Well Control Optimization using Derivative-Free Algorithms and a Multiscale Approach

Smart well technologies, which allow remote control of well and production processes, make the problem of determining optimal control strategies a timely endeavour. In this paper, we use numerical optimization algorithms and a multiscale approach in order to find an optimal well management strategy over the life of the reservoir. Optimality is measured in terms of the values of the net present value objective function. The large number of well rates for each control step make the optimization problem more difficult and at a high risk of achieving a suboptimal solution. Moreover, the optimal number of adjustments is not known a priori. Adjusting well controls too frequently will increase unnecessary well management and operation cost, and an excessively low number of control adjustments may not be enough to obtain a good yield. We investigate three derivative-free optimization algorithms, chosen for their robust and parallel nature, to determine optimal well control strategies. The algorithms chosen include generalized pattern search (GPS), particle swarm optimizaX. WANG Department of Petroleum Engineering, China University of Petroleum (Huadong), Qingdao, Shandong, China Department of Mathematics & Statistics, Memorial University, St. John’s, NL, Canada Tel.: +86.132.8085.6026 E-mail: [email protected] R.D. Haynes Department of Mathematics & Statistics, Memorial University, St. John’s, NL, Canada Tel.: +1.709.864.8825 Fax: +1.709.864.3010 E-mail: [email protected] Q. Feng Department of Petroleum Engineering, China University of Petroleum (Huadong), Qingdao, Shandong, China E-mail: [email protected] tion (PSO) and covariance matrix adaptation evolution strategy (CMA-ES). These three algorithms encompass the breadth of available black–box optimization strategies: deterministic local search, stochastic global search and stochastic local search. In addition, we hybridize the three derivative-free algorithms with a multiscale regularization approach. Starting with a reasonably small number of control steps, the control intervals are subsequently refined during the optimization. Results for experiments studied indicate that CMA-ES performs best among the three algorithms in solving both small and large scale problems. When hybridized with a multiscale regularization approach, the ability to find the optimal solution is further enhanced, with the performance of GPS improving the most. Topics affecting the performance of the multiscale approach are discussed in this paper, including the effect of control frequency on the well control problem. The parameter settings for GPS, PSO, and CMA-ES, within the multiscale approach are considered.