Efficient approximate spectral method to delineate stochastic well capture zones in nonstationary groundwater flow systems

This study presents an unconditional approximate spectral method (ASM) to delineate well capture zones in nonstationary groundwater systems. Taking advantages of spectral theories in solving unmodeled small-scale variability in hydraulic conductivity (K), the proposed spectral method can efficiently estimate flow uncertainties. Such velocity uncertainties associated with the concept of particle tracking can delineate well capture zones for groundwater systems with practical complexities and scales. In this study the developed ASM is assessed to quantify the accuracy of delineated well capture zones under a variety of conditions, including bounded flow domains, flow systems with multiple wells, multiple hydraulic conductivity scales, and nonstationary flows caused by complex sources and sinks in the modeling areas. The ASM solutions are systematically compared with the corresponding numerical solutions of nonstationary spectral method (NSM) and Monte Carlo simulation (MCS). Simulation results reveal that the proposed ASM is computationally efficient and the solutions of velocity variances agree well with the corresponding numerical solutions of NSM and MCS. Based on the simple and efficient approximations, the developed ASM can delineate accurately the mean and variance dynamics of capture zones in complex large-scale groundwater flow systems.