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



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.


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Bear, J. 1988 Dynamics of Fluids in Porous Media. Dover.
Bickle, M., Chadwick, A., Huppert, H. E., Hallworth, M. A. & Lyle, S. 2007 Modelling carbon-dioxide accumulation at Sleipner: implications for underground carbon storage. Earth Planet. Sci. Lett. 255, 164176.
Bleaney, B. I. & Bleaney, B. 1976 Electricity and Magnetism. Oxford University Press.
Lake, L. 1989 Enhanced Oil Recovery. Prentice Hall.
Neufeld, J. A., Vella, D. & Huppert, H. E. 2009 The effect of a fissure on storage in a porous medium. J. Fluid Mech. 639, 239259.
Neufeld, J. A., Vella, D., Huppert, H. E. & Lister, J. R. 2010 Leakage from a gravity current in a porous medium. Part 1. A localized sink. J. Fluid Mech. doi:10.1017/S002211201000488X.
Pacala, S. & Socolow, R. 2004 Stabilization wedges: solving the climate problem for the next 50 years with current technologies. Science 305, 968972.
Phillips, O. M. 2009 Geological Fluid Dynamics: Sub-Surface Flow and Reactions. Cambridge University Press.
Pritchard, D. 2007 Gravity currents over fractured substrates in a porous medium. J. Fluid Mech. 584, 415431.
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