Semi-analytical solution for solute radial transport dynamic model with scale-dependent dispersion
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abstract
A novel mathematical model to describe reactive solute transport in a radially divergent flow field with scale-dependent dispersion is presented in this study. The model is based on the convection-dispersion equation in cylindrical coordinates but the dispersivity is a linear function of travel distance from the injection well, considering kinetic adsorption and first-order degradation of the solute. The Laplace transform technique and de Hoog numerical inversion method are applied to solve the proposed model. The proposed scale-dependent dispersion model (SDM) is compared with the constant dispersion model (CDM) to illustrate the effect of scale-dependent dispersion and reactive processes on solute transport behavior. The results indicate that with the increase of scale-dependent dispersion the spreading of the breakthrough curves (BTCs) increases, and the peak concentrations of the BTCs and their arrival time decrease. The solute concentration distribution curves exhibit nearly similar features as the BTCs except that the scale-dependent dispersion has little effect on arrival distances of the peak concentrations. The CDM can produce a breakthrough curve with nearly same shape as that from the SDM. This correspondence occurs when the ratio between the dispersivity of CDM and the maximum dispersivity of SDM is 4/5. However, the discrepancy of this correspondence increases lightly with the increase of scale-dependent dispersion for SDM. In addition, as a result of adsorption and degradation, the solute concentration is reduced and the transport of the solute is delayed. A set of previous radial dispersion experimental data is interpreted by SDM and CDM. The analytical results indicate that SDM is more satisfactory than CDM for describing solute radial transport in heterogeneous porous media.
