Simulation of groundwater age distributions

The objective of our work is to examine how to simulate the age of groundwa ter 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, toge ther with its inability to account for mixing processes, makes it inadequat e for comparison with age measurements, which are the result of some averag ing of the age distribution in the water sample (the type of averaging depe nds on the measurement procedure). Therefore we go on to write the equation s for the cumulative distribution function of residence time under transien t flow conditions. This allows us to derive transient equations for the mea n age, as well as for the higher-order moments of its distribution, which g eneralize previous results by others. These moments can be used for approxi mating age measurements, which need not be equal to the mean age of the wat er 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. I ncluding a second-order correction (variance of residence time distribution ) always improves results. On the other hand, higher-order approximations c onverge slowly for old (compared to half-life) waters, to the point that th ird-order approximations often worsen the results.