On the relevance of molecular diffusion for travel time distributions inferred from different water isotopes

Abstract

Water isotopes are a tool of choice for assessing travel time distributions of water in soils, aquifers and rivers. However, the question of whether different water isotopes tag the same travel time distributions of the water molecule, or whether the inferred travel time distribution is specific to the chosen water isotope, remains under debate. Here we conjecture that the latter is correct. We state that (a) travel time distributions of water and any tracer reflect the spectrum of fluid velocities and diffusive/dispersive mixing between the flow lines connecting the system in- and outlet, and (b) the diffusion coefficients of deuterium, tritium and 18O differ by as much as 10 %. Using particle tracking simulations, we show that these differences do indeed affect the variance of the travel time distribution – as one would expect for wellmixed advective-dispersive transport. Moreover, our simulations suggest that in the case of imperfect mixing, also the average travel time becomes sensitive to the differences in diffusion coefficients. We find that when advective trapping occurs in low conductive zones, an isotope with a smaller diffusion coefficient remains there for longer times compared to a substance exhibiting faster diffusion. This implies that for imperfectly mixed transport, average transit times ultimately increase with a decreasing diffusion coefficient: deuterium has the longest average travel time, followed by tritium, followed by 18O. Depending on the type of simulated system, we find differences in average travel times ranging from 10 d to more than 2 years. As these differences are in relative terms usually of order 5 %–10 %, one might erroneously explain them as measurement errors. Our findings suggest instead that these relative differences are physics based and may reach up to 50 % for strongly heterogeneous systems, persisting and even growing with increasing space and time scales rather than being averaged out. We thus conclude that travel time distributions inferred from O-H isotopes of the water molecule are conditioned by the chosen water isotope.