High resolution geostatistics on coarse unstructured flow grids

in: Geostatistics Banff, Proc. of the seventh International Geostatistics Congress, pages 703-712, Kluwer, Dordrecht

Abstract

Although closely related to each other, Geostatistics and simulation of physical processes have different, often conflicting, requirements about their discretization support. While geostatistical methods can be efficiently implemented on high-resolution regular grids, process simulation calls for coarse flexible grids to minimize computational cost without loss of accuracy. Adapting geostatistical methods to such flexible grids is difficult, since unstructured neighborhood lookup is time-consuming, and cell volumes may vary significantly throughout the grid. Instead, we propose to disconnect the representation of properties from the representation of geometry using the concept of geo-chronological space: the coarse flexible grid in present geometrical space (x, y, z) is mapped onto a high-resolution cartesian grid in geo-chronological space (u, v, t), where u and v are planar topographic coordinates at deposition time, and t is the geological time. The calculation of this 3D mapping is probably the most challenging part of the method. Here, we describe how to derive it by the extrusion of a reference stratigraphic surface, possibly discontinuous across faults. This mapping can be used to infer spatial covariance models and run geostatistical algorithms directly in geo-chronological space. The practicality of the method is demonstrated on actual reservoir data.

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BibTeX Reference

@INCOLLECTION{Caumon04HRG,
    author = { Caumon, Guillaume and Grosse, Olivier and Mallet, Jean-Laurent },
    editor = { Leuangthong, Oy and Deutsch, C. V. },
     title = { High resolution geostatistics on coarse unstructured flow grids },
 booktitle = { Geostatistics Banff, Proc. of the seventh International Geostatistics Congress },
    volume = { 2 },
   chapter = { 0 },
      year = { 2004 },
     pages = { 703-712 },
 publisher = { Kluwer, Dordrecht },
       doi = { 10.1007/978-1-4020-3610-1_71 },
  abstract = { Although closely related to each other, Geostatistics and simulation of physical processes have different, often conflicting, requirements about their discretization support. While geostatistical methods can be efficiently implemented on high-resolution regular grids, process simulation calls for coarse flexible grids to minimize computational cost without loss of accuracy. Adapting geostatistical methods to such flexible grids is difficult, since unstructured neighborhood lookup is time-consuming, and cell volumes may vary significantly throughout the grid. Instead, we propose to disconnect the representation of properties from the representation of geometry using the concept of geo-chronological space: the coarse flexible grid in present geometrical space (x, y, z) is mapped onto a high-resolution cartesian grid in geo-chronological space (u, v, t), where u and v are planar topographic coordinates at deposition time, and t is the geological time. The calculation of this 3D mapping is probably the most challenging part of the method. Here, we describe how to derive it by the extrusion of a reference stratigraphic surface, possibly discontinuous across faults. This mapping can be used to infer spatial covariance models and run geostatistical algorithms directly in geo-chronological space. The practicality of the method is demonstrated on actual reservoir data. }
}