A New Mixing-Cell-in-Series Model to Predict Breakthrough Curve in Chemically Heterogeneous Media at Column Scale

Abstract

International audienceThe paper aims at modelling linearly adsorbed solute breakthrough curves into chemically heterogeneous media at column scale. The model was developed according to the mixing-cell-in-series approach and provided a general expression of the reduced variance for either water tracer or linearly adsorbed solute into either chemically homogeneous or heterogeneous medium. According to the experimental investigation of Semra et al. (2008), medium activity was assumed discrete with a known mean capacity. The chemical heterogeneity scale was assessed by the inverse of the ratio of active grains number to the total grains one. Discussion of the heterogeneous model results was accomplished considering breakthrough curve moments. Moment analysis showed that respective effects of interaction and transport are no longer independent from each other even when adsorption is linear. For a constant mean capacity and a constant hydrodynamic dispersion, the effective dispersion, accounted for by the temporal reduced variance, increases linearly with the chemical heterogeneity scale and the breakthrough spreading increase is favoured by high capacities. Moreover, mathematical form of the reduced variance predicts asymmetric breakthrough curves even in the case of equilibrium assumption. Considering kinetics, the model shows additive but independent effects of kinetics and hydrodynamics as in the case of chemically homogeneous media; it shows also independent kinetic effects from heterogeneity. Finally, modelling results were coherent with experimental observations made by Semra et al