A theoretical model for the flux of radon from rock to ground water

A model is derived to predict the abundance of ²²²Rn in ground water in contact with a rock of known uranium content. The model assumes that secular equilibrium is attained in the rock-water system as a whole, but is independent of any microscopic geometric properties of the system. The key variables in the model are bulk properties such as porosity, uranium content of the rock, emanating efficiency, and rock density, all of which are measurable. Thus, the model is simplified by the averaging effects of a macroscopic view of the system. Although less rigorous than other models presented in the literature, it is more generally applicable to natural systems because it does not rely on microscopic properties of the system, which are impossible to quantify. Application of the model to crystalline aquifers in the eastern United States shows that bulk emanation rates of radon are generally less than about 30%.