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.