Statistical physics and immiscible displacements through porous media

This talk briefly reviews the subject of fluid flow through disordered media. First, we use two-dimensional percolation networks as a simple model for porous media to investigate the dynamics of viscous penetration when the ratio between the viscosities of displaced and injected fluids is very large. The results indicate the possibility that viscous displacement through critical percolation networks constitutes a single universality class, independent of the viscosity ratio. We also focus on the sorts of considerations that may be necessary to move statistical physics from the description of idealized flows in the limit of zero Reynolds number to more realistic flows of real fluids moving at a nonzero velocity, when inertia effects may become relevant. We discuss several intriguing features, such as the surprisingly change in behavior from a "localized" to a "delocalized" flow structure (distribution of flow velocities) that seems to occur at a critical value of Re which is significantly smaller than the critical value of Re where turbulence sets in.

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Immiscible displacements of two-phase non-Newtonian fluids in porous media

Physics Letters A ◽

10.1016/s0375-9601(99)00561-7 ◽

1999 ◽

Vol 261 (3-4) ◽

pp. 174-178 ◽

Cited By ~ 7

Author(s):

Ju-Ping Tian ◽

Kai-Lun Yao

Keyword(s):

Porous Media ◽

Newtonian Fluids ◽

Two Phase ◽

Immiscible Displacements

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Numerical models and experiments on immiscible displacements in porous media

Journal of Fluid Mechanics ◽

10.1017/s0022112088000953 ◽

1988 ◽

Vol 189 ◽

pp. 165-187 ◽

Cited By ~ 845

Author(s):

Roland Lenormand ◽

Eric Touboul ◽

Cesar Zarcone

Keyword(s):

Phase Diagram ◽

Porous Media ◽

Numerical Models ◽

Viscous Fingering ◽

Capillary Forces ◽

Viscous Effects ◽

Dimensionless Numbers ◽

Diffusion Limited Aggregation ◽

Viscous Forces ◽

Immiscible Displacements

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.

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