Iterative Multi-Scale Method for Anisotropic Porous Media Flow
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Solution Overview
Problem
Current multi-scale methods for simulating fluid flow in subsurface reservoirs face challenges in accurately modeling complex, heterogeneous domains due to errors introduced by localization assumptions, especially in the presence of large permeability contrasts and varying boundary conditions, which can lead to divergent solutions from standard fine-scale simulations.
Innovation Solution
The iterative multi-scale method employs line relaxation and iterative smoothing procedures to improve the localization assumptions, creating a fine grid, coarse grid, and dual coarse grid, calculating dual basis functions, and integrating a source term of an elliptic pressure equation to compute pressure using an iterative method, allowing for the reconstruction of a solution that models fluid flow in subsurface reservoirs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If multi-scale methods are used to reduce computational complexity, then computational cost is reduced, but accuracy deteriorates due to errors introduced by localization assumptions
Solution Approach 1:
The patent implements an iterative feedback mechanism where the coarse-scale solution is repeatedly refined by incorporating fine-scale information. The method computes fine-scale corrections based on the coarse-scale pressure solution, then feeds these corrections back to improve the coarse-scale operator and boundary conditions. This iterative feedback loop continues until convergence, progressively reducing the error introduced by localization assumptions while maintaining computational efficiency.
Solution Approach 2:
The patent performs preliminary computation of fine-scale basis functions and local solutions on coarse-scale control volumes before the main simulation. These pre-computed fine-scale components capture the essential fine-scale heterogeneity effects, which are then incorporated into the coarse-scale operator. This preliminary action allows the coarse-scale model to account for fine-scale details without requiring full fine-scale computation during the main simulation.
2Device complexity
If coarse-scale modeling is used to simplify the reservoir model, then device complexity is reduced, but manufacturing precision deteriorates in modeling fine-scale velocity fields
Solution Approach 1:
The patent segments the velocity field computation into two distinct parts: a coarse-scale pressure solution obtained from the simplified coarse model, and fine-scale velocity corrections computed locally using pre-computed basis functions. This segmentation allows the complex fine-scale velocity reconstruction to be performed locally on coarse control volumes, maintaining accuracy while avoiding the need for a full fine-scale pressure solution.
Solution Approach 2:
The patent introduces fine-scale basis functions as an intermediary between the coarse-scale pressure solution and the fine-scale velocity field. These basis functions, computed once on each coarse control volume, act as mediators that translate the coarse-scale pressure information into accurate fine-scale velocity fields, bridging the gap between coarse modeling and fine-scale accuracy requirements.
3Measurement precision
If standard numerical schemes are used on fine grids to achieve reference solutions, then measurement precision is improved, but productivity deteriorates due to high computational cost
Solution Approach 1:
The patent applies partial fine-scale action by computing fine-scale basis functions and corrections only on coarse-scale control volumes where they are needed, rather than performing a complete fine-scale simulation everywhere. The fine-scale computation is applied selectively to capture essential fine-scale effects while avoiding the full computational burden of a complete fine-scale solution, achieving a balance between accuracy and efficiency.
Data Source
AI summary
Computer-implemented iterative multi-scale methods and systems are provided for handling simulation of complex, highly anisotropic, heterogeneous domains. A system and method can be configured to achieve simulation of structures where accurate localization assumptions do not exist. The iterative system and method smoothes the solution field by applying line relaxation in all spatial directions. The smoother is unconditionally stable and leads to sets of tri-diagonal linear systems that can be solved efficiently, such as by the Thomas algorithm. Furthermore, the iterative smoothing procedure, for the improvement of the localization assumptions, does not need to be applied in every time step of the computation.