# History Matching for Geological Carbon Storage using Data-Space Inversion with Spatio-Temporal Data Parameterization

arXiv: https://arxiv.org/abs/2310.03228 · HTML: https://mlsanity.com/paper/2310.03228/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 53 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media](https://mlsanity.com/paper/1807.00882/) (2018)
- [Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration](https://mlsanity.com/paper/2303.04778/) (2023)
- [Training-image based geostatistical inversion using a spatial generative adversarial neural network](https://mlsanity.com/paper/1708.04975/) (2017)
- [3D CNN-PCA: A Deep-Learning-Based Parameterization for Complex Geomodels](https://mlsanity.com/paper/2007.08478/) (2020)
- [A Robust Deep Learning Workflow to Predict Multiphase Flow Behavior during Geological CO2 Sequestration Injection and Post-Injection Periods](https://mlsanity.com/paper/2107.07274/) (2021)
- [Surrogate Model for Geological CO2 Storage and Its Use in Hierarchical MCMC History Matching](https://mlsanity.com/paper/2308.06341/) (2023)
- [Deep-learning-based coupled flow-geomechanics surrogate model for CO2 sequestration](https://mlsanity.com/paper/2105.01334/) (2021)
- [Data-Space Inversion Using a Recurrent Autoencoder for Time-Series Parameterization](https://mlsanity.com/paper/2005.00061/) (2020)

## Built on by (most cited first, 5 of 5)

- [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)
- [Likelihood-Free Inference and Hierarchical Data Assimilation for Geological Carbon Storage](https://mlsanity.com/paper/2410.15302/) (2024)
- [GeoFUSE: A High-Efficiency Surrogate Model for Seawater Intrusion Prediction and Uncertainty Reduction](https://mlsanity.com/paper/2410.20118/) (2024)
- [PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers](https://mlsanity.com/paper/2609.20794/) (2026)
- [Prediction of Fault Slip Tendency in CO2 Storage using Data-space Inversion](https://mlsanity.com/paper/2601.05431/) (2026)

## Abstract (arXiv)

History matching based on monitoring data will enable uncertainty reduction, and thus improved aquifer management, in industrial-scale carbon storage operations. In traditional model-based data assimilation, geomodel parameters are modified to force agreement between flow simulation results and observations. In data-space inversion (DSI), history-matched quantities of interest, e.g., posterior pressure and saturation fields conditioned to observations, are inferred directly, without constructing posterior geomodels. This is accomplished efficiently using a set of O(1000) prior simulation results, data parameterization, and posterior sampling within a Bayesian setting. In this study, we develop and implement (in DSI) a deep-learning-based parameterization to represent spatio-temporal pressure and CO2 saturation fields at a set of time steps. The new parameterization uses an adversarial autoencoder (AAE) for dimension reduction and a convolutional long short-term memory (convLSTM) network to represent the spatial distribution and temporal evolution of the pressure and saturation fields. This parameterization is used with an ensemble smoother with multiple data assimilation (ESMDA) in the DSI framework to enable posterior predictions. A realistic 3D system characterized by prior geological realizations drawn from a range of geological scenarios is considered. A local grid refinement procedure is introduced to estimate the error covariance term that appears in the history matching formulation. Extensive history matching results are presented for various quantities, for multiple synthetic true models. Substantial uncertainty reduction in posterior pressure and saturation fields is achieved in all cases. The framework is applied to efficiently provide posterior predictions for a range of error covariance specifications. Such an assessment would be expensive using a model-based approach.