Surrogate reservoir models have emerged as efficient alternatives to approximate full-physics reservoir simulation while reducing computational costs. Even though existing studies have used synthetic models to test the feasibility of surrogate models, the application to actual reservoirs is limited. To employ the surrogate model in real-life history matching and field development optimization, key geological properties and frequent development operations need to be jointly considered. This study develops a full-scale surrogate reservoir model based on the Koopman neural operator (KNO) for actual three-dimensional (3D) oil reservoirs under waterflood operations. The model integrates static reservoir properties (permeability, net-to-gross ratio, and relative permeability) and dynamic development parameters (well placement and controls) as model inputs. A scientific sampling method that considers geological principles and monthly production operations ensures feasible and diverse training samples. The proposed 3D KNO architecture incorporates a learned grid layer to handle corner-point grids and leverages Fourier transforms to linearize nonlinear dynamics in high-dimensional space. After validating on a real oil field in China, the method demonstrates great capability in predicting pressure and saturation changes and oil production rates. By comparing the prediction performance with a baseline physics informed neural network model, the KNO model greatly outperforms the convolution neural network-based discrete mapping model. The prediction results by the KNO model align well with numerical simulations, which offers a robust and efficient tool for history matching and field development optimization.
Ye et al. (Sun,) studied this question.
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