Semi-analytical solution for reactive solute transport in the convergent flow to an extraction well considering scale-dependent dispersion
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abstract
To account for the scale-dependent dispersion in radial solute transport, a novel and simplified mathematical model to describe reactive solute transport in the convergent flow to an extraction well is presented. The model is based on the convection-dispersion equation in cylindrical coordinates, but the dispersivity is a linear function of travel distance from solute input source. Kinetic adsorption and first-order degradation of solute are considered in the model. The Laplace transform technique and de Hoog numerical inversion method are applied to solve the proposed model. The accuracy of semi-analytical solution is verified by a hybrid Laplace transform finite difference method. Moreover, the proposed scale-dependent dispersion model (SDM) is compared with the constant dispersion model (CDM) to illustrate the effect of scale-dependent dispersion on reactive solute transport behavior. The results indicate that with the increase of scale-dependent dispersion the peak concentrations of the breakthrough curves (BTCs) and their arrival time decrease. The CDM can produce a BTC at the extraction well with nearly the 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 1/4. In addition, as a result of adsorption and degradation, the solute concentration is reduced and the transport of solute is delayed. A previous radial dispersion experiment conducted in laboratory tank is interpreted by SDM and CDM. The modeling results indicate that SDM is more satisfactory than CDM for describing solute transport to an extraction well in porous media.
