Multilevel field development optimization under uncertainty using a sequence of upscaled models

Advisors

Louis Durlofsky, primary advisor
Roland N. Horne, advisor
Oleg Volkov, advisor

Abstract

Determining the well locations and settings that maximize reservoir performance is a key issue in reservoir management. Computational optimization procedures are commonly applied for this purpose. In conventional optimization methods, flow simulation is performed over the basic reservoir model. If optimization under uncertainty is considered, multiple geological realizations, which quantify reservoir uncertainty, are typically used. This can result in great computational expense, as commonly used optimization methods may require thousands of function evaluations (each of which entails multiple flow simulations). Efficient surrogate models, which can be used to reduce the computational requirements, would thus be highly beneficial. In this thesis, 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 is applicable for use with any type of optimization algorithm. In this work it is implemented within the context of a 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 proposed by the optimizer at each grid level. 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 value, relative to the ranking that would be computed using fine-scale simulations. This enables the optimization algorithm to appropriately select and discard candidate solutions. The multilevel optimization framework is further extended for use in optimization under geological uncertainty. Toward this goal, we introduce an accelerated multilevel optimization procedure, in which the full PSO-MADS algorithm is used only at the coarsest grid level. At subsequent grid levels, standalone MADS (a local optimization algorithm) is applied. An optimization with sample validation (OSV) procedure is also incorporated into the multilevel method. This approach enables us to optimize over a limited set of geological realizations. The combined use of accelerated multilevel optimization and OSV leads to substantial speedup compared to direct application of the standard multilevel optimization procedure. Optimization results for two- and three-dimensional example cases, which involve both single and multiple geological realizations, are presented. The multilevel procedure for single realizations is shown to provide optimal solutions that are comparable, and in some cases better, than those from the conventional (single-level) approach. Computational speedups of about a factor of five to ten are achieved. For optimization under uncertainty, we use the accelerated multilevel procedure with sample validation to further reduce the computational cost of the optimization. Speedups of a factor of 10--20 are achieved by the accelerated multilevel approach relative to the conventional procedure for examples with ten realizations. An additional speedup factor of about two is observed through incorporation of OSV for cases involving 100 realizations. Our overall findings thus suggest that this framework may be quite useful for practical field development. We also investigate the application of the multilevel Monte Carlo approach for field development optimization under geological uncertainty as an alternative to the multilevel optimization technique. Although this approach provides speedup relative to the conventional (single-level) treatment, it is not as efficient as the multilevel procedure developed in this work.