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Numerical models and experiments on immiscible displacements in porous media

Published online by Cambridge University Press:  21 April 2006

Roland Lenormand ,
Eric Touboul  and
Cesar Zarcone
Roland Lenormand
Affiliation:
Dowell Schlumberger, B.P. 90, 42003 Saint Etienne Cedex 1, France
Eric Touboul
Affiliation:
Dowell Schlumberger, B.P. 90, 42003 Saint Etienne Cedex 1, France
Cesar Zarcone
Affiliation:
Institut de Mécanique des Fluides, 2 rue C. Camichel, 31071 Toulouse Cedex, France.
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Abstract

Immiscible displacements in porous media with both capillary and viscous effects can be characterized by two dimensionless numbers, the capillary number C, which is the ratio of viscous forces to capillary forces, and the ratio M of the two viscosities. For certain values of these numbers, either viscous or capillary forces dominate and displacement takes one of the basic forms: (a) viscous fingering, (b) capillary fingering or (c) stable displacement. We present a study in the simple case of injection of a non-wetting fluid into a two-dimensional porous medium made of interconnected capillaries. The first part of this paper presents the results of network simulators (100 × 100 and 25 × 25 pores) based on the physical rules of the displacement at the pore scale. The second part describes a series of experiments performed in transparent etched networks. Both the computer simulations and the experiments cover a range of several decades in C and M. They clearly show the existence of the three basic domains (capillary fingering, viscous fingering and stable displacement) within which the patterns remain unchanged. The domains of validity of the three different basic mechanisms are mapped onto the plane with axes C and M, and this mapping represents the ‘phase-diagram’ for drainage. In the final section we present three statistical models (percolation, diffusion-limited aggregation (DLA) and anti-DLA) which can be used for describing the three ‘basic’ domains of the phase-diagram.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 189 , April 1988 , pp. 165 - 187
Copyright
© 1988 Cambridge University Press

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References

Bachmat, Y. & Bear, J. 1986 Macroscopic modeling of transport phenomena in porous media. 1: The continuum approach. Transp. Por. Med. 1, 213–240.Google Scholar
Chan, D. Y. C., Hughes, B. D. & Paterson, L. 1986 Fluctuations, viscous fingering, and diffusion-limited aggregation. Phys. Rev. A 34, 4079–4082.Google Scholar
Chen, J. D. & Wilkinson, D. 1985 Pore-scale viscous fingering in porous media. Phys. Rev. Lett. 55, 1892–1895.Google Scholar
Dias, M. M. & Payatakes, A. C. 1986a Network models for two-phase flow in porous media. Part 1. Immiscible microdisplacement of non-wetting fluids. J. Fluid Mech. 164, 305–336.Google Scholar
Dias, M. M. & Payatakes, A. C. 1986b Network models for two-phase flow in porous media. Part 2. Motion of oil ganglia. J. Fluid Mech. 164, 337–358.Google Scholar
Houi, D. & Lenormand, R. 1984 Particle deposition on a filter medium. In Kinetics of Aggregation and Gelation (ed. F. Family & D. P. Landau), pp. 173–176. Elsevier.
Kadanoff, L. P. 1985 Simulating hydrodynamics: a pedestrian model. J. Stat. Phys. 39, 267–283.Google Scholar
Koplik, J. & Lasseter, T. J. 1985 One and two-phase flow in network models of porous media. Chem. Engng Commun. 26, 285–295.Google Scholar
Lenormand, R. 1985 Différents mécanismes de déplacements visqueux et capillaires en milieu poreux: Diagramme de phase. C.R. Acad. Sci. Paris II 301, 247–250.Google Scholar
Lenormand, R. 1986 Scaling laws for immiscible displacements with capillary and viscous fingering. SPE 15390 61th Annual Tech. Conf. and Exhib. of SPE, New Orleans, La, Oct. 5–8.
Lenormand, R. & Bories, S. 1980 Description d'un mécanisme de connexion de liaisons destiné à l'étude du drainage avec piégeage en milieu poreux. C.R. Acad. Sci. Paris 291 B, 279–280.Google Scholar
Lenormand, R. & Zarcone, C. 1984a Role of roughness and edges during imbibition in square capillaries. SPE 13264, 59th Annual Tech. Conf. and Exhib. of SPE, Houston, Texas, Sept. 16–19.
Lenormand, R. & Zarcone, C. 1984b Two-phase flow experiments in a two-dimensional permeable medium. Proc. Physiochemical Hydrodynamics 5th International Conference, Tel-Aviv; Phys. Chem. Hydrodyn. 6, 497–506, 1985.Google 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, 337–353.Google Scholar
Måløy, K. J., Feder, J. & Jøssang, T. 1985 Viscous fingering fractals in porous media. Phys. Rev. Lett. 55, 1885–1891.Google Scholar
Meakin, P. & Deutch, J. M. 1986 The formation of surfaces by diffusion limited annihilation. J. Chem. Phys. 85, 2320–2325.Google Scholar
Niemeyer, L., Pietronero, L. & Wiesmann, H. J. 1984 Fractal dimension of dielectric breakdown. Phys. Rev. Lett. 52, 1033–1036.Google Scholar
Nittmann, J. & Stanley, H. E. 1986 Tip splitting without interfacial tension and dendritic growth patterns arising from molecular anisotropy. Nature 321, 663–668.Google Scholar
Paterson, L. 1984 Diffusion-limited aggregation and two-fluid displacements in porous media. Phys. Rev. Lett. 52, 1621–1624.Google Scholar
Sherwood, J. D. 1987 Unstable fronts in a porous medium. J. Comp. Phys. 68, 485–500.Google Scholar
Wilkinson, D. 1985 Multiphase flow in porous media. In Physics of Finely Divided Matter (ed. N. Boccara & M. Daoud), pp. 280–288. Springer.
Witten, T. A. & Sander, L. M. 1983 Diffusion limited aggregation. Phys. Rev. B27, 5686–5697.Google Scholar