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Effective two-phase flow through highly heterogeneous porous media: Capillary nonequilibrium effects

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Abstract

We consider the two-phase flow through a dual-porosity medium, characterized by a period of heterogeneity ω, a ratio of global permeabilities ∈K, and a ratio of the order of capillary forces ∈c. The limit when ω tends to zero at different values of ∈K and ∈c gives four classes of global behavior, differing by the type of elementary flows at the one-cell level. We propose a diagram of their predominance. A macro-scale model is constructed by formal homogenization techniques for one of these classes; it shows a nonlinear kinetic relationship for the averaged capillary pressure functions, and leads to a decomposition for the effective phase permeability tensors. A capillary relaxation time is explicitly determined.

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Authors and Affiliations

  1. Equipe d’Analyse Numérique, UMR 5585, Université de Saint-Etienne, 23 rue P. Michelon, F-42023, St-Etienne Cedex 02, France

    Alain Bourgeat

  2. Russian Academy of Sciences, Oil and Gas Research Institute, 63, Leninsky prospekt, Moscow, 117917, Russia

    Mikhail Panfilov

Authors
  1. Alain Bourgeat
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  2. Mikhail Panfilov
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Bourgeat, A., Panfilov, M. Effective two-phase flow through highly heterogeneous porous media: Capillary nonequilibrium effects. Computational Geosciences 2, 191–215 (1998). https://doi.org/10.1023/A:1011502303588

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