Active Learning for Well Control Optimization with Surrogate Models

Abstract

Summary Optimization of well controls in waterflooding operations has been established as an effective strategy to increase oil recovery efficiency and to reduce operating costs. Optimization problems, however, entail hundreds of full-scale reservoir simulation runs, which can be computationally expensive and impractical for field-scale applications. Fit-for-purpose surrogate models present more efficient alternatives that can be deployed for faster implementation and to enable real-time applications. In recent years, machine learning (ML)-based surrogate models have gained traction in building efficient proxy models to facilitate reservoir engineering and management workflows. For high-dimensional control variables that are frequently encountered in life cycle optimization, gradient-based local search methods have proven to be the optimization algorithms of choice, especially when adjoint models are available to provide the required gradient information in a computationally efficient manner. The use of local search optimization techniques implies that the surrogate models should be locally accurate and adapted to the optimization path that is traversed during the iterations. The adaptation can be accomplished through active learning, where the training of the surrogate model is performed online (throughout the iterations) and tied to the optimization iterations. This paper presents an active learning framework that is tuned to the local search nature of the optimization problem by updating an initially trained surrogate model based on new samples that are generated during the optimization iterations. Specifically, at each iteration, the full reservoir simulation model is performed to evaluate the true objective function and provide the new simulated data to update the surrogate model, thereby enhancing its local prediction accuracy. As the optimization progresses, older samples that become less relevant to the solution at the current iteration are dropped to preserve the local nature of the surrogate model. Various aspects of designing an active learning-based proxy model for well control optimization are discussed and the framework is applied to waterflooding problems to demonstrate its efficiency and superior performance compared to the traditional offline training approach.