考虑弥散尺度效应的抽水井附近溶质运移模型及半解析解

Semi-analytical solution for reactive solute transport in the convergent flow toan extraction well considering scale-dependent dispersion

为考虑溶质径向运移的弥散尺度效应,将弥散度概化为径向距离的线性函数,并考虑溶质的吸附和降解,建立了抽水井附近溶质运移的简化模型(SDM,Scale-dependent Dispersion Model),通过Laplace变换和de Hoog数值反演方法求得SDM的半解析解,并采用混合拉普拉斯变换有限差分法验证了半解析解的正确性。通过SDM与弥散度为常数的溶质径向运移模型(CDM,Constant Dispersion Model)的比较,分析了弥散尺度效应对反应性溶质径向运移过程的影响,并利用渗流槽中的径向弥散实验资料检验模型的适用性。结果表明:随着弥散尺度效应的增强,抽水井处溶质穿透曲线分布范围越广,浓度峰值越小且达到浓度峰值所需的时间越短;当CDM的弥散度为SDM弥散度最大值的1/4时,CDM和SDM模拟的抽水井处穿透曲线近似一致;由于吸附和降解作用,溶质在运移过程中会出现消耗和滞后的现象;与CDM相比,SDM的模拟结果与径向弥散实验结果吻合更好,说明本文建立的考虑弥散尺度效应的简化模型可以用来模拟较大区域上溶质的径向运移过程。

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.