Optimal control of water flooding reservoir using proper orthogonal decomposition

Abstract

Optimal control of water flooding reservoir is performed to calculate the optimal set of well controls to maximize economic profitability. However, calculating the optimal well controls requires major computational resources, which restricts its implementation in actual reservoir production. In this paper a reduced-order optimal control methodology mainly based on POD (Proper Orthogonal Decomposition) is proposed to optimize the operation of wells in water flooding reservoir. The methodology is decomposed into the ‘offline’ and ‘online’ calculations. The offline calculation consists in determining a reduced set of POD basis from several ‘snapshots’ obtained using reservoir simulator over a pre-determined set of time instants and well control parameters. In the online calculation, knowing the current economic parameters, the optimal well controls are determined only using a nonlinear programming method and POD reconstruction. The methodology is approved on a small scale, two-dimensional, water flooding reservoir model. The results show that the NPV obtained by the reduced-order optimal control methodology is approached to within 99% of the NPV obtained by the adjoint-gradient based methodology, besides, it is quite fast, where the achieved increase in calculation speed is several dozens of times, and its advantage of calculation speed significantly increases as the number of grid blocks increases.