Voronoi Grids Conformal to 3D Structural Features

in: 13th European Conference on the Mathematics of Oil Recovery (ECMOR)

Abstract

When simulating flow in a reservoir, errors due to upscaling can have a significant impact on the quality of results. To reduce these errors, the cells of the simulation grid should be as homogeneous as possible, hence conform to horizons and faults. In this paper, we optimize the coordinates of the 3D Voronoi seeds so that cell facets honor the structural features. These features are modeled by piecewise linear complex (PLC). The optimization consists in minimizing a function made of two parts: • A barycentric function, called Centroidal Voronoi Tessellation (CVT) function, which ensures that the cells will be of good quality by maximizing their compactness. • A conformal function, which measures the proportion of cells that is on the "wrong side" of the structural features (if the cell is cut in two by a structural feature, the "good side" contains the Voronoi seed). The novelty in this paper concerns the method of cutting cells by structural features which are locally approximated inside the Voronoi cells. These methods used jointly with an adaptive gradient solver allow dealing with complex 3D geological cases, presented in the paper.

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    BibTeX Reference

    @INPROCEEDINGS{Merland2012ECMOR,
        author = { Merland, Romain and Levy, Bruno and Caumon, Guillaume },
         title = { Voronoi Grids Conformal to 3D Structural Features },
         month = { September },
     booktitle = { 13th European Conference on the Mathematics of Oil Recovery (ECMOR) },
          year = { 2012 },
       address = { Biarritz, France },
      abstract = { When simulating flow in a reservoir, errors due to upscaling can have a significant impact on the quality of results. To reduce these errors, the cells of the simulation grid should be as homogeneous as possible, hence conform to horizons and faults.
    In this paper, we optimize the coordinates of the 3D Voronoi seeds so that cell facets honor the structural features. These features are modeled by piecewise linear complex (PLC).
    The optimization consists in minimizing a function made of two parts:
    • A barycentric function, called Centroidal Voronoi Tessellation (CVT) function, which ensures that the cells will be of good quality by maximizing their compactness.
    • A conformal function, which measures the proportion of cells that is on the "wrong side" of the structural features (if the cell is cut in two by a structural feature, the "good side" contains the Voronoi seed).
    The novelty in this paper concerns the method of cutting cells by structural features which are locally approximated inside the Voronoi cells.
    These methods used jointly with an adaptive gradient solver allow dealing with complex 3D geological cases, presented in the paper. }
    }