This study investigates the integration of machine learning (ML) and data assimilation (DA) techniques, focusing on implementing surrogate models for Geological Carbon Storage (GCS) projects while maintaining the high fidelity physical results in posterior states. Initially, we evaluate the surrogate modeling capability of two distinct machine learning models, Fourier Neural Operators (FNOs) and Transformer UNet (T-UNet), in the context of CO₂ injection simulations within channelized reservoirs. We introduce the Surrogate-based hybrid ESMDA (SH-ESMDA), an adaptation of the traditional Ensemble Smoother with Multiple Data Assimilation (ESMDA). This method uses FNOs and T-UNet as surrogate models and has the potential to make the standard ESMDA process at least 50% faster or more, depending on the number of assimilation steps. Additionally, we introduce Surrogate-based Hybrid RML (SH-RML), a variational data assimilation approach that relies on the randomized maximum likelihood (RML) where both the FNO and the T-UNet enable the computation of gradients for the optimization of the objective function, and a high-fidelity model is employed for the computation of the posterior states. Our comparative analyses show that SH-RML offers a better uncertainty quantification when compared to the conventional ESMDA for the case study.

In this comprehensive study, we discuss a novel approach to enhance data assimilation and uncertainty quantification in the field of Geological Carbon Sequestration (GCS). We specifically address the complexities of channelized reservoirs, which pose significant challenges due to non-Gaussian permeability distributions and the intricate non-linear physics of CO2 injection processes. Our innovative method integrates Fourier Neural Operators (FNOs) and Transformer UNet (T-UNet) with advanced data assimilation techniques - the Surrogate-based Hybrid Ensemble Smoother with Multiple Data Assimilation (SH-ESMDA) and the Surrogate-based Hybrid Randomized Maximum Likelihood (SH-RML). These techniques make use of the very efficient computation of gradients that neural networks provide and they not only improves the speed of data processing but also enhances the accuracy of predictions in synthetic data assimilation experiments for GCS applications. A key element of our approach is the use of proxy models alongside high-fidelity simulations, ensuring the consistency and reliability of physical posterior distributions. We utilized Alluvsim for detailed geological modeling and the Delft Advanced Research Terra Simulator (DARTS) for comprehensive fluid flow simulations, providing a comprehensive understanding of reservoir dynamics. A synthetic case study on a channelized reservoir model for CO2 sequestration demonstrates the effectiveness of these methods, with improvements in predicting CO2 plume migration and pressure dynamics within the reservoir. The results of our study show that the integration of FNOs and T-UNet with SH-ESMDA and SH-RML leads to enhanced prediction capabilities, particularly in the challenging context of channelized reservoirs. The SH-ESMDA method proves to be highly efficient in speeding up the data assimilation process without compromising accuracy, while SH-RML demonstrates a more effective history matching compared to standard Ensemble Smoother with Multiple Data Assimilation (ESMDA) techniques, indicating a robust strategy for assimilating complex data. This research not only contributes to the realm of GCS but also presents a novel solution for the integration of artificial intelligence with traditional methodologies that can be applied in various fields where data assimilation and uncertainty quantification are crucial. Our study paves the way for future advancements in this domain, highlighting the potential of AI-driven techniques in enhancing data assimilation and uncertainty quantification for GCS projects.