Oscillation Mitigation In Subsurface And Surface Couplings Using PID Controllers

Abstract

Simulation of coupled subsurface (reservoir) and surface (network) systems is a challenging problem and can become a daunting task if one considers computationally intensive multi-reservoir models and realistic surface network facilities. Accurate production forecast is especially important in long-term field development plans. Integration of production systems, including reservoir, wellbore and surface facilities can be done using separate simulators (explicit) or in a seamless fashion by creating a large scale model (fully implicit) that can take into account all of the individual components in a single software. Unlike the implicit formulation, the explicit method is very flexible, allowing the integration of commercial-of-the-shelf simulators. However, as a drawback, it can yield inaccurate and oscillatory solutions. In this work, a new framework for mitigating explicit coupling instabilities (oscillations) is developed by recasting the problem in a control setting. Results from this work allow fast turn arounds in large-scale simulation of coupled surface-subsurface models. Explicit coupling can present error and consequently oscillation that can grow unmanageably throughout the simulation, because the IPR curve and operating point flow rate (q_OP) exchanged at the beginning of a time step between reservoir simulator and coupling program, may not be representative for the entire coupling interval. In order to mitigate the numerical oscillations, a feedback control system, namely a PID (i.e., proportional, integral and derivative) controller is applied. The PID controller, with parameters (K_C,τ_I,τ_D) tuned manually for a group of well settings, adjusts the IPR curves generated by the reservoir simulator so that the error between the bottom-hole pressure calculated by the reservoir simulator (BHP_RS) and the bottom-hole pressure obtained in the operating point (BHP_OP) is minimal. In this case, a corrected value of the operating flow rate (q_OP) is obtained. The new methodology was tested in a synthetic numerical model (UNISIM-I-D) based on Namorado field (Campos Basin-Brazil), which is comprised by 36,739 active cells and 20 satellite wells (7 injectors and 13 producers). The results indicate that the PID control indeed reduce the rate and pressure oscillations as expected by a more theoretical control point of view, and outperforms the base scenario, which represents the network system of producer wells by proper pressure drop tables.