BEACON: Bayesian Experimental design Acceleration with Conditional Normalizing flows $-$ a case study in optimal monitor well placement for CO$_2$ sequestration

TL;DR

The paper tackles the challenge of monitoring CO$_2$ plumes under uncertain reservoir properties by optimally placing a limited number of monitoring wells. It introduces BEACON, a Bayesian Experimental Design method that combines a conditional normalizing flow with a probabilistic well-density to maximize information gain, quantified as $EIG(M) = E_{p(y_k|M)}[ D_{KL}( p(x_k|y_k) || p(x_k) ) ]$, and integrates this within a Digital Twin framework for iterative plume updating. Training data are generated via fluid-flow solvers forecasting plume states, with corrupted observations and a budget-enforcing mask to simulate real-world constraints, yielding outputs: a density over optimal locations $\hat{\mathbf{w}}$ and an amortized generator $f_{\hat{\theta}}$. The approach scales to three-dimensional domains and is validated on a synthetic Compass permeability case, showing reduced posterior uncertainty and lower RMSE compared with random-well baselines across four iterative cycles, highlighting practical benefits for monitoring CO$_2$ sequestration projects.

Abstract

CO$_2$ sequestration is a crucial engineering solution for mitigating climate change. However, the uncertain nature of reservoir properties, necessitates rigorous monitoring of CO$_2$ plumes to prevent risks such as leakage, induced seismicity, or breaching licensed boundaries. To address this, project managers use borehole wells for direct CO$_2$ and pressure monitoring at specific locations. Given the high costs associated with drilling, it is crucial to strategically place a limited number of wells to ensure maximally effective monitoring within budgetary constraints. Our approach for selecting well locations integrates fluid-flow solvers for forecasting plume trajectories with generative neural networks for plume inference uncertainty. Our methodology is extensible to three-dimensional domains and is developed within a Bayesian framework for optimal experimental design, ensuring scalability and mathematical optimality. We use a realistic case study to verify these claims by demonstrating our method's application in a large scale domain and optimal performance as compared to baseline well placement.

Figures (2)

• Figure 1: BEACON workflow integrated to digital twin for CO$_2$ sequestration monitoring. The sequence starts with prior samples of the plumes that are passed through the fluid simulator to generate plume forecasts. These forecasts are used to define the training observations of both well observations and seismic images. After training the normalizing flow and finding the optimal well location density, we simulate a field observation $\mathbf{y}_k^{o}$ from the ground truth plume and sample from the amortized posterior. The posterior samples become the prior samples of the next iteration and the sequence continues.
• Figure 2: BEACON compared with random well placement baseline.