[Paper Review] Real-time high-resolution CO$_2$ geological storage prediction using nested Fourier neural operators

Gege Wen, Zongyi Li+4 more|arXiv (Cornell University)|Oct 31, 2022

Reservoir Engineering and Simulation Methods18 citations

TL;DR

This paper introduces Nested Fourier Neural Operator (Nested FNO), a machine learning framework that accelerates high-resolution 3D CO2 geological storage simulations by up to 700,000× compared to traditional numerical methods. By learning the solution operator for PDEs governing multiphase flow across hierarchical resolution levels, Nested FNO enables real-time, generalizable predictions of pressure buildup and CO2 plume migration under diverse reservoir conditions and injection schemes.

ABSTRACT

Carbon capture and storage (CCS) plays an essential role in global decarbonization. Scaling up CCS deployment requires accurate and high-resolution modeling of the storage reservoir pressure buildup and the gaseous plume migration. However, such modeling is very challenging at scale due to the high computational costs of existing numerical methods. This challenge leads to significant uncertainties in evaluating storage opportunities, which can delay the pace of large-scale CCS deployment. We introduce Nested Fourier Neural Operator (FNO), a machine-learning framework for high-resolution dynamic 3D CO2 storage modeling at a basin scale. Nested FNO produces forecasts at different refinement levels using a hierarchy of FNOs and speeds up flow prediction nearly 700,000 times compared to existing methods. By learning the solution operator for the family of governing partial differential equations, Nested FNO creates a general-purpose numerical simulator alternative for CO2 storage with diverse reservoir conditions, geological heterogeneity, and injection schemes. Our framework enables unprecedented real-time modeling and probabilistic simulations that can support the scale-up of global CCS deployment.

Motivation & Objective

• Address the critical bottleneck in carbon capture and storage (CCS) deployment caused by high computational costs of high-fidelity reservoir simulations.
• Overcome the limitations of conventional numerical simulators that are too slow for probabilistic, repetitive, or real-time applications in site selection and optimization.
• Develop a machine learning framework that generalizes across diverse geological heterogeneities, reservoir conditions, and injection strategies without retraining.
• Enable real-time, high-resolution dynamic simulations of CO2 storage at basin scale, including both near-well pressure buildup and far-field plume migration.
• Provide a scalable, general-purpose alternative to numerical simulators for large-scale CCS project evaluation and decision-making.

Proposed method

• Propose a hierarchical machine learning framework using multiple Fourier Neural Operators (FNOs) at different resolution levels, forming a nested architecture.
• Train each FNO to learn the solution operator of the governing multiphase flow PDEs (based on Darcy’s law with immiscible and soluble CO2-water flow) at a specific resolution level.
• Use coarse-to-fine information flow: lower-resolution FNO outputs (e.g., pressure) are fed as inputs to higher-resolution FNOs (e.g., gas saturation), enabling multi-scale modeling.
• Leverage the Fourier transform in FNOs to efficiently capture long-range spatial dependencies and learn the solution operator across diverse input conditions.
• Train the entire nested system end-to-end on high-fidelity simulation data from multiple reservoir configurations, ensuring generalization across geological and operational variations.
• Use local grid refinement (LGR) data from numerical simulations as training data to preserve accuracy at fine scales near injection wells and coarse scales for far-field pressure propagation.

Experimental results

Research questions

• RQ1 Can a deep learning framework achieve real-time, high-resolution 3D CO2 storage simulations across diverse geological and operational conditions?
• RQ2 How can a neural operator be structured to handle multi-scale reservoir responses—both near-well pressure buildup and basin-scale plume migration—simultaneously?
• RQ3 To what extent can a hierarchical FNO architecture improve computational efficiency while maintaining accuracy compared to standard numerical simulators?
• RQ4 Can a single trained model generalize across varying reservoir permeability, injection rates, and well configurations without retraining?
• RQ5 Can such a model enable probabilistic simulations and rapid decision support for CCS site selection and optimization?

Key findings

• Nested FNO achieves a speedup of nearly 700,000× over conventional numerical simulators for high-resolution 3D CO2 storage simulations.
• The framework accurately predicts both near-well pressure buildup and far-field plume migration at resolutions as fine as 1–2 meters.
• The model generalizes across diverse geological heterogeneities, injection schemes, and reservoir conditions without requiring retraining.
• By learning the solution operator of the PDE family, Nested FNO enables real-time simulation and probabilistic analysis essential for large-scale CCS deployment.
• The hierarchical design ensures that coarse-scale outputs (e.g., pressure) inform fine-scale predictions (e.g., saturation), improving physical consistency and accuracy.
• The method maintains high fidelity even in complex, multi-physics scenarios involving immiscible and soluble CO2-water flow, as validated against high-resolution numerical simulations.