Determination of the initial 14C activity of the total dissolved carbon: A review of the existing models and a new approach

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Abstract
Carbon 14 age calculations are based upon the assumption that the initial activity of the material to be dated was 100% of modern CO2 activity (100 pmc). This assumption is generally good for material of organic origin (wood and, to some extent, shells). Dissolved carbon in groundwater has two main sources: active carbon from the soil zone and less active (or even ‘dead’) carbon of inorganic origin. Furthermore, the existence of a three‐phase system (gaseous CO2 and aqueous and solid carbon) allows significant isotopic exchange. The estimation of the initial activity of the total dissolved carbon requires the use of a model. Existing models for the determination of the initial 14C activity (A0) of total dissolved carbon are (1) Vogel's model (A0 = 85 ± 5% of modern carbon), (2) Tamers' model (A0 is the activity of dissolved carbon of organic origin diluted by dissolved carbon of inorganic origin), (3) Pearson's model (A0 is the mixing of these same sources of carbon, evidenced by their stable isotope content), and (4) Mook's model (same as Tamers' model plus a correcting term accounting for an isotopic exchange in closed system with aqueous CO2). A new model is presented which assumes the simple mixing of the end‐members of the system (gaseous CO2 and solid carbonate). Their relative proportions are given by comparison of the molality of total dissolved carbon (measured bicarbonates and calculated H2CO3, assuming equilibrium at the temperature of the aquifer) to the molality of dissolved carbon of inorganic origin (DIC). The DIC is determined on the basis of the alkaline‐earth molal concentration corrected for gypsum dissolution and base exchange. This treatment can be more simply substituted for by the measurement of field alkalinity, whose value, expressed in molal concentration, is identical to twice the molal concentration of DIC. In addition to the mixing, which also leads to Tamers' expression, an isotope exchange term is calculated, assuming that a part of the contribution of either soil CO2 or solid carbonate is in isotopic equilibrium, in an open system, with the other carbon reservoir. The different models are applied to the results of the confined aquifer of the ‘calcaires carbonifères’ in northern France and Belgium. A value of −24‰ (equivalent to about −22.8‰ for gaseous CO2) is adopted for the 13C content of aqueous carbon dioxide. Values for the isotope fractionation which occurs between carbon‐bearing compounds at aquifer temperatures are adopted from values of Mook et al. (1974) and Deines et al. (1974). It is assumed that ∈14C% ≃0.2∈13C‰. Radiometric ages obtained from the Vogel and Tamers approaches are undercorrected. The model of Mook appears very sensitive to the variations of δ 13C of the total dissolved carbon and can lead to overcorrected values. The model of Pearson is generally in rather good agreement with our treatment in the range of average values of A0. For extremely high and low values of A0 our model provides larger corrections. The ages obtained from the different models are also discussed on the basis of the 18O content of the waters, which appear too high to be attributed to glacial epochs. Average flow velocities calculated from our model range from 1.70 m yr−1 to 0.73 m yr−1.