The curved 14 C vs. δ 13 C relationship in dissolved inorganic carbon: A useful tool for groundwater age- and geochemical interpretations
Determination of the 14 C content of dissolved inorganic carbon (DIC) is useful for dating of groundwater. However, in addition to radioactive decay, the 14 C content in DIC ( 14 C DIC ) can be affected by many geochemical and physical processes and numerous models have been proposed to refine radiocarbon ages of DIC in groundwater systems. Changes in the δ 13 C content of DIC (δ 13 C DIC ) often can be used to deduce the processes that affect the carbon isotopic composition of DIC and the 14 C value during the chemical evolution of groundwater. This paper shows that a curved relationship of 14 C DIC vs. δ 13 C DIC will be observed for groundwater systems if (1) the change in δ 13 C value in DIC is caused by a first-order or pseudo-first-order process, e.g. isotopic exchange between DIC and solid carbonate, (2) the reaction/process progresses with the ageing of the groundwater, i.e. with decay of 14 C in DIC, and (3) the magnitude of the rate of change in δ 13 C of DIC is comparable with that of 14 C decay. In this paper, we use a lumped parameter method to derive a model based on the curved relationship between 14 C DIC and δ 13 C DIC . The derived model, if used for isotopic exchange between DIC and solid carbonate, is identical to that derived by Gonfiantini and Zuppi (2003). The curved relationship of 14 C DIC vs. δ 13 C DIC can be applied to interpret the age of the DIC in groundwater. Results of age calculations using the method discussed in this paper are compared with those obtained by using other methods that calculate the age of DIC based on adjusted initial radiocarbon values for individual samples. This paper shows that in addition to groundwater age interpretation, the lumped parameter method presented here also provides a useful tool for geochemical interpretations, e.g. estimation of apparent rates of geochemical reactions and revealing the complexity of the geochemical environment.