Nested FNO is a machine learning framework that offers a general-purpose numerical simulator alternative to provide high-resolution CO ₂ storage predictions in real time.

Carbon capture and storage (CCS) is an essential technology for achieving carbon neutrality. Depositional environments with sandstone and interbedded shale layers are promising for CO${}_2$ storage because they can retain CO${}_2$ beneath continuous and discontinuous shale layers. However, conventional numerical simulation of shale–sandstone systems is computationally challenging due to the large contrast in properties between the shale and sandstone layers and significant impact of thin shale layers on CO${}_2$ migration. Extending recent advancements in Fourier neural operators (FNOs), we propose a new deep learning architecture, the RU-FNO, to predict CO${}_2$ migration in complex shale–sandstone reservoirs under various reservoir conditions, injection designs, and rock properties. The gas saturation plume and pressure buildup predictions of the RU-FNO model are 8000-times faster than traditional numerical models and exhibit remarkable accuracy. We utilize the model’s fast prediction to investigate the impact of shale layer characteristics on plume migration and pressure buildup. These case studies show that shale–sandstone reservoirs with moderate heterogeneity and spatial continuity can minimize the plume footprint and maximize storage efficiency.

Numerical simulation is an essential tool for understanding subsurface flow in porous media problems, yet often suffers from computational challenges due to the highly non-linear governing equations, multi-physics problem nature, and need for high spatial resolutions to capture multi-scale heterogeneity. The inherent parameter uncertainties in the subsurface porous media

Quantification of uncertainty in production/injection forecasting is an important aspect of reservoir simulation studies. Conventional approaches include intrusive Galerkin-based methods (e.g., generalized polynomial chaos (gPC) and stochastic collocation (SC) methods) and non-intrusive Monte Carlo (MC) based methods. Nevertheless, the quantification is conducted in reformulations of the underlying stochastic PDEs with fixed well controls. If one wants to take various well control plans into account, expensive computations need to be repeated for each well design independently. In this project, we take advantages of the equation-free spirit of convolutional neural network (CNN) to overcome this challenge and thus achieve the flexibility of efficient uncertainty quantification with various well controls. We are interested in the development of surrogate models for uncertainty quantification and propagation in reservoir simulations using a deep convolutional encoder-decoder network as an analogue to the image-to-image regression tasks in computer science. First, a U-Net architecture is applied to replace conventional expensive deterministic PDE solver. Then we adopt the idea from shape-guided image generation using variational U-Net and design a new variational U-Net architecture for "control-guided" reservoir simulation. Backward propagation is learned in the network to extract the hidden physical quantities and then predict the future production by the learned forward propagation using the hidden variable with various well controls. Comparisons in computational efficiency are made between our proposed CNN approach and conventional MC approach. Significant improvements in computational speed with reasonable accuracy loss are observed in the numerical tests.