# A Robust Deep Learning Workflow to Predict Multiphase Flow Behavior during Geological CO2 Sequestration Injection and Post-Injection Periods

arXiv: https://arxiv.org/abs/2107.07274 · HTML: https://mlsanity.com/paper/2107.07274/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 24 references that are in the map.
- First posted on arXiv 15 Jul 2021.

## Builds on (most cited first, 3 of 3)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems](https://mlsanity.com/paper/1908.05823/) (2019)

## Built on by (most cited first, 10 of 10)

- [Partial Differential Equations Meet Deep Neural Networks: A Survey](https://mlsanity.com/paper/2211.05567/) (2022)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Model-Parallel Fourier Neural Operators as Learned Surrogates for Large-Scale Parametric PDEs](https://mlsanity.com/paper/2204.01205/) (2022)
- [Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure management](https://mlsanity.com/paper/2206.10718/) (2022)
- [Multi-fidelity Fourier Neural Operator for Fast Modeling of Large-Scale Geological Carbon Storage](https://mlsanity.com/paper/2308.09113/) (2023)
- [History Matching for Geological Carbon Storage using Data-Space Inversion with Spatio-Temporal Data Parameterization](https://mlsanity.com/paper/2310.03228/) (2023)
- [Accelerated training of deep learning surrogate models for surface displacement and flow, with application to MCMC-based history matching of CO2 storage operations](https://mlsanity.com/paper/2408.10717/) (2024)
- [SciAI4Industry -- Solving PDEs for industry-scale problems with deep learning](https://mlsanity.com/paper/2211.12709/) (2022)
- [Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data](https://mlsanity.com/paper/2305.11913/) (2023)
- [Physics-informed Partitioned Coupled Neural Operator for Complex Networks](https://mlsanity.com/paper/2410.21025/) (2024)

## Abstract (arXiv)

This paper contributes to the development and evaluation of a deep learning workflow that accurately and efficiently predicts the temporal-spatial evolution of pressure and CO2 plumes during injection and post-injection periods of geologic CO2 sequestration (GCS) operations. Based on a Fourier Neuron Operator, the deep learning workflow takes input variables or features including rock properties, well operational controls and time steps, and predicts the state variables of pressure and CO2 saturation. To further improve the predictive fidelity, separate deep learning models are trained for CO2 injection and post-injection periods due the difference in primary driving force of fluid flow and transport during these two phases. We also explore different combinations of features to predict the state variables. We use a realistic example of CO2 injection and storage in a 3D heterogeneous saline aquifer, and apply the deep learning workflow that is trained from physics-based simulation data and emulate the physics process. Through this numerical experiment, we demonstrate that using two separate deep learning models to distinguish post-injection from injection period generates the most accurate prediction of pressure, and a single deep learning model of the whole GCS process including the cumulative injection volume of CO2 as a deep learning feature, leads to the most accurate prediction of CO2 saturation. For the post-injection period, it is key to use cumulative CO2 injection volume to inform the deep learning models about the total carbon storage when predicting either pressure or saturation. The deep learning workflow not only provides high predictive fidelity across temporal and spatial scales, but also offers a speedup of 250 times compared to full physics reservoir simulation, and thus will be a significant predictive tool for engineers to manage the long term process of GCS.