Analytic solutions to the advective contaminant transport equation with non-linear sorption

This paper considers advective transport of a soluble contaminant through saturated soil with non-linear sorption of the contaminant onto a stationary porous media. The non-linear sorption isotherms considered in the transport analysis are the Langmuir and Freundlich sorption isotherms. A special case of the Freundlich sorption isotherm is the linear sorption isotherm, and it is shown that in this case transport through a homogeneous soil results in the initial concentration profile simply being translated in the direction of the groundwater flow. However, when the sorption isotherm is non-linear the initial concentration profile distorts as it is translated with the groundwater flow, leading to the development of concentration shock fronts and rarefactions. Analytic solutions to the non-linear first-order hyperbolic equations are developed for a number of contaminant transport problems of practical significance. It is shown that in the case of the Langmuir sorption isotherms, shock fronts develop at the leading edge of the concentration profile while for the Freundlich sorption isotherm shock fronts may develop at either the leading or trailing edge of the concentration profile. Copyright © 1999 John Wiley & Sons Ltd.     

非平衡-非线性吸附情况下填埋场污染物运移分析

采用Langmuir等温吸附线方程描述非线性吸附性能, 基于改进的混合元方法，通过数值计算与分析，探讨了非平衡吸附条件下污染物运移过程及其机理。计算结果表明: 当考虑非平衡、非线性吸附性能时, 污染物穿透曲线即浓度的时程变化曲线尖锐而狭窄、峰值点前移, “拖长尾”现象不明显, 由此说明，土颗粒对污染物的非平衡、非线性吸附使得污染物的穿透能力增强, 滞留能力下降。进一步的变动参数比较分析表明：Langmuir等温线方程中的参数B、压实粘土衬里的渗透性及地下水渗流速度对污染物运移过程具有显著的影响。     

考虑非等温环境下污染物在黏土中的运移解析模型

利用广义积分变换法推导了非等温条件下污染物在压实黏土衬垫中的运移解析解。所提出的解析解考虑了分子扩散、对流、吸附和热扩散的耦合效应,并考虑了压实黏土的渗透系数、分布系数和有效扩散系数3个参数随温度的变化。通过与热扩散试验结果、已有的解析解和基于COMSOL软件的数值模型的对比,验证了所提出的解析解。利用经过验证的解析解,研究了非等温环境以及压实黏土的渗透系数、有效扩散系数和分布系数3个参数随温度的变化对甲苯在压实黏土衬垫系统中迁移的影响。结果表明,非等温环境以及压实黏土的渗透系数、有效扩散系数和分布系数随温度的变化均对甲苯在压实黏土衬垫中迁移有着显著的影响。不考虑非等温环境的影响将极大低估污染物的溢出量和污染物的击穿时间。既有解析解忽略压实黏土的渗透系数和有效扩散系数随温度的变化会极大低估甲苯的流出速率,而忽略压实黏土分布系数随温度的变化会极大高估甲苯击穿衬垫系统的时间和达到稳态的时间。所提出的解析解能够考虑热扩散作用,同时考虑了压实黏土的渗透系数、分布系数和有效扩散系数3个参数随温度的变化,较既有解析解更贴近工程实际,能够为压实黏土衬垫系统的设计和服役性能评价提供指导和借鉴。     

裂隙岩体中污染物运移过程的数值模拟

基于双重介质理论模型建立了污染物在地下环境中运移的耦合数学模型,给出了有限元离散的数值格式。并以核废料储存过程中核素90Sr为例,采用所建立的数值模型模拟其在裂隙岩体中运移过程,预测了污染物的浓度分布范围和发展趋势。模拟结果表明:核素90Sr在处置库中运行40年后,下游地区的抽水井的浓度可达到3 100 Bq/m3,超出了国家规定的标准,为固体废物场址的选择以及污染的控制提供了决策依据。     

Numerical study of soil heterogeneity effects on contaminant transport in unsaturated soil (model development and validation)

The movement of chemicals through soil to groundwater is a major cause of degradation of water resources. In many cases, serious human and stock health implications are associated with this form of pollution. The study of the effects of different factors involved in transport phenomena can provide valuable information to find the best remediation approaches. Numerical models are increasingly being used for predicting or analyzing solute transport processes in soils and groundwater. This article presents the development of a stochastic finite element model for the simulation of contaminant transport through soils with the main focus being on the incorporation of the effects of soil heterogeneity in the model. The governing equations of contaminant transport are presented. The mathematical framework and the numerical implementation of the model are described. The comparison of the results obtained from the developed stochastic model with those obtained from a deterministic method and some experimental results shows that the stochastic model is capable of predicting the transport of solutes in unsaturated soil with higher accuracy than deterministic one. The importance of the consideration of the effects of soil heterogeneity on contaminant fate is highlighted through a sensitivity analysis regarding the variance of saturated hydraulic conductivity as an index of soil heterogeneity. Copyright © 2011 John Wiley & Sons, Ltd.     

大变形黏土防渗层中的污染物迁移和转化规律研究

国内湖泊疏浚污染底泥堆场一般以较厚的黏土层作为主要防渗层,由于在上覆底泥作用下黏土层会发生较大的固结变形,因此,在研究黏土防渗层中的污染物运移和转化规律时,应该考虑土体变形的影响。基于Gibson一维大变形固结理论和饱和多孔介质中的污染物对流扩散方程,建立了二者耦合的可变形多孔介质中污染物的运移和转化模型,其中首次考虑了土体自重和生物降解作用的影响。利用所建立模型的数值解,研究了在可变形黏土防渗层中的污染物运移和转化规律,同时分析了模型中不同项和主要参数的作用和影响。研究结果表明,土体大变形对黏土防渗层中污染物的运移有着较复杂的影响,一方面土体变形会加速污染物的运移;另一方面土体固结带来的渗透性减小会增加污染物的穿透时间,二者的不同作用取决于众多的影响因素,如土层厚度和吸附作用等。研究结果对于评估天然黏土防渗层对污染物的阻隔作用有重要的指导意义。     

Modelling of contaminant transport through landfill liners using EFGM

Modelling of contaminant transport through landfill liners and natural soil deposits is an important area of research activity in geoenvironmental engineering. Conventional mesh‐based numerical methods depend on mesh/grid size and element connectivity and possess some difficulties when dealing with advection‐dominant transport problems. In the present investigation, an attempt has been made to provide a simple but sufficiently accurate methodology for numerical simulation of the two‐dimensional contaminant transport through the saturated homogeneous porous media and landfill liners using element‐free Galerkin method (EFGM). In the EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no characterization of the interrelationship of the nodes is needed. The EFGM employs moving least‐square approximants to approximate the function and uses the Lagrange multiplier method for imposing essential boundary conditions. The results of the EFGM are validated using experimental results. Analytical and finite element solutions are also used to compare the results of the EFGM. In order to test the practical applicability and performance of the EFGM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the EFGM and the field investigation data. Copyright © 2009 John Wiley & Sons, Ltd.     

考虑土体固结变形的污染物运移模型

土体的固结压缩变形对污染物的运移具有重要的影响,而目前国内关于污染物在变形多孔介质中运移规律的研究尚处于空白,在国外也是近几年才有人开始这方面的研究工作。在Biot固结理论和污染物运移理论相结合的基础上,提出了污染物在黏土防渗层中迁移转化的一维数学模型,该模型的最大特点是考虑了土体受力变形对污染物运移的影响,在合理简化的基础上给出了模型的解析解,并将计算结果与太湖疏浚污染底泥堆场的实测结果进行了比较分析,模拟计算的结果在一定程度上能够反映实际土层中污染物的运移情况。     

Numerical modelling of competitive components transport with non‐linear adsorption

A characteristic finite element (CFE) algorithm for modelling contaminant transport problems coupled with non‐linear competitive adsorption is presented. An alternative algorithm, termed as the transport‐equilibrium Petrov–Galerkin (TEPG) methods in this paper, is also presented for comparison. Through analyses of a number of examples with Peclet number ranging from zero to infinity, it is shown that the CFE algorithm is very competitive with the middle–point TEPG method in terms of accuracy, stability and efficiency. The fully explicit and fully implicit TEPG methods are found to be less appropriate for transport problems coupled with non‐linear equilibrium equations. Copyright © 2000 John Wiley & Sons, Ltd.     

渗透作用下多孔介质中循环浓度污染物的迁移过程研究

根据饱和多孔介质中考虑释放效应的一维渗透作用的可溶性污染物的迁移控制方程,通过Laplace变换和Fourier变换及其逆变换求得相应的通解形式。根据半无限体表面可溶性污染物点源注入情形下的基本解,通过积分方法得到半无限体表面圆形区域上作用循环浓度污染物后,在多孔介质内部污染物迁移过程的求解方法。作为一个典型算例,对渗透作用下循环浓度污染源引起的多孔介质中的迁移过程进行分析。算例表明,当污染源浓度为周期变化时,多孔介质内部污染物的浓度随时间增长由不稳定的周期变化过程逐渐过渡到稳定的循环过程,而某一深度处污染物浓度的相位则相应滞后。此时,稳定后的污染物浓度周期与污染源浓度周期相同。实际上,随多孔介质表面污染源浓度的周期变化,在靠近多孔介质表面一定深度范围内的污染物浓度在深度方向也呈增大或减小的交替变化过程。另一方面,在污染源循环变化过程中污染物不断向深处推进,而最终其影响范围限定在某一深度内。     

One‐dimensional contaminant transport through a deforming porous medium: theory and a solution for a quasi‐steady‐state problem

Contaminant migration through soil is usually modelled mathematically using the dispersion–advection equation. This type of model finds application when planning the remediation of contaminated land, predicting the movement of polluted groundwater and designing engineered landfills. Usually the analysis assumes that the porous media through which the contaminant migrates is stationary. However, the construction of landfills on clay soils means that the soil beneath the landfill will undergo time‐dependent deformation as the soil consolidates. To date, there are no published data on the effect a deforming porous media may have on contaminant transport beneath a landfill; indeed, there appears to be no theory of contaminant migration through a deforming soil. In this paper, a one‐dimensional theory of contaminant migration through a saturated deforming porous media is developed based on a small and large strain analysis of a consolidating soil and conservation of contaminant mass. By selection of suitable parameters, the new transport equation reduces to the familiar one‐dimensional dispersion–advection equation for a saturated soil with linear, reversible, equilibrium controlled sorption of the contaminant onto the soil skeleton. Analytic solutions to a quasi‐steady‐state contaminant transport problem for a deforming media are presented, and a preliminary assessment made of the potential importance of soil deformation on the results of a contaminant migration analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

基于非达西渗流的软土一维非线性固结半解析解

在土中渗流遵循非达西渗流定律的前提下,考虑软土在固结过程中的非线性固结特性,根据饱和土体一维固结的连续条件,推导出基于非达西渗流的软土一维非线性固结控制方程。利用半解析方法对其进行求解,并与差分计算结果进行对比,验证半解析方法的可靠性。最后,着重分析非达西渗流与达西定律之间非线性固结性状的差别,以及不同自重应力分布方式对固结速率的影响。结果表明,考虑非达西渗流下的非线性固结速率比达西定律下要慢,且指数和临界水力坡降越大,非线性固结速率越慢。而且,作用的外荷载越小、地基土层越厚,非达西渗流下非线性固结速率的减慢愈明显。自重应力均匀分布下的非线性固结速率要比自重应力线性分布下慢,但随着荷载的增大、土层的变薄,两者之间的差别会越来越小。     

污染泥堆场处置中自重固结与污染物迁移的耦合分析

基于一维固结方程和对流-弥散方程,提出了一种用于污染泥堆场处置中自重固结与污染物迁移耦合问题的求解方法,其中,自重固结方程由解析解直接求解,污染物迁移方程由显示差分法求解。在自重固结方面,新方法可考虑线性的压缩关系和渗透关系;在污染物迁移方面,新方法能够考虑对流、扩散、机械弥散、线性和非线性吸附以及孔隙率相依的有效扩散系数。新方法与CST1数值模型进行了对比,验证了新方法的正确性。基于所提出的解,分析了固结效应、压缩系数、渗透系数和污染物初始分布形式对污染物在淤泥中迁移过程的影响。计算结果表明:固结效应、压缩性、渗透性和污染物的初始分布形式对污染物的迁移过程有着显著的影响;固结效应能显著地加速污染物的流出;土体的压缩系数越大其污染物累计流出质量越大;土体的渗透系数越大其污染物累计流出质量越大;污染物的初始分布形式对污染物的流出速率影响较大。     

渗透系数的空间变异性对污染物运移的影响研究

随机水文地质学方法,较传统的确定性方法而言,是解决非均质含水层中水流和溶质运移问题的一种更为合理的手段。据以往研究,假设渗透系数场遵循对数正态分布,利用直接傅立叶变换方法来生成渗透系数随机场。应用基于随机理论的蒙特卡罗方法,来研究渗透系数的空间变异性对污染物运移结果的影响。实例研究表明,污染物在含水层中运移过程中污染羽的展布范围(二阶矩)随着渗透系数空间变异方差的增大而扩大,而污染羽在空间上的质心位置(一阶矩)基本不受方差的影响,仅取决于渗透系数随机场的均值大小。另外还分析了污染羽在各点的浓度变化方差和变异系数分别随渗透系数变异方差的变化状况。     

Numerical model of contaminant transport through conduit-porous matrix system

A mathematical model for determining solute concentrations at a point within a cylindrically symmetrical conduit-porous matrix system is described. Both convection and diffusion are considered within the conduit subsystem, whereas only diffusion is considered within the porous matrix subsystem. The two subsystems are coupled through continuity conditions imposed at their interface boundary. The transport equations are solved utilizing an alternating-direction implicit-method technique. The solute concentration profiles resulting from this model are then sketched and discussed.     

结构性土一维非线性大应变固结半解析解

以结构性较强的天然饱和软黏土为研究对象,考虑了沉积作用对其自重应力的影响,以及压缩性和渗透性的非线性变化,推导了任意加载条件下结构性土一维大应变固结控制方程,并采用半解析的方法对方程进行求解计算。再将其退化为无结构性的饱和软黏土固结解,与已有的大应变固结解进行了对比,验证了该解的正确性。最后将该半解析解计算结果与小应变固结理论解、不考虑结构性的固结理论解计算结果进行对比分析。结果表明:大应变固结理论的沉降计算值大于小应变固结理论的计算值,且二者的差值随着荷载的增加而增加;当考虑土体的结构性时,地表沉降计算值小于不考虑土体结构性的沉降计算值。     

我国北方型裂隙岩溶水流及污染物运移数值模拟研究进展

简要回顾了近几十年来我国北方型裂隙岩溶水流及污染物运移数值模拟方面的研究成果,评述了裂隙岩溶水资源评价和污染物运移模拟的计算方法和模拟技术,其中对一些与数值模拟相关的重要问题、近年来研究的热点问题,如模型参数识别及其尺度效应问题、数值弥散和数值振荡问题、Non-Darcy流和Non-Fickian运移问题以及随机方法研究等进行了重点评述,对已有的解决办法进行了比较和对照,并探讨了今后的研究趋势.     

A general approach to the modelling of contaminant transport through composite landfill liners with intact or leaking geomembranes

Finite‐element models of contaminant transport through composite landfill liners require highly refined meshes around the interface between the geomembrane and the clay layer, especially if leakage through holes in the geomembrane is considered. In addition, no general formulation for transport through leaking geomembranes can be found in the literature. The paper develops a general approach to time‐dependent contaminant migration through composite liners with intact or leaking geomembranes. Equations are derived for various combinations of system conditions including Dirichlet and Neumann boundary conditions in the waste, constant mass of contaminants in the waste, steady state or transient transport in the geomembrane, and steady state or transient seepage velocities in the mineral liner. The effect of the geomembrane on transport in the soil is converted into an equivalent boundary condition applicable at the top of the clay layer. Hence, only the media underlying the top geomembrane are explicitly represented in the numerical model, yielding a computationally efficient algorithm. The new formulation is validated in conjunction with finite‐layer, finite‐element and boundary‐element methods, by comparing its predictions to those of more conventional approaches which represent the geomembrane explicitly. The scope of the method is illustrated by modelling a landfill liner with a geomembrane leaking in five locations. Copyright © 2007 John Wiley & Sons, Ltd.     

CCL吸附特性及孔隙率降低对污染物运移的影响

假定孔隙均匀地分布于土体的物质空间内和土骨架对污染物的吸附特性服从平衡线性,对基本体积质量关系进行分析,提出了由于土体对污染物的吸附而引起的孔隙率降低的估算公式。在考虑土体孔隙率变化的条件下,建立了污染物一维运移的控制方程,并考虑垃圾生物降解效应、压实黏土衬里（CCL）防渗层、下覆有限厚度含水层等实际情况,确定了初始条件和边界条件。对所建立的初边值问题进行了数值求解,且对某假想填埋场情况进行了变动参数与对比计算,结果表明,由于土颗粒对污染物的吸附所引起的孔隙率降低,显著地降低了污染物对压实黏土衬里的穿透能力。与常孔隙率情况相比,CCL中污染物的峰值浓度降低近10 %,含水层中污染物浓度降低更显著。当考虑土体孔隙率变化时,弥散对污染物运移具有控制作用,分布系数对污染物的运移具有重要影响。     

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。