Bias of apparent tracer ages in heterogeneous environments

The interpretation of apparent ages often assumes that a water sample is composed of a single age. In heterogeneous aquifers, apparent ages estimated with environmental tracer methods do not reflect mean water ages because of the mixing of waters from many flow paths with different ages. This is due to nonlinear variations in atmospheric concentrations of the tracer with time resulting in biases of mixed concentrations used to determine apparent ages. The bias of these methods is rarely reported and has not been systematically evaluated in heterogeneous settings. We simulate residence time distributions (RTDs) and environmental tracers CFCs, SF₆, ⁸⁵Kr, and ³⁹Ar in synthetic heterogeneous confined aquifers and compare apparent ages to mean ages. Heterogeneity was simulated as both K-field variance (σ²) and structure. We demonstrate that an increase in heterogeneity (increase in σ² or structure) results in an increase in the width of the RTD. In low heterogeneity cases, widths were generally on the order of 10 years and biases generally less than 10%. In high heterogeneity cases, widths can reach 100s of years and biases can reach up to 100%. In cases where the temporal variations of atmospheric concentration of individual tracers vary, different patterns of bias are observed for the same mean age. We show that CFC-12 and CFC-113 ages may be used to correct for the mean age if analytical errors are small.