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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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