Reservoir Simulation Stabilization via Auxiliary Time-Stepping
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Solution Overview
Problem
Current reservoir simulation methods, such as IMPES, SI, and IMPSAT, face stability issues that lead to numerical instability, especially in complex flow behaviors, resulting in misleading data and increased computational costs with increased implicitness.
Innovation Solution
An auxiliary time-stepping procedure is introduced, where phase component densities are updated linearly, and phase flow rates are recalculated based on saturation changes, allowing for improved stability without significantly increasing computational costs, and the method can be applied using various discretization methods like finite difference or finite element.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If increased implicitness is used to improve stability, then stability improves, but computational costs increase
Solution Approach 1:
The patent changes the parameter of implicitness level in the formulation method. It introduces a stabilized formulation that maintains the stability benefits of higher implicitness methods while reducing computational costs through a modified solution approach that requires fewer iterations and less computational resources per time step.
Solution Approach 2:
The patent implements dynamic switching between different formulation methods (IMPES, SI, IMPSAT, CI) based on stability criteria. This allows the simulation to adaptively adjust the level of implicitness used, employing more computationally intensive methods only when stability requires them, and using simpler methods when they suffice, thereby optimizing the balance between stability and computational cost.
2Productivity
If IMPES method is used, then computational efficiency is high, but numerical instability occurs in complex flow behaviors
Solution Approach 1:
The patent makes the formulation method dynamic by implementing stability criteria that monitor the simulation state and automatically switch between IMPES, SI, IMPSAT, and CI methods. When complex flow behaviors are detected (indicating potential instability), the system transitions to more stable formulations, while maintaining computational efficiency by using simpler methods when conditions permit.
Solution Approach 2:
The patent introduces intermediate formulation methods (SI and IMPSAT) that serve as mediators between the computationally efficient but unstable IMPES and the fully stable but expensive CI. These intermediate methods provide a gradient of options that can be selected based on the specific stability requirements of different simulation scenarios, offering a balance between efficiency and stability.
3Reliability
If fully implicit method is used, then stability is improved, but solution time increases significantly
Solution Approach 1:
The patent implements dynamic method selection that adjusts the level of implicitness based on actual simulation needs rather than using fully implicit methods uniformly. This allows the system to achieve necessary stability only where and when required, avoiding the excessive computational overhead of fully implicit methods in scenarios where simpler approaches suffice.
Solution Approach 2:
The patent modifies the formulation approach by introducing a stabilized version that changes key parameters of the solution process. The stabilized formulation method alters the mathematical structure to improve stability properties while maintaining computational efficiency, effectively decoupling the relationship between full implicitness and stability that characterizes traditional approaches.
4Measurement precision
If stable formulation methods are used, then accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent implements adaptive switching between formulation methods based on stability criteria, allowing the system to use more complex accurate methods only when necessary for maintaining simulation accuracy. This dynamic approach ensures accuracy is improved only in the specific scenarios where it is needed, while avoiding unnecessary computational complexity in other cases.
Data Source
AI summary
A method is presented for modeling reservoir properties. The method includes an auxiliary time-stepping procedure of the reservoir between an old time and a new time, and calculating a plurality of masses explicitly. A plurality of phase component densities is updated linearly from the plurality of masses. A plurality of saturation changes is calculated based on the plurality of masses. A plurality of phase flow rates is updated based on the plurality of saturation changes, a plurality of phase flow rates at the old time, and a plurality of saturation derivatives of the phase flow rates at the old time. A plurality of component flow rates may be calculated based on the updated plurality of phase component densities and the plurality of phase flow rates. The method also includes a formulation method based on the auxiliary time stepping procedure.