Mathematical results new and revisited on the distribution of groundwater age

The equation governing the distribution of groundwater age under transient, 3D flow conditions is analyzed under several simplifying cases to illustrate some relations among groundwater age equations and some results about steady-state and transient age distributions. First linkages are made among the various groundwater age equations recently published, showing them all to be different simplifications of the same equation. The most basic analysis in 1D shows that groundwater age is at lease inverse-Gaussian distributed. More generally, steady state age moments, when they exist, are given by breakthrough curve moments and this allows us to use the temporal moment results from the solute transport literature as steady state age moments. In particular, age moment equations with arbitrary diffusive mass transfer (two-domain, radial microscopic, powerlaw) at steady state are already available as the temporal flux moment equations for solute transport under analogous boundary conditions. Lastly transient simulations of age in 1D are calculated to illustrate several aspects of the evolution of groundwater age distributions in time in the presences of multidomain diffusive transport.