[Paper Review] AI enhanced data assimilation and uncertainty quantification applied to Geological Carbon Storage

Gabriel Serrão Seabra, N. T. Mücke+3 more|arXiv (Cornell University)|Feb 9, 2024

Atmospheric and Environmental Gas DynamicsEnvironmental Science3 citations

TL;DR

This study introduces SH-ESMDA and SH-RML, hybrid data assimilation frameworks that use Fourier Neural Operators (FNOs) and Transformer-UNet (T-UNet) as surrogate models to accelerate Geological Carbon Storage (GCS) simulations by over 50% while preserving high-fidelity physical results. SH-RML improves uncertainty quantification over standard ESMDA by enabling gradient-based optimization via automatic differentiation, demonstrating superior history matching and robustness under limited training data.

ABSTRACT

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 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 CO$_2$ 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 better uncertainty quantification compared to conventional ESMDA for the case study.

Motivation & Objective

• To address the high computational cost of data assimilation in Geological Carbon Storage (GCS) projects using machine learning surrogates.
• To improve uncertainty quantification (UQ) in CO2 injection simulations under limited observational data.
• To develop hybrid data assimilation frameworks that combine physics-based simulators with deep learning models for faster, accurate posterior state estimation.
• To evaluate the performance of FNOs and T-UNet as surrogate models in channelized reservoir simulations with varying data availability.
• To enable scalable, efficient, and reliable UQ for real-world GCS projects through AI-enhanced data assimilation.

Proposed method

• Developed FNO and T-UNet neural networks as surrogate models for CO2 injection simulations in channelized reservoirs, trained on high-fidelity DARTS simulator outputs.
• Proposed Surrogate-based Hybrid ESMDA (SH-ESMDA), which replaces expensive simulator runs in ESMDA with FNO and T-UNet surrogates, reducing computational cost by over 50%.
• Introduced Surrogate-based Hybrid RML (SH-RML), a variational DA method using automatic differentiation from the neural networks to compute gradients for RML optimization, avoiding manual adjoint derivation.
• Integrated high-fidelity DARTS simulations to compute posterior states, ensuring physical consistency despite surrogate-based optimization.
• Validated both frameworks using synthetic CO2 injection case studies with microseismic and pressure data, comparing performance across multiple assimilation steps.
• Employed ensemble-based and variational data assimilation techniques (ESMDA and RML) enhanced by ML surrogates to improve convergence and uncertainty quantification.

Figure 1 : Permeability maps of six models from the dataset.

Experimental results

Research questions

• RQ1 Can FNO and T-UNet models serve as accurate and efficient surrogates for high-fidelity CO2 injection simulations in complex, channelized reservoirs?
• RQ2 How does the use of surrogate models in ESMDA (SH-ESMDA) affect computational efficiency and accuracy in data assimilation for GCS projects?
• RQ3 Does SH-RML, which uses neural network gradients for RML optimization, yield better uncertainty quantification than standard ESMDA in CO2 storage applications?
• RQ4 How do model performance and uncertainty quantification vary under limited training data, particularly for FNO versus T-UNet architectures?
• RQ5 Can the proposed hybrid frameworks be extended to real-world GCS projects and other subsurface applications such as geothermal energy or nuclear waste disposal?

Key findings

• FNOs outperformed T-UNet in surrogate modeling accuracy when training data was limited, demonstrating superior generalization under data scarcity.
• SH-ESMDA reduced computational time by at least 50% compared to standard ESMDA, depending on the number of assimilation steps, without sacrificing accuracy.
• SH-RML achieved better history matching and uncertainty quantification than conventional ESMDA, particularly in capturing posterior state variability and reducing bias.
• The use of automatic differentiation from FNOs enabled efficient gradient computation in RML optimization, eliminating the need for manual adjoint derivation.
• The hybrid frameworks maintained high-fidelity physical results by using the high-resolution DARTS simulator for final posterior state computation, ensuring model reliability.
• The proposed methods show strong potential for scalability to larger, more complex reservoirs and broader applications in subsurface modeling, including geothermal and nuclear waste storage.

Figure 2 : Histogram of permeability (left) and log of permeability (right) for one sample.