In general, the purpose of a simulation is to mimic a real system in order to study its behavior. Among the first steps in a simulation study is the proper definition of the spatial discretization. This abstraction process of the space domain produces the simulation model and is essential for the result of the simulation.

A new approach for the simulation of faulted hydrocarbon reservoirs is proposed. The described algorithm iteratively generates a constrained Voronoi grid suitable for two-point flux approximation schemes. The algorithm is based on a Delaunay triangulation and is characterized by its robustness, efficiency and the iterative modeling approach. Initially, a Delaunay triangulated mesh is calculated for a given point distribution. Using the triangulated mesh, the proper Voronoi grid is derived. Constraints (faults, pinch-outs, boundaries) are aligned sequentially on the derived Voronoi cell and integrated into the Delaunay mesh. The alignment is necessary to ensure that the use of two-point flux approximation methods on the generated reservoir grid model is correct. The higher the resolution of the point distribution in the area of the constraint, the better the aligned constraint matches the actual constraint. Finally, all Voronoi cells touching the integrated constraints are reconstructed using the Delaunay mesh. Similar to the insertion of new constraints, local grid refinements or model elements can be added without reconstructing the entire model. All modifications of the reservoir model result in local grid adjustments.

The runtime complexity of the algorithm depends on constructing the underlying Delaunay mesh and can be estimated as O(n log n) plus some overhead O(n) for deriving the Voronoi grid.

This new approach reduces the construction and updating times for reservoir grid models considerably and results in grid models ranging from structured, Cartesian-type of grid to high complex unstructured models depending on the original distribution of grid points.

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