Advanced History Matching Workflow by Deep Learning Surrogates with Knowledge-Based Graph Neural Networks

Reservoir simulation is a cornerstone of geoscience, underpinning important applications such as hydrocarbon recovery and carbon dioxide sequestration. Accurate predictions of reservoir behavior under varying geological and operational conditions are essential for optimizing extraction processes, enhancing resource management, and mitigating environmental impacts. Traditional simulation techniques, while effective, rely on computationally intensive numerical methods, making them impractical in simulation intensive optimization applications. Recent advances in machine learning have introduced promising approaches to address this drawback of traditional methods providing the possibility of speeding up reservoir simulations by two or more orders of magnitude when searching in a determined solution space efficiently spanned by a training set of well selected traditional simulations. The first approaches rely on Convolutional Neural Network (Liu et al. [2018]) where the reservoir is treated as a pixelized image. Recently Graph Neural Networks (GNNs) were also used for modeling complex spatio-temporal relationships in dynamic systems (Sasal et al. [2024]), leveraging the inherent graph structure of physical phenomena such as geological reservoirs. By representing geological data as graphs, GNNs can capture important spatial dependencies and adapt to irregular reservoir topologies, enabling accurate modeling of fluid flow and pressure dynamics. Despite their advantages, GNNs primarily rely on data-driven learning, which can result in physically inconsistent predictions, particularly when faced with limited or noisy data. Physics-Informed Machine learning methods (e.g. Karniadakis et al. [2021]), on the other hand, offer a complementary approach by adding the governing physical equations as an additional loss function to be minimized and potentially offering more generality. By integrating physical laws, we enforce consistency with the underlying dynamics of the system, providing enhanced interpretability and robustness that allow us to address the reservoir control optimization problem (Elabid et al. [2024a]).