Redick, Brian Samuel (2017-08). PID Controlled Adaptive Time-Stepping in Coupled Surface-Subsurface Simulation: A Tool for Reducing Non-Physical Oscillation. Master's Thesis.
Surface-subsurface coupling in simulation is required to model large, complex and often offshore projects. The most optimal form of coupling is the partially implicit method. The partially implicit method typically balances accuracy and computational costs. However, the partially implicit method can suffer from non-physical oscillations. Nonphysical oscillations are a result of incorrect assumptions made during coupled simulation. Non-physical oscillations are solely artifacts of less than ideal coupled simulation- they do not have physical significance. As such, non-physical oscillations in coupling are treated as simulation complications, as opposed to reservoir or network dynamics. Although many coupling solutions exist, many are complex and difficult to implement in commercial software packages. In this study, we investigate the use of PID control to select time-steps in coupled surface-subsurface simulation. PID control is not often used in oil and gas applications, however it is well established in other engineering fields. The PID controller performs automatic, adaptive time-stepping in the coupled simulation. The controller operated by reducing oscillations in coupling error. The results show that the PID controlled time-stepping reduces non-physical oscillations, the total number of time-steps executed, and the computational cost of coupled simulation. Importantly, one PID controlled experiment decreased simulation time by 300%, with less than 0.5% error (in cumulative production) as compared to Schlumberger's standard coupling settings. We performed a set of manual tuning experiments that highlight opportunity for controller optimization, as well as motivate future work. The PID controlled coupled simulation we created can be implemented in any software where the user can select the time-steps.