Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 65
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Zheng, Zhong Rongy, Laurence and Stone, Howard A. 2015. Viscous fluid injection into a confined channel. Physics of Fluids, Vol. 27, Issue. 6, p. 062105.

    Pegler, Samuel S. Bain, Emily L. Huppert, Herbert E. and Neufeld, Jerome A. 2015. Fluid invasion of an unsaturated leaky porous layer. Journal of Fluid Mechanics, Vol. 777, p. 97.

    Mathias, Simon A. McElwaine, Jim N. and Gluyas, Jon G. 2014. Heat transport and pressure buildup during carbon dioxide injection into depleted gas reservoirs. Journal of Fluid Mechanics, Vol. 756, p. 89.

    MacMinn, Christopher W. and Juanes, Ruben 2009. A mathematical model of the footprint of the CO2 plume during and after injection in deep saline aquifer systems. Energy Procedia, Vol. 1, Issue. 1, p. 3429.

    MacMinn, C. W. Szulczewski, M. L. and Juanes, R. 2011. CO2 migration in saline aquifers. Part 2. Capillary and solubility trapping. Journal of Fluid Mechanics, Vol. 688, p. 321.

    Afanasyev, Andrey A. 2015. On the Riemann problem for supercritical CO2 injection into an aquifer. International Journal of Greenhouse Gas Control, Vol. 42, p. 629.

    Leahy, M.J. Ennis-King, J. Hammond, J. Huppert, H.E. and Neufeld, J. 2009. Application of gravity currents to the migration of CO2 in heterogeneous saline formations. Energy Procedia, Vol. 1, Issue. 1, p. 3331.

    Hidalgo, Juan J. MacMinn, Christopher W. and Juanes, Ruben 2013. Dynamics of convective dissolution from a migrating current of carbon dioxide. Advances in Water Resources, Vol. 62, p. 511.

    Qi, R. Laforce, T.C. and Blunt, M.J. 2010. Developments and Innovation in Carbon Dioxide (CO2) Capture and Storage Technology.

    Szulczewski, M. L. and Juanes, R. 2013. The evolution of miscible gravity currents in horizontal porous layers. Journal of Fluid Mechanics, Vol. 719, p. 82.

    FARCAS, ADRIAN and WOODS, ANDREW W. 2009. The effect of drainage on the capillary retention of CO2 in a layered permeable rock. Journal of Fluid Mechanics, Vol. 618, p. 349.

    Zheng, Zhong Shin, Sangwoo and Stone, Howard A. 2015. Converging gravity currents over a permeable substrate. Journal of Fluid Mechanics, Vol. 778, p. 669.

    Okwen, Roland T. Stewart, Mark T. and Cunningham, Jeffrey A. 2011. Analytical model for screening potential CO2 repositories. Computational Geosciences, Vol. 15, Issue. 4, p. 755.

    MacMinn, Christopher W. and Juanes, Ruben 2009. Post-injection spreading and trapping of CO2 in saline aquifers: impact of the plume shape at the end of injection. Computational Geosciences, Vol. 13, Issue. 4, p. 483.

    Riaz, Amir and Cinar, Yildiray 2014. Carbon dioxide sequestration in saline formations: Part I—Review of the modeling of solubility trapping. Journal of Petroleum Science and Engineering, Vol. 124, p. 367.

    Guo, Bo Zheng, Zhong Celia, Michael A. and Stone, Howard A. 2016. Axisymmetric flows from fluid injection into a confined porous medium. Physics of Fluids, Vol. 28, Issue. 2, p. 022107.

    GOLDING, MADELEINE J. NEUFELD, JEROME A. HESSE, MARC A. and HUPPERT, HERBERT E. 2011. Two-phase gravity currents in porous media. Journal of Fluid Mechanics, Vol. 678, p. 248.

    Kalisch, H. Mitrovic, D. and Nordbotten, J. M. 2016. Rayleigh–Taylor instability of immiscible fluids in porous media. Continuum Mechanics and Thermodynamics, Vol. 28, Issue. 3, p. 721.

    Doster, F. Nordbotten, J.M. and Celia, M.A. 2013. Impact of capillary hysteresis and trapping on vertically integrated models for CO2 storage. Advances in Water Resources, Vol. 62, p. 465.

    GOLDING, MADELEINE J. NEUFELD, JEROME A. HESSE, MARC A. and HUPPERT, HERBERT E. 2011. Two-phase gravity currents in porous media. Journal of Fluid Mechanics, Vol. 678, p. 248.

  • Journal of Fluid Mechanics, Volume 577
  • April 2007, pp. 363-383

Gravity currents in horizontal porous layers: transition from early to late self-similarity

  • M. A. HESSE (a1), H. A. TCHELEPI (a1), B. J. CANTWEL (a2) and F. M. ORR (a1)
  • DOI:
  • Published online: 25 April 2007

We investigate the evolution of a finite release of fluid into an infinite, two-dimensional, horizontal, porous slab saturated with a fluid of different density and viscosity. The vertical boundaries of the slab are impermeable and the released fluid spreads as a gravity current along a horizontal boundary. At early times the released fluid fills the entire height of the layer, and the governing equation admits a self-similar solution that is a function of the viscosity ratio between the two fluids. This early similarity solution describes a tilting interface with tips propagating as xt1/2. At late times the released fluid has spread along the boundary and the height of the current is much smaller than the thickness of the layer. The governing equation simplifies and admits a different similarity solution that is independent of the viscosity ratio. This late similarity solution describes a point release of fluid in a semi-infinite porous half-space, where the tip of the interface propagates as xt1/3. The same simplification of the governing equation occurs if the viscosity of the released fluid is much higher than the viscosity of the ambient fluid. We have obtained an expression for the time when the solution transitions from the early to the late self-similar regime. The transition time increases monotonically with increasing viscosity ratio. The transition period during which the solution is not self-similar also increases monotonically with increasing viscosity ratio, for mobility ratios larger than unity. Numerical computations describing the full evolution of the governing equation show good agreement with the theoretical results. Estimates of the spreading of injected fluids over long times are important for geological storage of CO2, and for the migration of pollutants in aquifers. In all cases it is important to be able to anticipate when the spreading regime transitions from xt1/2 to xt1/3.

Corresponding author
Author to whom correspondence should be addressed.
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

G. I. Barenblatt & Ya. B. Zeldovich 1972 Self-similar solutions as intermediate asymptotics. Ann. Rev. Fluid Mech. 4, 285312.

Y. C. Yortsos 1995 A theoretical analysis of vertical flow equilibrium. Transp. Porous Media 18, 107129.

J. Bear 1972 Dynamics of Fluids in Porous Media. American Elsevier.

R. J. Leveque 2002 Finite Volume Methods for Hyperbolic Problems. Cambridge University Press.

J. Bear & V. Ryzhik 1998 On displacement of NAPL lenses and plumes in a phreatic aquifer. Transp. Porous Media 33, 227255.

S. Lyle , H. E. Huppert , M. Hallworth , M. Bickle & A. Chadwick 2005 Axisymmetric gravity currents in a porous medium. J. Fluid Mech. 543, 293302.

S. Bachu 2003 Screening and ranking of sedimentary basins for sequestration of CO2 in geological media in response to climate change. Environmental Geology 44, 277289.

G. I. Barenblatt 1996 Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press.

J. R. Hunt , N. Sitar & K. S. Udell 1995 Nonaqueous phase liquid transport and cleanup. Part 1. Analysis of mechanisms. Water Resour. Res. 24, 12471258.

J. M. Nordbotten , M. A. Celia & S. Bachu 2005 Injection and storage of CO2 in deep saline aquifers: Analytical solution for the CO2 plume evolution during plume injection. Transp. Porous Media 58, 339360.

H. E. Huppert 1982 Propagation of two-dimensional viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 4358.

H. E. Huppert & A. W. Woods 1995 Gravity-driven flows in porous media. J. Fluid Mech. 292, 5569.

A. Riaz & H. A. Tchelepi 2006 Numerical simulation of immiscible two-phase flow in porous media. Phys. Fluids 18 014104.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *