3D conforming power diagrams for radial LGR in CPG reservoir grids

Abstract

Mesh generation becomes a crucial step in reservoir flow simulation of new generation. The mesh must faithfully represent the architecture of the reservoir and its heterogeneity. In (Flandrin et al. in IJNME 65(10):1639–1672, 2006) a three-dimensional hybrid mesh model was proposed to capture the radial characteristics of the flow around the wells. In this hybrid mesh, the reservoir is described by a non-uniform Cartesian structured mesh and the drainage areas around the wells are represented by structured radial circular meshes. Unstructured polyhedral meshes are used to connect these two kinds of structured grids. The construction of these transition meshes is based on 3D power diagrams (Aurenhammer in SIAM J Comput 16(1):78–96, 1987) to ensure finite volume properties such as mesh conformity, dual orthogonality and cell convexity. In this paper, we propose an extension of this hybrid model to the case where the reservoir is described by a corner point geometry (CPG) grid. At first, the CPG grid is mapped, in a reference space, into a non-uniform Cartesian grid by minimizing the mapping deformation. Then, a hybrid mesh is generated in this reference space using the previous method. Finally, this mesh is mapped back into the real space. Some quality criterions are introduced to measure and improve the quality of the polyhedral transition mesh.