A Control Perspective to Adaptive Time-Stepping in Reservoir Simulation
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Copyright 2017, Society of Petroleum Engineers In this paper, we formulate an adaptive time-stepping strategy in a control system framework for efficient reservoir simulation. Current simulators achieve a trade-off between stability and computational effort by means of heuristically-based time-stepping strategies during the simulation runs of complex reservoirs. This can lead to larger computational time and unrealistic time-steps. To this end, we assess the effectiveness of a PID (proportional-integral-derivative) controller at regulating the time steps used during the time discretization of a simulator. We also evaluate the robustness of a PID controller using various metrics - computing time, total number of time steps, and number of rejected steps - and compare it to adaptive time-stepping techniques currently used in the industry. Feedback control strategies are extensively applied in the upstream and downstream of the oil and gas industry in the sense of controlling fluid flow displacement. In particular, PID controllers are preferred for their ease of implementation and robustness. We test our methodology using a two-phase flow reservoir simulator. The goal is to determine if the use of the PID controller can significantly reduce the computational cost while maintaining the same level of accuracy. The results show that the PID controller can improve the efficiency of the reservoir simulator as long as it is tuned properly. We recorded a lower rise time in the PID time-step response, a lower number of total time-step used for the time discretization and a near identical accuracy in the solution obtained. In most of the scenarios run, the PID controller consistently outperformed the basic controller while achieving the same accuracy in the pressure and saturation solutions. This trend was observed in a wide range of permeability and well locations.
