3D-Parameterization of the 3D Geological Space – The GeoChron Model
Résumé
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.