One-dimensional two-region model for reactive solute transport with scale-dependent dispersion and its application
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abstract
This study proposed a two-region model (TRM) to describe reactive solute transport with scale-dependent dispersion in heterogeneous porous media. The model was derived from the conventional TRM but assumed the dispersivity to be a linear and exponential function of travel distance. The linear adsorption and first-order degradation of solute were also considered in the model. The Laplace transform technique and de Hoog numerical inversion method were applied to solve the developed model. The break-through curves (BTCs) obtained from TRM with scale-dependent and constant dispersion were compared, and the effective dispersivity for TRM with scale-dependent dispersion 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, but discrepancy will occur if the dispersion effect is great. The applicability of the proposed model was tested with concentration data obtained from a 1250 cm long and highly heterogeneous soil column. The simulation results indicated that the TRM with constant and linear distance-dependent dispersivity were unable to describe the measured BTCs in the column adequately, while the TRM with exponential distance-dependent dispersivity satisfactorily captured the evolution of BTCs. Therefore, the proposed TRM with scale-dependent dispersion by assuming the dispersivity to be a function of distance is a simple and practical approach to describe solute transport at relatively large scale in heterogeneous porous media, but the increase of dispersivity with distance is limited as it has bounds.
