Abstract
This paper presented a stochastic approach to identify time-related capture zones of solute in pumping wells in geostatistically generated hydraulic conductivity fields based on field data. Random walk particle tracking was applied to assess the travel time and subsequent spatial probability distributions of introduced ensemble lattice cells having the probability that particles located initially within cells reach the pumping wells during a certain time of the pumping. Proposed methodologies provided a few proper time-related outcomes corresponding to the boundary conditions, pumping rates and pumping locations. Based on the probability of each lattice cell, entropy was introduced for computing a quantitative measure expressing the uncertainty relevant to the spatial probability distributions of the solute capture zones, resulting in the increase of the entropy with the extension of the solute capture zone. Moreover, it was demonstrated that the magnitude of the time-related capture zones of groundwater, which was identified using backward particle tracking from a pumping well, was smaller than that of the time-related capture zones of solute due to the effect of solute dispersion phenomena.
