Implicit Function Refinement for Subterranean Modeling
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Solution Overview
Problem
Current implicit structural modeling of subterranean volumes faces challenges in accurately representing structural discontinuities due to the assumption of smoothness, leading to poor data fitting and increased computation times with finer mesh resolutions, which may not meet the resolution requirements for fluid flow simulations and rock volume computations.
Innovation Solution
The method involves generating a refined implicit function using a meshless technique with weighted curvature minimization, allowing for adaptive resolution matching the input data quality, thereby improving the accuracy of iso-surface definition near discontinuities while maintaining computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If mesh resolution is increased to improve accuracy of implicit function approximation, then manufacturing precision improves, but productivity deteriorates due to longer computation runtimes and larger model sizes
Solution Approach 1:
The patent divides the computational domain into two distinct parts: a coarse mesh background mesh for global modeling and a fine mesh local mesh for refined regions. This segmentation allows the model to achieve high accuracy in specific areas of interest without requiring the entire domain to be modeled at fine resolution, thus reducing overall computational cost while maintaining local precision.
Solution Approach 2:
The patent applies different mesh qualities to different regions of the domain. The background mesh uses coarse resolution for areas where high accuracy is not critical, while the local mesh provides fine resolution in regions requiring detailed representation. This local quality approach ensures computational resources are concentrated where they are most needed, improving efficiency without sacrificing necessary accuracy.
2Measurement precision
If mesh resolution is increased to improve data fitting accuracy, then measurement precision improves, but loss of time increases due to longer computation runtimes
Solution Approach 1:
The patent segments the modeling process into two stages: first solving the system on the coarse background mesh to obtain a global solution, then solving a refined system on the fine local mesh only in regions where high accuracy is required. This segmentation eliminates the need to solve the entire domain at fine resolution, significantly reducing computation time while maintaining measurement precision in critical areas.
Solution Approach 2:
The patent applies fine mesh resolution only partially to specific local regions rather than uniformly across the entire domain. This partial action approach provides excessive accuracy only where necessary (in the local mesh region) while using coarse resolution elsewhere, thereby achieving the required measurement precision without the proportional time cost of full-domain fine meshing.
3Manufacturing precision
If uniform fine mesh resolution is used throughout the volume, then manufacturing precision improves, but device complexity increases due to larger model sizes in memory
Solution Approach 1:
The patent segments the memory structure into two parts: a compact background mesh storing coarse-resolution data for the entire domain, and a smaller local mesh storing fine-resolution data only for specific regions. This segmentation reduces the total memory footprint compared to a uniform fine mesh while maintaining the ability to represent detailed features where needed.
Solution Approach 2:
The patent implements local quality by storing high-resolution mesh data only in specific local regions where it is required, rather than uniformly across the entire volume. This approach reduces the overall model size in memory while maintaining high manufacturing precision in the regions that require it, avoiding the memory overhead of uniform fine meshing throughout the entire domain.
Data Source
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AI summary
Methods, computing systems, and computer-readable media for modeling a subterranean volume, of which the methods include receiving data representing a geology of the subterranean volume, calculating a mesh for a digital model of the subterranean volume, generating the digital model using the mesh and the data, wherein generating the digital model comprises defining an implicit function for isostratigraphic surfaces of the subterranean volume. calculating values for a plurality of data points in the model using the implicit function, determining a discrepancy value for the individual data points, identifying a sample domain in the digital model, determining a refined implicit function for the sample domain, and modeling the subterranean volume using the refined implicit function for the sample domain and the implicit function for an area outside of the sample domain in the digital model.