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Leakage from gravity currents in a porous medium. Part 2. A line sink

Published online by Cambridge University Press:  06 January 2011

DOMINIC VELLA ,
JEROME A. NEUFELD ,
HERBERT E. HUPPERT  and
JOHN R. LISTER
DOMINIC VELLA*
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CMS, Wilberforce Road, Cambridge, CB3 0WA, UK
JEROME A. NEUFELD
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CMS, Wilberforce Road, Cambridge, CB3 0WA, UK
HERBERT E. HUPPERT
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CMS, Wilberforce Road, Cambridge, CB3 0WA, UK
JOHN R. LISTER
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CMS, Wilberforce Road, Cambridge, CB3 0WA, UK
*
†Email address for correspondence: dominic.vella@cantab.net
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Abstract

We consider the propagation of a buoyancy-driven gravity current in a porous medium bounded by a horizontal, impermeable boundary. The current is fed by a constant flux injected at a point and leaks through a line sink at a distance from the injection point. This is an idealized model of how a fault in a cap rock might compromise the geological sequestration of carbon dioxide. The temporal evolution of the efficiency of storage, defined as the instantaneous ratio of the rate at which fluid is stored without leaking to the rate at which it is injected, is of particular interest. We show that the ‘efficiency of storage’ decays like t−2/5 for times t that are long compared with the time taken for the current to reach the fault. This algebraic decay is in contrast to the case of leakage through a circular sink (Neufeld et al., J. Fluid Mech., vol. 2010) where the efficiency of storage decays more slowly like 1/lnt. The implications of the predicted decay in the efficiency of storage are discussed in the context of geological sequestration of carbon dioxide. Using parameter values typical of the demonstration project at Sleipner, Norway, we show that the efficiency of storage should remain greater than 90% on a time scale of millennia, provided that there are no significant faults in the cap rock within about 12km of the injection site.

JFM classification

Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 666 , 10 January 2011 , pp. 414 - 427
Copyright
Copyright © Cambridge University Press 2011

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References

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