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Numerical methods for flow in a porous medium with internal boundaries

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Abstract

Flow of fluids and transport of solutes in porous media are subjects of wide interest in several fields of applications: reservoir engineering, subsurface hydrology, chemical engineering, etc. In this paper we will study two-phase flow in a model consisting of two different types of sediments. Here, the absolute permeability, the relative permeabilities and the capillary pressure are discontinuous functions in space. This leads to interior boundary value problems at the interface between the sediments. The saturation Sw will be discontinuous or experience large gradients at the interface. A new solution procedure for such problems will be presented. The method combines the modified method of characteristics with a weak formulation where the basis functions are discontinuous at the interior boundary. The modified method of characteristics will provide a good first approximation for the jump in the discontinuous basis functions, which leads to a fast converging iterative solution scheme for the complete problem.

The method has been implemented in a two-dimensional simulator, and results from numerical experiments will be presented.

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Authors and Affiliations

  1. Statoil, N-5020, Bergen, Norway

    Brit Gunn Ersland

  2. Department of Mathematics, University of Bergen, N-5008, Bergen, Norway

    Magne S. Espedal

  3. Norsk Hydro, N-5020, Bergen, Norway

    Roger Nybø

Authors
  1. Brit Gunn Ersland
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  2. Magne S. Espedal
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  3. Roger Nybø
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Ersland, B.G., Espedal, M.S. & Nybø, R. Numerical methods for flow in a porous medium with internal boundaries. Computational Geosciences 2, 217–240 (1998). https://doi.org/10.1023/A:1011554320427

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