Abstract

In a stratified porous medium, foam can divert the flow from high permeability to low permeability layers. This interesting behavior found several practical applications in some reservoirs and aquifers. Moreover, experimental results have shown that foam blocking effect is maximum when the layers are isolated, i. e., when there is no capillary crossflow. Foam blocking in high permeability layers can be explained through the concept of limiting capillary pressure, P*c, which is the maximum value of capillary pressure above which liquid films separating bubbles are broken.

In this study, we present a numerical simulation of foam displacement in a stratified system made of two non-communicating layers with a permeability ratio of 5.4.

Numerical simulations are performed using a bubble-population correlation that allows us to compute explicitly foam texture in each layer from the physical properties of the rock (porosity, permeability and capillary pressure). We observe clearly the blocking effect of foam in high permeability layer, diverting gas to low permeability layer, due to capillary pressure difference.

Numerical results are qualitatively in good accordance with experimental data published in the literature.

Introduction

Gas injection in porous media is used in petroleum engineering and will be used more extensively in the future because gas flaring is more and more controlled and gas injection is a good alternative.

Gas injected together with surfactant solution generates foam in the porous medium. Consequently, gas mobility is drastically reduced compared to what is observed when gas is injected alone.

Practical applications of foam in porous media are in EOR processes (steam foam process), profile control (foam as blocking agent), well stimulation (acidizing), environment (clean up of polluted soils).

Foam in porous media

Foam is a dispersion of gas in a continuous liquid phase. The thin films, called lamellae, that separate gas bubbles, are stabilized by the presence of surfactant molecules.

There are several papers (see for example the book edited by Schramm, 1994) describing generation, coalescence, rheology and propagation of foam in porous media. Here below we describe briefly these points.

Foam generation.

Three mechanisms are listed in the literature.

  1. Capillary snap-off

  2. Lamellae division

  3. Leave behind

These three mechanisms occur at the pore scale. Consequently gas bubbles generated in a porous medium will have the same size than the pores where they are generated.

Foam destruction.

Foam is destructed when gas diffuses through the lamellae and when lamellae are broken due to capillary forces.

This last effect can be explained through the DLVO theory that expresses the forces acting in a thin film.

In a lamella, which is assimilated to a thin film, capillary pressure is expressed by the augmented Young-Laplace equation,

Pc=2sC+?(h)(1)

Where Pc is the capillary pressure, s the interfacial tension, C the interface curvature and ?(h) is the disjoining pressure that is a function of the film thickness h.

Foam generation.

Three mechanisms are listed in the literature.

  1. Capillary snap-off

  2. Lamellae division

  3. Leave behind

These three mechanisms occur at the pore scale. Consequently gas bubbles generated in a porous medium will have the same size than the pores where they are generated.

Foam destruction.

Foam is destructed when gas diffuses through the lamellae and when lamellae are broken due to capillary forces.

This last effect can be explained through the DLVO theory that expresses the forces acting in a thin film.

In a lamella, which is assimilated to a thin film, capillary pressure is expressed by the augmented Young-Laplace equation,

Pc=2sC+?(h)(1)

Where Pc is the capillary pressure, s the interfacial tension, C the interface curvature and ?(h) is the disjoining pressure that is a function of the film thickness h.

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