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An Adaptive Newton's Method for Implicit Dynamic Local Grid Refinement for Simulation of IOR/EOR Processes
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, IOR 2019 – 20th European Symposium on Improved Oil Recovery, Apr 2019, Volume 2019, p.1 - 18
Abstract
Dynamic Local Grid Refinement (DLGR) is a well-known computational method to improve the performance of reservoir simulations by dynamically adapting the grid resolution to local physical phenomena at each location in time. This enables reservoir simulators to achieve similar accuracy with only a fraction of the number of grid cells that it would otherwise utilize. This is particularly useful for IOR/EOR processes due to the small scale and complexity of the physical and chemical processes involved.
A challenge in using DLGR is the adaptation of the local grid resolution in advance of dynamic changes in physical phenomena, such as moving thermal or oil displacement fronts. Failure to intercept such changes up front by a locally high resolution grid will lead to loss of numerical accuracy. A Repeat Time Step (RTS) method that iteratively repeats time steps to implicitly evaluate the grid adaptation criteria at the next time node was previously proposed. However, the results in this paper show that using the RTS method for DLGR leads on average to considerably higher computational time spent in the linear solver. As a result, it was found that it is more efficient in most cases to tighten the tolerances for the grid adaptation criteria in order to create a buffer zone of fine grid cells in regions that require high grid resolution instead of using the RTS method.
This report proposes an iDLGR-ANM method in which an Adaptive Newton's Method (ANM) is used to further reduce computational overhead spent in repeat time steps performed by DLGR. The ANM leads to reduced simulation times by only considering unconverged and adjacent grid cells in each NR iteration. Furthermore, the added benefit of ANM to the RTS method is that ANM can immediately be restricted to refined grid cells and adjacent cells from the first NR iteration in the repeat time steps rather than solving the full system of linearized equations. In order to compare the performance of the RTS method with and without the ANM, eight examples are considered involving various IOR/EOR applications and numerical schemes. Results show that iDLGR-ANM is nearly as fast in terms of CPU time spent in the linear solver as DLGR without using the RTS method. Moreover, if a post-Newton material balance smoothing technique is applied, iDLGR-ANM results in production forecasts with the same accuracy as DLGR when the RTS method is used without ANM, with differences within machine accuracy.