Voronoi Meshing to Accurately Capture Geological Structure in Subsurface Simulations

Abstract

Mesh generation lies at the interface of geological modeling and reservoir simulation. Highly skewed or very small grid cells may be necessary to accurately capture the geometry of geological features, but the resulting poorly scaled or small grid cells can have a substantial negative impact on simulator accuracy and speed. One way to minimize numerical errors caused by gridding complex structures is to simulate on high-quality Voronoi meshes, which reduce grid orientation effects in fluid flow. This work presents a complete methodology to create Voronoi simulation grids, model fluid flow in complex geological systems, and visualize the results. A recently developed Voronoi meshing method that can automatically generate provably good unstructured meshes that conform to input surfaces creating closed volumes is used. Initially an analytical benchmark simulation is presented to validate the quality of the meshes and simulation results and demonstrate the superiority of simulation results using Voronoi meshes over flexed-hexahedral meshes on a domain with internal features. Next, meshes are created for test structures representing four of the most common geological features in the subsurface: layering, pinch-out, an interior lens that tapers to zero thickness on all sides and a fault with offset. Two benchmark flow simulations are run for each test structure. Finally, a realistic geological example for CO$$_2$$ 2 injection into an anticline is simulated. Three realizations of the Voronoi mesh at the same resolution are generated for the simulations. Each mesh is highly refined near the injection wells and coarse in areas of less interest. These three meshes are used to model the CO$$_2$$ 2 plume in the subsurface as it migrates to the top of the structure and then fills downward. Simulations on the meshes with randomly generated elements inside the input volumes each give slightly different fingering patterns for the viscous-unstable buoyant gas flow. The results presented in this work show a promising step towards utilizing fully automated Voronoi meshing for subsurface flow simulations in complex geology.

A Comparison of Cartographic and Toponymic Databases in a Multilingual Environment: A Methodology for Detecting Redundancies Using ETL and GIS Tools

“…For the comparison of the elements of each origin, for computational efficiency reasons, the centroids of the cadastral parcels (CP) were superimposed on areas of influence around the NGO-CAE place names. For areas where the parcel extension was large, it was decided to generate a continuous surface of the Voronoi diagram, as has been used in other recent cartographic works [96][97][98]; these are usually forestry and pasture areas. In most cases, the municipality owns the land, either as public domain or as patrimonial land.…”