow in a confined aquifer with a vertical gradient of permeability. J. Fluid Mech. 848, 411–429.CrossRefGoogle Scholar
Huppert, H.E. 1986 The intrusion of fluid mechanics into geology. J. Fluid Mech. 173, 557–594.CrossRefGoogle Scholar
Huppert, H.E. & Neufeld, J.A. 2014 The fluid mechanics of carbon dioxide sequestration. Annu. Rev. Fluid Mech. 46 (1), 255–272.CrossRefGoogle Scholar
Huppert, H.E., Neufeld, J.A. & Strandkvist, C. 2013 The competition between gravity and flow focusing in two-layered porous media. J. Fluid Mech. 720, 5–14.CrossRefGoogle Scholar
Huppert, H.E. & Woods, A.W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292, 55–69.CrossRefGoogle Scholar
Kampman, N., et al. 2014 Drilling and sampling a natural CO$_2$ reservoir: implications for fluid flow and CO$_2$-fluid–rock reactions during CO$_2$ migration through the overburden. Chem. Geol. 369, 51–82.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.CrossRefGoogle Scholar
Nordbotten, J.M. & Celia, M.A. 2006 Similarity solutions for fluid injection into confined aquifers. J. Fluid Mech. 561, 307–327.CrossRefGoogle Scholar
Pegler, S.S., Huppert, H.E. & Neufeld, J.A. 2014 Fluid injection into a confined porous layer. J. Fluid Mech. 745, 592–620.CrossRefGoogle Scholar
Pegler, S.S., Huppert, H.E. & Neufeld, J.A. 2016 Stratified gravity currents in porous media. J. Fluid Mech. 791, 329–357.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.CrossRefGoogle Scholar
Pegler, S.S., Maskell, A.S.D., Daniels, K.A. & Bickle, M.J. 2017 Fluid transport in geological reservoirs with background flow. J. Fluid Mech. 827, 536–571.CrossRefGoogle Scholar
Saffman, P.G. & Taylor, G.I. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245 (1242), 312–329.Google Scholar
Zheng, Z., Guo, B., Christov, I.C., Celia, M.A. & Stone, H.A. 2015 Flow regimes for fluid injection into a confined porous medium. J. Fluid Mech. 767, 881–909.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