A Bayesian approach to stochastic capture zone delineation incorporating tracer arrival times, conductivity measurements, and hydraulic head observations

Abstract

This paper presents a methodology to invert tracer arrival times and to incorporate travel time data in the delineation of well capture zones. Within a Bayesian framework the observed arrival times are used to obtain probability-based weights for each realization of the hydraulic conductivity field. Realizations that closely reproduce the observed arrival times are more likely to represent the "true" or real conductivity field than realizations yielding worse predictions, and are consequently characterized by a higher conditional probability. In the prediction of the capture zones the realizations are weighted by their respective probability. We combine the arrival time data with conductivity measurements and head observations to delineate stochastic capture zones. The conductivity measurements update the prior distributions specified for the unknown structural parameters of the conductivity field, and are used as conditioning data in the generation of conditional conductivity fields. The parameter values used to generate the conductivity realizations are sampled by Monte Carlo from the updated parameter distributions. The head and travel time observations are subsequently used to assign probability-based weights to the conductivity realizations by applying Bayes' theorem. The hyperparameters of the error model are assumed unknown, and their effect is accounted for by marginalization. A synthetic flow setup consisting of a single extraction well in a fully confined aquifer under a regional gradient is used to illustrate the method. We evaluate the relative worth of the different data types by introducing them sequentially in the inverse methodology. Results indicate that the different data types are complementary and that the travel time data are essential to improve the predictions of the capture zones. This is confirmed by the results for the case where uncertainty in the homogeneous porosity is accounted for.