Production Optimization in Closed-Loop Reservoir Management

Abstract

Abstract In closed-loop reservoir management, one periodically updates the reservoir model(s) 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 updating and 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. A simple but representative example, indicates that the steepest ascent algorithm is the best of those tried, but if the required adjoint software for calculating the gradient of NPV with respect to the controls is not available, we show that if properly implemented, iteration using an easily computed stochastic gradient can yield a good estimate of the optimal NPV. For the problem considered, it is shown that NPV is a nonlinear function of the controls, but the final controls from cases with both known true geology and uncertain geology present "Bang-Bang" behavior. Introduction In recent years, the concept of "closed-loop" management has attracted intensive research interest1,2,3,4. This approach enables one to adjust the reservoir production control parameters to optimize the reservoir production performance with geological uncertainty, while assimilating dynamic production data in real-time. There are two optimization steps in the approach: the first step is the dynamic data assimilation (history matching) and the second step is to optimize the reservoir performance by adjusting the well controls based on the history-matched reservoir models. Studies in the literature have been focusing on one of the steps and only a few researchers investigated the conjunction of the two5,6. For data integration problems of interest in reservoir modeling and characterization, Bayesian statistics provides a convenient framework for characterizing and evaluating uncertainty. The method introduced into reservoir characterization by Oliver et al.7 and also considered briefly by Kitanidis8, which is now most commonly referred to as Randomized Maximum Likelihood (RML) method, has frequently been used to generate an approximate sampling of pdf for a reservoir model conditional to production and/or seismic data9,10,11. However, this method often takes the computational equivalent of 50 to 100 reservoir simulation runs to generate a single plausible reservoir model (realization or ensemble) and its implementation requires efficient adjoint code. The implementation of the adjoint method is not a trivial task and it appears that an optimal implementation of the adjoint can only be done with detailed knowledge of the reservoir simulator. In contrast, the ensemble Kalman filter (EnKF) method requires only one reservoir simulation run per ensemble member. EnKF was proposed by Evensen12 in the context of ocean dynamics literature as a Monte Carlo approximation of the Kalman filter. Since its introduction into the petroleum engineering literature13,14, it has been used by many researchers for assimilating production and seismic data to update reservoir variables including gridblock rock properties15,16, boundaries between facies17 and initial fluid contacts18.