Using the rare gas concentrations in the aquifers of the Paris Basin (see part 1 of this series), a numerical model of a two-dimensional cross section of the entire Paris Basin was built to simulate groundwater flow and the transport of He-3, He-4, and Ar-40 isotopes. The model included seven aquifers separated by seven aquitards in a steady state flow regime. Transport of the gases is by advection, diffusion, and dispersion in steady or transient states. The He-4 transport was simulated first and made it possible to calibrate both the crustal flux of this isotope and the average permeability of each aquifer, which were then favorably compared with measured values. These values present a high variability from aquifer to aquifer, between 8.5 x 10(-7) and 3.5 x 10(-4) m s(-1). The water velocities and average residence times were also estimated, Average turnover limes for the different aquifers are highly variable, ranging from 8700 years for the shallowest one (Ypresian) to 30 Myr for the deepest one (Trias) The calibrated model was also able to correctly represent the distribution of He-3 and Ar-40 in the basin. Diffusion proved to be an important mechanism for vertical transfer through the aquitards of the helium isotopes, as opposed io Ar-40, which is transported mainly by advection. On the basis of the (He-4/Ar-40) radiogenic ratio a constant value of 10(-11) m s(-1) was attributed to the permeability of all the aquitards, A sensitivity study showed that the permeability of the aquitards situated in the lower part of the basin (Lias and aquitards in the Triassic and Dogger) could not be higher than 10(-11) m s(-1) given the observed distribution of the radiogenic He-4/Ar-40 ratio, but a lower limit could not be defined. The crustal fluxes of He-3, He-4, and Ar-40 in the basin were estimated at 4.33 x 10(-13) mol m(-2) yr(-1), 4 x 10(-6) mol m(-2) yr(-1) and 2.52 x 10(-7) mol m-2 yr(-1), respectively, The simulation of the He-3 and He-4 transport showed that the R/R-a ratio (value of the measured R = He-3/He-4 ratio normalized to the atmospheric ratio R-a) entering at the base of the Trias from the bedrock remained constant while crossing the basin except in the zones close to the recharge areas where it is influenced by the atmospheric component, This constancy is due to the low radiogenic/nucleogenic production rate of these isotopes inside the basin, as compared to the crustal flux.
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