3D Geological Feature Honored Cell-centered and Vertex-centered Unstructured Grid Generation, and CVD-MPFA Performance

Grid generation for reservoir simulation, must honor classical key geological features and multilateral wells. For the purpose of grid generation, the geological features are classified into two groups; 1) involving layers, faults, pinchouts and fractures, and 2) involving well distributions. In the former, control-volume boundary aligned grids(BAGs) are required, while in the latter, control-point well aligned grids(WAGs) are required. In reservoir simulation a choice of grid type and consequent control-volume type is made, i.e. either primal or dual-cells are selected as control-volumes. Regardless of control-volume type, the control-point is defined as the centroid of the control-volume. Three-dimensional unstructured grid generation methods are proposed that automate control-volume boundary alignment to geological features and control point alignment to wells, yielding essentially PEBI-meshes either with respect to primal or dual-cells depending on grid type. In the grid generation methods presented, for both primal and dual-cell feature based meshes, both frameworks use primal-cells (tetrahedra, pyramids, prisms and hexahedra) as grid elements. Dual-cell feature honored grids are derived from underlying primal-meshes such that features are recovered in the dual-setting. Geological features are honored by using the idea of protection spheres, and protection halos around key geological features. Halo construction requires the use of prisms and/or hexahedra. Pyramids are used as transition elements providing interfaces between quad faces of the halo elements and triangular faces of the main tetra-mesh. A novel method for constructing pyramids as transition elements in an unstructured mesh together with a novel technique for ensuring fully constrained recovery of geological features is proposed. The grids generated are employed to study comparative performance of cell-vertex versus cell-centred CVD-MPFA finite-volume formulations using equivalent degrees of freedom. The benefits of both types of approximation are presented in terms of flow resolution relative to the respective degrees of freedom employed. The cell vertex method proves to be the most beneficial with respect to accuracy and efficiency.