Semi-analytical solution for reactive solute transport dynamic model with scale-dependent dispersion and immobile water
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This study proposed a novel two-region model with scale-dependent dispersion (TRMS) to describe reactive solute transport in heterogeneous soils. The model was derived from the conventional TRM but assumed the dispersivity to be an asymptotic function of travel distance, considering the linear adsorption and first-order degradation of solute. The Laplace transform technique and de Hoog numerical inversion method were applied to solve the proposed model. The accuracy of semi-analytical solution was verified by a hybrid Laplace transform finite difference method. The TRMS and the two-region model with constant dispersion (TRMC) were compared to interpret the effect of scale-dependent dispersion, and the effective dispersivity for TRMS was calculated by averaging the distance-dependent dispersivity with arithmetic method. This effective dispersivity could reflect the accumulated scale-dependent dispersion effect over the entire travel domain. The TRMC with effective dispersivity could produce nearly similar breakthrough curves (BTCs) as those from TRMS. The applicability of TRMS was tested with concentration data from a 1,250-cm long and highly heterogeneous soil column. The simulation results indicated that the TRMC was unable to adequately describe the measured BTCs in the column, while the TRMS satisfactorily captured the evolution of BTCs. Therefore, this study suggests that the proposed TRMS is a simple and practical approach to describe solute transport at relatively large scale in heterogeneous porous media.
