On stochastic study of well capture zones in bounded, randomly heterogeneous media

Accurately determining well capture zones is of great importance in aquifer cleanup and for the protection of drinking water. Earlier models in delineating capture zones assumed the medium to be homogeneous. Recently, stochastic approaches have been applied to studying capture zones in heterogeneous media. The Monte Carlo method is commonly used to infer the probability distribution of the resulting capture zones from multiple realizations of the aquifer of interest. In this study, we present a moment-equation-based approach to derive the time-dependent mean capture zones and their associated uncertainties. The flow statistics are obtained by solving the first two moments of flow, and the mean capture zones are determined by reversely tracking the nonreactive particles released at a small circle around each pumping well. The uncertainty associated with the mean capture zones is calculated based on the particle displacement covariance Xij for nonstationary flow fields. For comparison purposes, we also conducted Monte Carlo simulations. It has been found that our model results are in excellent agreement with Monte Carlo results.