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Real-Space Renormalization Estimates for Two-Phase Flow in Porous Media

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Abstract

We present a spatial renormalization group algorithm to handle immiscibletwo-phase flow in heterogeneous porous media. We call this algorithmFRACTAM-R, where FRACTAM is an acronym for Fast Renormalization Algorithmfor Correlated Transport in Anisotropic Media, and the R stands for relativepermeability. Originally, FRACTAM was an approximate iterative process thatreplaces the L × L lattice of grid blocks, representing the reservoir,by a (L/2) × (L/2) one. In fact, FRACTAM replaces the original L× L lattice by a hierarchical (fractal) lattice, in such a way thatfinding the solution of the two-phase flow equations becomes trivial. Thistriviality translates in practice into computer efficiency. For N=L ×L grid blocks we find that the computer time necessary to calculatefractional flow F(t) and pressure P(t) as a function of time scales as τ∼ N1.7 for FRACTAM-R. This should be contrasted with thecomputational time of a conventional grid simulator τ ∼N2.3. The solution we find in this way is an accurateapproximation to the direct solution of the original problem.

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Authors and Affiliations

  1. Fraction a.s., Tåsenveien 74 C, 0873, Oslo, Norway

    Alex Hansen, Stéphane Roux Roux, Amnon Aharony, Jens Feder & Torstein Jøssang

  2. Institutt for Fysikk, Norges Teknisk Naturvitenskapelige Universitetet, 7034, Trondheim, Norway

    Alex Hansen

  3. Laboratoire de physique et Mécanique de la Matière Hétérogéne Ecole Supérieure de physique et Chimie Industrielle de Paris URA CNRS 857, 10 rue Vauquelin, F-75231, Paris Cédex 05, France

    Stéphane Roux Roux

  4. Department of Physics, University of Oslo, Box 1048, Blindern, 0316, Oslo, Norway

    Amnon Aharony, Jens Feder & Torstein Jøssang

  5. Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel-Aviv University, Tel-aviv, 69978, Israel

    Amnon Aharony

  6. Conoco Inc., Geoscience and Reservoir Research, Ponca City, Oklahoma, 74603, U.S.A

    H. H. Hardy

Authors
  1. Alex Hansen
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  2. Stéphane Roux Roux
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  3. Amnon Aharony
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  4. Jens Feder
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  5. Torstein Jøssang
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  6. H. H. Hardy
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Hansen, A., Roux, S.R., Aharony, A. et al. Real-Space Renormalization Estimates for Two-Phase Flow in Porous Media. Transport in Porous Media 29, 247–279 (1997). https://doi.org/10.1023/A:1006593820928

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