A Monte Carlo-Based Approach for Determining Traveltime-Related Capture Zones of Wells Using Convex Hulls as Confidence Regions

Determination of traveltime-related capture zones of wells in instances where there is a lack of adequate or reliable site-specific values of hydraulic parameters and/or the heterogeneous character of the geologic materials may lead to designation and management of wellhead-protection areas of dubious function. In these instances, Monte Carlo simulation can be used to determine traveltime-related capture zones that account for the uncertainty in values of hydraulic and geologic parameters that cannot be accounted for by deterministically based flow models. Monte Carlo simulations using 100 randomly generated values of hydraulic conductivity and effective porosity were used to determine one-year capture zones based on determination of percentile confidence regions from reverse-tracked flowpaths emanating from a well completed in a leaky-confined aquifer. The mean of the lognormal distribution used to generate the hydraulic-conductivity values was taken to be 3.89 ft/d, the log of the average value from an aquifer test, and a standard deviation of 1.0 ft/d was used. The normal distribution used to generate the effective porosity values had a mean of 25 percent and a standard deviation of 3.5 percent. The values of hydraulic conductivity and effective porosity were ordered and then paired to induce correlation. Other relevant hydraulic and geologic parameters were fixed at average or observed values from the available data. Simulations were made using an analytical flow model in conjunction with a particle-tracking program to obtain 100 sets of endpoint coordinates for 36 reverse-tracked, one-year flowpaths emanating from the well. Wellhead-protection areas based on the 90th- and 75th-percentile confidence regions of the distribution of 3,600 endpoints were determined by deleting the 10 and 25 most-extreme (distant) endpoints, respectively, from the 100 sets of flowpath endpoints of the 36 flowpaths. Delineation of the wellhead-protection areas was based on determination of the convex hull of the remaining endpoints. The distribution of remaining endpoints around the well also was used to determine optimum locations for construction of sentinel wells to detect contaminants moving toward the well along the most probable flowpaths.