Three-Dimensional Geological Boundary Aligned Unstructured Grid Generation, and CVD-MPFA Flow Computation

Abstract Three-dimensional unstructured grid generation for reservoirs with geological layers, faults, pinchouts, fractures and wells is presented. Grids are generated for example cases, and pressure fields and flow fields computed by the cell-centered and vertex-centered control-volume distributed multi-point flux approximation (CVD-MPFA) schemes are compared and contrasted together with the methods. Grid generation for reservoir simulation, must honour classical key geological features and multilateral wells. 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. The control-point is defined as the centroid of the control-volume for any grid type. 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 perpendicular bisector (PEBI) meshes either with respect to primal or dual-cells depending on grid type. Both primal and dual-cell boundary aligned grid generators use primal-cells (tetrahedra, pyramids, prisms and hexahedra) as grid elements. Dual-cell feature aligned grids are derived from underlying primal-meshes, such that features are recovered, with control-volume faces aligned with interior feature boundaries. The grids generated enable a comparative performance study of cell- vertex versus cell-centered 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. Stability limits of the methods are also explored. For a given mesh the cell-vertex method uses approximately a fifth of the unknowns used by a cell-centered method and proves to be the most beneficial with respect to accuracy and efficiency, which is verified by flow computation. Novel techniques for generating three-dimensional unstructured hybrid essentially PEBI-grids, honouring geological features are presented. Geological boundary aligned grid generation is performed for primal and dual-cell grid types. Flow results show that vertex-centered CVD-MPFA methods outperform cell-centered CVD-MPFA methods.