Exploring Sparsity-Promoting Dynamic Mode Decomposition for Data-Driven Reduced Order Modeling of Geological CO2 Storage
Authors: James Omeke , Alokla Kassem , Voulanas Dimitrios , Okoroafor Rita 
Published: September 2024

Abstract
In the context of addressing climate change, advanced computational methods are crucial for enhancing the efficiency and efficacy of carbon capture and storage (CCS) technologies. This study explores the application of Sparsity-Promoting Dynamic Mode Decomposition (Sp-DMD) for developing reduced-order models (ROMs) that effectively manage the computational complexity of subsurface CO2 storage simulations. By focusing on critical state variables—reservoir pressure and CO2 plume saturation—this research aims to investigate whether Sp-DMD can accurately capture the dynamic characteristics of CO2 behavior in geological formations over extended periods.
This study is centered on the Illinois Basin Decatur Project (IBDP), a CCS initiative targeting CO2 injection into a deep saline reservoir. The pre-existing IBDP Eclipse300 open-source simulation model, originally calibrated with both permeability and porosity modifications, required 8 hours to simulate a 3-year CO2 injection history. By revising the history-matching process to focus solely on permeability modification, and re-calibrating using multi-level pressure readings from a monitoring well and bottom-hole pressure data from the injection well, we reduced the runtime to 3 hours for the historical period. Additionally, we extended the simulation to include a 9-year post-injection monitoring phase, culminating in a total runtime of 4 hours over 12 years. From this calibrated full-order model (FOM), we developed a ROM by extracting 3D pressure and CO2 saturation data at various timesteps, which were then flattened into vectors to form a comprehensive snapshot matrix. This matrix was segmented into 109 months (9 years) for ROM training and 27 months for validation using Sp-DMD which employs advanced data-driven techniques such as Singular Value Decomposition (SVD) and eigen decomposition, enhanced with L1 norm regularization, to effectively capture and model the coherent fluid dynamics within the complex geological settings.
The ROM achieved mean absolute errors (MAE) of 4.78E-05 for CO2 plume saturation and 0.63 psi for pressure during its training phase. When tested on the remaining 27 months, it yielded an MAE of 1.17 psi for pressure and 0.009 for saturation. Remarkably, this ROM reconstructed a 12-year dataset in just 1 minute and 43 seconds—significantly faster than the full-order model's 4-hour requirement. Moreover, it demonstrated the capability to forecast up to 500 years within only 1 hour and 40 minutes, establishing itself as a potent tool for long-term CO2 storage monitoring. This performance not only significantly reduces computational demands but also facilitates efficient and rapid long-term forecasting of CO2 saturation and pressure, thus streamlining the transition from a data-intensive FOM to an expedient ROM. This project utilized a workstation with a 12th Gen Intel(R) Core(TM) i9-12900H, 2.50 GHz, and 16 GB RAM, supporting extensive ROM computational demands.
Our Sp-DMD approach provides a meaningful balance between speed and accuracy in modeling complex geological storage systems. Although still in the exploratory phase, the study paves the way for further investigations into the scalability and robustness of Sp-DMD applications in CCS simulation.