Tracer travel and residence time distributions in highly heterogeneous aquifers: Coupled effect of flow variability and mass transfer

The driving mechanism of tracer transport in aquifers is groundwater flow which is controlled by the heterogeneity of hydraulic properties. We show how hydrodynamics and mass transfer are coupled in a general analytical manner to derive a physically-based (or process-based) residence time distribution for a given integral scale of the hydraulic conductivity; the result can be applied for a broad class of linear mass transfer processes. The derived tracer residence time distribution is a transfer function with parameters to be inferred from combined field and laboratory measurements. It is scalable relative to the correlation length and applicable for an arbitrary statistical distribution of the hydraulic conductivity. Based on the derived residence time distribution, the coefficient of variation and skewness of residence time are illustrated assuming a log-normal hydraulic conductivity field and first-order mass transfer. We show that for a low Damkohler number the coefficient of variation is more strongly influenced by mass transfer than by heterogeneity, whereas skewness is more strongly influenced by heterogeneity.