ABSTRACT
Tracer flow in stratified porous media is dominated by the interaction between convective transport and transverse diffusive mixing. By averaging the tracer concentration in the transverse direction, a one-dimensional non-Fickian dispersion model is derived. The model accounts for the relaxation process that reduces the convective transport to dispersive mixing. This process is (short-) time correlated and partially reversible upon reversal of flow direction. For multiscale velocity fields, the relaxation is a multiscale process. To date only single scale processes have been successfully upscaled. Our procedure extends this to multiscale processes, using scale separation. The model parameters can be calculated a priori based on the velocity profile. For periodic flow reversal, the results are essentially the same. Despite the non-Fickian behavior during a cycle, the net contribution of each cycle to the spreading relaxes to a Fickian process in a similar way as for unidirectional flow. The cycle time averaged dispersion coefficient is a monotonically increasing function of the reversal time. It asymptotically converges towards the effective dispersion coefficient in the absence of flow reversal.