Voronoi Grids Conforming to 3D Structural Features

in: Computational Geosciences, 18:3-4 (373-383)

Abstract

Flow simulation in a reservoir can be highly impacted by upscaling errors. These errors can be reduced by using simulation grids with cells as homogeneous as possible, hence conformable to horizons and faults. In this paper, the coordinates of 3D Voronoi seeds are optimized so that Voronoi cell facets honor the structural features. These features are modeled by piecewise linear complex (PLC). The optimization minimizes a function made of two parts: (1) a barycentric function, which ensures that the cells will be of good quality by maximizing their compactness; and (2) a conformity function, which allows to minimize the volume of cells that is isolated from the Voronoi seed w.r.t., a structural feature. To determine the isolated volume, a local approximation of the structural feature inside the Voronoi cells is used to cut the cells. It improves the algorithm efficiency and robustness compared to an exact cutting procedure. This method, used jointly with an adaptive gradient solver to minimize the function, allows dealing with complex 3D geological cases. It always produces a Voronoi simulation grid with the desired number of cells.

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BibTeX Reference

@ARTICLE{,
    author = { Merland, Romain and Caumon, Guillaume and Levy, Bruno and Collon, Pauline },
     title = { Voronoi Grids Conforming to 3D Structural Features },
   journal = { Computational Geosciences },
    volume = { 18 },
    number = { 3-4 },
      year = { 2014 },
     pages = { 373-383 },
       doi = { 10.1007/s10596-014-9408-0 },
  abstract = { Flow simulation in a reservoir can be highly impacted by upscaling errors. These errors can be reduced by using simulation grids with cells as homogeneous as possible, hence conformable to horizons and faults. In this paper, the coordinates of 3D Voronoi seeds are optimized so that Voronoi cell facets honor the structural features. These features are modeled by piecewise linear complex (PLC). The optimization minimizes a function made of two parts: (1) a barycentric function, which ensures that the cells will be of good quality by maximizing their compactness; and (2) a conformity function, which allows to minimize the volume of cells that is isolated from the Voronoi seed w.r.t., a structural feature. To determine the isolated volume, a local approximation of the structural feature inside the Voronoi cells is used to cut the cells. It improves the algorithm efficiency and robustness compared to an exact cutting procedure. This method, used jointly with an adaptive gradient solver to minimize the function, allows dealing with complex 3D geological cases. It always produces a Voronoi simulation grid with the desired number of cells. }
}