Statistical Formulation of Generalized Tracer Retention in Fractured Rock

We study tracer retention in fractured rock by combing Lagrangian and time domain random walk frameworks, as well as a statistical representation of the retention process. Mass transfer is quantified by the retention time distribution that follows from a Lagrangian coupling between advective transport and mass exchange processes, applicable for advection‐dominated transport. A unifying parametrization is presented for generalized diffusion using two rates denoted byk1andk2wherek1is a forward rate andk2a reverse rate, plus an exponent as an additional parameter. For the Fickian diffusion model,k1andk2are related to measurable retention properties of the fracture‐matrix by the method of moments, whereas for the non‐Fickian case dimensional analysis is used. The derived retention time distributions are exemplified for interpreting tracer tests as well as for predictive modeling of expected tracer breakthrough. We show that non‐Fickian effects can be notable when transport is upscaled based on a non‐Fickian interpretation of a tracer test for which deviations from Fickianity are relatively small. The statistical representation of retention clearly shows the significance of the forward ratek1which depends on the active specific surface area and is the most difficult parameter to characterize in the field.