Hierarchical Electrical Model for Thin Feature Simulation
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Solution Overview
Problem
Finite element modeling of thin features or processes in large computational domains leads to computationally explosive calculations, causing significant processing time and making real-time monitoring impractical, especially in applications like oilfield geophysics during fracking operations.
Innovation Solution
A hierarchical electrical model is introduced for unstructured finite element meshes, augmenting volume-based conductivity with facet and edge-based conductivity, allowing for a coarse representation of thin conductors and fractures, reducing the computational burden by localizing conductivity properties to edges and facets rather than distributing them across entire elements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If finite element modeling is applied to thin features or processes, then modeling accuracy is improved, but computational complexity becomes explosive
Solution Approach 1:
The patent segments the computational domain into volumetric elements and identifies thin features within them. By separating the representation of thin features from the bulk volumetric modeling, the method avoids the need to refine the entire mesh, thus reducing computational complexity while maintaining accuracy for thin structures.
Solution Approach 2:
The patent introduces a hierarchical approach where thin features are represented in reduced dimensions (edges and facets) rather than full volumetric elements. This dimensional reduction allows accurate modeling of thin structures without the computational burden of fine volumetric meshing throughout the entire domain.
2Measurement precision
If a large number of finite elements are used to characterize thin features, then modeling precision is improved, but processing time increases significantly
Solution Approach 1:
The patent applies local quality by assigning different levels of detail to different parts of the model. Thin features are represented with high precision using edge and facet-based conductivity, while the surrounding volumetric elements use coarser discretization. This localized refinement maintains modeling precision for thin features without requiring fine meshing everywhere, thus reducing processing time.
3Area of stationary object
If volumetric finite element modeling is used for thin conductors, then comprehensive coverage is achieved, but computational resources are excessively consumed
Solution Approach 1:
The patent extracts thin conductor features from the volumetric mesh and represents them separately using edge and facet-based conductivity models. This extraction allows the method to maintain comprehensive spatial coverage while avoiding the computational expense of volumetric discretization for thin structures, thus reducing computational resource consumption.
4Measurement precision
If fine meshing is applied to model thin features accurately, then characterization accuracy is improved, but real-time monitoring becomes impractical
Solution Approach 1:
The patent implements a dynamic modeling approach where the computational complexity is adapted to the specific features being modeled. By using hierarchical conductivity models that can represent thin features efficiently without requiring fine meshing throughout the entire domain, the method enables real-time monitoring while maintaining characterization accuracy for thin structures.
Data Source
AI summary
A computer-implemented method of preventing computationally explosive calculations. The method includes obtaining, by a processor of the computer, measured data of one of a physical process or a physical object; performing hierarchical numerical modeling of a physical process inclusive of an Earth model containing at least one of (a) infrastructure in the ground and (b) a formation feature in the ground, wherein predicted data is generated; comparing the measured data to the predicted data to calculate an estimated error; analyzing the estimated error via an inversion process to update the at least one of the Earth model and infrastructure model so as to reduce the estimated error and to determine a final composite Earth model of at least one of the infrastructure and the feature; and using the final composite Earth model to characterize at least one of the process and the physical object.