Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-26T01:19:01.044Z Has data issue: false hasContentIssue false
  • English
  • Français

Buoyancy-driven dispersion in a layered porous rock

Published online by Cambridge University Press:  12 February 2015

Adrian Farcas  and
Andrew W. Woods
Adrian Farcas
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
Andrew W. Woods*
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: andy@bpi.cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the longitudinal dispersion of a passive tracer by a gravity-driven flow in a porous medium consisting of a series of independent horizontal layers connected to a constant pressure source. We show that in a formation of given vertical extent, the total flux is only weakly dependent on the number of layers, and is very similar to that in a single layer of the same total depth. However, although the flow speed in each layer is approximately uniform, the speed gradually increases with layer depth. As a result, if a pulse of tracer is released in the flow it will migrate more rapidly through the lower layers, leading to longitudinal dispersion of the tracer. Eventually, the location of the tracer in the different layers may become separated in space so that a sufficiently distant observation well would detect a series of discrete pulses of tracer rather than the original coherent input, as would occur in a single permeable layer. For a constant pressure source, at long times, the standard deviation of the longitudinal distribution of tracer asymptotes to a fraction of order 0.1 of the position of the centre of mass, depending on the number of layers and the overpressure of the source.

JFM classification

Mass Transport: Dispersion
Type
Papers
Information
Journal of Fluid Mechanics , Volume 767 , 25 March 2015 , pp. 226 - 239
Check for updates
Copyright
© 2015 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

Barenblat, G. I. 1996 Scaling, Self-Similarity and Intermediate Asymptotics. Cambridge University Press.CrossRefGoogle Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Elsevier.Google Scholar
Bear, J. & Cheng, A. H.-D. 2010 Modeling Groundwater Flow and Contaminant Transport. Springer.CrossRefGoogle Scholar
Bijelic, J., Muggeridge, A. & Blunt, M. 2004 Pore scale modeling of longitudinal dispersion. Water Resour. Res. WR003567.CrossRefGoogle Scholar
Ciriello, V., Di Federico, R., Archetti, S. & Longo, S. 2013 Effect of variable permeability on the propagation of thin gravity currents in porous media. Intl J. Non-Linear Mech. 57, 168–175.CrossRefGoogle Scholar
Croucher, A. E. & O’Sullivan, M. J. 1995 The Henry problem of salt-water intrusion. Water Resour. Res. 31, 1809–1814.CrossRefGoogle Scholar
Dagan, G. 1989 Flow and Transport in Porous Formations. Springer.CrossRefGoogle Scholar
Dagan, G., Fiori, A. & Jankovic, I. 2003 Flow and transport in highly heterogeneous formations. Water Resour. Res. 39 (9), 1268–1270.CrossRefGoogle Scholar
Delgado, J. M. P. Q. 2007 Longitudinal and transverse dispersion in porous media. Chem. Engng Res. Des. 85 (A9), 1245–1252.CrossRefGoogle Scholar
Di Federico, V., Longo, S., Chiapponi, L., Archetti, R. & Ciriello, V. 2014 Radial gravity currents in vertically graded porous media: theory and experiments for Newtonian and power-law fluids. Adv. Water Resour. 70, 65–76.CrossRefGoogle Scholar
Diersch, H.-J. & Kolditz, O. 2002 Variable-density flow and transport in porous media: approaches and challenges. Adv. Water Resour. 25, 899–944.CrossRefGoogle Scholar
Eames, I. & Bush, J. 1999 Longitudinal dispersion by bodies fixed in a potential flow. Proc. R. Soc. Lond. A8 445 (1990), 3665–3686.CrossRefGoogle Scholar
Flowers, T. & Hunt, J. 2007 Viscous and gravitational contributions to mixing during vertical brine transport in water-saturated porous media. Water Resour. Res. 43 (1), 4773–4790.CrossRefGoogle ScholarPubMed
Hesse, M. A. & Woods, A. W. 2010 Buoyant dispersal of $\text{CO}_{2}$ during geological storage. Geophys. Res. Lett. 37, L01403.CrossRefGoogle Scholar
Huppert, H. E. & Woods, A. W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292, 55–69.CrossRefGoogle Scholar
Gelhar, L. W., Welty, C. & Rehfeldt 1992 A critical review of data on field-scale dispersion in aquifers. Water Resour. Res. 7, 1955–1974.CrossRefGoogle Scholar
King, A. & Woods, A. W. 2003 Dipole solutions for viscous gravity currents. Theory and experiment. J. Fluid Mech. 483, 91–109.CrossRefGoogle Scholar
Kueper, B. H., Wealthall, G. P., Smith, J. W. N., Leharne, S. A. & Lerner, D. N.2003 An illustrated handbook of DNAPL transport and fate in the subsurface. U.K. Environment Agency R&D Publication No. 133, 2003.Google Scholar
Li, L., Lockington, D. L., Barry, D. A., Parlange, M. A. & Perrochet, P. 2003 Confined–unconfined flow in a horizontal confined aquifer. J. Hydrol. 271, 150–155.CrossRefGoogle Scholar
Menand, T. & Woods, A. W. 2005 Dispersion, scale, and time dependence of mixing zones under gravitationally stable and unstable displacements in porous media. Water Resour. Res. 41 (5), W05014.CrossRefGoogle Scholar
Phillips, O. M. 1991 Flow and Reactions in Permeable Rocks. Cambridge University Press.Google Scholar
Rayward-Smith, W. J. & Woods, A. W. 2011 Dispersal of buoyancy-driven flow in porous media with inclined baffles. J. Fluid Mech. 689, 517–528.CrossRefGoogle Scholar
Saffman, P. 1959 A theory of dispersion in a porous medium. J. Fluid Mech. 6, 321–349.CrossRefGoogle Scholar
Scheidegger, A. E. 1961 General theory of dispersion in porous media. J. Geophys. Res. 66, 3273–3274.CrossRefGoogle Scholar
Woods, A. W. & Norris, S. 2010 On the role of caprock and fracture zones in dispersing gas plumes in the subsurface. Water Resour. Res. 46, W08522.CrossRefGoogle Scholar
Young, W. R. & Jones, S. W. 1991 Dispersion in an unconsolidated porous medium. Phys. Fluids A 310, 2468–2470.CrossRefGoogle Scholar