# Surrogate Model for Geological CO2 Storage and Its Use in Hierarchical MCMC History Matching

arXiv: https://arxiv.org/abs/2308.06341 · HTML: https://mlsanity.com/paper/2308.06341/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 44 references that are in the map.
- First posted on arXiv 11 Aug 2023.

## Builds on (most cited first, 1 of 1)

- [Dimension-Robust MCMC in Bayesian Inverse Problems](https://mlsanity.com/paper/1803.03344/) (2018)

## Built on by (most cited first, 9 of 9)

- [History Matching for Geological Carbon Storage using Data-Space Inversion with Spatio-Temporal Data Parameterization](https://mlsanity.com/paper/2310.03228/) (2023)
- [Deep Learning Framework for History Matching CO2 Storage with 4D Seismic and Monitoring Well Data](https://mlsanity.com/paper/2408.01575/) (2024)
- [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)
- [GeoFUSE: A High-Efficiency Surrogate Model for Seawater Intrusion Prediction and Uncertainty Reduction](https://mlsanity.com/paper/2410.20118/) (2024)
- [STONet: A neural operator for modeling solute transport in micro-cracked reservoirs](https://mlsanity.com/paper/2412.05576/) (2024)
- [Deep operator network for surrogate modeling of poroelasticity with random permeability fields](https://mlsanity.com/paper/2509.11966/) (2025)
- [PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers](https://mlsanity.com/paper/2609.20794/) (2026)
- [Data assimilation for subsurface flow using latent diffusion model parameterization: performance of ensemble-Kalman and Monte Carlo techniques](https://mlsanity.com/paper/2606.11140/) (2026)
- [Multimodal Auto-regressive Transformer Surrogate for Modeling Variable Operations and Quantifying Uncertainty in Geological Carbon Storage](https://mlsanity.com/paper/2608.02629/) (2026)

## Abstract (arXiv)

Deep-learning-based surrogate models show great promise for use in geological carbon storage operations. In this work we target an important application - the history matching of storage systems characterized by a high degree of (prior) geological uncertainty. Toward this goal, we extend the recently introduced recurrent R-U-Net surrogate model to treat geomodel realizations drawn from a wide range of geological scenarios. These scenarios are defined by a set of metaparameters, which include the horizontal correlation length, mean and standard deviation of log-permeability, permeability anisotropy ratio, and constants in the porosity-permeability relationship. An infinite number of realizations can be generated for each set of metaparameters, so the range of prior uncertainty is large. The surrogate model is trained with flow simulation results, generated using the open-source simulator GEOS, for 2000 random realizations. The flow problems involve four wells, each injecting 1 Mt CO2/year, for 30 years. The trained surrogate model is shown to provide accurate predictions for new realizations over the full range of geological scenarios, with median relative error of 1.3% in pressure and 4.5% in saturation. The surrogate model is incorporated into a hierarchical Markov chain Monte Carlo history matching workflow, where the goal is to generate history matched geomodel realizations and posterior estimates of the metaparameters. We show that, using observed data from monitoring wells in synthetic `true' models, geological uncertainty is reduced substantially. This leads to posterior 3D pressure and saturation fields that display much closer agreement with the true-model responses than do prior predictions.