Multilevel Field Development Optimization Under Uncertainty Using a Sequence of Upscaled Models

The robust optimization of reservoir performance under geological uncertainty typically requires the simulation of multiple geological realizations at each iteration of the optimization run. This results in high computational expense, particularly when simulation models are highly resolved and many realizations are employed to characterize geological uncertainty. In recent work we introduced a multilevel optimization procedure that uses a sequence of upscaled models to accelerate field development optimization. The core optimizer is a particle swarm optimization–mesh adaptive direct search (PSO–MADS) hybrid technique. Coarse-scale models are constructed from the fine-grid geological characterization using an accurate global transmissibility upscaling procedure. In this paper we extend the multilevel framework to enable efficient optimization under uncertainty. New treatments include the use of a sample validation procedure for realization selection and the use of the standalone MADS optimizer (rather than PSO–MADS) after the first optimization stage. Numerical results are presented for two example systems, and for each case optimization over both ten and 100 realizations is performed. For ten-realization cases we achieve comparable results, and speedups of a factor of 10 or more, relative to the conventional single-level optimization procedure. Speedups are estimated to be even more substantial for 100 realization cases, for which conventional optimization is not practical. We also investigate the application of a multilevel Monte Carlo approach as an alternative to our proposed techniques for optimization under uncertainty. Although this method is faster than the conventional approach, it is not as efficient as the multilevel procedures developed in this work.