Fourier Neural Operator based surrogates for $CO_2$ storage in realistic geologies

TL;DR

The paper addresses the need for fast, high-fidelity screening of CO$_2$ storage sites by developing Fourier Neural Operator surrogates within NVIDIA's Modulus framework to predict 3D CO$_2$ plume migration in realistic geologies. It shows that these surrogates can achieve substantial speedups around $O(10^5)$ with minimal accuracy loss, and it investigates super-resolution, mass-conservation regularization, and outlier detection to enhance reliability. The approach enables rapid, scalable site screening and paves the way for digital twins in subsurface CCS and related energy storage domains. The methods and strategies are extendable to geothermal reservoir modeling and hydrogen storage, supporting broader applications of fast physics-informed surrogates in subsurface engineering.

Abstract

This study aims to develop surrogate models for accelerating decision making processes associated with carbon capture and storage (CCS) technologies. Selection of sub-surface $CO_2$ storage sites often necessitates expensive and involved simulations of $CO_2$ flow fields. Here, we develop a Fourier Neural Operator (FNO) based model for real-time, high-resolution simulation of $CO_2$ plume migration. The model is trained on a comprehensive dataset generated from realistic subsurface parameters and offers $O(10^5)$ computational acceleration with minimal sacrifice in prediction accuracy. We also explore super-resolution experiments to improve the computational cost of training the FNO based models. Additionally, we present various strategies for improving the reliability of predictions from the model, which is crucial while assessing actual geological sites. This novel framework, based on NVIDIA's Modulus library, will allow rapid screening of sites for CCS. The discussed workflows and strategies can be applied to other energy solutions like geothermal reservoir modeling and hydrogen storage. Our work scales scientific machine learning models to realistic 3D systems that are more consistent with real-life subsurface aquifers/reservoirs, paving the way for next-generation digital twins for subsurface CCS applications.

Figures (11)

• Figure 1: Schematic of the layered reservoir geometries. Different colors correspond to varying permeability. The parts of the reservoir protruding above ground level (reservoir ceiling), shaded in black, represent void-blocks (inactive regions), and changes based on reservoir dip angle and other input parameters (first row of Table \ref{['tab:params']}).
• Figure 2: Visualization of fields. (a) 3D permeability map of the reservoir along with injection location. Distance is measured in km and permeability (K) in milliDarcy (mD). (b) $\overline{m}_{\textrm{CO}_2}$, measured in $kg/m^3$, as viewed on the XZ plane (c) Cross sectional views of various fields at the injection location. $m_{\textrm{CO}_2}$ and $S_g$ are shown at final time whereas $\delta p$ at initial time because of their respective importance in decision making.
• Figure 3: Error metrics (a) MAE for $m_{\textrm{CO}_2}$ and $S_g$, with $<MAE>$ representing average in time (b) $R^2$ correlation plots of $90\%$ plume mass migration distance. (c) Maximum pointwise error in $\delta p$ (d) [red circles] $R^2$ correlation plots of $\delta p$ at maximum pressure location corresponding to the test sample. [blue circles] Correlation plots $\delta p$ for randomly selected locations within the active domain of the test sample.
• Figure 4: Performance metrics when a soft constraint on total mass in the system is imposed (a) Mean relative error (MRE) of total mass, $\int_V m_{\textrm{CO}_2}$, over all time instances as weighing factor in the loss function ($\alpha$) is varied. (b) MAE for $m_{\textrm{CO}_2}$ and $S_g$ along with $R^2$ of $p_{90}[m_{\textrm{CO}_2}]$
• Figure 5: Super resolution experiments (a) Error metrics for different cases – base case (black circles), model trained on vol. avg coarse grid and evaluated on fine grid (orange square), model trained on vol. avg coarse grid and evaluated on vol. avg coarse grid (orange triangle), model trained on discretely down-sampled coarse grid and evaluated on fine grid (blue square), model trained on discretely down-sampled coarse grid and evaluated on discretely down-sampled coarse grid (blue triangle), (b, c, d) 2D visualization of fields along the Y axis.