Abstract
A multilevel optimization procedure, in which optimization is performed over a sequence of upscaled models, is developed for use in combined well placement and control problems. The multilevel framework, which can be incorporated with any type of optimization algorithm, is implemented here with a derivative-free Particle Swarm Optimization – Mesh Adaptive Direct Search (PSO–MADS) hybrid technique. An accurate global transmissibility upscaling procedure is applied to generate the coarse-model parameters required at each grid level. Distinct upscaled models are constructed using this approach for each candidate solution evaluated by the optimization algorithm. We demonstrate that the coarse models are able to capture the basic ranking of the candidate well location and control scenarios, in terms of objective function, relative to the ranking that would be computed using fine-scale simulations. This enables the optimization algorithm to appropriately select and discard candidate solutions. Two- and three-dimensional example cases are presented, one of which involves optimization over multiple geological realizations. The multilevel procedure is shown to provide optimal solutions that are comparable, and in some cases better, than those from the conventional (single-level) approach, but with computational speedups of about an order of magnitude.
