Integrated framework for constrained optimization of well placement and control in subsurface operations

The use of formal optimization procedures for hydrocarbon production and geological CO2 storage enables the most effective operating strategies to be identified. These optimizations are challenging computationally because they require many expensive function evaluations (which entail a full reservoir simulation) and they often involve complex and multimodal objective functions (due in part to reservoir heterogeneity). An efficient and general optimization framework, with suitable algorithms and constraint treatments, would thus be highly beneficial for these problems. In this dissertation, we first integrate an existing procedure for handling nonlinear geometric constraints into a general optimization framework. This constraint treatment entails a solution-repair procedure that consists of a gradient-based optimization performed prior to flow simulation. The goal of the repair procedure is to reduce constraint violations via projection of the infeasible solutions onto (or toward) feasible space while minimizing the difference between the repaired and original solutions. The repair procedure is implemented with three different core optimization algorithms -- particle swarm optimization (PSO), iterative Latin hypercube sampling (ILHS), and differential evolution (DE). Using extensive numerical experiments involving the placement of multiple deviated wells in 3D models, we demonstrate the necessity of tuning the hyperparameters in the core optimization algorithms when these optimizers are used with the repair procedure. Improvement in the objective function values and satisfaction of the constraints are observed when tuned hyperparameters are used. Results also indicate that the tuned hyperparameters are to some extent transferable between related problems. We then expand the capability of the framework to treat constraints that appear in well control problems. In this case, well placement and control optimizations for geological CO2 storage is considered. We first perform (separate) single-objective optimizations for two different objective functions, the minimization of mobile CO2 fraction and the maximization of storage efficiency, both evaluated at the end of the simulation time frame. Practical linear and nonlinear constraints involving well geometry, injection rates, and injected mass are considered. For both problems, we assess the performance of two core optimization algorithms -- PSO and DE. A multifidelity approach involving three levels of grid resolution, with the finer grids generated by refining the coarse model, is applied to achieve computational efficiency in the optimizations. Compared with results from all-fine-scale optimizations, the optimized solutions from the multifidelity approach display advantages in both solution quality and computational requirements. The framework is then used to perform biobjective optimization, in which both objective functions are considered together, for a realistic field model. The multifidelity approach is again used here, and a set of Pareto-optimal solutions is identified. Finally, a transmissibility upscaling approach based on global, single-phase, pseudo-steady-state solutions is developed for CO2 storage problems. Two different well treatments, near-well local grid refinement (LGR) and well-index upscaling, are used in the upscaled models. For a base-case with four deviated wells, and for a large set of well configurations and controls generated from optimization, we show that the LGR approach provides more accurate bottomhole pressure results than well-index upscaling. Improved coarse-scale results for mobile CO2 fraction and storage efficiency are also achieved when near-well LGR is used. The upscaled models with LGR are then incorporated into the multifidelity optimization framework (in contrast to the grid refinement approach mentioned previously). The objective function in these runs is the minimization of the time-averaged mobile CO2 fraction. The multifidelity approach, which uses upscaled models followed by fine-scale models, again displays advantages over the all-fine-scale optimization in terms of final objective function value and computational demands.

Keywords: Sustainability.
Energy Resources Engineering.
Advisor: Durlofsky Louis
Horne Roland N.
Volkov Oleg