A Control Perspective to Adaptive Time Stepping in Reservoir Simulation
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Reservoir modelling is an important tool in the management of hydrocarbon reservoirs. In fact, reservoir models are often a cost effective and time efficient alternative to a trial-and- error field management approach. Reservoir models allow oil companies to simulate various reservoir conditions and management strategies without having to spend considerable amount of money and time. Consequently, it is crucial to find ways to generate fast and accurate reservoir models to assist in making these crucial decisions. Within a reservoir simulator, the time discretization scheme is one of the most sensitive and computer intensive steps of the entire simulator. As a result, it is vital to find an efficient ways to perform this step in order to optimize the performance of the simulator. During the time discretization process, the choice of the time-step is a crucial decision. In fact, the time-step affects the computation time, the convergence, the accuracy and the amount of memory space used by the computer to run the simulation. We have to pick a time-step that is small enough to allow the solution to converge, but also sufficiently large to avoid high computation times. In order to tackle this problem, there are several adaptive time-stepping methods developed to automatically adjust the time-step and make sure that it remains within an optimal range. In this study, we investigate the effectiveness of using the Proportional-Integral-Derivative controller (PID) to regulate the error and the variations in pressure and saturation during the simulation of a reservoir system. We compare the performance of the PID controller with the basic controller conventionally used in adaptive time-stepping. The results show that PID algorithm used to control the variations in pressure and saturation can be more efficient than the basic controller as long as the proper PID coefficients are used in the simulation. We were able to reduce the computation cost with the use of the PID controller while maintaining the same level of accuracy as the basic method. The manual tuning of the controller can be time-consuming and future would have to include automatic tuning algorithms specifically tailored for adaptive time-stepping purposes. Otherwise, the benefit associated with using the PID controller would be dwarfed by the time-consuming manual tuning process. We also tested the PID controller to regulate the error within the Newton-Raphson loop. The results showed that the use of the PID controller inside this loop results in instabilities that cause the reservoir simulator to run inefficiently.
Akakpo, Dany Elom (2016). A Control Perspective to Adaptive Time Stepping in Reservoir Simulation. Master's thesis, Texas A & M University. Available electronically from