Mixing effect on reactive transport in a column with scale dependent dispersion

Controlled column tracer test (CTT) experiments become indispensable tools in understanding the physical, chemical, and biochemical behaviors of solute transport in the subsurface, especially for parameter estimation purpose. Here, we find that previous CTT models perform well in calibration when interpreting experimental data under multiple flow rates, but not well in prediction, probably because they have not taken into consideration of the boundary effect, mixing effect, and scale effect concurrently. In this study, new mathematic models and analytical solutions have been developed, where the mixing effect has been considered in the pre-inlet reservoir, and two scale-dependent models (linear-asymptotic and exponential) are employed to describe the dispersivity. A series of new controlled laboratory experiments and finite-difference numerical simulations have also been conducted to test the new models. The results show that the newly proposed model performs better than previous models when interpreting breakthrough curves of CIT. Both scale effect and mixing effect play important roles in the transport processes. The long standing controversy of boundary conditions at the inlet of the column has been resolved by considering the linear-asymptotic or the exponentially scale-dependent dispersivity models and the mixing effect of the pre-inlet reservoir. Specifically, such new models effectively eliminate the problem of simultaneously satisfying the mass flux continuity and the resident concentration continuity at the inlet of the column. The Danckwerts condition commonly used in previous studies for describing the boundary condition at the column exit is found to be a special case of this study when the after-outlet reservoir is absent.