Production Optimization in Closed-Loop Reservoir Management

Abstract

Summary In closed-loop reservoir management, one periodically updates reservoir models by integrating production data and then solves an optimal control problem to determine optimum operating conditions to maximize hydrocarbon production or net present value (NPV) for the remaining expected life of the reservoir. The cycle of model updating and production optimization is repeated at specified times. Here, to account for geological uncertainty, we suggest using the ensemble Kalman filter for reservoir model updating and consider three different algorithms for production optimization. Two simple but representative examples indicate that the steepest ascent algorithm is the best of the optimization methods. If the required adjoint software for calculating the gradient of NPV with respect to the controls is not available, we show that iteration using an easily computed stochastic gradient can yield a good estimate of the optimal NPV if properly implemented. For the problem considered, it is shown that NPV is a nonlinear function of the controls, but the final controls from the cases with both known true geology and uncertain geology show "bang-bang" behavior.