Summary In this paper, we present both simultaneous and sequential algorithms for the joint optimization of well trajectories and their life-cycle controls. The trajectory of a well is parameterized in terms of six variables that define a straight line in three dimensions. In the simultaneous joint optimization algorithm, the set of controls of a well throughout the life cycle of the reservoir is constructed as a linear combination of the left singular vectors that correspond to the largest singular values of a specified temporal covariance matrix. This covariance matrix is used to impose a temporal correlation on the controls at each well. In this approach, well controls are parameterized in terms of a few optimization parameters to reduce the dimension of the joint optimization problem. Moreover, the imposed smoothness on the well controls will result in temporally smooth well controls. We use an implementation of the covariance matrix adaptation–evolution strategy (CMA-ES) optimization algorithm to solve the defined optimization problem. In the sequential optimization algorithm, first, the trajectories of the wells are optimized with the CMA-ES optimization algorithm whereas the controls of the wells are prespecified. After the optimum trajectories of the wells are obtained, the life-cycle production optimization step is performed to find the optimal well controls for the specified well trajectories. For the production optimization step, we compare the performance of three optimization algorithms that are the standard ensemble-based optimization algorithm (EnOpt), the standard CMA-ES algorithm, and a variant of the CMA-ES algorithm in which we set the initial covariance matrix equal to a prespecified covariance that imposes a temporal correlation on the controls of each well. The performance of the proposed algorithms is tested for the joint optimization of well trajectories and controls of injectors and producers for the PUNQ reservoir model. The proposed simultaneous well placement/well control optimization algorithm obtained better results than did the sequential optimization framework. The CMA-ES algorithm performed well for both well placement and production optimization purposes. Moreover, the CMA algorithm with a prespecified covariance that imposes a temporal correlation on the well controls obtained a higher net present value compared with EnOpt for the life-cycle production optimization step of the sequential framework.

In this paper, we present both simultaneous and sequential algorithms for the joint optimization of well trajectories and their lifecycle controls. The trajectory of a well is parameterized in terms of six variables which define a straight line in 3D. In the simultaneous joint optimization algorithm, the set of controls of a well throughout the life-cycle of the reservoir is parameterized in terms of the singular vectors corresponding to the largest singular values of a pre-specified temporal covariance matrix which imposes a temporal correlation on the controls at each well. In this approach, well controls are parameterized in terms of a few optimization parameters which significantly reduces the dimension of the joint optimization problem. Moreover, the imposed smoothness on the well controls will result in temporally smooth well controls. We use an implementation of the Covariance Matrix Adaptation -Evolution Strategy (CMA-ES) optimization algorithm to solve the defined optimization problem. In the sequential optimization algorithm, first the trajectories of the wells are optimized using CMA-ES optimization algorithm while the controls of the wells are pre-specified. Once the optimum trajectories of the wells are obtained, the life cycle production optimization step is performed in order to find the optimal well controls for the specified well trajectories. For the production optimization step, we compare the performance of three production optimization algorithms which are: the standard EnOpt algorithm, the standard CMA-ES algorithm for production optimization and, a variant of the CMA-ES algorithm for production optimization in which we set the initial covariance matrix equal to a pre-specified covariance which imposes a temporal correlation on the controls of each well. The performance of the proposed algorithms is tested for the joint optimization of well trajectories and controls of injectors and producers for the PUNQ reservoir model. The proposed simultaneous well placement-well control optimization algorithm obtained slightly better results than the sequential optimization framework. CMA-ES algorithm showed good performance for both well placement and production optimization purposes. Moreover, the CMA algorithm with a pre-specified covariance that imposes a temporal correlation on the well controls showed a superior performance compared to EnOpt for the life cycle production optimization step of the sequential framework. General well placement optimization problemWell placement optimization is the key element in the decision making process for preparing the optimal development plan for a reservoir. To solve a "general well placement optimization" problem, the number of wells, their trajectory and controls should be optimized in order to maximize a prescribed objective function, which is typically the net present value (NPV) of the hydrocarbon production from the reservoir. However, very few papers have addressed this general problem as it is too computationally expensive. Yeten et al. (2002) proposed ...