Variable fidelity surrogate well control optimization with multilevel wavelet based grids

Abstract

Well control optimization is a complex task that, typically, requires a large number of flow simulations. These simulations are often computationally expensive, which imposes challenges for practical applications. This paper presents a variable fidelity surrogate framework for well control optimization that reduces the computational budget. The method associates a multilevel wavelet based local grid refinement with upscaling procedures to build proxy models in a hierarchical trust-region optimization framework. In the initial stage, lower fidelity samples are used to construct a surrogate model, representing the underlying trends of the objective function and guiding the optimizer in the exploration phase. In the next stages, higher fidelity wavelet based models are used to build new surrogate models, increasing the accuracy. Results are presented for two-dimensional immiscible gas injection and a three-dimensional water injection model. A comparison with the traditional single-level high fidelity surrogate optimization is conducted. Additionally, we verify the reliability of the trust-region update scheme based only on low fidelity samples. We show that the proposed strategy was able of achieving similar or better results than the traditional surrogate optimization, saving about 90% of the computation cost. Also, the low fidelity models were capable to correctly guide the trust-region update scheme.