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Capillary entry pressure and the leakage of gravity currents through a sloping layered permeable rock

Published online by Cambridge University Press:  10 January 2009

ANDREW W. WOODS  and
ADRIAN FARCAS
ANDREW W. WOODS*
Affiliation:
BP Institute, University of Cambridge, Cambridge CB3 0EZ, UK
ADRIAN FARCAS
Affiliation:
BP Institute, University of Cambridge, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

We examine the motion of a buoyant fluid injected into a water-saturated porous rock as it spreads along a thin inclined low-permeability barrier. We account for leakage of the fluid across the barrier once the current is sufficiently deep so that the pressure exceeds the capillary threshold. We show that at some distance from the source, the pressure decreases below this threshold, and all the remaining flux spreads laterally along the barrier. We examine the controls on the partitioning of the flow between the draining flux and the laterally spreading flux and also the controls on the lateral extent of the draining region for the case of an instantaneous release and a maintained release of fluid. We consider the implications of our work for the dispersal of CO2 plumes which may be sequestered in deep saline aquifers.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 618 , 10 January 2009 , pp. 361 - 379
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Ames, W. F. 1977 Numerical Methods for Partial Differential Equations. Academic.Google Scholar
Barenblatt, G. I. 1996 Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press.CrossRefGoogle Scholar
Barenblatt, G. I., Entov, V. M. & Ryzhik, V. M. 1990 Theory of Fluid Flows through Natural Rocks. Kluwer.Google Scholar
Bear, J. 1970 Dynamics of Flow in Porous media. Dover.Google Scholar
Bear, J., & Ryzhik, V. 1998 On the displacement of NAPL lenses and plumes in a phreatic aquifer. Trans. Porous Med. 33, 227–255.Google Scholar
Bickle, M., Chadwick, A., Huppert, H. E., Hallworth, M. & Lyle, S. 2007 Modelling carbon dioxide accumulation at Sleipner: Implications for underground carbon storage. Earth Planet. Sci. Lett. 255, 164–176.CrossRefGoogle Scholar
Dake, L. 1978 Fundamentals of Reservoir Engineering. Elsevier.Google Scholar
Farcas, A. & Woods, A. W. 2009 The effect of drainage on the capillary retention of CO2 in a layered permeable rock. J. Fluid Mech. 618, 349–359.Google Scholar
Hesse, M. A., Tchelepi, H. A., Cantwell, B. J. & Orr, F. M. Jr., 2006 Scaling analysis of the migration of CO2 in saline aquifers: SPE 102796. SPE Annu. Tech. Conf. and Exhibition. San Antonio, TX, USA.Google Scholar
Hesse, M. A., Tchelepi, H. A., Cantwell, B. J. & Orr, F. M. Jr., 2007 Gravity currents in horizontal porous layers: transition from early to late self-similarity. J. Fluid Mech. 577, 363–383.CrossRefGoogle Scholar
Holloway, S. 2001 Storage of fossil fuel derived carbon dioxide beneath the surface of the earth. Annu. Rev. Energy Environ. 26, 245–266.Google Scholar
Huppert, H. E. & Woods, A. W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292, 55–69.CrossRefGoogle Scholar
Kumar, A., Ozah, R., Noh, M., Pope, G. A., Bryant, S., Sephernoori, K. & Lake, L. W. 2005 Reservoir simulation of CO2 storage in deep saline aquifers Soc. Petrol Engng J. 336-248, 307–327.Google Scholar
Mathunjwa, J. S. & Hogg, A. 2005 Self-similar gravity currents in porous media: linear stability of the Barenblatt–Pattle solution revisited. Euro J. Mech. B 25 (3), 360–378.Google Scholar
Mitchell, V. & Woods, A. W. 2006 Gravity driven flow in confined aquifers. J. Fluid Mech. 566, 345–355.CrossRefGoogle Scholar
Nordbotten, J. M., Celia, M. A. & Bachu, S. 2005 Injection and storage of CO2 in deep saline aquifers: analytical solution for the CO2 plume evolution during plume injection. Trans. Porous Med. 58, 339–360.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
Phillips, O. M. 1991 Flow and Reactions in Permeable Rocks. Cambridge University Press.Google Scholar
Pritchard, D. 2007 Gravity currents over fractured substrates in a porous medium. J. Fluid Mech. 584, 415–431.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
Riaz, A., Hesse, M., Tchelepi, H. A. & Orr, F. M. Jr., 2006 Onset of convection in a gravitationally unstable diffusive boundary layer in porous media. J. Fluid Mech. 548, 87–111.Google Scholar
Vella, D. & Huppert, H. E. 2006 Gravity currents in a porous medium at an inclined plane. J. Fluid Mech. 555, 353–362.CrossRefGoogle Scholar
Woods, A. W. 2002 Gravity driven flows in porous rocks: effects of layering, reaction, boiling and double advection. In Transport Phenomena in Porous Media (ed. Ingham, D. B. & Pop, I.), vol. 2, pp. 397–423. Pergamon.CrossRefGoogle Scholar