Reaction-transport models for radiocarbon in groundwater: The effects of longitudinal dispersion and the use of Sr isotope ratios to correct for water-rock interaction

We expand a model for isotope ratios in groundwater-rock systems to consider the ratio of ¹⁴C to dissolved inorganic carbon, or 'percent modern carbon' The model couples one-dimensional advection and dispersion with water-rock interaction and radioactive decay. We use a Fickian formulation to model longitudinal macrodispersion and present a formula for the groundwater velocity error introduced when dispersion is ignored, as a function of dispersivity and decrease in percent modern carbon. For example, if the longitudinal dispersivity were one tenth the length of observation and percent modern carbon decreased tenfold along a flow path, the error would be 23%. We also present a method for inversion of ⁸⁷Sr/⁸⁶Sr and ¹⁴C data to obtain carbonate dissolution rates and dissolution-corrected water velocities and apply this technique using published data from the Lincolnshire aquifer, England. The results are similar to those obtained using the δ¹³C method.