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Leakage from gravity currents in a porous medium. Part 1. A localized sink

Published online by Cambridge University Press:  06 January 2011

JEROME A. NEUFELD ,
DOMINIC VELLA ,
HERBERT E. HUPPERT  and
JOHN R. LISTER
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
DOMINIC VELLA
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: [email protected]
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Abstract

We consider the buoyancy-driven flow of a fluid injected into a semi-infinite porous medium bounded by a horizontal impermeable barrier through which a single localized sink allows leakage of the injected fluid. Our study is motivated by the geological sequestration of carbon dioxide (CO2), which is less dense than the ambient water, and the possibility that fissures in the bounding ‘cap’ rock may therefore compromise the long-term storage of CO2. A theoretical model is presented in which the leakage through the sink, or fissure, is driven by the hydrostatic pressure at the sink of the injected buoyant fluid. We determine numerical solutions for the evolution of the gravity current in the porous medium and for the quantity of fluid that escapes through the sink as a function of time. A quantity of considerable interest is the efficiency of storage, which we define as the flux of fluid that is stably stored relative to the amount injected. At the later stages in the evolution of the current, the region near the source and sink reaches a quasi-steady state. We find analytical solutions to this asymptotic state which show that the efficiency of storage decreases to zero like 1/lnt, where t is the time since initiation of the current, and predict a dependence on the properties of the sink in agreement with our numerical results. The implications of this result for the geological sequestration of CO2 are discussed.

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. 391 - 413
Copyright
Copyright © Cambridge University Press 2011

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