Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestration

Abstract

Geological carbon sequestration (GCS) involves injecting CO2 into subsurface geological formationsfor permanent storage. Numerical simulations could guide decisions in GCS projects by predictingCO 2 migration pathways and the pressure distribution in storage formation. However, these simula-tions are often computationally expensive due to highly coupled physics and large spatial-temporalsimulation domains. Surrogate modelling with data-driven machine learning has become a promis-ing alternative to accelerate physics-based simulations. Among these, the Fourier neural operator(FNO) has been applied to three-dimensional synthetic subsurface models. Despite its good accuracyin simulating CO 2 plume migration, it requires large computational resources in training and alsolacks generalizability. Here, to further improve performance, we have developed a nested Fourier-DeepONet by combining the expressiveness of the FNO with the modularity of a deep operatornetwork (DeepONet). This new framework is twice as efficient as a nested FNO for training and has atleast 80% lower GPU memory requirement due to its flexibility to treat temporal coordinates sepa-rately. These performance improvements are achieved without compromising prediction accuracy.In addition, the generalization and extrapolation ability of nested Fourier-DeepONet beyond thetraining range has been thoroughly evaluated. Nested Fourier-DeepONet outperformed the nestedFNO for extrapolation in time with more than 50% reduced error. It also exhibited good extrapolationaccuracy beyond the training range in terms of reservoir properties, number of wells, and injectionrate.