Simulation of groundwater age distributions

The objective of our work is to examine how to simulate the age of groundwater in such a way that it can be compared to actual measurements. We start by showing that computation of kinematic age, the one obtained by tracking water along streamlines, is ill posed in heterogeneous aquifers. This, together with its inability to account for mixing processes, makes it inadequate for comparison with age measurements, which are the result of some averaging of the age distribution in the water sample (the type of averaging depends on the measurement procedure). Therefore we go on to write the equations for the cumulative distribution function of residence time under transient flow conditions. This allows us to derive transient equations for the mean age, as well as for the higher-order moments of its distribution, which generalize previous results by others. These moments can be used for approximating age measurements, which need not be equal to the mean age of the water sample. Using both a synthetic and a real example, we show that mean age is an acceptable estimate of radiometric age measurements in many cases. Including a second-order correction (variance of residence time distribution) always improves results. On the other hand, higher-order approximations converge slowly for old (compared to half-life) waters, to the point that third-order approximations often worsen the results.

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