Source-linked AI summary
Real-time high-resolution CO$_2$ geological storage prediction using nested Fourier neural operators
Gege Wen, Zongyi Li, Qirui Long, Kamyar Azizzadenesheli, Anima Anandkumar, Sally M. Benson
TL;DR
CO2 storage deployment needs accurate high-resolution forecasts, but multiphase, multi-physics, and multi-scale numerical simulations are costly. The paper introduces Nested FNO, a hierarchy of Fourier neural operators integrated with local grid refinement to model dynamic 3D storage responses across resolution levels. It reports inference 700,000 times faster than a state-of-the-art numerical solver, supporting real-time probabilistic assessments and other repetitive CCS analyses.
Problem
High-resolution 3D CO2 storage modeling must represent multiphase, multi-physics, and multi-scale responses, while existing numerical simulations are computationally expensive.
Method
Nested FNO combines a hierarchy of FNO models with semi-adaptive local grid refinement to predict 3D pressure buildup and gas saturation across multiple resolutions.
Results
700,000 times faster inference than the state-of-the-art numerical solver enables real-time forecasts and probabilistic assessments of pressure buildup and CO2 plume footprints.
Takeaways & Limitations
Nested FNO can support repetitive CCS tasks including probabilistic assessment, site selection, storage optimization, and seismic inversion.
Takeaways & Limitations
The evaluated dataset covers CO2 injection into 3D saline reservoirs over 30 years with specified reservoir, injection, and permeability variables.
Abstract
from arXiv · showhide
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.
Introduction
CCS storage forecasting requires high-resolution 3D multiphase simulations across large spatial and temporal scales, but conventional numerical methods are computationally expensive. Nested FNO addresses this challenge with a hierarchy of FNOs that models basin-scale CO2 storage at multiple resolutions and enables substantially faster predictions.
- Motivation: High-resolution CO2 storage forecasts must capture fine-scale plume migration, near-well pressure effects, and pressure propagation across hundreds of kilometers.The gaseous plume may require one- to two-meter resolution, while pressure buildup can extend far beyond the plume and affect other injection operations.
- Motivation: Existing machine-learning approaches struggle with the multi-scale requirements of realistic CCS reservoirs, including 3D geometry, multiple wells, and geological heterogeneity.Prior models were limited to simplified flat single-well settings or coarse 3D resolutions that could miss essential physics.
- Nested FNO: Nested FNO combines FNO architecture with semi-adaptive local grid refinement to predict dynamic 3D pressure buildup and gas saturation across five resolution levels.The framework uses a hierarchy of FNOs to represent different spatial resolutions and model basin-scale CO2 storage responses.
- Results: Nested FNO exceeds the prediction resolution of several benchmark CO2 storage simulations while generalizing from fewer than 2,500 coarse-resolution and about 6,000 fine-resolution training samples.The model is reported to generalize to problems with millions of cells and diverse practical input variables.
- Results: 700,000 times faster inference than the state-of-the-art numerical solver enables real-time forecasts and probabilistic assessments that would otherwise be prohibitively expensive.A probabilistic assessment of maximum pressure buildup and plume footprint took 2.8 seconds with Nested FNO compared with nearly two years using numerical simulators.
Results & Discussion
Nested FNO predicts high-resolution 3D CO2 plume saturation and pressure buildup across multiple refinement levels, reservoir conditions, and injection schemes. It achieves low errors, rapid inference, and probabilistic assessment capabilities while retaining broad generalization.
- Model and data: The framework represents practical CCS scenarios with varied reservoir conditions, multiple injection wells, injection rates, perforation intervals, and heterogeneous permeability fields.Its training data are generated with semi-adaptive local grid refinement, reducing cell sizes by 80x in x,y and 10x in z near wells.
- Model and data: Nested FNO uses a sequence of FNO models across five resolution levels to predict 3D pressure buildup and gas saturation over 30 years.The model inputs include permeability, initial hydrostatic pressure, temperature, injection scheme, and spatial-temporal encoding.
- Gas saturation prediction: Nested FNO captures plume shapes, saturation distributions, and near-well dry-out zones across complex multiphase flow conditions.Dry-out zones occur near injection perforations where gas saturation is almost one.
- Gas saturation prediction: 1.8% is the testing-set average gas saturation error, compared with 1.2% for the training set.The reported accuracy supports applications including sweep-efficiency estimation and plume-footprint forecasting.
- Pressure buildup prediction: 0.5% is the testing-set relative pressure buildup error, compared with 0.3% for the training set.The model captures both local well responses and global pressure interactions relevant to injection-rate decisions and regulatory assessment.
- Computational speed and probabilistic assessment: 400,000 to 700,000 times is the reported speedup over ECLIPSE, with prediction times ranging from 0.025s to 0.085s.The speedup enables ensemble modeling and probabilistic assessment that would otherwise require nearly two years of numerical simulation.
- Generalizability: Nested FNO generalizes to millions of cells using 2,408 training samples for the coarsest model and 5,916 for finer models.The paper attributes this generalizability to fine-tuning for the nested architecture and the global kernels of FNO.
Conclusions
Nested FNO provides fast, high-resolution dynamic 3D predictions of CO2 gas saturation and pressure buildup. Its speed supports repeated simulations for probabilistic assessment, site selection, optimization, and seismic inversion, while broadening access to high-quality forecasts.
- Core contribution: Nested FNO predicts high-resolution dynamic 3D gas saturation and pressure buildup for CO2 storage problems.The model is presented as a tool for repeated forward simulations in CCS deployment tasks.
- Supported applications: Its fast predictions support probabilistic assessment, site selection, storage optimization, and seismic inversion.These applications involve repeated forward simulations or simulation outputs and gradients.
- Implications: The framework can help reduce uncertainties and accelerate CCS deployment scale-up by facilitating rigorous analyses.The stated scope includes CCS project analysis rather than a guarantee of deployment outcomes.
- Broader access: High-quality forecasts can benefit small- to mid-sized developers and communities seeking independent evaluation of proposed projects.The paper identifies these groups as previously lacking access to such forecasts.
Experimental
The study evaluates Nested FNO through multilevel pressure and gas-saturation prediction, sequential-error analysis, and fine-tuning experiments. Random perturbation fine-tuning reduces error accumulation, especially for fine pressure predictions.
- Training procedure: Nested FNO uses nine independently trained models across refinement levels for pressure buildup and gas saturation.The models are trained concurrently from ground-truth numerical simulation inputs, then used for multilevel inference.
- Prediction procedure: Inference constructs predictions sequentially across refinement levels, using coarser-level pressure or saturation outputs as inputs to finer models.Algorithm 1 applies the level-wise models to predict pressure buildup and gas saturation for reservoirs with multiple injection wells.
- Separate versus sequential prediction: 13 times: level-4 validation error increased by this factor under sequential rather than separate pressure prediction.Separate prediction uses ground-truth simulator inputs, whereas sequential prediction uses predicted coarser-level outputs and accumulates error toward finer levels.
- Separate versus sequential prediction: Gas-saturation predictions show less error accumulation than pressure-buildup predictions during sequential refinement.This indicates that gas-saturation prediction relies less heavily on coarser-level models.
- Fine-tuning: Randomly sampled coarser-level errors provide the best validation performance and smallest overfitting among the tested perturbation options.The method exposes finer models to structured upstream error; sample-specific perturbations overfit, while Gaussian perturbations produce the largest errors.
- Fine-tuning: More than 50%: level-4 pressure-buildup validation error decreased after applying the selected fine-tuning procedure.Sequential prediction errors decreased for both pressure buildup and gas saturation after fine-tuning.
- Error structure: A few principal components describe nearly a third of the prediction error, supporting structured rather than Gaussian perturbations.The authors characterize errors as lying in a perturbed low-dimensional manifold, whereas Gaussian noise occupies an infinite-dimensional space.
Web application
The trained Nested FNO models are hosted in the CCSNet.ai web application for real-time predictions.
- Web application: CCSNet.ai provides public real-time predictions from the trained Nested FNO models.The application was made available upon publication.
Conflicts of interest
The authors report no conflicts of interest.
- Conflicts of interest: The authors declare no conflicts of interest.
Notes and references
The paper’s notes and references list sources supporting CCS motivation, modeling methods, evaluation, and related work.
- References: The references include sources on CCS deployment, climate pathways, and related energy-system research.
- References: The references include regulatory guidance, reservoir-simulation software, and geological-storage studies.