Combining Karhunen-Loève expansion and stochastic modeling for probabilistic delineation of well capture zones in heterogeneous aquifers

The delineation of well capture zones (WCZs), particularly for water supply wells, is of utmost importance to ensure water quality. This task requires a comprehensive understanding of the aquifer's hydrogeological parameters for precise delineation. However, the inherent uncertainty associated with these parameters poses a significant challenge. Traditional deterministic methods bear inherent risks, emphasizing the demand for more resilient and probabilistic techniques. This study introduces a novel approach that combines the Karhunen-Loeve expansion (KLE) technique with stochastic modeling to probabilistically delineate well capture zones in heterogeneous aquifers. Through numerical examples involving moderate and strong heterogeneity, the effectiveness of KLE dimension reduction and the reliability of stochastic simulations are explored. The results show that increasing the number of KL-terms significantly improves the statistical attributes of the samples. When employing more KL-terms, the statistical properties of the hydraulic conductivity field outperform those of cases with fewer KL-terms. Notably, particularly in scenarios of strong heterogeneity, achieving a convergent probabilistic WCZs map requires a greater number of KL-terms and stochastic simulations compared to cases with moderate heterogeneity.