Simulation of Groundwater Age Distributions Using Radioactive Solutes in Double-Porosity Media

We use reactive transport modeling to investigate the control of diffusive mass transfer rate on isotope distribution and groundwater residence time in hypothetical flow regimes. For stable isotopes, the mean arrival time is independent of mass transfer coefficient heterogeneity, regardless of the spatial variability of groundwater velocity. Radioactive isotopes are affected by diffusion because the isotopes can be lost to decay while in the immobile zone. If the solute is radioactive, then heterogeneity associated with diffusive mass transfer affects the mean arrival time and all higher temporal moments such that the effects of diffusion are evident in the accumulated mass, mean concentration, spread, and skewness. We develop temporal moments for solute concentration subject to first order mass transfer rates for steady state transport with decay. In our approach, the distributions of arrival times for solute at any location using moments of concentration can be calculated for a number of boundary conditions including localized pulse input in a heterogeneous field, decaying solute at the boundary (e.g.3H), or a continuous source of decaying solute (e.g.14C). Reactive transport with decay cannot be readily modeled with traditional transport codes because the inclusion of decay in the governing equation affects the matrix of equations, not just the load function.