地下水水质的教学模擬(二)——水动力弥散方程与水动力弥散系数

地下水水质的数学模型可分为纯对流型与对流弥散型两种。纯对流模型忽略弥散的作用,不考虑过渡带,即认为溶质的运移完全由流速场的分布所确定。这类模型比较简单,也比较容易处理,在研究大范围内的水质变化时经常采用。但是,要想得到溶质浓度的精确分布,限于纯对流模型则不能满足要求,     

基于流网单元的污染物优势运移数值模型

垃圾填埋场滤出液、入侵海水、核废物及生产生活废水等污染物随地下水的迁移威胁人类生存。地下水渗流的随机性导致溶质运移问题更加复杂。根据流网特点,利用流线与水头等势线对求解域进行离散,基于质量守恒原理建立流网单元内溶质浓度求解的隐式有限体积差分格式。基于多孔介质孔隙流速分布规律,利用蒙特卡洛法建立流管单元随机流速场进行溶质运移过程的数值模拟,最后根据数值模拟和模型试验的结果对比,验证了数值模拟方法的准确性。基于流网单元的数值模型中沿流线方向的物质交换由对流和扩散共同作用,而流管间的物质交换只有扩散作用,因此,可在不使用弥散系数下进行污染物运移的模拟。引入随机方法确定流管内流速为研究非均匀流场中染污物的优势迁移提供了新的思路。     

LNAPL在二维含水介质中运移规律的研究

为研究LNAPL(轻质非水相液体)污染物在均匀含水介质中的运移规律,本文建立微元模型推导出LNAPL在均匀含水介质中的对流--弥散方程。针对不同的介质模型,对二维对流--弥散方程运用差分法进行数值模拟,求其数值解。分析LNAPL污染物的运移特征,得出在均匀介质和非均匀层状介质中运移规律:LNAPL污染物在含水介质中的运移规律遵循对流--弥散方程,介质的弥散系数是影响LNAPL污染物运移的主要因素。     

土石混合介质中非反应性阴离子运移试验研究

为探讨化学物质在土石混合介质中的运移过程和机理,采用饱和稳态流下的Cl-1混合置换试验,测定水流和溶质运移过程,分析土石混合介质的溶质穿透曲线特征及碎石组成和含量对运移过程的影响。选用CXTFIT2.1的平衡和物理非平衡对流弥散模型,对参数弥散系数D和滞留因子R进行反求。结果显示:不同土石比的D变异较大:0.258~22.31 cm2/h。R的波动范围为0.6~1.54;碎石含量影响土石介质的溶质运移过程表现为平均孔隙流速、弥散系数、弥散度均与土石比成负指数的幂函数关系。对碎石粒径与溶质运移参数进行相关分析发现,小粒径的碎石含量增加,则孔隙流速和弥散系数有减少的趋势,而大于10 mm的碎石有利于溶质的运移。通过土石介质的非反应性阴离子的混合置换试验研究,可以为非均一介质中化学物质运移提供参考。     

地下水溶质运移数值模拟中减少误差的新方法

地下水中污染物运移的数值模拟方法一直是学界的研究热点问题.而如何减少与消除对流-弥散方程数值解中浓度陡锋面附近的数值振荡与数值弥散,更是研究的前沿与难点.提出了一种地下水溶质运移数值模拟中减少数值弥散的新方法.该方法的核心思想是在水动力弥散系数上加上一个数值弥散估算值,得到一个修正弥散系数,用其替代方程中有明确物理意义的水动力弥散系数进行计算.并提出了一个参数——数值弥散因子(μ_NDF),可以根据研究需要进行参数分区并适当调节该因子的大小,从而达到控制数值振荡,减小数值弥散的目的.从一维到二维的多个数值算例的模拟计算结果表明,该方法能在消除数值振荡的基础上,较好地减少数值弥散,达到满意的精度.     

稳定流场中饱和均质土壤盐分迁移的传递函数解

通过对淹灌条件下砂质壤土的盐水入渗试验,以传递函数模型作为数学模拟的工具,探讨了对流占优运移机制下土壤盐分的迁移特征,得到了盐分在45cm土层的迁移时间概率分布函数与迁移时间概率密度函数及土壤盐分平均孔隙流速和水动力弥散系数,进行了盐分出流过程的数学模拟,同时对描述稳定流场中土壤盐分对流迁移特征的有关参量进行了初步分析。     

弥散度及其在地下水污染模型中的作用

弥散理论是污染质在含水层中运移模型的基本理论.但在实际应用中存在着不少问题和争议.本文对污染质在含水层中运移的弥散作用进行了分析探讨.并应用MOC水质模型对弥散参数的作用进行了分析,证明了在一般情况下,污染质在含水层中的运移主要受对流作用控制,弥散参数的变化对水质模型结果的影响相对较小.在特定的水文地质条件下,弥散作用对污染质的运移是重要的.     

改进时间分数阶模型模拟非Fick溶质运移

通过将经典时间分数阶对流-弥散方程的等待时间分布函数的尾部修改为指数型,推导出了改进时间分数阶对流-弥散方程,并提出有效的时空算子分裂数值求解方法。对两个理想算例和一个实际算例进行计算,结果表明,改进的时间分数阶对流-弥散方程继承了时间分数阶对流-弥散方程能模拟穿透曲线幂率型拖尾分布的优点,还可模拟穿透曲线尾部由幂率型转换到指数型的过程;特征时间λ、分数阶指数γ和两相容量比例系数β共同决定了运移行为。改进的新模型可以区分非均质介质中流动相和非流动相中的溶质浓度, 更细微地模拟非Fick溶质运移行为。     

水箱-管道系统溶质运移实验研究及其岩溶水文地质意义

为了研究岩溶管道中溶潭对溶质运移的影响,在实验室内构建水箱-管道系统,在不同管道结构和水流条件下进行定量示踪实验并得到相应的穿透曲线(BTCs);采用Qtracer2软件分析溶质运移参数,采用滞后系数R分析实验结果与一维经典对流弥散方程解析解之间的差别。实验结果显示:随着水箱数量的增加,示踪剂(NaCl)峰值质量浓度逐渐降低,弥散系数和弥散度逐渐增加,穿透曲线拖尾逐渐增长,表明水箱的瞬态存储使溶质运移滞后;与不对称水箱相比,对称水箱BTC拖尾较长;峰现时间随着不对称水箱数量的增多明显滞后;出口流量增加时,弥散度减小,BTC拖尾变短。一维经典对流弥散方程解析解仅对单管道最大流量条件下的BTC拟合较好,对流量较小的单管道和水箱-管道系统的BTC拟合较差,需研究适用的模型解释其拖尾现象。     

判定地下水二维水动力弥散参数的直线图解法

弥散参数的求得，是正确认识地下水污染运移及对其控制的前提。本文根据极值理论和非线性方程线性化手段，导出了浓度和时间变化的线性关系，得出了确定弥散参数的直线图解法。它可以弥补其它方法的不足。借用实际弥散试验资料对其进行了检验，表明所建数学模型与实际模型之间吻合良好，即所求得的参数结果可信。     

Analytical solutions of one-dimensional advection-diffusion equation with variable coefficients in a finite domain

Analytical solutions are obtained for one-dimensional advection-diffusion equation with variable coefficients in a longitudinal finite initially solute free domain, for two dispersion problems. In the first one, temporally dependent solute dispersion along uniform flow in homogeneous domain is studied. In the second problem the velocity is considered spatially dependent due to the inhomogeneity of the domain and the dispersion is considered proportional to the square of the velocity. The velocity is linearly interpolated to represent small increase in it along the finite domain. This analytical solution is compared with the numerical solution in case the dispersion is proportional to the same linearly interpolated velocity. The input condition is considered continuous of uniform and of increasing nature both. The analytical solutions are obtained by using Laplace transformation technique. In that process new independent space and time variables have been introduced. The effects of the dependency of dispersion with time and the inhomogeneity of the domain on the solute transport are studied separately with the help of graphs.     

Effects of Local Dispersion and Kinetic Sorption on Evolution of Concentration Variance in a Heterogeneous Aquifer

A Eulerian stochastic method is applied to develop a theory of concentration variance for solute transport in a heterogeneous medium. The study focuses on the effects of kinetic sorption and local dispersion on solute dissipation. Spatial distribution of the concentration variance is obtained by scaling the zero local dispersion form of σ_c ². The scaling function resulting from the local dispersion and kinetic sorption is derived in a closed integral form. It satisfies the measurement of total concentration variance resulting from the Eulerian mass balance using spatially integrated concentration moments. The spatially integrated moments bypass the need for classical closures applied to joint moments between concentration and velocity fields. The study results indicate that kinetic sorption reduces the total development of concentration variance in comparison with non-reactive solute transport. Kinetic sorption acts as a reduction mechanism, but not as a dissipating mechanism like the local dispersion. Kinetic sorption and local dispersion are not additive processes and their effects on the concentration variance depend on the stage of transport time.     

One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

The one-dimensional linear advection–diffusion equation is solved analytically by using the Laplace integral transform. The solute transport as well as the flow field is considered to be unsteady, both of independent patterns. The solute dispersion occurs through an inhomogeneous semi-infinite medium. Hence, velocity is considered to be an increasing function of the space variable, linearly interpolated in a finite domain in which solute dispersion behaviour is studied. Dispersion is considered to be proportional to the square of the spatial linear function. Thus, the coefficients of the advection–diffusion equation are functions of both the independent variables, but the expression for each coefficient is considered in degenerate form. These coefficients are reduced into constant coefficients with the help of a new space variable, introduced in our earlier works, and new time variables. The source of the solute is considered to be a stationary uniform point source of pulse type.     

区域地下水溶质运移随机理论的研究与进展

在总结近年来国内外区域地下水溶质运动研究的基本理论、方法和部分成果的基础上,论述了溶质在大区域运动的主要影响因素为区域介质的空间变异性。首先总结了野外条件下饱和介质和非饱和介质土壤渗透性能的空间变异性结果,由于野外渗透介质严重的空间变异性,研究溶质在野外条件下的运动采用了随机理论方法。基于Lagrange方法和Euler方法,研究结果表明,在渗透系数为对数正态二阶平稳及一阶扰动近似条件下,平均浓度满足对流－弥散方程,方程中宏观弥散度决定于介质渗透性能的统计特征,总结了一系列宏观弥散系数的表达形式,在此基础上,指出了需要进一步研究的问题。     

Three-dimensional temporally dependent dispersion through porous media: analytical solution

A three-dimensional model for non-reactive solute transport in physically homogeneous subsurface porous media is presented. The model involves solution of the advection-dispersion equation, which additionally considered temporally dependent dispersion. The model also account for a uniform flow field, first-order decay which is inversely proportional to the dispersion coefficient and retardation factor. Porous media with semi-infinite domain is considered. Initially, the space domain is not solute free. Analytical solutions are obtained for uniform and varying pulse-type input source conditions. The governing solute transport equation is solved analytically by employing Laplace transformation technique (LTT). The solutions are illustrated and the behavior of solute transport may be observed for different values of retardation factor, for which simpler models that account for solute adsorption through a retardation factor may yield a misleading assessment of solute transport in ‘‘hydrologically sensitive’’ subsurface environments.     

Experimental investigation of contaminant migration in filled fracture

Experiment equipments involved in the single tube fracture and double tube fracture models are designed to research the characteristics of groundwater flow and solute transport in filled fracture. During the experiment, the state of groundwater flow can be characterized as linear flow, and satisfies Darcy’s law. Therefore, based on the pipe flow of hydraulics and Darcy’s law, the flow rate and water flow velocity can be calculated. Also, dispersion parameters were calculated with the fitting of observed data and analytical solution in the single tube fracture model. Furthermore, effects of some factors on solute transport are involved in the double tube fracture model, and length of branch fracture, particles’ diameter and flow rate in water inlet have been discussed. Results show that the arrival time of concentration peak value in the single tube fracture model is faster than that in the double tube fracture model, and two concentration peak values exist in the double tube fracture model. Arrival time of concentration peak value is faster with the increase of branch fracture length. Furthermore, if the branch fracture is longer, arrival time of the first concentration peak value is faster, while arrival time of the second concentration peak value is slower, relative to short branch fracture.     

Analytical solutions for advective–dispersive solute transport in double‐layered finite porous media

Analytical solutions for advection and dispersion of a conservative solute in a one‐dimensional double‐layered finite porous media are presented. The solutions are applicable to five scenarios that have various combinations of fixed concentration, fixed flux and zero concentration gradient conditions at the inlet and outlet boundaries that provide a wide number of options. Arbitrary initial solute concentration distributions throughout the media can be considered via explicit formulations or numerical integration. The analytical solutions presented have been verified against numerical solutions from a finite‐element‐based approach and an existing closed‐form solution for double‐layered media with an excellent correlation being found in both cases. A practical application pertaining to advective transport induced by consolidation of underlying sediment layers on contaminant movement within a capped contaminated sediment system is presented. Comparison of the calculated concentrations and fluxes with alternative approaches clearly illustrates the need to consider advection processes. Consideration of the different features of contaminant transport due to varying pore‐water velocity fields in primary consolidation and secondary consolidation stages is achieved via the use of non‐uniform initial concentration distributions within the proposed analytical solutions. Copyright © 2010 John Wiley & Sons, Ltd.     

Simulation of chloride transport in an aggregated soil using three conceptual models

Breakthrough curves (BTCs) of chloride displaced through columns of loessial soil aggregates of different sizes were measured under saturated steady flow conditions. The data were simulated using three conceptual models. Model I (CDE) assumed that all soil water was mobile and physical equilibrium existed in the system. Model II (two-region model) partitioned the soil water into mobile and immobile regions, and convective diffusive solute transport was limited to the mobile water region. Model III (two-flow region model) also divided the soil water into two regions based on their flow velocities, but both of the regions had a non-zero flow rate. Transfer of the chloride solute between the two soil water regions was assumed to occur at a rate proportional to the difference in solute concentration. The two unknown parameters in model I, three in model II, and four in model III were estimated by fitting the experimental data. The three models could well describe all the BTCs measured for columns packed with all the aggregate sizes at the low pore water velocity (0.68 cm/h); however, the values of the fitted parameters varied greatly. The Peclet numbers derived from both the two-region (model II) and two-flow region (model III) models behaved similarly and increased with increases in aggregate size. But the Peclet numbers derived from the convection dispersion equation (model I) were about two orders of magnitude greater than those derived from the other two models. The mobile water fraction obtained for the two-flow region model decreased with increases of aggregate size. The mass transfer coefficient decreased with an increase in pore water velocity due to the shorter residence time of the chloride solute in the soil columns.     

溶质入渗土工合成衬垫的化学-渗透特性研究

溶质在土工合成衬垫（GCL）长期入渗过程中具有明显的化学-渗透特性。室内渗透试验表明：阳离子之间的置换效应对GCL衬垫渗透系数影响较大,10 mM的CaCl2溶液使渗透系数上升至2.5×10-11 m/s,而30 mM的CaCl2溶液使渗透系数上升至5.6×10-11 m/s。渗透液体浓度的增加缩短了溶质穿透GCL的时间,且预饱和处理试剂对GCL渗透系数的变化影响较大,采用蒸馏水作为预饱和试剂处理GCL衬垫对其渗透系数的影响明显小于CaCl2溶液;建立了考虑膜效应和离子交换效应条件下溶质运移耦合动力学模型,并对GCL穿透试验过程中溶质浓度的变化进行了预测,仿真计算结果表明,10 mM和30 mM两种CaCl2溶液渗透条件下,Ca2+浓度变化的试验结果和计算结果均相吻合,验证了耦合动力学模型的可靠性;从Ca2+浓度及流量穿透曲线分布可知,化学-渗透效应可有效地延缓溶质的迁移速度。随着溶质浓度的降低,阻滞作用更显著。因此,在分析GCL衬垫中溶质入渗特征时,必须考虑化学-渗透效应的影响。     

Quantification of electrical resistance to estimate NaCl behavior in a column under controlled conditions

Accurate prediction of solute transport processes in surface water and its underlying bed is an important task not only for proper management of the surface water but also for pollution control in these water bodies. Key issue in this task is an estimation of parameters as diffusion coefficient and velocity for solute transport both in water body and in the underlying bed. This estimation would greatly help us to understand the deposition and release mechanism of solute across the water-bed interface. In this study, a column experiment was conducted in laboratory to estimate the velocity and diffusion coefficient of sodium chloride (NaCl) in water body and underlying sand layer (bed). The column used with a diameter of 30 cm and a height of 100 cm, was filled with sand at the lower half part and water at the upper half part. Total 64 stainless steel electrodes were installed on its surface around. The sodium chloride solution was injected from the top of the column, and electrical resistance between electrodes was monitored for 71 h. Then the dimensionless resistance breakthrough curve was fitted with one dimensional analytic solution for solute transport and the related diffusion coefficient and velocity parameters were estimated. The results show that the NaCl transport velocity was high in the water body but extremely low in the underlying sand layer (bed). The diffusion coefficient estimated in sand layer coincides with those reported well. This indicates that the electrical resistance based solute transport parameter estimation method is not only effective but also has an advantage of multipoints monitoring. This is useful both in mapping solute transport parameter for solute transport process analysis and in providing parameter input for solute transport numerical modeling.