Joint optimization of number of wells, well locations and controls using a gradient-based algorithm - Forouzanfar, Fahim; Reynolds, A.C. (Chemical engineering research & design, 2014)
•Well placement optimization is converted to a continuous optimization problem.•The number of wells, their locations and controls are optimized simultaneously.•The algorithm is based on adjoint gradient and it is very efficient.•The algorithm incorporates a procedure to honor BHP constraints of the wells.•A procedure is devised for the algorithm to escape from a local maximum. This paper presents a detailed algorithm for solving the general well-placement optimization problem in which the number of wells, their locations and rates are simultaneously optimized with an efficient gradient-based algorithm. The proposed well-placement optimization algorithm begins by placing a large number of wells in the reservoir, where, the well rates are the optimization variables. During iterations of the algorithm, most of the wells are eliminated by setting their rates to zero. The remaining wells and their controls determine the optimal number of wells, their optimum locations and rates. The well-placement algorithm consists of two optimization stages. In the initialization stage, the appropriate total reservoir production rate (or the total injection rate) for the set of to-be-optimized producers (or injectors) is estimated by maximizing the net-present-value for the specified operational life of the reservoir. In the second stage, a modified net-present-value functional which also considers the drilling cost of the wells is maximized subject to the a total rate constraint determined in the initialization stage. Both stages of the algorithm use gradient projection to enforce the linear and bound constraints, where the required gradients are computed with the adjoint method. The bottomhole pressure constraints on the wells are enforced using a practical approach. The applicability and robustness of our well-placement algorithm is discussed through several example problems.