A Method for Calibrating the Transient Storage Model from the Early and Late-Time Behavior of Breakthrough Curves

Solute transport in rivers is controlled by mixing processes that occur over a wide spectrum of spatial and temporal scales. Deviations from the classic advection–dispersion model observed in tracer test studies are known to be generated by the temporary trapping of solutes in storage zones where velocities and mixing rates are relatively small. In this work, the relation between the early and late-time behavior of solute breakthrough curves (BTCs) and the key parameters of the Transient Storage Model (TSM) is analyzed using non-asymptotic approximations of the model equations. Two main slopes are identified corresponding to the rising and decreasing limbs of the BTCs which are linked by specific relationships to transport and storage parameters. The validity of the proposed approximations is demonstrated with both synthetic and experimental data. Consistent with the TSM assumptions, the range of validity of the proposed approximations represents the limit of separability between surface dispersion and transient storage and can be expressed as a function of a nondimensional parameter. The results of this work can help environmental scientists identify solute transport and transient storage parameters and support the design of enhanced field tracer experiments.