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

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。     

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

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de Hoog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.     

考虑弥散尺度效应与不动水体的反应性溶质运移动力学模型及半解析解

将弥散度概化为运移距离的渐进函数,并考虑土壤孔隙中存在的不动水体以及溶质的吸附和降解,建立了考虑弥散尺度效应的溶质运移两区模型(TRMS,Two-Region Model with Scale-dependent Dispersion),通过Laplace变换和de Hoog数值反演方法求得了模型的半解析解,并运用混合拉普拉斯变换有限差分法验证了半解析解的准确性。通过TRMS与弥散度为常数的两区模型(TRMC,Two-Region Model with Constant Dispersion)之间的比较,分析了弥散尺度效应对溶质运移过程的影响,并利用算术平均方法计算了TRMS的等效弥散度,最后应用TRMS和TRMC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:TRMS的等效弥散度反映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,采用等效弥散度时,TRMC描述的穿透曲线与TRMS的模拟结果基本一致;TRMC的模拟结果与非均质长土柱的浓度实测值存在较大偏差,而TRMS的模拟精度有了较大程度的提高,能够更好地模拟非均质长土柱中溶质的不规则运移过程,说明本文建立的TRMS能够较好地模拟非均质介质中溶质在较大尺度上的运移过程。     

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

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de Hoog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...     

考虑弥散尺度效应的两点吸附溶质运移模型及半解析解

该文考虑弥散尺度效应,建立了有限土柱中溶质运移的两点吸附降解模型。采用Laplace变换和数值反演方法求得了模型的半解析解,并应用试验资料对模型进行了验证。应用半解析解模拟分析了弥散尺度效应、平衡吸附点位所占比例及边界条件对溶质运移过程的影响。结果表明:弥散尺度效应越强土壤溶质运移锋面越远,分布范围越广,溶质浓度峰值越小。平衡吸附点位所占比例越小溶质运移锋面越远,但对溶质分布范围与浓度峰值影响不大。当经验常数a为1.0 m-1时,有限土柱和半无限土柱中溶质浓度几乎一致,出口附近处有限土柱中浓度模拟结果较高;当经验常数a小于1.0 m-1时,模拟结果恰好相反。     

不流动水对包气带溶质运移的影响研究进展

本文对考虑不流动水影响下的溶质运移模型、可动-不动区溶质运移模型、考虑吸附与降解作用的不流动水溶质运移模型进行了综述。指出对不流动水的研究已从盲端水扩展到内聚体间不动的水和远离流动区的水。其中，用可动-不动区模型可解释溶质运移中穿透曲线不对称的现象；用压力圆盘渗透仪可直接测量不动区的含水量使上述模型易于操作。并指出今后不流动水研究的方向应为不流动水分类的完善、不流动水对包气带水流的影响研究、参数的不确定性和尺度效应研究。     

一维非饱和溶质随机运移模型的谱分析

本文根据宏观尺度条件下溶质运移的随机特征，在不考虑孔隙弥散的条件下，对一维非饱和溶质运移方程进行了简化。假设流速场及溶质浓度无普空间平稳随机函数，通过对一维非饱和溶运移的简化方程进行平均处理，导出了与小尺度对流一弥散方程相似的宏观尺度溶质运移的基本方程，并由谱分析导出了宏观弥散系数及溶质浓度方差的表达式。应用宏观尺度溶驼移方程为基础的数学模型对野外盐分迁移过程进行了模拟。模拟所得的溶质平均浓度及浓     

考虑弥散系数尺度效应的溶质运移模型研究

基于多空介质溶质运移的基本方程,利用erfc(x)的近似公式反求地下水溶质运移的纵向弥散参数,分析了其与尺度之间的相关关系,并运用分维理论确定了尺度效应的分维数,导出了弥散参数的表达式.结果表明:①弥散系数与尺度之间呈幂相关关系;②考虑弥散系数尺度效应的方法可较好地模拟均质的溶质迁移.     

稳定流条件下土壤溶质运移两区模型的准解析解及数值模拟

将弥散度概化为运移距离的指数函数，给出了稳定流条件下，非均质土壤中考虑水动力弥散尺度效应及不动水体存在时，一维溶质运移的两区模型。在初始浓度为零，半无限一维空间内定通量边界条件下，推导出了可动区和不动区溶质相对浓度的准解析表达式。用特征有限元法建立了相应的数值模型，从数值解和准解析解的计算数据可以看出：数值计算所产生的误差很小，能满足实际工作对计算精度的要求。     

稳态条件下土壤溶质运移的两区模型及其解析解

给出了稳态水流条件下，非均质土壤中考虑水动力弥散尺度效应以及不动水体存在时，一维溶质运移的两区模型。并在初始浓度为零，半无限一维空间内第一类边界条件下，推导出了可动区和不动区溶质相对浓度的解析表达式。给出了利用Matlab软件包计算相对浓度的计算方法，并对一假设试验情形进行了计算，从计算结果可以看出：该模型的模拟结果符合土壤中溶质运移的规律。最后，用特征有限元法对模型进行了数值计算，从而验证了所得解析解的正确性。     

Analytical solution and analysis for solute transport in streams with diffusive transfer in the hyporheic zone

Solute transport in streams with diffusive transfer in the hyporheic zone is studied. Analytical solution of the diffusive transfer model is obtained by means of Laplace transform. Solutions are derived for a general situation, in which the concentration at the injection point is a function of time. In order to illustrate the use of present analytical solution, physical transport parameters are estimated for the observed data of Uvas Creek tracer experiment for chloride concentration and also of Wkra river tracer experiment. The concentration–time breakthrough curves obtained from the analytical solutions are found to be in good agreement with the observed as well as numerical concentration–time breakthrough curve. Step concentration–time profile and continuous concentration–time profile are considered as upstream boundary conditions for conservative solute. An instantaneous injection of solute is taken as an upstream boundary condition for reactive solute. It is noticed that with the increase in the value of porosity, the solute concentration in the main channel decreases. With the decrease in the value of Péclet number in the hyporheic zone, the overall solute concentration in the main channel decreases. Due to increase in the value of the sorption rate coefficient in the hyporheic zone, solute particles once enter into the hyporheic zone, reside for a longer time in the hyporheic zone. A sensitivity analysis is performed in order to identify the critical parameters for conservative as well as for reactive solute. It is found that the ratio of cross-sectional areas is much more sensitive compared to the other parameters for conservative solute. The Damköhler number in the hyporheic zone is the most sensitive parameter among all the parameters for reactive solute. The above observations indicate that the analytical solution can be reliably applied for the analysis of tracer experiments.     

土壤溶质运移的边界层运动

本文以半无限土壤溶质运移的对流——弥散方程为例研究边界层运动规律。运用Laplace变换方法推导土壤溶质运移的边界层方程。数学分析表明边界层上溶质通量假设对于计算边界层运动距离和溶质浓度是可行的。边界层运动方程的一个重要应用是估算溶质运移参数，这个估算参数方法在数学上更简单、信息利用更全面，是一个值得研究和发展的新方法。     

Modeling atrazine transport in soil columns with HYDRUS-1D

Both physical and chemical processes affect the fate and transport of herbicides. It is useful to simulate these processes with computer programs to predict solute movement. Simulations were run with HYDRUS-1D to identify the sorption and degradation parameters of atrazine through calibration from the breakthrough curves (BTCs). Data from undisturbed and disturbed soil column experiments were compared and analyzed using the dual-porosity model. The study results show that the values of dispersivity are slightly lower in disturbed columns, suggesting that the more heterogeneous the structure is, the higher the dispersivity. Sorption parameters also show slight variability, which is attributed to the differences in soil properties, experimental conditions and methods, or other ecological factors. For both of the columns, the degradation rates were similar. Potassium bromide was used as a conservative non-reactive tracer to characterize the water movement in columns. Atrazine BTCs exhibited significant tailing and asymmetry, indicating non-equilibrium sorption during solute transport. The dual-porosity model was verified to best fit the BTCs of the column experiments. Greater or lesser concentration of atrazine spreading to the bottom of the columns indicated risk of groundwater contamination. Overall, HYDRUS-1D successfully simulated the atrazine transport in soil columns.     

双重介质示踪剂径向输运问题的一组新解析解

本文研究示踪剂在裂隙－孔隙双重介质中的输运问题。假设对流弥散仅发生在裂隙系统中，孔隙系统只作为一种贮客场所，并考虑其中的均衡吸附。另外，示踪剂的输运处于径向的稳定渗流场中。描述这一问题的数学模型是一组交系数的微分方程，通过Ｌａｐｌａｃｅ变换，我们给出了由Ａｉｒｙ函数表示的形式较为简洁的解析解。文中研究了有关参量的影响作用，这对于识别地层信息具有很大的帮助，可以用来分析示踪剂试验，拟合求参。也可用于预测废水回注时浓度及范围。本解准确，计算量少，便于实际应用，许多特殊情况下的解可由简化本解而得，故它还有较广泛的适应性。     

Analytical solutions for temporally and spatially dependent solute dispersion of pulse type input concentration in one-dimensional semi-infinite media

A linear advection–diffusion equation with variable coefficients in a one-dimensional semi-infinite medium is solved analytically using a Laplace transformation technique, for two dispersion problems: temporally dependent dispersion along a uniform flow and spatially dependent dispersion along a non-uniform flow. Uniform and varying pulse type input conditions are considered. The variable coefficients in the advection–diffusion equation are reduced into constant coefficients with the help of two transformations which introduce new space and time variables, respectively. It is observed that the temporal dependence of increasing nature causes faster solute transport through the medium than that of decreasing nature. Similarly the effect of inhomogeneity of the medium on the solute transport is studied with the help of a function linearly interpolated in a finite space domain.