Robust Optimization under Geological Uncertainty Using a TransUNet-Based Surrogate Model with EnOpt Algorithm

As a crucial step in closed-loop reservoir management, robust optimization is defined as maximizing or minimizing the expected value of a predefined objective function, such as net present value (NPV), across geological uncertainties. The computational cost of performing extensive forward simulations with traditional solvers is often prohibitive. To efficiently and reliably address this issue, we introduce for the first time a TransUNet-based surrogate model, coupled with the ensemble optimization (EnOpt) algorithm for robust optimization. TransUNet is a deep learning network that integrates the self-attention mechanism of the transformer with the encoder-decoder architecture of U-Net, efficiently fusing features at various scales to capture both local and global image information. The trained model can predict time-varying production responses for scenarios with different permeability realizations and well rate sequences. Specifically, the surrogate model takes geological uncertainties and well control sequences as inputs, predicting pressure and saturation distributions, and subsequently deriving production dynamics using Peaceman’s formula. Ultimately, with NPV as the target function, the model is integrated with the EnOpt algorithm to optimize production. The proposed surrogate-based optimization framework has been validated using a water flooding reservoir, specifically a three-dimensional benchmark channelized Egg model. On the test set, our surrogate-based optimization framework achieved root mean square error (RMSE) of less than 0.005 for pressure and saturation predictions, with oil and water production coefficients of determination ( \(R^2\) $R^2$ ) reaching 0.952 and 0.988, respectively. By integrating the model with the EnOpt algorithm, we perform injection rate optimizations that account for geological uncertainty. This approach achieves a 40.2% reduction in the total computational time for the robust optimization task, and improves the NPV by 10.8% compared to the result without optimized well operations. Our results demonstrate that this optimization method based on TransUNet and EnOpt can efficiently and accurately predict the reservoir production and development state, facilitating rapid decision-making and robust optimization in water flooding reservoirs.