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Gravity currents with residual trapping

Published online by Cambridge University Press:  25 September 2008

M. A. HESSE ,
F. M. ORR JR  and
H. A. TCHELEPI
M. A. HESSE
Affiliation:
Department of Energy Resources Engineering, Stanford University, Stanford CA 94305, USA
F. M. ORR JR
Affiliation:
Department of Energy Resources Engineering, Stanford University, Stanford CA 94305, USA
H. A. TCHELEPI*
Affiliation:
Department of Energy Resources Engineering, Stanford University, Stanford CA 94305, USA
*
†Author to whom correspondence should be addressed.
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Abstract

Motivated by geological carbon dioxide (CO2) storage, we present a vertical-equilibrium sharp-interface model for the migration of immiscible gravity currents with constant residual trapping in a two-dimensional confined aquifer. The residual acts as a loss term that reduces the current volume continuously. In the limit of a horizontal aquifer, the interface shape is self-similar at early and at late times. The spreading of the current and the decay of its volume are governed by power-laws. At early times the exponent of the scaling law is independent of the residual, but at late times it decreases with increasing loss. Owing to the self-similar nature of the current the volume does not become zero, and the current continues to spread. In the hyperbolic limit, the leading edge of the current is given by a rarefaction and the trailing edge by a shock. In the presence of residual trapping, the current volume is reduced to zero in finite time. Expressions for the up-dip migration distance and the final migration time are obtained. Comparison with numerical results shows that the hyperbolic limit is a good approximation for currents with large mobility ratios even far from the hyperbolic limit. In gently sloping aquifers, the current evolution is divided into an initial near-parabolic stage, with power-law decrease of volume, and a later near-hyperbolic stage, characterized by a rapid decay of the plume volume. Our results suggest that the efficient residual trapping in dipping aquifers may allow CO2 storage in aquifers lacking structural closure, if CO2 is injected far enough from the outcrop of the aquifer.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 611 , 25 September 2008 , pp. 35 - 60
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Bachu, S. & Bennion, B. 2007 Effects of in-situ conditions on relative permeability characteristics of CO2–brine systems. Environ. Geol. doi 10.1007/s00254-007-0946-9.CrossRefGoogle Scholar
Barenblatt, G. I. 1996 Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press.CrossRefGoogle Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Elsevier.Google Scholar
Bear, J. & Ryzhik, V. 1998 On displacement of NAPL lenses and plumes in a phreatic aquifer. Transport Porous Med. 33, 227–255.CrossRefGoogle Scholar
Benson, S. M., Tomutsa, L., Silin, D. & Kneafsey, T. 2006 Core scale and pore scale studies of carbon dioxide migration in saline formations. In Proc. GHGT-8, Trondheim, Norway.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
Ennis-King, J. & Paterson, L. 2002 Engineering aspects of geological sequestration of carbon dioxide. In Asia Pacific Oil and Gas Conf. and Exhibition, Melbourne, Australia.CrossRefGoogle Scholar
Ennis-King, J., Preston, I. & Paterson, L. 2005 Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions. Phys. Fluids 17 (8), 084107.CrossRefGoogle Scholar
Hassanzadeh, H., Pooladi-Darvish, M. & Keith, D. W. 2007 Scaling behavior of convective mixing, with application to geological storage of CO2. AIChE J. 53 (5), 1121–1131.CrossRefGoogle Scholar
Hesse, M. A., Tchelepi, H. A. & Orr, F. M. Jr 2006 Scaling analysis of the migration of CO2 in saline aquifers. In SPE Annu. Tech. Conf. and Exhibition, San Antonio, TX.CrossRefGoogle Scholar
Hesse, M. A., Riaz, A. & Tchelepi, H. A. 2007 a Convective dissolution of CO2 in saline aquifers. Geochim. Cosmochim. Acta 71 (15), A401.Google Scholar
Hesse, M. A., Tchelepi, H. A., Cantwell, B. J. & Orr, F. M. Jr 2007 b Gravity currents in horizontal porous layers: transition from early to late self-similarity. J. Fluid Mech. 577, 363–383.CrossRefGoogle Scholar
Holloway, S & Savage, D. 1993 The potential for aquifer disposal of carbon-dioxide in the UK. Energy Convers. Manage. 34 (9–11), 925–932.CrossRefGoogle Scholar
Huppert, H. E. & Woods, A. W. 1995 Gravity-driven flows in porous media. J. Fluid Mech. 292, 55–69.CrossRefGoogle Scholar
Ide, S. T., Jessen, K. & Orr, F. M. Jr 2007 Storage of CO2 in saline aquifers: effects of gravity, viscous, and capillary forces on amount and timing of trapping. Intl J. Greenh. Gas Control 1 (4), 481–491.Google Scholar
Juanes, R., Spiteri, E. J., Orr, F. M. Jr & Blunt, M. J. 2006 Impact of relative permeability hysteresis on geological CO2 storage. Water Resour. Res. 42 (W12418), 1–13.CrossRefGoogle Scholar
Kochina, I. N., Mikhailov, N. N. & Filinov, M. V. 1983 Groundwater mound damping. Intl J. Engng Sci. 21, 413–421.CrossRefGoogle Scholar
Koperna, G. J. & Kuuskraa, V. A. 2006 Assessing technical and economic recovery of oil resources in residual oil zones. Tech. Rep. Advanced Resources International, 4501 Fairfax Drive, Suite 910, Arlington, VA 22203 USA.Google Scholar
Kumar, A., Ozah, R., Noh, M., Pope, G. A., Bryant, S., Sepehrnoori, K. & Lake, L. W. 2005 Reservoir simulation of CO2 storage in deep saline aquifers. Soc. Petrol. Engrs J. September pp. 336–348.CrossRefGoogle Scholar
Leveque, R. J. 2002 Finite Volume Methods for Hyperbolic Problems. Cambridge University Press.CrossRefGoogle Scholar
Lindeberg, E. & Wessel-Berg, D. 1997 Vertical convection in an aquifer column under a gas cap of CO2. Energy Conserv. Manage. 38, SS229–SS234.CrossRefGoogle Scholar
Lister, J. R. 1992 Viscous flows down an inclined plane from point and line sources. J. Fluid Mech. 242, 631–653.CrossRefGoogle Scholar
Lyle, S., Huppert, H. E., Hallworth, M., Bickle, M. & Chadwick, A. 2005 Axisymmetric gravity currents in a porous medium. J. Fluid Mech. 543, 293–302.CrossRefGoogle Scholar
Metz, B., Davidson, O., de Coninck, H., Loos, M. & Meyer, L. (ed.) 2006 Special Report on Carbon Dioxide Capture and Storage. Cambridge University Press.Google Scholar
Michael, K., Bachu, S., Buschkuehle, B. E., Haug, K., Grobe, M. & Lytviak, A. T. 2006 Comprehensive characterization of a potential site for CO2 geological storage in central Alberta, Canada. In Proc. CO2SC Symp. 2006, Berkeley, CA.Google Scholar
Mo, S., Zweigel, P., Lindeberg, E. & Akervoll, I. 2005 Effect of geologic parameters on CO2 storage in deep saline aquifers. In SPE Eurospec/EAGE Annu. Conf. Madrid, Spain.CrossRefGoogle Scholar
Nicot, J.-P. 2007 Evaluation of large-scale carbon storage on fresh-water sections of aquifers: a Texas study. Intl J. Greenh. Gas Control (in press).Google 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. Transport Porous Med. 58, 339–360.CrossRefGoogle Scholar
Riaz, A. & Meiburg, E. 2004 Linear stability of radial displacements in porous media: influence of velocity-induced dispersion and concentration-dependent diffusion. Phys. Fluids 16 (10), 3592.CrossRefGoogle Scholar
Riaz, A. & Tchelepi, H. A. 2006 Numerical simulation of immiscible two-phase flow in porous media. Phys. Fluids 18 (014104).CrossRefGoogle Scholar
Riaz, A., Hesse, M., Tchelepi, H. & Orr, F. M. Jr 2006 Onset of convection in a gravitationally unstable, diffusive boundary layer in porous media. J. Fluid Mech. 548, 87–111.CrossRefGoogle Scholar
Saffman, P. G. & Taylor, G. I. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more visous fluid. Proc. R. Soc. Lond. A 245, 312–329.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
Verdon, J. & Woods, A. W. 2007 Gravity driven reacting flows in a confined porous aquifer. J. Fluid Mech. 588, 29–41.CrossRefGoogle Scholar
Yortsos, Y. C. 1995 A theoretical analysis of vertical flow equilibrium. Transport Porous Med. 18, 107–129.CrossRefGoogle Scholar
Yortsos, Y. C. & Hickernell, F. J. 1989 Linear stability of immiscible displacement in porous media. SIAM J. Appl. Maths 49, 730–748.CrossRefGoogle Scholar