Production optimization using derivative free methods applied to Brugge field case

Recently production optimization has achieved increasing attention in upstream petroleum industry. Here, we evaluate derivative free optimization methods for determination of the optimal production strategy using a numerical reservoir model which was prepared for a comparative study at the SPE Applied Technology Workshop in Brugge, June 2008. The pattern search Hooke–Jeeves, the reflection simplex Nelder–Mead, a new line-search derivative-free and a generalized pattern search methods are applied to the optimization problem. The line-search derivative-free algorithm is developed based on the existing line-search derivative free algorithms in combination with the Hooke–Jeeves pattern search method. The derivative free optimization results are compared with a gradient based sequential quadratic programming algorithm, but we clearly identify some issues limiting the performance of gradient based algorithms. In real applications our optimization problem is facing very costly function evaluations and at the same time one might have limitations in the computational budget. Therefore we are interested in methods that can improve the objective function with few function evaluations. The line-search derivative-free method performs more efficient and better than the other optimization methods. Ranking among the other four methods is somewhat more difficult, except that the Nelder–Mead method clearly has the slowest performance among these methods. We also observed that optimization with sequential quadratic programming had a high risk of getting trapped in a local optimum, which could be explained by properties of the objective function.