A hierarchical spatial model for well yield in complex aquifers

Efficiently siting and managing groundwater wells requires reliable estimates of the amount of water that can be produced, or the well yield. This can be challenging to predict in highly complex, heterogeneous fractured aquifers due to the uncertainty around local hydraulic properties. Promising statistical approaches have been advanced in recent years. For instance, kriging and multivariate regression analysis have been applied to well test data with limited but encouraging levels of prediction accuracy. Additionally, some analytical solutions to diffusion in homogeneous porous media have been used to infer "effective" properties consistent with observed flow rates or drawdown. However, this is an under-specified inverse problem with substantial and irreducible uncertainty. We describe a flexible machine learning approach capable of combining diverse datasets with constraining physical and geostatistical models for improved well yield prediction accuracy and uncertainty quantification. Our approach can be implemented within a hierarchical Bayesian framework using Markov Chain Monte Carlo, which allows for additional sources of information to be incorporated in priors to further constrain and improve predictions and reduce the model order. We demonstrate the usefulness of this approach using data from over 7,000 wells in a fractured bedrock aquifer.