Oscillation Mitigation in Subsurface and Surface Couplings Using PID Controllers

Simulation coupling subsurface (reservoir) and surface (network) systems is a challenging problem, especially for computationally intensive multi-reservoir models and complex surface network facilities. Integration of petroleum systems can be done using different simulators (explicit coupling) or considering all individual components of the system in one simulator (implicit coupling). The explicit method is more flexible, allowing the integration of commercial-off-the-shelf simulators. However, as a drawback, it can yield oscillatory solutions. In this work, a new framework for mitigating explicit coupling numerical instabilities (oscillations) is developed by recasting the problem in a control setting. Results from this work show that explicit coupling without a mechanism to avoid numerical instabilities presents oscillations that can grow throughout the simulation. In order to mitigate the numerical oscillations we develop a framework based on a feedback control system, namely a PID (Proportional, Integral and Derivative) controller. The PID controller, with parameters (KC,τI,τD) tuned manually for a group of well settings, adjusts the traditional IPR curve generated by the reservoir simulator so that the error between the bottom-hole pressure calculated by the reservoir simulator (BHPRS) and the bottom-hole pressure defined in the operating point (BHPOP) is minimal. In this case, a qOP value representative for the entire time step (next time step) is obtained. The new methodology was tested in a synthetic numerical model (UNISIM-I-D) based on Namorado field (Campos Basin – Brazil), comprised by 20 satellite wells (7 injectors and 13 producers). The PID control reduces the rate and pressure oscillations in the case study, and results converge with base case scenario, which represents the network system of producer wells by proper pressure drop tables.