The generation of reservoir grids has to take into account numerous flow parameters, static and dynamic, from the fine-scale geological models to minimize discretization errors. These parameters are generally encoded separately as constraints on cell size, orientation and aspect ratio. In this paper, we propose to encode them all at a time in a Riemannian metric tensor field and to apply a global optimization method. This method is based on Centroidal Voronoi Tesselation algorithms under Lp norm and generates unstructured hex-dominant reservoir grids, optimum in terms of sampling.
We apply these principles to generate flow-based reservoir grids. We use a fine-scale velocity field to compute the norm and the directions of the metric tensor: the generated grids are refined in regions of high flow and the cell facets are oriented along the streamline directions. The grids are therefore suitable to a discretization with two-point-flux approximation. The simulation results obtained with these grids are then compared with those computed on a standard Cartesian grid of the same size. These first results are encouraging and need further investigation.
The method is general, and can account for other dynamic parameters, such as vorticity, that can be weighted and introduced in the metric tensor. Furthermore, CVT algorithms can be adapted to take into account fine-scale static features in the grid generation process. Because the gridding is fully automatic, a possible extension of this work is to update the grid between simulation time steps to reflect changes in boundary conditions.