Influence of transverse mixing on the breakthrough of sorbing solute in a heterogeneous aquifer

The temporal moments associated with the breakthrough of a sorbing solute in a heterogeneous aquifer are investigated assuming an anisotropic distribution of hydraulic conductivity and deterministic linear sorption kinetics. The expressions for the temporal moments are based on a solution to the advection-dispersion equation with constant coefficients which implies that they are valid in the large-time regime. For the evaluation of the “macrodispersion” coefficient we use the asymptotic results of Fiori [1996], who quantified the effect of pore-scale dispersion on nonreactive solute and showed that porescale dispersion affects field-scale transport primarily through transverse mixing between flow paths. The present study shows that linear sorption kinetics decrease the effect of transverse mixing on the temporal moments as compared to the nonreactive case. It is concluded that in the considered large-time regime, the pure-advection approach to quantify field-scale spreading is appropriate under the conditions encountered in most natural formations.