Hexahedral Mesh Subdivision for Stable Basin Simulation
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Solution Overview
Problem
Current basin simulation tools face instability and numerical issues when modeling sedimentary basins with thin layers and stratigraphic bevels, leading to inaccurate stress field modeling and potential failure in numerical simulations due to the use of flattened hexahedral meshes.
Innovation Solution
The method involves subdividing hexahedral meshes into pyramidal meshes and applying a face-based smoothed finite element method (FS-FEM) to stabilize the numerical simulation of poromechanics equilibrium equations, ensuring accurate determination of stress and strain fields even in hexa-dominant meshes with unfavorable geometries.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If a hexa-dominant mesh representation is used for basin modeling, then the mesh structure is simplified and easier to construct, but numerical instability and inaccurate stress field modeling occur when modeling thin layers and stratigraphic bevels
Solution Approach 1:
The patent applies segmentation by dividing the hexahedral mesh into multiple tetrahedral elements. Each hexahedral cell is subdivided into six tetrahedra by connecting the centroid to each face, creating a finer-grained mesh that can accurately represent thin layers and complex geometries without the numerical instability associated with flattened hexahedral cells.
Solution Approach 2:
The patent changes the fundamental parameter of mesh topology from hexahedral dominance to tetrahedral dominance. This parameter change allows the mesh to adapt to complex geological structures like thin layers and bevels while maintaining numerical stability, as tetrahedral elements are more flexible in accommodating various geometric configurations.
2Productivity
If hexahedral meshes are used for sedimentary basin simulation, then computational efficiency is improved, but accurate modeling of thin geological layers becomes difficult
Solution Approach 1:
The patent segments each hexahedral cell into six tetrahedral elements, creating a finer mesh that can resolve thin geological layers with high precision. This segmentation allows the mesh to capture the geometry of thin layers accurately while maintaining the overall computational efficiency of the simulation by using a systematic division approach.
Solution Approach 2:
The patent transitions from a two-face-dominated hexahedral representation to a four-face-dominated tetrahedral representation, adding dimensional flexibility. This dimensional change enables the mesh to better represent the third dimension (thickness of thin layers) while maintaining computational efficiency through the systematic tetrahedralization process.
3Device complexity
If flattened hexahedral meshes are used to represent thin layers, then the mesh construction is simplified, but the quality of the numerical solution deteriorates
Solution Approach 1:
The patent segments flattened hexahedral cells into tetrahedral elements, eliminating the need for flattened geometries. This segmentation produces a mesh that maintains simple construction while achieving high measurement precision for stress field calculations, as tetrahedral elements can accurately represent thin layers without the numerical artifacts introduced by flattened hexahedra.
Solution Approach 2:
The patent changes the mesh topology parameter from hexahedral to tetrahedral dominance, which fundamentally alters how thin layers are represented. This parameter change eliminates the need for flattened geometries while maintaining construction simplicity and significantly improving the accuracy of stress field calculations through better geometric representation.
Data Source
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AI summary
The present invention relates to a method for modeling a sedimentary basin by means of a numerical basin simulation that solves at least one poromechanical equilibrium equation using a face-based smoothed finite element method to determine at least one stress field and one strain field. The method according to the invention includes, in particular, the following steps for each meshed representation of a basin state comprising hexahedral cells: a) a second meshed representation of the basin state is determined by subdividing each of the hexahedral cells of the initial meshed representation into six pyramidal cells; b) the basin is modeled by determining at least the displacement field and the stress field using the numerical simulation applied to the second meshed representation.