Isometric Unfolding of Stratigraphic Grid Units for Accurate Property Populating – Mathematical Concepts

In traditional methods used to populate stratigraphic units, the distortions can be very important and affect the setting up of the static and dynamic parameters necessary to the reservoir simulation, hence the simulation results. These distortions result from the mapping between the original curvilinear stratigraphic grid and the intermediate cartesian grid in which the property populating is processed. To minimize the deformation and improve the populating process, we propose a new original isometric unfolding process based on the minimization of the elastic tensor deformation. This method could be applied for every type of deposit: horizontal, parallel to top, parallel to bottom, proportional. Starting from a structural model defined into a coordinate line grid, the user chooses a reference iso-chronological level represented by a triangulated surface. The contacts between this surface and fault surfaces are explicitly extracted as coincident edges. These coincident edges are used to constraint an unfolding process, respecting the above constraints, join the fault lips opened by geological tectonic events. In this paper we will focus on mathematical concepts of the algorithms used in the whole unfolding process and present some results throw actual case studies.