Streamlines in Geochron G-Grids.

@inproceedings{Royer1GM2011,
 abstract = { Geochron objects are made of two grids. The first one in the so-called G-space, is a tetrahedral unstructured grid used to describe geological objects such as faults, sub-horizontal layers, and lithological contacts. The second one, named G-space, is a Voxet regular grid used to describe chronostratigraphic events and properties. It is equivalent to 3D Wheeler diagram used for describing sedimentation processes through time. Classically, fluid flows are described by a set of partial differential equations (PDE) with boundary conditions solved in the G-space. Pressure, velocity and saturation values are then available at each node of a regular Voxet or Sgrid grid, or at the center of an tetrahedral TSolid. Streamlines are then calculated from a set of injection/production wells and boundary conditions. They are then mapped in the G-space.
This paper suggests to write the set of fluid flow equations in the curvilinear G-space accounting for adapted boundary conditions and for the anisotropy and heterogeneity induced by the mapping of the Gspace into the G-space. The resulting complexity introduced in the flow equations, mainly due to anisotropy and heterogeneity is compensated by the time gained at the solving stage as solving PDE in regular grids is notably faster than on unstructured grids. Classical solver like commercial solvers (Eclipse, Comsol), can be used to solve the fluid flow problem in the G-space. Once the velocity field is calculated, the streamlines can be drawn virtually in the G-space using classical Pollock or Runge-Kunta algorithms, or commercial streamline simulator Streamsim [2004], and mapped back onto the G-space using Geochron coordinate transform functions. The theory necessary to implement the above method is described in this work. },
 author = { Royer, Jean-Jacques },
 booktitle = { Proc. 31st Gocad Meeting, Nancy },
 title = { Streamlines in Geochron G-Grids. },
 year = { 2011 }
}