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

Vella, D. and Neufeld, J. A. and Huppert, H. E. and Lister, J.R. (2011) Leakage from gravity currents in a porous medium. Part 2. A line sink. Journal of Fluid Mechanics, 666. pp. 414-427. ISSN 0022-1120 DOI 10.1017/S002211201000491X

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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.

Item Type: Article
Uncontrolled Keywords: 2010AREP; IA61
Subjects: 99 - Other
Divisions: 99 - Other
Journal or Publication Title: Journal of Fluid Mechanics
Volume: 666
Page Range: pp. 414-427
Identification Number: 10.1017/S002211201000491X
Depositing User: Sarah Humbert
Date Deposited: 06 Dec 2011 11:38
Last Modified: 23 Jul 2013 10:02
URI: http://eprints.esc.cam.ac.uk/id/eprint/2259

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