A model for the groundwater transport of naturally occurring U, Th, Ra, and Rn nuclides in the238U and232Th decay series is discussed. The model developed here takes into account transport by advection and the physico-chemical processes of weathering, decay, α-recoil, and sorption at the water-rock interface. It describes the evolution along a flowline of the activities of the238U and232Th decay series nuclides in groundwater. Simple sets of relationships governing the activities of the various species in solution are derived, and these can be used both to calculate effective retardation factors and to interpret groundwater data. For the activities of each nuclide, a general solution to the transport equation has been obtained, which shows that the activities reach a constant value after a distance ϰi, characteristic of each nuclide. Where ϰi is much longer than the aquifer length, (for238U,234U, and232Th), the activities grow linearly with distance. Where gKi is short compared to the aquifer length, (for234Th,230Th,228Th,228Ra, and224Ra), the activities rapidly reach a constant or quasi-constant activity value. For226Ra and222Rn, the limiting activity is reached after 1 km.
High δ234U values (proportional to the ratioɛ234Th/W238U) can be obtained through high recoil fraction and/or low weathering rates. The activity ratios230Th/232Th,228Ra/226Ra and224Ra/226Ra have been considered in the cases where either weathering or recoil is the predominant process of input from the mineral grain. Typical values for weathering rates and recoil fractions for a sandy aquifer indicate that recoil is the dominant process for Th isotopic ratios in the water. Measured data for Ra isotope activity ratios indicate that recoil is the process generally controlling the Ra isotopic composition in water. Higher isotopic ratios can be explained by different desorption kinetics of Ra. However, the model does not provide an explanation for228Ra/226Ra and224Ra/226Ra activity ratios less than unity.
From the model, the highest222Rn emanation equals 2ɛ. This is in agreement with the hypothesis that222Rn activity can be used as a first approximation for input by recoil (Krishnaswamiet al 1982). However, high222Rn emanation cannot be explained by production from the surface layer as formulated in the model. Other possibilities involve models including surface precipitation, where the surface layer is not in steady-state.