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Multiresolution Wavelet Scale Up of Unstable Miscible Displacements in Flow Through Heterogeneous Porous Media

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Abstract

We describe scale up of geological models of field-scale porous media using a new method based on the wavelet transformations. The porous media of interest contain broadly-distributed and correlated permeabilities. Wavelet transformation of the permeability field of such porous media coarsens the geological model from smallest to largest length scales, drastically reduces the number of equations to be solved, preserves the important information on the permeability field at all the relevant length scales, and yields numerical results for any fluid flow property that are as accurate as those that are obtained with the highly detailed geological model of the same porous media. To test this method, we carry out extensive computer simulations of unstable miscible displacement processes and the associated viscous fingering phenomenon in highly heterogeneous porous media, both with the fine-scale geological model and the coarsened model. Excellent agreement is found between the results of the two sets of simulations.

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Authors and Affiliations

  1. Department of Physics, Ferdowsi University of Mashhad, Mashhad, Iran

    Fatemeh Ebrahimi

  2. Faculty of Sciences, University of Birjand, Birjand, Iran

    Fatemeh Ebrahimi

  3. Department of Chemical Engineering, University of Southern California, Los Angeles, CA, 90089-1211, USA

    Fatemeh Ebrahimi & Muhammad Sahimi

Authors
  1. Fatemeh Ebrahimi
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  2. Muhammad Sahimi
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Ebrahimi, F., Sahimi, M. Multiresolution Wavelet Scale Up of Unstable Miscible Displacements in Flow Through Heterogeneous Porous Media. Transport in Porous Media 57, 75–102 (2004). https://doi.org/10.1023/B:TIPM.0000032742.05517.06

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  • DOI: https://doi.org/10.1023/B:TIPM.0000032742.05517.06

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