考虑弥散尺度效应的溶质径向运移动力学模型及半解析解  

Semi-analytical solution for solute radial transport dynamic model with scale-dependent dispersion

作　　者：高光耀[1] 冯绍元[1] 霍再林[1] 詹红兵 黄冠华[1,3] 

机构地区：[1]中国农业大学中国农业水问题研究中心,北京100083 [2]美国德克萨斯农工大学地质与地球物理系,美国德州77843 [3]中国农业大学中国-以色列国际农业研究培训中心,北京100083

出　　处：《水动力学研究与进展（A辑）》2009年第2期156-163,共8页Chinese Journal of Hydrodynamics

基　　金：国家重点基础研究发展规划项目(2006CB403406);国家自然科学基金(50779066);教育部长江学者创新团队项目(IRT0657);北京市重点学科"水文学及水资源"建设项目

摘　　要：将弥散度概化为径向距离的线性函数,并考虑溶质的动态吸附和一阶降解,建立了考虑弥散尺度效应的注水井附近反应性溶质径向运移动力学模型(SDM,Scale-dependent Dispersion Model),采用Laplace变换和deHoog数值反演方法对模型求解,并与弥散度为常数的溶质径向运移模型(CDM,Constant Dispersion Model)进行对比,分析弥散尺度效应与吸附和降解对溶质运移的影响。结果表明:随着弥散尺度效应的增强,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,浓度分布曲线也有类似的变化规律,但弥散尺度效应对浓度分布曲线中浓度峰的运移过程没有显著影响;当CDM的弥散度为SDM弥散度最大值的4/5时,CDM和SDM模拟的穿透曲线近似一致,但是这种近似的精确程度会随着SDM弥散度与距离比值的增大而有所降低;由于吸附和降解的存在,溶质在运移过程中会出现损耗和滞后的现象。为检验模型的适用性,本文还应用SDM和CDM模拟室内的径向弥散实验。结果表明,与CDM相比,SDM能更好地描述非均质介质中溶质径向运移过程。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.

关 键 词：弥散尺度效应 径向运移 反应性溶质 LAPLACE变换 半解析解 

分 类 号：X523[环境科学与工程—环境工程]