Nitsche Continuity Enforcement for Non-Conforming Subsurface Meshes
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Solution Overview
Problem
Current numerical methods for subsurface modeling in hydrocarbon exploration struggle to accurately capture the effects of subsurface features like fractures, faults, and wellbores, leading to precision loss when mesh geometry changes over time, and require meshes that conform to complex geometries, which can be inaccurate and unstable.
Innovation Solution
A method involving the generation of a background mesh that does not honor subsurface features, splitting it along these features to create a mesh that does, identifying non-conforming edges, and performing numerical simulations with mass or traction balance enforced on these edges using the Nitsche method, allowing for discontinuities and local refinement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a mesh is generated to honor complex subsurface feature geometries, then the accuracy of geometric representation is improved, but the mesh generation complexity and computational cost increase
Solution Approach 1:
The computational domain is divided into multiple subdomains separated by discontinuity surfaces (faults, fractures). Each subdomain is independently meshed, allowing the use of simpler background meshes within each subdomain while still capturing the complex geometry through the discontinuity surfaces. This segmentation approach reduces overall mesh generation complexity while maintaining geometric accuracy.
Solution Approach 2:
Discontinuity surfaces act as intermediaries between the background mesh and the complex subsurface features. These surfaces embed the geometric information of faults and fractures without requiring the background mesh to conform to them, thereby simplifying mesh generation while preserving geometric representation accuracy.
2Measurement precision
If the mesh is refined to capture high gradients around wellbores, then the simulation accuracy is improved, but the computational cost and mesh complexity increase
Solution Approach 1:
The mesh density is varied locally across different regions of the domain. Background meshes with coarser resolution are used in regions with low gradients, while refined meshes are applied only in localized areas with high gradients (e.g., around wellbores). This local refinement strategy maintains simulation accuracy in critical regions while reducing overall computational cost.
3Adaptability or versatility
If the mesh evolves to accommodate changing subsurface features, then the adaptability to reservoir changes is improved, but the precision of parameter mapping during mesh evolution deteriorates
Solution Approach 1:
Discontinuity surfaces are defined and embedded in the mesh structure in advance, before reservoir evolution occurs. This preliminary setup allows the mesh to naturally adapt to changing subsurface features by activating or deactivating specific discontinuity surfaces, avoiding the need for complex mesh remeshing and parameter mapping operations that would otherwise be required to accommodate reservoir changes.
4Ease of manufacture
If non-conforming meshes are used to simplify mesh generation, then the ease of mesh generation is improved, but the stability of numerical simulations deteriorates
Solution Approach 1:
Discontinuity surfaces serve as intermediaries that reconcile the use of simple background meshes with the need for accurate geometric representation. These surfaces are embedded within elements of the background mesh, allowing non-conforming mesh topology while maintaining numerical stability through proper formulation of the governing equations at the discontinuity surfaces.
Data Source
AI summary
A method for modeling a subsurface reservoir system, the method including: generating, with a computer, a background mesh that does not honor at least one subsurface feature included in the subsurface reservoir system; splitting, with a computer, the background mesh along the subsurface feature included in the subsurface reservoir system such that a resulting mesh honors a geometry of the subsurface features; identifying, with a computer, element faces or edges where the resulting mesh is non-conforming and/or the element faces or edges lie on subsurface features; and performing a computer-based numerical simulation utilizing the resulting mesh to model at least one fluid-related or geomechanical reservoir response, wherein mass or traction balance is enforced on the identified element faces or edges.