BEACON: Bayesian Experimental design Acceleration with Conditional
  Normalizing flows $-$ a case study in optimal monitor well placement for
  CO$_2$ sequestration
Rafael Orozco Abhinav Gahlot Felix J. Herrmann
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.