  In the well placement problem, as well as in 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. 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 to
estimate the objective function instead of using multiple simulations on
multiple realizations. This approach is combined with the stochastic optimizer
CMA-ES. The proposed approach is shown on the benchmark reservoir case PUNQ-S3
to be able to capture the geological uncertainty using a smaller number of
reservoir simulations. This approach is compared to the reference approach
using all the possible realizations for each well configuration, and shown to
be able to reduce significantly the number of reservoir simulations (around
80%).
