Unstructured Cut-Cell Grids for Modeling Complex Reservoirs

Effective workflows for translating Earth models into simulation models require grids that preserve geologic accuracy, offer flexible resolution control, integrate tightly with upscaling, and can be generated easily. Corner-point grids and pillar-based unstructured grids fail to satisfy these objectives; hence, a truly 3D unstructured approach is required. This paper describes unstructured cut-cell gridding tools that address these needs and improve the integration of our overall reservoir-modeling workflows. The construction of simulation grids begins with the geologic model: a numerical representation of the reservoir structure, stratigraphy, and properties. Our gridding uses a geochronological (GeoChron) map from physical coordinates to an unfaulted and unfolded depositional coordinate system. The mapping is represented implicitly on a tetrahedral mesh that conforms to faults, and it facilitates accurate geostatistical modeling of static depositional properties. In the simplest use case, we create an explicit representation of the geologic model as an unstructured polyhedral grid. Away from faults and other discontinuities, the cells are hexahedral, highly orthogonal, and arranged in a structured manner. Geometric cutting operations create general polyhedra adjacent to faults and explicit contact polygons across faults. The conversion of implicit models to explicit grids is conceptually straightforward, but the implementation is nontrivial because of the limitations of finite precision arithmetic and the need to remove small cells formed in the cutting process. In practice, simulation grids are often constructed at coarser resolutions than Earth models. Our implementation of local grid coarsening and refinement exploits the flexibility of unstructured grids to minimize upscaling errors and to preserve critical geologic features. Because the simulation grid and the geologic model are constructed by use of the same mapping, fine cells can be nested exactly inside coarse cells. Therefore, flow-based upscaling can be applied efficiently without resampling onto temporary local grids. This paper describes algorithms and data structures for constructing, storing, and simulating cut-cell grids. Examples illustrate the accurate modeling of normal faults, y-faults, overturned layers, and complex stratigraphy. Flow results, including a field-sector model, show the suitability of cut-cell grids for simulation.