Adaptive Newton Reservoir Simulation Convergence
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Solution Overview
Problem
Reservoir simulation methods like Newton's Method require solving all equations at each iteration, even after some cells have converged, leading to excessive computational time and resources due to the 'weakest link' phenomenon, where uniform convergence is not achieved across the entire grid.
Innovation Solution
Adaptive iterative methods that focus only on unconverged cells and their neighbors, adjusting the size of the system of equations at each iteration based on convergence criteria, reducing the number of cells needed to be solved and thus minimizing computational resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Newton's Method is used to solve all equations at each iteration, then the solution converges to the true solution, but the computational time and resources are excessive due to solving already-converged cells
Solution Approach 1:
The patent segments the computational domain into active cells and inactive cells based on convergence status. Only active cells (those not yet converged) are included in the system of equations at each iteration, while inactive cells are excluded. This segmentation allows the solver to focus computational resources only on regions requiring further iteration, significantly reducing computational time while maintaining solution accuracy for the entire reservoir.
Solution Approach 2:
The patent applies partial action by solving only a subset of the total equations at each iteration - specifically, only those equations corresponding to active cells that have not yet converged. This partial approach avoids the excessive computation of re-solving already-converged cells, while still achieving complete convergence across the entire system through iterative refinement of the active cell set.
2Stability of the object's composition
If all cells are included in the system of equations at each iteration, then uniform convergence is achieved, but the device complexity and computational resources increase
Solution Approach 1:
The patent implements a dynamic cell activation strategy where the set of active cells changes at each iteration based on convergence criteria. Cells are dynamically transitioned from active to inactive status as they converge, and the system of equations is dynamically reconstructed to include only currently active cells. This dynamic approach adapts the computational system to the current state of convergence, reducing complexity while maintaining stability.
Solution Approach 2:
The patent applies local quality by allowing different cells to have different convergence statuses and computational treatment. Rather than uniformly processing all cells, the method identifies and treats active cells (requiring further solution) differently from inactive cells (already converged). This localized approach optimizes the system by applying computational effort only where needed, reducing overall system complexity while maintaining convergence uniformity.
3Productivity
If the number of cells to be solved is reduced to only unconverged cells, then computational resources are minimized, but the convergence criterion may not be satisfied across the entire grid
Solution Approach 1:
The patent applies preliminary action by identifying and marking converged cells at each iteration before reconstructing the system of equations. The convergence criterion is checked preliminarily for all cells, and those satisfying the criterion are preemptively excluded from the next iteration's active set. This preliminary identification ensures that the reduced system of active cells will converge reliably while maintaining high computational efficiency throughout the simulation.
Data Source
AI summary
A method of performing a simulation of a subsurface hydrocarbon reservoir. The reservoir is approximated by a reservoir model having a plurality of cells. Each cell has an equation set representing a reservoir property. An initial guess is provided to a solution for a system of equations formed using the equation set for each of the cells. An iterative root-finding method and the initial guess are used to solve for a solution to the system of equations. When the number of non-converged cells is greater than a predetermined amount, neighboring converged cells are added to the non-converged cells. Parts of the method are repeated, substituting the solved solution for the initial guess and the equation sets corresponding to the non-converged cells for the first system of equations, until substantially all equation sets satisfy the convergence criterion. The solved solution is outputted as a simulation of the subsurface reservoir.