Reservoir Simulation Velocity Model Stabilization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current reservoir simulators using Sequential Implicit (SI) and Sequential Fully Implicit (SFI) methods can lead to unstable solutions, especially in cases with high capillary pressure and multi-regions, due to overshooting issues.
Innovation Solution
A new velocity model is introduced that employs an estimated end of time step capillary pressure, based on a modification coefficient derived from capillary pressure derivatives, to stabilize the phase velocity calculation, improving the accuracy and stability of the reservoir simulation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional Sequential Implicit (SI) or Sequential Fully Implicit (SFI) methods are used to solve the discrete form of nonlinear partial differential equations, then the reservoir simulation can be performed with standard computational approaches, but the solution becomes unstable and overshoots in cases with high capillary pressure and multi-regions
Solution Approach 1:
The patent changes the parameter used in capillary pressure calculation from explicit saturation to an estimated end-of-time-step saturation. This parameter change stabilizes the solution by using a predicted future state rather than the current state, preventing overshooting in high capillary pressure scenarios while maintaining computational efficiency
Solution Approach 2:
The patent performs preliminary estimation of the end-of-time-step saturation before solving the full system of equations. This preliminary action provides a more accurate basis for capillary pressure calculation, preventing instability and overshooting that would occur with standard explicit saturation approaches
2Productivity
If explicit saturation is used for capillary pressure calculation in traditional velocity models, then the computational process is simpler and faster, but the accuracy deteriorates significantly in high capillary pressure scenarios
Solution Approach 1:
The patent changes the saturation parameter from explicit (current time step) to estimated (end of time step), which improves accuracy in high capillary pressure scenarios while maintaining the computational efficiency of the Sequential Implicit and Sequential Fully Implicit methods through the use of modified pressure equations
Data Source
AI summary
Improved reservoir simulation methods and systems are provided that employ a new velocity model in conjunction with a sequential implicit (SI) formulation or Sequential Fully Implicit (SF) formulation for solving the discrete form of the system of nonlinear partial differential equations. In embodiments, the new velocity model employs a fluid transport equation part based on calculation of phase velocity for a number of fluid phases that involves capillary pressure and a modification coefficient. In embodiments, the modification coefficient can be based on a derivative of capillary pressure with respect to saturation. In another aspect, the new velocity model can employ an estimate of the phase velocity of the water phase vw_est that is based on one or more derivatives of capillary pressure of the water phase as a function of water saturation.