Abstract
An unstructured grid generation method is presented that automates control-volume boundary alignment to geological objects and control point alignment to complex wells. The grid generation method is coupled with an iterative acute mesh reconstruction technique, to construct essentially acute triangulations, while satisfying quite general geometric constraints. For well aligned grids control points are constrained to the well trajectory and protection circles are used, whereas for boundary aligned grids halo construction is performed. Unstructured Delaunay triangulations (DT) have the desirable locally orthogonal perpendicular bisectional (PEBI) property, required by the industry standard two-point flux approximation for consistency for isotropic fields. The PEBI property can only be exploited if such grids are comprised of acute simplexes, with circumcentres located inside their respective elements. The method presented enables acute DT layered mesh generation while honoring internal boundaries and wells in a two dimensional space. A dual (Voronoi) grid derived from a feature honored simplicial mesh is then projected in the vertical direction generating 2.5D PEBI grids. Effectiveness of the method to construct acute PEBI grids honoring geological objects and complex wells is demonstrated by meshing representative reservoir geometries. Numerical results are presented that verify consistency of the two-point flux on the resulting boundary-aligned acute PEBI grids. Development of an unstructured grid generation method which 1) Automates interior boundary alignment, 2) Honors features with respect to control point and/or control volume, and 3) Generates acute PEBI grids for reservoir geometries is presented. A unique workflow is presented to generate boundary aligned acute PEBI grids for complex geometries. Development of boundary aligned grids that honor both geological objects and multilateral complex wells, together with mesh reconstruction to ensure circumcenter containment is presented. Further, 3D PEBI grid generation method which can limit refinement to well perforations and geological objects is also described.
Linear variational principle for Riemann mappings and discrete conformality
