From simulator to surrogate: GANs for spatiotemporal modeling of subsurface flow in porous media

Deep learning-based surrogate models provide a powerful alternative to traditional numerical simulations for addressing subsurface multiphase flow challenges, such as those encountered in Geological Carbon Storage (GCS). In this work, we utilized Generative Adversarial Networks (GANs) to model the evolution of CO₂ saturation and pressure buildup. GANs, with their generator-discriminator framework, excel at capturing intricate spatial and temporal patterns, enabling accurate predictions of CO₂ plume saturation and pressure buildup in saline aquifers. By leveraging adversarial training, GANs effectively model structured data, preserving spatial relationships and generating high-resolution outputs. In this study, we have first developed physics-based numerical simulation models to represent both the injection and post-injection phases of GCS. Using Latin-Hypercube sampling, we created a diverse set of reservoir and decision parameters, forming a comprehensive simulation database. The GANs were trained and evaluated on two different cases, including a single well in a 2D model and multiple wells in five spot patterns to assess the GANs performance. During training, we employed Mean Squared Error (MSE) and spatial derivative-based loss functions to optimize the model hyperparameters. The GANs demonstrated strong performance, achieved R² values of 0.989 and 0.996 for saturation and pressure buildup predictions, respectively. The Normalized Absolute Relative Error (NARE) remained consistently around 1% across all predictions, highlighting the model’s accuracy in capturing the temporal and spatial evolution of CO₂ saturation. Additionally, the GANs demonstrated remarkable computational efficiency, with prediction times of just 0.01 s per case, compared to 1000 s for the 2D model using physics-based simulations. These results underscore the potential of GANs to deliver highly accurate predictions while significantly reducing computational costs.