Hybrid Multiscale Reservoir Simulation Using Super-Resolution Deep Learning for Well-Control Optimization

by Billal Aslam, Haotian Li, Bicheng Yan
Year: 2026 DOI: https://doi.org/10.1007/s11004-026-10333-6

Extra Information

Math Geosci (2026)

Abstract

Robust field development strategies rely on optimizing well placement and dynamic well control using massive high-resolution reservoir simulation evaluations. However, the computational cost of these simulations can be prohibitive. To address this challenge, this study develops an efficient dynamic workflow for well-control optimization by applying a super-resolution deep neural network (SR-DNN) model to alleviate the computational burden of the fine-scale simulation stage. The SR-DNN is trained on paired coarse- and fine-scale reservoir simulations to learn the nonlinear mapping between coarse-scale state variables (e.g., pressure and saturation) and their fine-scale counterparts. The SR-DNN is integrated with an efficient coarse-scale simulator, forming a hybrid forward model that accurately predicts well production rates. Further, differential evolution is employed for dynamic well-control optimization by tuning the water injection rates and production bottom-hole pressures at each control step. The workflow is validated using dynamic well-control optimization for a waterflooding process in a channelized reservoir. The SR-DNN achieves excellent prediction accuracy, with an average root mean square error of 76.1 psi for pressure and 0.046 for saturation across a 10-year prediction time horizon. The structural similarity index measure confirms high fidelity, averaging 0.9899 for pressure and 0.9129 for saturation. The hybrid forward model strongly aligns with fine-scale simulations, yielding relative L2-norm errors of 1.93% and 5.55% for cumulative oil and water production, respectively. The predicted net present value (NPV) obtained using the hybrid model reaches an R2 score of 0.98 relative to the fine-scale simulation model. Compared with direct optimization using the fine-scale model, the proposed method delivers a 16× computational acceleration while maintaining the best-case NPV within 3.78% of the fine-scale result due to the corrective capability of the SR-DNN. Another advantage is the ability to recover high-resolution saturation and pressure fields from coarse-scale simulations, which can support reservoir monitoring and visualization of the remaining oil without incurring additional fine-scale simulation costs. By integrating SR-DNN with a physically consistent coarse-scale simulation, the proposed framework enables scalable, accurate, and dynamic well-control optimization with practical feasibility for real-world field applications.