Adaptive Formulation for Reservoir Simulation Convergence
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Reservoir simulation methods, such as Newton's Method, face inefficiencies due to the need to solve all equations at each iteration, even after some cells have converged, leading to excessive computational resources and time requirements, especially in large and highly nonlinear systems.
Innovation Solution
The method involves dynamically assigning cells to either explicit or implicit formulations based on stability criteria, constructing a reduced nonlinear system with unconverged cells for implicit solution and others for explicit solution, until all cells satisfy convergence and stability criteria.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Newton's Method is used to solve all equations at each iteration, then convergence is achieved, but computational time and resources are excessively consumed
Solution Approach 1:
The patent segments the reservoir grid into multiple regions based on convergence status. Cells are classified as converged or unconverged, and only unconverged cells are included in the implicit formulation system to be solved at each iteration. This segmentation allows the solver to focus computational effort only where needed, rather than solving the entire system of equations repeatedly.
Solution Approach 2:
The patent implements a dynamic formulation selection mechanism where the formulation type (implicit or explicit) is determined based on the convergence status of each cell. The system dynamically adapts during the simulation process, switching between implicit and explicit formulations for different cells depending on whether they have converged, thereby optimizing computational efficiency while maintaining convergence reliability.
2Stability of the object's composition
If all cells are solved using implicit formulation, then numerical stability is maintained, but computational complexity and resource requirements increase
Solution Approach 1:
The patent applies different formulation qualities to different parts of the computational domain. Converged cells use explicit formulation (simpler, less computationally intensive), while unconverged cells use implicit formulation (more stable but computationally heavier). This local differentiation allows the system to maintain numerical stability where needed while reducing overall computational complexity.
Solution Approach 2:
The patent changes the formulation parameter (implicit vs. explicit) based on the convergence status of each cell. This parameter change is driven by the convergence criterion, allowing the system to adapt the computational approach dynamically. Cells that have converged change from implicit to explicit formulation, reducing computational complexity while maintaining stability where necessary.
3Productivity
If reduced system is constructed with only unconverged cells, then computational efficiency is improved, but formulation selection complexity increases
Solution Approach 1:
The patent implements a dynamic formulation selection process where the formulation type for each cell is determined at each iteration based on convergence status. The system automatically updates which cells are included in the implicit system and which use explicit formulation, creating a dynamic adaptation mechanism that improves computational efficiency while managing selection complexity through automated criteria.
Solution Approach 2:
The patent uses feedback from the convergence criterion to guide formulation selection. The convergence status of each cell feeds back into the formulation selection process, determining whether implicit or explicit formulation should be used. This feedback mechanism automates the complex selection process, improving computational efficiency by systematically identifying which cells require implicit treatment based on their convergence behavior.
Data Source
AI summary
A method for performing a simulation of a subsurface hydrocarbon reservoir is disclosed. Each cell in a reservoir model has an equation set representing a reservoir property. A stability limit is determined for each cell. Each cell is assigned to an explicit or implicit formulation. A solution to the system of equations is solved for using an initial guess and an explicit or implicit formulation. A stability limit is calculated for the converged cells. When the number of unconverged cells is greater than a predetermined amount, a reduced nonlinear system is constructed with a list of unconverged cells. The reduced nonlinear system is solved with the implicit formulation, and other cells are solved with the explicit formulation. Parts of the method are repeated until all equation sets satisfy a convergence criterion and a stability criterion, and the solved solution is output.