Constrained Voronoi Grid Generation for Reservoir Simulation

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Solution Overview

Problem

Existing methods for generating two-dimensional Voronoi grids in bounded regions with internal features fail to accurately account for polylinear internal and boundary features, leading to unstable and inaccurate numerical solutions, especially in petroleum reservoir simulations.

Innovation Solution

The method involves approximating boundaries and internal features with polylines, constructing protected polygons or points around these features, and modifying Delaunay triangulation to conform to the polylines, with additional steps like grid smoothing to improve accuracy and adaptivity based on specified density criteria.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Manufacturing precision

If existing methods for Voronoi grid generation are used, then the grid can be generated in bounded regions, but the internal features and their intersections are not accurately accounted for, leading to unstable and inaccurate numerical solutions

Engineering Contradiction:

Improvegrid alignment with internal featuresVSAvoidstability of numerical solutions

Core Design Contradiction:

Manufacturing precisionVSReliability

Solution Approach 1:

The domain is divided into multiple Voronoi cells, each associated with a node, such that the grid naturally conforms to internal features. The segmentation allows the grid to adapt to complex geometries while maintaining accuracy at feature intersections through the Voronoi construction process.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The Voronoi grid provides local adaptivity by allowing different cell sizes and shapes in different regions. The grid can be refined locally around internal features and their intersections, ensuring high resolution where needed while maintaining coarser resolution in other areas, thus improving both accuracy and numerical stability.

Inventive Principle:

Principle #3Local quality

2Adaptability or versatility

If Voronoi grids are generated with free node location selection, then the grid has flexibility to represent widely varying domain geometry, but the ability to accurately represent internal and boundary features is compromised

Engineering Contradiction:

Improveflexibility to represent domain geometryVSAvoidaccuracy of feature representation

Core Design Contradiction:

Adaptability or versatilityVSManufacturing precision

Solution Approach 1:

Nodes are strategically positioned before grid generation to ensure that internal features and boundary features are accurately captured. The node locations are chosen in advance to honor the geometric constraints of the domain, allowing the subsequent Voronoi construction to naturally produce cells that conform to these features.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The grid allows different regions to have different properties: areas with internal features have refined, conforming cells, while other areas can have coarser cells. This local adaptivity maintains overall geometric flexibility while ensuring high precision where features require accurate representation.

Inventive Principle:

Principle #3Local quality

3Manufacturing precision

If protected polygons are constructed around polylines and Delaunay triangulation is modified to conform to features, then the constrained Voronoi grid precisely aligns with internal features, but the grid generation process becomes more complex

Engineering Contradiction:

Improvealignment precision with internal featuresVSAvoidcomplexity of grid generation process

Core Design Contradiction:

Manufacturing precisionVSDevice complexity

Solution Approach 1:

Protected polygons are introduced as an intermediary structure between the input polylines and the final Voronoi grid. These polygons serve as a bridge that translates the feature geometry into a form suitable for Delaunay triangulation, simplifying the overall process by providing a clear intermediate representation.

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

The method combines multiple techniques: protected polygon construction, Delaunay triangulation modification, and Voronoi grid generation. By merging these steps into an integrated workflow, the complexity is managed systematically, with each step building on the previous one to achieve precise feature alignment.

Inventive Principle:

Principle #5Merging (Combining)

Data Source

PatentUS8212814B2Generation of constrained Voronoi grid in a plane

Publication Date: 2012.07.03 EXXONMOBIL UPSTREAM RESEARCH COMPANY(US)

AI summary

A computer-implemented method for generating a constrained Delaunay triangulation for a planar domain with boundaries and internal features. The boundaries and internal features of the domain are approximated with polylines. Unconstrained Delaunay triangulation is constructed for the domain. The unconstrained Delaunay triangulation is modified to conform triangle sides to the polylines. The modified triangulation is corrected to make it a constrained Delaunay triangulation. At least one of the steps of the method is implemented using a computer.