考虑弥散尺度效应的一维反应性溶质运移两区模型及应用  

One-dimensional two-region model for reactive solute transport with scale-dependent dispersion and its application

作　　者：高光耀[1,3] 冯绍元[2,3] 马英[2] 詹红兵 

机构地区：[1]中国科学院生态环境研究中心,城市与区域生态国家重点实验室,北京100085 [2]扬州大学水利科学与工程学院,江苏扬州225009 [3]中国农业大学中国农业水问题研究中心,北京100083 [4]美国德克萨斯农工大学地质与地球物理系,美国德克萨斯州77843

出　　处：《水利学报》2011年第6期631-640,共10页Journal of Hydraulic Engineering

基　　金：十二五国家科技支撑计划课题;国家自然科学基金(91025018);黄土高原土壤侵蚀与旱地农业国家重点实验室开放基金(10501-280)

摘　　要：为考虑溶质运移的弥散尺度效应,将弥散度概化为运移距离的线性和指数函数,并考虑溶质的吸附和降解,建立了非均质介质中溶质运移的一维两区模型(TRM),采用Laplace变换和deHoog数值逆变换方法求得了模型的半解析解,分析了考虑弥散尺度效应与弥散度为常数的TRM之间的对应关系,利用算术平均方法计算了考虑弥散尺度效应的TRM的等效弥散度,并应用模型模拟了长度为1250cm的一维非均质土柱中的溶质运移过程。结果表明:等效弥散度反应了弥散尺度效应的影响,可以近似作为区域弥散度的平均值,但当弥散尺度效应增强时,这种近似会有一定误差;不考虑弥散尺度效应或将弥散度概化为运移距离线性函数的TRM的模拟结果与实测值存在较大偏差,而弥散度为运移距离指数函数时的TRM的模拟精度有了较大提高,能够更好地模拟非均质长土柱中溶质的不规则运移过程。这说明,非均质介质中弥散度并不是随距离无限制地增加,弥散度为运移距离指数函数时的TRM能够较好地模拟溶质在较大尺度上的运移过程。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 breakthrough 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 1 250cm 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.

关 键 词：弥散尺度效应 两区模型 反应性溶质 模型应用 

分 类 号：S152[农业科学—土壤学]