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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: [email protected]
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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
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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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