Skip to main content
SpringerLink
Log in

Foam Drainage in Porous Media

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

In this paper we present a simple analysis of liquid drainage in foams confined in porous media. First we derive the equation for the evolution of the liquid saturation using general mass and momentum conservation arguments and phenomenological relations between the transport parameters and liquid saturation. We find an unusual ‘foam drainage equation’ in which the determinant terms express the competition between the external force field, represented here by the gravity field, and capillary pressure gradient. We present analytical solutions of the drainage equation in three cases: (a) gravity forces are dominant over capillary forces, (b) capillary forces are dominant over gravity forces, and (c) capillary and gravity forces are comparable in order of magnitude.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abramowitz, M. and Stegun, I. A.: 1970, Handbook of Mathematical Functions, Dover, New York.

    Google Scholar 

  • Bear, J.: 1972, Dynamics of Fluids in Porous Media, Dover, New York.

    Google Scholar 

  • Bernard, G. G. and Holm, L. W.: 1965, Effect of foam on permeability of porous media to gas, Soc. Petrol. Eng. J., December, 295–300.

  • Bernard, G. G., Holm, L. W. and Jacobs, W. L.: 1965, Effect of foam on trapped gas saturation and on permeability of porous media to water, Soc. Petrol. Eng. J. 5(4), 295–300.

    Google Scholar 

  • Carslaw, H. S. and Jaeger, J. C.: 1959, Conduction of Heat in Solids, Oxford.

  • Debnath, L.: 1997, Non-linear Partial Differential Equations, Birkhauser, Boston.

    Google Scholar 

  • de Gennes, P.-G.: 1992, Conjectures on foam mobilization, FrReview de l'Institut Français du Pétrole 47, 249–254.

    Google Scholar 

  • Goldfarb, I. I., Kann, K. B. and Shreiber, I. R.: 1998, Liquid flow in foams, Fluid Dyn. (Official English Translation of Transactions of USSR Academy of Sciences, Ser. Mech. Liquids Gas) 23, 244–249.

    Google Scholar 

  • Goldshtein, V., Goldfarb, I. and Shreiber, I.: 1996, Drainage waves structure in gas–liquid foam, Int. J. Multiphase Flow 22(5), 991–1003.

    Google Scholar 

  • Hanssen, J. E. and Dalland, M.: 1994, Gas blocking foams, in: L. L. Schramm (ed.), Foams: Fundamentals and Applications in the Petroleum Industry, ACS.

  • Henssen, J. E.: 1993, Foam as a gas-blocking agent in reservoirs. II. Mechanisms of gas blockage by foam, J. Petrol. Sci. Eng. 10, 135–156.

    Google Scholar 

  • Holm, L. W.: 1968, The mechanism of gas and liquid flow through porous media in the presence of foam, Soc. Petrol. Eng. J., December, 359–369.

  • Koehler, S. A., Hilgenfeldt, S. and Stone, H.: 1999, Liquid flow through aqueous foams: the nodedominated foam drainage equation, Phys. Rev. Lett. 82(21), 4232–4235.

    Google Scholar 

  • Koehler, S. A., Stone, H. A., Brenner, M. P. and Eggers, J.: 1998, Dynamics of foam drainage, Phys. Rev. E 50(2), 2097–2106.

    Google Scholar 

  • Kornev, K. G., Neimark, A. V. and Rozhkov, A. N.: 1999, Foam in porous media: thermodynamic and hydrodynamic peculiarities, Adv. Coll. Interf. Sci. 82, 127–187.

    Google Scholar 

  • Kovscek, A. R. and Radke C. J.: 1994, Fundamentals of foam transport in porous media, in: Foams: Fundamentals and Applications in the Petroleum Industry, ACS Advances in Chemistry Series, No. 242, American Chemical Society, Washington, DC.

    Google Scholar 

  • Owete, O. S. and Brigham, W. E.: 1987, Flow behaviour of foam: a porous micromodel study, SPE Reservoir Eng., August, 315–323.

  • Patzek, T. W.: 1988, In: Surfactant Based Mobility Control Progress in Miscible-Flood Enhanced Oil Recovery, ACS Symposium Series 373, Chemical Society, Washington, DC.

    Google Scholar 

  • Rossen, W. R.: 1996, Foams in enhanced oil recovery, In: R. K. Prud'homme and S. Khan (eds), Chapter 12 in Foams: Theory, Measurements and Applications, Marcel Dekker, New York.

    Google Scholar 

  • Verbist, G., Weaire, D. and Kraynik, A. M.: 1996, The foam drainage equation, J. Phys.: Condensed Matter 8, 3715–3731.

    Google Scholar 

  • Weaire, D., Hutzler, S., Verbist, G. and Peters, E.: 1997, A review of foam drainage, in: I. Prigogine and S. A. Rice (eds), Advances in Chemical Physics, Wiley, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Earth Sciences, Delft University of Technology, Mijnbouwstraat 120, 2628 RX, Delft, The Netherlands

    Pacelli L. J. Zitha

Authors
  1. Pacelli L. J. Zitha
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zitha, P.L.J. Foam Drainage in Porous Media. Transport in Porous Media 52, 1–16 (2003). https://doi.org/10.1023/A:1022366809721

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022366809721

Search

Navigation