Well Placement Optimization under Uncertainty with CMA-ES Using the Neighborhood

In the well placement problem, as well as in many other field development optimization problems, geological uncertainty is a key source of risk affecting the viability of field development projects. Well placement problems under geological uncertainty are formulated as optimization problems in which the objective function is evaluated using a reservoir simulator on a number of possible geological realizations. The existing approaches to cope with geological uncertainty require multiple reservoir simulations (on the possible realizations) to estimate the expected field performance for a given well configuration, which is often very demanding in CPU time and impractical when dealing with real field cases. In this paper, we present a new approach to handle geological uncertainty for the well placement problem with a reduced number of reservoir simulations. The proposed approach uses already simulated well configurations in the neighborhood of each well configuration for the objective function evaluation. We use thus only one single reservoir simulation performed on a randomly chosen realization together with the neighborhood of each well configuration to estimate the objective function instead of using multiple simulations on multiple realizations. This approach is combined with the stochastic optimizer CMA-ES (Covariance Matrix Adaptation- Evolution Strategy)