A new mobile-immobile model for reactive solute transport with scale-dependent dispersion

This study proposed a new mobile-immobile model (MIM) to describe reactive solute transport with scale-dependent dispersion in heterogeneous porous media. The model was derived from the conventional MIM but assumed the dispersivity to be a linear or exponential function of travel distance. The linear adsorption and the first-order degradation of solute were also considered in the model. The Laplace transform technique and the de Hoog numerical Laplace inversion method were applied to solve the developed model. Solute breakthrough curves (BTCs) obtained from MIM with scale-dependent and constant dispersions were compared, and a constant effective dispersivity was provided to reflect the lumped scale-dependent dispersion effect. The effective dispersivity was calculated by arithmetically averaging the distance-dependent dispersivity. With this effective dispersivity, MIM could produce similar BTC as that from MIM with scale-dependent dispersion in porous media with moderate heterogeneity. The applicability of the proposed new model was tested with concentration data from a 1,250-cm long and highly heterogeneous soil column. The simulation results indicated that MIM with constant and linear distance-dependent dispersivities were unable to adequately describe the measured BTCs in the column, while MIM with exponential distance-dependent dispersivity satisfactorily captured the evolution of BTCs.