Advertisement

Capillary and Viscous Fingering in an Etched Network

  • Roland Lenormand
Part of the Springer Proceedings in Physics book series (SPPHY, volume 5)

Abstract

We present an original set-up for studying the different mechanisms associated with the displacement of immiscible fluids in porous media. A molding technique, using a transparent polyester resin and a photographically etched network has been developed to visualize the front during the displacement. At very low flow-rate we can observe the growth of very thin fingers, even when the displacing fluid is the more viscous. This capillary fingering is very well described by invasion percolation theory and the measured fractal dimension agrees with computer simulations. When the injected fluid is the less viscous fluid, the fingers become more and more dendritic as the flow rate increases; this mechanism seems to be related to a cross-over between invasion percolation and diffusion-limited aggregation (D.L.A.). When the injected fluid is the more viscous fluid, increasing the flow rate decreases the fingering. This mechanism can be described as a cross-over between invasion percolation and a flat interface.

Keywords

Porous Medium Fractal Dimension Capillary Number Viscosity Ratio Immiscible Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Lenormand and C. Zarcone, Two-phase flow experiments in a two-dimensional medium, in proceedings of the Vth Int. Meet. Phys. Chem. Hydro., Tel-Aviv, (Dec. 1984).Google Scholar
  2. 2.
    H. S. Hele Shaw, Investigation of the nature of surface resistance of water and of stream-line motion under certain experimental conditions, Trans. Instn. Nav. Archit., Lond, 40, 21, (1898).Google Scholar
  3. 3.
    P. G. Saffman and G. I. Taylor, The penetration of a fluid into a porous medium or Hele Shaw cell containing a more viscous liquid, Proc. R. Soc. Lond., A 245, 311–329, (1958).ADSMathSciNetGoogle Scholar
  4. 4.
    R. Lenormand and S. Bories, Description d’un mecanisme de connexion de liaison destine a l’etude du drainage avec piegeage en milieu poreux, C. R. Acad. Sci. Paris, 291 B, 279–280 (1980).Google Scholar
  5. 5.
    R. Chandler, J. Koplik, K. Lerman and J. F. Willemsen, Capillary displacement and percolation in porous media, J. Fluid Mech., 119, 249–267, (1982).CrossRefMATHADSGoogle Scholar
  6. 6.
    P. G. De Gennes and E. Guyon, Lois generales pour l’injection d’un fluide dans un milieu poreux aleatoire, J. Mecanique, 17, 403–442, (1977).Google Scholar
  7. 7.
    J. Bonnet and R. Lenormand, Realisation de micromodeles pour l’etude des ecoulements polyphasiques en milieu poreux, Rev. Inst. Franc. Petr., 42, 447–480, (1977).Google Scholar
  8. 8.
    R. Lenormand, Deplacements polyphasiques en milieu poreux sous l’influence des forces capillaires. Modelisation de type percolation, Thesis, University of Toulouse, (1981).Google Scholar
  9. 9.
    R. Lenormand and C. Zarcone, Role of roughness and edges during imbibition in square capillaries, S.P.E paper no 13264, (1984).Google Scholar
  10. 10.
    T. A. Witten and L. M. Sander, Diffusion-limited aggregation, Phys. Rev. B, 27, 9, 5686–5697, (1983).CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    P. Meakin, Diffusion-controlled cluster formation in 2–6 dimensional space, Phys. Rev. A, 27, 3, 1495–1507, (1983).CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    L. Paterson, Diffusion-limited aggregation and two-fluid displacements in porous media, Phys. Rev. let, 52, 18, 1621–1624, (1984).CrossRefADSGoogle Scholar
  13. 13.
    J. Nittmann, G. Daccord and H. E. Stanley, Fractal growth of viscous fingers: quantitative characterization of a fluid instability phenomenon, Nature, 314, 14, 141–144, (1985).CrossRefADSGoogle Scholar
  14. 14.
    R. Lenormand and C. Zarcone, Invasion Percolation in an etched network: measurement of a fractal dimension, to be published in Phys. Rev. Let., (1985).Google Scholar
  15. 15.
    D. Wilkinson and J. F. Willemsen, Invasion Percolation: a new form of percolation theory, J. Phys. A, 16, 3365–3376, (1983).ADSMathSciNetGoogle Scholar
  16. 16.
    R. Lenormand, C. Zarcone and A. Sarr, Mechanisms of the displacement of one fluid by another in a network of capillary ducts, J. Fluid Mech., 135, 337–353, (1983).CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Roland Lenormand
    • 1
  1. 1.Schlumberger-Doll ResearchRigdefieldUSA

Personalised recommendations