Effective flux boundary conditions for upscaling porous media equations

T. C. Wallstrom, M. A. Christie, L. J. Durlofsky, D. H. Sharp

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    35 Citations (Scopus)

    Abstract

    We introduce a new algorithm for setting pressure boundary conditions in subgrid simulations of porous media flow. The algorithm approximates the flux in the boundary cell as the flux through a homogeneous inclusion in a homogeneous background, where the permeability of the inclusion is given by the cell permeability and the permeability of the background is given by the ambient effective permeability. With this approximation, the flux in the boundary cell scales with the cell permeability when that permeability is small, and saturates at a constant value when that permeability is large. The flux conditions provide Neumann boundary conditions for the subgrid pressure. We call these boundary conditions effective flux boundary conditions (EFBCs). We give solutions for the flux through ellipsoidal inclusions in two and three dimensions, assuming symmetric tensor permeabilities whose principal axes align with the axes of the ellipse. We then discuss the considerations involved in applying these equations to scale up problems in geological porous media. The key complications are heterogeneity, fluctuations at all length scales, and boundary conditions at finite scales.

    Original languageEnglish
    Pages (from-to)139-153
    Number of pages15
    JournalTransport in Porous Media
    Volume46
    Issue number2-3
    DOIs
    Publication statusPublished - Feb 2002

    Keywords

    • Effective flux boundary conditions
    • Scale up

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  • Cite this

    Wallstrom, T. C., Christie, M. A., Durlofsky, L. J., & Sharp, D. H. (2002). Effective flux boundary conditions for upscaling porous media equations. Transport in Porous Media, 46(2-3), 139-153. https://doi.org/10.1023/A:1015075210265