Fractionation, concentration and flow: A model coupling stable isotope ratios to fluid travel time and chemical reactivity

Abstract:

From the point of infiltration to the point of discharge, the chemical signature imparted to fluid flowing through catchments represents the weathering flux from the landscape. The magnitude of this flux is linked to both the time water spends in the system and the time required for reactions to influence fluid chemistry. The ratio of these characteristic times is often represented as a Damköhler number (Da), which links the parameters governing reactivity and flow. Stable isotope ratios are now commonly applied to identify and even quantify the processes and rates of primary mineral weathering, secondary mineral formation and biogeochemical cycling within catchments. Here, we derive a series of fractionation-discharge relationships for a variety of governing chemical rate laws utilizing Da coefficients. These equations can be used to isolate and quantify the effects of (1) fluid travel time distributions and (2) chemical weathering efficiency on observed stable isotope ratios. The analytical solutions are verified against multi-component reactive transport simulations of stable isotope fractionation in homogeneous and spatially correlated heterogeneous flow fields using the CrunchTope code and evaluated against field observations.

We demonstrate that for an irreversible reaction, the relationship between stable isotope enrichment and reactant concentration obeys a Rayleigh-type model across a wide range of reaction rates. However, this relationship is violated when a heterogeneous travel time distribution is considered. This observation highlights an important discrepancy in the commonly assumed relationship between fractionation and concentration for irreversible reactions. We further extend our derivation to consider isotope fractionation associated with a reversible reaction (i.e. a kinetically controlled approach to equilibrium) in a steady-state flow field. Due to the dependence of the observed isotope ratio on the flow rate, kinetic enrichment and equilibrium fractionation, our results suggest that a simple concentration – fractionation relationship does not exist for this type of reaction.