3{D}-Parameterization of the 3{D} geological space - The {G}eo{C}hron model

in: Proc. European Conference on the Mathematics of Oil Recovery (ECMOR IX)

Abstract

One of the key points in reservoir modeling is the building of a complex 3D-mesh, which must integrate various constraints: respecting the geometry of the fault network, taking into account stratigraphic knowledge, computing petrophysical properties by geostatistical methods, allowing upscaling and/or flow simulation… The building of this mesh relies on the use of a parametric coordinate system (u,v,t) such that (u,v) corresponds to “horizontal” curvilinear coordinates tangent to the horizons while (t) corresponds to the “vertical” curvilinear axis approximately orthogonal to the horizons. So far, common practice consists in covering the geological domain with a “regular structured stratigraphic grid” with hexahedral cells and then to use the (i,j,k) indexes of the nodes of these cells as a sampling of the (u,v,t) coordinates. This kind of structured mesh is necessary to geostatistics, and to a lesser point flow simulation, which rely heavily on the implicit structure of the mesh to define neighborhoods and relationships between cells. However, such a regular grid may lead to errors or approximation, for example when trying to model complex faults networks or heavily folded horizons in such a way that edges' cells never cross these structural surfaces. In this article, we propose a completely new approach based on the recently introduced “GeoChron” model where the (u,v,t) parameterization of the geological space is computed independently of any stratigraphic grid. This approach allows a consistent 3D-parameterization to be built whatever the complexity of the fault network, using only a tetrahedral mesh respecting the faults. Stratigraphic data, such as unconformity or sedimentation styles, can be taken into account in the construction of such a parameterization. The main benefit of such a parameterization of the 3D geological space is to allow past, present and future geostatistical methods to be implemented in the (u,v,t) parametric space without using any stratigraphic grid. As a consequence, it is then possible to populate polyhedral grids with the petrophysical properties computed in the parametric space.

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    BibTeX Reference

    @INPROCEEDINGS{Moyen04,
        author = { Moyen, Rémi and Mallet, Jean-Laurent and Frank, Tobias and Leflon, Bruno and Royer, Jean-Jacques },
         title = { 3{D}-Parameterization of the 3{D} geological space - The {G}eo{C}hron model },
     booktitle = { Proc. European Conference on the Mathematics of Oil Recovery (ECMOR IX) },
       chapter = { 0 },
          year = { 2004 },
      abstract = { One of the key points in reservoir modeling is the building of a complex 3D-mesh, which must
    integrate various constraints: respecting the geometry of the fault network, taking into account
    stratigraphic knowledge, computing petrophysical properties by geostatistical methods, allowing
    upscaling and/or flow simulation… The building of this mesh relies on the use of a parametric
    coordinate system (u,v,t) such that (u,v) corresponds to “horizontal” curvilinear coordinates
    tangent to the horizons while (t) corresponds to the “vertical” curvilinear axis approximately
    orthogonal to the horizons. So far, common practice consists in covering the geological domain
    with a “regular structured stratigraphic grid” with hexahedral cells and then to use the (i,j,k)
    indexes of the nodes of these cells as a sampling of the (u,v,t) coordinates. This kind of
    structured mesh is necessary to geostatistics, and to a lesser point flow simulation, which rely
    heavily on the implicit structure of the mesh to define neighborhoods and relationships between
    cells. However, such a regular grid may lead to errors or approximation, for example when
    trying to model complex faults networks or heavily folded horizons in such a way that edges'
    cells never cross these structural surfaces. In this article, we propose a completely new approach
    based on the recently introduced “GeoChron” model where the (u,v,t) parameterization of the
    geological space is computed independently of any stratigraphic grid. This approach allows a
    consistent 3D-parameterization to be built whatever the complexity of the fault network, using
    only a tetrahedral mesh respecting the faults. Stratigraphic data, such as unconformity or
    sedimentation styles, can be taken into account in the construction of such a parameterization.
    The main benefit of such a parameterization of the 3D geological space is to allow past, present
    and future geostatistical methods to be implemented in the (u,v,t) parametric space without using
    any stratigraphic grid. As a consequence, it is then possible to populate polyhedral grids with the
    petrophysical properties computed in the parametric space. }
    }