Generation of unstructured PEBI-grids for geological reservoirs utilizing offset curves with L-BFGS optimization

Date

2025-7

Author

Hasanzade, Parviz

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A well-constructed static model is essential for accurate reservoir simulations. Structured grids are easy to generate but often fail to conform to geological features or meet the orthogonality conditions required by standard flux approximation schemes. Unstructured Perpendicular Bisector (PEBI) grids, by contrast, offer local orthogonality and adaptability to complex geometries. Part of the Voronoi seeds, which are called fixed seeds, are predefined to capture the geological features, and the reservoir seeds that cover the rest of the reservoir are often placed using Delaunay triangulation. Reservoir seeds that are placed based on a uniform random distribution, or utilizing a Cartesian grid, are relocated by the optimization algorithms that calculate the seed positions with the most uniform Voronoi cell distribution. This study introduces a novel seed placement method that systematically honors geological constraints. Fixed seeds are first positioned along faults and wells. Reservoir seeds are then generated and filtered to avoid constraint violations. To improve initial coverage, a polygon offsetting algorithm is applied to place seeds along inner offset curves of the domain. This offset-based approach reduces degenerate cases during the boundary cell clipping and accelerates the energy function minimization that governs grid compactness. The proposed workflow was tested on realistic geological models. Finally, a compressible multiphase flow simulation was conducted on both corner-point and PEBI grids of a homogeneous reservoir to assess the impact on pressure distribution and displacement behavior. Results demonstrate improved grid quality and simulation accuracy, validating the effectiveness of the offset-based seed placement strategy for PEBI grid generation.

Subject Keywords

PEBI grids, Voronoi diagrams, Reservoir simulation, Polygon offsetting

URI

https://hdl.handle.net/11511/115421

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Graduate School of Natural and Applied Sciences, Thesis