Upscalling Relative Permeability with gOcad using a strealine-based Approach

Jean-Jacques Royer and Jean-Charles Voillemont and D. Thenin. ( 2002 )
in: 22nd Gocad Meeting, Nancy

Abstract

Upscaling aims at determining equivalent homogeneous parameters at a coarse-scale from a spatially heterogeneous fine-scale parameter distribution. This homogenization technique is extensively used in reservoir oil simulators for manipulating a limited number of relatively large grid-blocks on which properties have been obtained from previous geological or geostatistical studies using well logging and/or seismic data. This paper proposes to compute the upscaled two-phase relative permeability at a coarse grid from a spatially fine-scale grid (SGrid) using numerical approximation methods. The propose method consists in solving the saturation equation using a stream-line approach in order to decouple the resolution of the continuity equation (Darcy’s law) and the saturation equation. The streamline approach offers substantial computational efficiency and numerical accuracy compared to traditional finite-element methods because it transforms a 3D transport problem into several 1D problems. This method uses a standard homogenization technique to estimate the total mobility by solving the continuity equation (Darcy’s law) by a finite-element method (Thermass plug-in). Then, at each step-time, the two-phase saturation equation (black oil model) is solved along the 1D stream-lines. The mobility is then mapped onto the fine-scale grid and the new streamline field is again estimated till the block is saturated in water. The up-scaled absolute permeability is then derived together with the relative permeability versus saturation curve. This approach has been applied to mono-phase case-studies for validating the methodology. For the two-phase case, it was validated on simple cases for which solutions are known.

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    BibTeX Reference

    @INPROCEEDINGS{,
        author = { Royer, Jean-Jacques and Voillemont, Jean-Charles and Thenin, D. },
         title = { Upscalling Relative Permeability with gOcad using a strealine-based Approach },
         month = { "jun" },
     booktitle = { 22nd Gocad Meeting },
       chapter = { 0 },
          year = { 2002 },
      location = { Nancy },
      abstract = { Upscaling aims at determining equivalent homogeneous parameters at a coarse-scale from a spatially heterogeneous
    fine-scale parameter distribution. This homogenization technique is extensively used in reservoir
    oil simulators for manipulating a limited number of relatively large grid-blocks on which properties
    have been obtained from previous geological or geostatistical studies using well logging and/or seismic
    data. This paper proposes to compute the upscaled two-phase relative permeability at a coarse grid from
    a spatially fine-scale grid (SGrid) using numerical approximation methods. The propose method consists
    in solving the saturation equation using a stream-line approach in order to decouple the resolution of the
    continuity equation (Darcy’s law) and the saturation equation. The streamline approach offers substantial
    computational efficiency and numerical accuracy compared to traditional finite-element methods because
    it transforms a 3D transport problem into several 1D problems.
    This method uses a standard homogenization technique to estimate the total mobility by solving
    the continuity equation (Darcy’s law) by a finite-element method (Thermass plug-in). Then, at each
    step-time, the two-phase saturation equation (black oil model) is solved along the 1D stream-lines. The
    mobility is then mapped onto the fine-scale grid and the new streamline field is again estimated till the
    block is saturated in water. The up-scaled absolute permeability is then derived together with the relative
    permeability versus saturation curve.
    This approach has been applied to mono-phase case-studies for validating the methodology. For the
    two-phase case, it was validated on simple cases for which solutions are known. }
    }