Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-17T21:17:10.781Z Has data issue: false hasContentIssue false

Two-phase gravity currents in porous media

Published online by Cambridge University Press:  26 April 2011

Department of Applied Mathematics and Theoretical Physics, Institute of Theoretical Geophysics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Department of Applied Mathematics and Theoretical Physics, Institute of Theoretical Geophysics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Department of Applied Mathematics and Theoretical Physics, Institute of Theoretical Geophysics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Department of Applied Mathematics and Theoretical Physics, Institute of Theoretical Geophysics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Email address for correspondence:


We develop a model describing the buoyancy-driven propagation of two-phase gravity currents, motivated by problems in groundwater hydrology and geological storage of carbon dioxide (CO2). In these settings, fluid invades a porous medium saturated with an immiscible second fluid of different density and viscosity. The action of capillary forces in the porous medium results in spatial variations of the saturation of the two fluids. Here, we consider the propagation of fluid in a semi-infinite porous medium across a horizontal, impermeable boundary. In such systems, once the aspect ratio is large, fluid flow is mainly horizontal and the local saturation is determined by the vertical balance between capillary and gravitational forces. Gradients in the hydrostatic pressure along the current drive fluid flow in proportion to the saturation-dependent relative permeabilities, thus determining the shape and dynamics of two-phase currents. The resulting two-phase gravity current model is attractive because the formalism captures the essential macroscopic physics of multiphase flow in porous media. Residual trapping of CO2 by capillary forces is one of the key mechanisms that can permanently immobilize CO2 in the societally important example of geological CO2 sequestration. The magnitude of residual trapping is set by the areal extent and saturation distribution within the current, both of which are predicted by the two-phase gravity current model. Hence the magnitude of residual trapping during the post-injection buoyant rise of CO2 can be estimated quantitatively. We show that residual trapping increases in the presence of a capillary fringe, despite the decrease in average saturation.

Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



Bear, J. & Ryzhik, V. 1998 On the displacement of NAPL lenses and plumes in a phreatic aquifer. Trans. Porous Med. 33, 227255.CrossRefGoogle Scholar
Bear, J., Ryzhik, V., Braester, C. & Entov, V. 1996 On the movement of an LNAPL lens on the water table. Trans. Porous Med. 25, 283311.CrossRefGoogle Scholar
Bennion, B. 2006 The impact of interfacial tension and pore-size distribution/capillary pressure character on CO2 relative permeability at reservoir conditions in CO2–brine systems. In SPE/DOE Symposium on Improved Oil Recovery, Tulsa, Oklahoma, U.S.A., April 22–26. (SPE 99325).CrossRefGoogle Scholar
Bennion, B. & Bachu, S. 2005 Relative permeability characteristics for supercritical CO2 displacing water in a variety of potential sequestration zones in the western Canada sedimentary basin. In SPE Annual Technical Conference and Exhibition, Dallas, Texas, October 9–12. SPE 95547.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, 164176.CrossRefGoogle Scholar
Brooks, R. H. & Corey, A. T. 1964 Hydraulic properties of porous media. Hydrology Papers 3. Colorado State University.Google Scholar
Bryant, S. L., Lakshminarasimhan, S. & Pope, G. A. 2008 Buoyancy-dominated multiphase flow and its effect on geological sequestration of CO2. Soc. Petrol. Engng J. 13 (4), 447454.Google Scholar
Corey, A. T. 1954 The interrelation between gas and oil relative permeabilities. Prod. Monthly 19 (1), 3841.Google Scholar
Ennis-King, J. & Paterson, L. 2005 Role of convective mixing in the long-term storage of carbon dioxide in deep saline formations. Soc. Petrol. Engng J. 10 (3), 349356.Google Scholar
Farcas, A. & Woods, A. W. 2009 The effect of drainage on the capillary retention of CO2 in a layered permeable rock. J. Fluid Mech. 618, 349359.CrossRefGoogle Scholar
Fetter, C. W. 2001 Applied Hydrogeology. Prentice-Hall.Google Scholar
Gasda, S. E., Bachu, S. & Celia, M. A. 2004 Spatial characterization of the location of potentially leaky wells penetrating a deep saline aquifer in a mature sedimentary basin. Environ. Geol. 46, 707720.CrossRefGoogle Scholar
Gasda, S. E., Nordbotten, J. M. & Celia, M. A. 2009 Vertical equilibrium with sub-scale analytical methods for geological CO2 sequestration. Comput. Geosci. 13, 469481.CrossRefGoogle Scholar
van Genuchten, M. Th. 1980 A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892898.CrossRefGoogle Scholar
Golding, M. J. & Huppert, H. E. 2010 The effect of confining impermeable boundaries on gravity currents in a porous medium. J. Fluid Mech. 649, 117.CrossRefGoogle Scholar
Green, C. P. & Ennis-King, J. 2010 Effect of vertical heterogeneity on long-term migration of CO2 in saline formations. Trans. Porous Med. 82, 3147.CrossRefGoogle Scholar
Hesse, M. A., Orr, F. M. Jr & Tchelepi, H. A. 2008 Gravity currents with residual trapping. J. Fluid Mech. 611, 3560.CrossRefGoogle Scholar
Hesse, M. A., Tchelepi, H. A., Cantwell, B. J. & Orr, F. M. Jr 2007 Gravity currents in horizontal porous layers: transition from early to late self-similarity. J. Fluid Mech. 577, 363383.CrossRefGoogle Scholar
Hesse, M. A. & Woods, A. W. 2010 Buoyant dispersal of CO2 during geological storage. Geophys. Res. Lett. 37, L01403.CrossRefGoogle Scholar
Huppert, H. E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 4358.CrossRefGoogle Scholar
Huppert, H. E. & Woods, A. W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292, 5569.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, 481491.Google Scholar
Johnson, J. W., Nitao, J. J & Knauss, K. G. 2004 Reactive transport modelling of CO2 storage in saline aquifers to elucidate fundamental processes, trapping mechanisms and sequestration partitioning. In Geological Storage of Carbon Dioxide (ed. Baines, S. J. & Worden, R. H.). The Geological Society of London.Google Scholar
Juanes, R., MacMinn, C. W. & Szulczewski, M. L. 2010 The footprint of the CO2 plume during carbon dioxide storage in saline aquifers: storage efficiency for capillary trapping at the basin scale. Trans. Porous Med. 82, 1930.CrossRefGoogle 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.CrossRefGoogle Scholar
Kochina, I. N., Mikhailov, N. N. & Filinov, M. V. 1983 Groundwater mound damping. Intl J. Engng Sci. 21 (4), 413421.CrossRefGoogle 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. Engng J. 10 (3), 336348.Google Scholar
Lake, L. W. 1996 Enhanced Oil Recovery. Prentice-Hall.Google Scholar
Land, C. S. 1968 Calculation of imbibition relative permeability for two- and three-phase flow from rock properties. Soc. Petrol. Engng J. 8 (2), 149156.CrossRefGoogle Scholar
Lenormand, R., Zarcone, C. & Sarr, A. 1983 Mechanisms of the displacement of one fluid by another in a network of capillary ducts. J. Fluid Mech. 135, 337353.CrossRefGoogle Scholar
Leverett, M. C. 1939 Flow of oil–water mixtures through unconsolidated sands. Trans. AIME 132, 149171.CrossRefGoogle Scholar
Leverett, M. C. 1941 Capillary behavior in porous solids. Trans. AIME 142, 152169.CrossRefGoogle Scholar
Li, K. & Horne, R. N. 2006 Comparison of methods to calculate relative permeability from capillary pressure in consolidated water-wet porous media. Water Resour. Res. 42, W06405.CrossRefGoogle Scholar
MacMinn, C. W. & Juanes, R. 2009 Post-injection spreading and trapping of CO2 in saline aquifers: impact of the plume shape at the end of injection. Comput. Geosci. 13, 483491.CrossRefGoogle Scholar
Metz, B., Davidson, O., de Coninck, H., Loos, M. & Meyer, L., (Ed.) 2005 IPCC Special Report on Carbon Dioxide Capture and Storage. Cambridge University Press, prepared by Working Group III of the Intergovernmental Panel on Climate Change.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, June 13–16. SPE 93952.Google Scholar
Neufeld, J. A. & Huppert, H. E. 2009 Modelling carbon dioxide sequestration in layered strata. J. Fluid Mech. 625, 353370.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Nordbotten, J. M. & Celia, M. A. 2006 Similarity solutions for fluid injection into confined aquifers. J. Fluid Mech. 561, 307327.CrossRefGoogle Scholar
Nordbotten, J. M., Celia, M. A., Bachu, S. & Dahle, H. K 2005 Semianalytical solution for CO2 leakage through an abandoned well. Environ. Sci. Technol. 39 (2), 602611.CrossRefGoogle ScholarPubMed
Parker, J. C. & Lenhard, R. J. 1989 Vertical integration of three-phase flow equations for analysis of light hydrocarbon plume movement. Trans. Porous Med. 5, 187206.CrossRefGoogle Scholar
Pentland, C. H., Al-Mansoori, S., Iglauer, S., Bijeljic, B. & Blunt, M. J. 2008 Measurement of non-wetting phase trapping in sand packs. In SPE Annual Technical Conf. and Exhibition, Denver, CO. SPE 115697.Google Scholar
Pinder, G. F. & Gray, W. G. 2008 Essentials of Multiphase Flow and Transport in Porous Media. Wiley.CrossRefGoogle Scholar
Riaz, A. & Tchelepi, H. A. 2006 Numerical simulation of immiscible two-phase flow in porous media. Phys. Fluids 18, 014104.CrossRefGoogle Scholar
Saadatpoor, E., Bryant, S. L. & Sepehrnoori, K. 2010 New trapping mechanisms in carbon sequestration. Trans. Porous Med. 82, 317.CrossRefGoogle Scholar
Vella, D. & Huppert, H. E. 2006 Gravity currents in a porous medium at an inclined plane. J. Fluid Mech. 555, 353362.CrossRefGoogle Scholar
Woods, A. W. & Farcas, A. 2009 Capillary entry pressure and the leakage of gravity currents through a sloping layered permeable rock. J. Fluid Mech. 618, 361379.CrossRefGoogle Scholar
Yortsos, Y. C. 1995 A theoretical analysis of vertical flow equilibrium. Trans. Porous Med. 18 (2), 107129.CrossRefGoogle Scholar