The analysis of pollutant migration through soil with linear hereditary time-dependent sorption

This paper presents a non-equilibrium sorption dispersion–advection transport model for the analysis of pollutant migration through soil. The formulation involves a convolution integral of the product of the rate of change of concentration and a time-dependent sorption coefficient, suggesting an integral transformation of the governing equations. This facilitates the primary purpose of this paper, to incorporate a time-dependent solute sorption process into a computationally efficient and accurate semi-analytic Laplace transform method. An application of the non-equilibrium sorption model for backfiguring dispersion–advection equation parameters from experimental data is presented, and the implications of non-equilibrium sorption on the design of landfill liners is explored by means of an illustrative example.     

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.     

A Symmetrical Streamline Stabilization scheme for high advective transport

An overview of numerical techniques and previous investigations related to the solution of advection‐dominated transport processes is presented. In addition a new Symmetrical Streamline Stabilization (S³) scheme is introduced. The basis of the technique is to treat the transport equation in two steps. In the first step the dispersion part is approximated by a standard Galerkin approach, while in the second step the advection is approximated by a least‐squares method. The two parts are reassembled, resulting in one system of equations. The resulting coefficients' matrix is symmetric. Only half of a sparse matrix needs to be stored. Robust iterative algorithms for symmetrical systems of equations such as the preconditioned conjugate gradient method (PCG) can be successfully used. The new method leads to an implicit introduction of an ‘artificial diffusion’ term. Solute transport with high Peclet and Courant numbers does not lead to oscillations due to an inherent upwind damping. The upwind effect acts only in flow direction. The efficiency of the new formulation in terms of accuracy and computation time is shown in comparison with the Galerkin approach for mesh parallel and mesh oblique high advective solute transport. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

Solute transfer during consolidation based on a solid‐fluid‐solute coupling model

The migration of contaminant through soil is usually modeled using the advection‐dispersion equation and assumes that the porous media is stationary without introducing a constitutive equation to represent soil structure. Consequently, time‐dependent deformation induced by soil consolidation or physical remediation is not considered, despite the need to consider these variables during planning for the remediation of contaminated ground, the prediction of contaminated groundwater movement, and the design of engineered landfills. This study focuses on the numerical modeling of solute transfer during consolidation as a first step to resolve some of these issues. We combine a coupling theory‐based mass conservation law for soil‐fluid‐solute phases with finite element modeling to simulate solute transfer during deformation and groundwater convection. We also assessed the sensitivity of solute transfer to the initial boundary conditions. The modeling shows the migration of solute toward the ground surface as a result of ground settlement and the dissipation of excess pore water pressure. The form of solute transport is dependent on the ground conditions, including factors such as the loading schedule, contamination depth, and water content. The results indicate that an understanding of the interaction between coupling phases is essential in predicting solute transfer in ground deformation and could provide an appropriate approach to ground management for soil remediation.     

Validity of a sharp-interface model in a confined coastal aquifer

 The problem of seawater intrusion is considered for the case of a confined coastal aquifer in which there is steady seaward flow of fresh water. Using the GWCH2O model, the problem is solved first for the case of no dispersion where a distinct interface exists separating the fresh water from the salt water. The problem is solved next by taking into account dispersion and diffusion of the salt-water component, along with the density effect. In this respect, a two-dimensional finite-element model, 2D-VDTRAN, is developed to simulate density-dependent solute transport. To investigate the limitation of the sharp-interface approach in coastal aquifers for conditions of both steady state and unsteady state, the problem is solved twice using the two models with different parameter values. These parameters are combined in dimensionless form, resulting in four named parameters: seepage factor (A); dispersion-to-advection ratio (B); geometry ratio (C); and time-scale factor (T). Using the density-dependent model, the dimensionless width of the transition zone (W/L) is determined for different values of A, B, C, and T. Steady-state simulations show that the sharp-interface approach is valid only when the system is dominated by advection, i.e., when 0<B≤5% for all values of A and C, or when A≥65% for all values of B and C. However, the unsteady-state analysis shows that the applicability of the sharp-interface approach is sufficiently accurate at early times. Received, October 1997 Revised, June 1998, October 1998 Accepted, November 1998     

Regional-scale analysis of karst underground flow deduced from tracing experiments: examples from carbonate aquifers in Malaga province,southern Spain

Tracer concentration data from field experiments conducted in several carbonate aquifers (Malaga province, southern Spain) were analyzed following a dual approach based on the graphical evaluation method (GEM) and solute transport modeling to decipher flow mechanisms in karst systems at regional scale. The results show that conduit system geometry and flow conditions are the principal factors influencing tracer migration through the examined karst flow routes. Solute transport is mainly controlled by longitudinal advection and dispersion throughout the conduit length, but also by flow partitioning between mobile and immobile fluid phases, while the matrix diffusion process appears to be less relevant. The simulation of tracer breakthrough curves (BTCs) suggests that diffuse and concentrated flow through the unsaturated zone can have equivalent transport properties under extreme recharge, with high flow velocities and efficient mixing due to the high hydraulic gradients generated. Tracer mobilization within the saturated zone under low flow conditions mainly depends on the hydrodynamics (rather than on the karst conduit development), which promote a lower longitudinal advection and retardation in the tracer migration, resulting in a marked tailing effect of BTCs. The analytical advection-dispersion equation better approximates the effective flow velocity and longitudinal dispersion estimations provided by the GEM, while the non-equilibrium transport model achieves a better adjustment of most asymmetric and long-tailed BTCs. The assessment of karst underground flow properties from tracing tests at regional scale can aid design of groundwater management and protection strategies, particularly in large hydrogeological systems (i.e. transboundary carbonate aquifers) and/or in poorly investigated ones.     

A general polynomial solution to convection–dispersion equation using boundary layer theory

A number of models have been established to simulate the behaviour of solute transport due to chemical pollution, both in croplands and groundwater systems. An approximate polynomial solution to convection–dispersion equation (CDE) based on boundary layer theory has been verified for the use to describe solute transport in semi-infinite systems such as soil column. However, previous studies have only proposed low order polynomial solutions such as parabolic and cubic polynomials. This paper presents a general polynomial boundary layer solution to CDE. Comparison with exact solution suggests the prediction accuracy of the boundary layer solution varies with the order of polynomial expression and soil transport parameters. The results show that prediction accuracy increases with increasing order up to parabolic or cubic polynomial function and with no distinct relationship between accuracy and order for higher order polynomials (\(n\geqslant 3\)). Comparison of two critical solute transport parameters (i.e., dispersion coefficient and retardation factor), estimated by the boundary layer solution and obtained by CXTFIT curve-fitting, shows a good agreement. The study shows that the general solution can determine the appropriate orders of polynomials for approximate CDE solutions that best describe solute concentration profiles and optimal solute transport parameters. Furthermore, the general polynomial solution to CDE provides a simple approach to solute transport problems, a criterion for choosing the right orders of polynomials for soils with different transport parameters. It is also a potential approach for estimating solute transport parameters of soils in the field.     

A new numerical method of considering local longitudinal dispersion in single fractures

The solutions of advection–dispersion equation in single fractures were carefully reviewed, and their relationships were addressed. The classic solution, which represents the resident or flux concentration within the semi‐infinite fractures under constant concentration or flux boundary conditions, respectively, describes the effluent concentration for a finite fracture. In addition, it also predicts the cumulative distribution of solute particle residence time passing through a single fracture under pulse injection condition, based on which a particle tracking approach was developed to simulate the local advection–dispersion in single fractures. We applied the proposed method to investigate the influence of local dispersion in single fractures on the macrodispersion in different fracture systems with relatively high fracture density. The results show that the effects of local dispersion on macrodispersion are dependent on the heterogeneity of fracture system, but generally the local dispersion plays limited roles on marodispersion at least in dense fracture network. This trend was in agreement with the macrodispersion in heterogeneous porous media. Copyright © 2013 John Wiley & Sons, Ltd.     

求解非稳定对流占优水质模型的非标准Galerkin有限元法

在求解非稳定地下水溶质运移模型时,若对流项占优,则模型表现出双曲方程的特性。针对这种特性,采用非标准Galerkin有限元方法进行求解是解决这类问题的有效途径。分别采用Wavelet-Galer-kin有限元方法、迎风有限元方法和特征有限元方法对强对流溶质运移模型进行了求解,并将其结果与标准Galerkin有限元和解析解进行对比。结果表明:标准Galerkin有限元方法会产生强烈的数值振荡;Wavelet-Galerkin有限元方法的时空定位效果好;迎风有限元方法能够有效降低数值振荡现象,但迎风因子对解的影响较大,而且会带来时间延迟;特征有限元方法能够提高解的精度,故可以认为特征有限元方法是求解强对流地下水溶质运移模型的首选方法。     

Field characterization of vertical bromide transport in a fractured glacial till

A study of the fracture distribution, hydraulic properties, groundwater levels and the transport of bromide was conducted to characterize vertical transport in the oxidized and reduced zones of a fractured glacial till. Detailed vertical profiles of groundwater levels and solute concentrations were obtained over a 4.5-year period. Vertical migration occurred at several time scales, as a low concentration front was rapidly transported at rates of 100–500 m/year ahead of a slower moving main plume, which advanced at rates of 0.2–0.8 m/year. Concentrations in the leading edge of the plume displayed a high degree of spatial variability over short vertical distances through day 1,000. Late in the test, the influence of matrix diffusion became apparent as concentration patterns developed from being irregular to more uniform distributions. Calculations show that the mass within the low concentration plume front accounts for less than 1% of the total solute mass. Simulation of the breakthrough curves using a simple one-dimensional advection-dispersion model of transport in porous media indicates that vertical transport is dominated by advection. Furthermore, the results indicate that vertical transport of solutes in oxidized and reduced zones of the till can be adequately simulated using an equivalent porous media.     

土柱变密度溶质运移试验推求水平及垂直方向弥散度研究

基于溶质运移对流弥散理论的变密度海水入侵模型广泛用于海水入侵研究,而水动力弥散系数是影响模型模拟效果的关键性参量之一。利用传统土柱溶质运移试验结合旁侧抽水,采用数值反演法成功获取了水平及垂直两方向弥散度。相对于传统方法,在不增加试验复杂度的前提下,同时推求了不同方向的弥散度,提高了试验效率,节约了试验成本,可广泛用于测定水动力弥散系数等参数。     

井内混合效应与尺度效应对注入井附近溶质径向弥散过程的影响

径向弥散是指溶质在径向流场下的迁移规律,被广泛用于描述含水层修复领域中污染物的迁移过程.然而,在现有描述径向弥散的模型中,往往忽略了井内混合效应对溶质径向弥散的影响.建立新的注入井附近溶质径向运移动力学模型,同时考虑井内混合效应与弥散度的尺度效应.采用Laplace变换推导该模型的半解析解,利用Stehfest数值逆变换获取溶质在实数空间的解.通过与不考虑混合效应的模型对比研究混合效应对溶质径向弥散的影响,并利用室内渗流槽中的溶质径向弥散实验数据验证模型的合理性与适用性.结果表明:混合效应和尺度效应对注水井附近溶质径向弥散有显著影响.具体地讲,井内的混合效应越显著,在井壁处及含水层中的穿透曲线越低,溶质浓度达到峰值所需时间越长,与不考虑混合效应模型的差异越明显;随尺度效应的增强,溶质提前穿透且扩散范围变大,溶质浓度达到峰值所需时间越长;与前人的模型相比,本研究模型能更好地模拟注水井附近的溶质径向弥散问题.      

地下水溶质迁移模拟研究进展

在地下水的相关研究中,农药和石油等地下水污染、土地盐碱化、海水入侵等诸多实际问题主要的研究方法都涉及地下水溶质迁移模拟. 相比地下水水流模拟的相对完善,对溶质迁移的模拟比较薄弱且迁移过程本身复杂性较高,目前地下水溶质迁移的研究工作还处在全面发展的阶段. 文中阐述了反映地下水溶质迁移机理和过程的数学模型,综述了溶质迁移模拟在地下水污染物防治、土地盐碱化、海水入侵、石油和放射性废物扩散等问题的诸多应用,归类了目前溶质迁移模拟所使用的对流迁移、对流-弥散模拟等主要数值方法,并对这些方法的优缺点和应用实例做了总结. 最后,分析了目前溶质迁移模拟中存在的不足,展望了未来在参数确定、裂隙介质运移机理和多相介质条件下运移模拟可能取得的突破.     

Godunov Mixed Methods on Triangular Grids for Advection–Dispersion Equations

A time-splitting approach for advection–dispersion equations is considered. The dispersive and advective fluxes are split into two separate partial differential equations (PDEs), one containing the dispersive term and the other one the advective term. On triangular elements a triangle-based high resolution Finite Volume (FV) scheme for advection is combined with a Mixed Hybrid Finite Element (MHFE) technique to solve dispersion. This approach introduces an error proportional to the time step and the overall scheme is only first order accurate if special care is not taken in the definition of the numerical flux approximation for advection. By incorporating the diffusive effects into the definition of this numerical flux, near second order accuracy (up to a logh factor) can be proved theoretically and validated by numerical experiments in both one- and two-dimensional cases.     

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.     

氯离子在黏土-膨润土屏障中迁移的离心试验研究

将对流-扩散试验装置置于土工离心机中,以50g离心加速度运行12 h,研究了黏土-膨润土混合土样中Cl-的迁移扩散,使用解析解对试验结果进行拟合确定相关参数,分析了试验的相似条件,使用商用软件对离心试验原型进行模拟,与试验结果进行比较,探讨了离心机用于溶质迁移分析的比尺效应,最后通过数值分析研究了试验的黏土-膨润土屏障用于老垃圾填埋场防渗帷幕补强的效果。结果表明,土工离心机试验中,按实际出流量计算的实际孔隙水流速小于临界流速,两试样中的佩克莱数（Pe数）小于临界Pe数,机械弥散的作用可以忽略,试验满足扩散的相似定律;离心机试验所模拟的2.5 m厚衬垫原型,在水头5 m和10 m作用下3.42 a后均未被击穿;常重力下试验土样的渗透系数为8.5×10-8 cm/s,有效扩散系数为7.82×10-7 cm2/s,对试验原型进行的数值模拟表明,n倍重力加速度下,土工离心机可以 尺寸的试样实现对原型的模拟,同时将对流和扩散作用下的溶质迁移时间缩短至原型的 ;试验的黏土-膨润土屏障用于老垃圾填埋场防渗补强,可显著减缓溶质迁移,防渗补强后可满足渗滤液迁移扩散的控制要求。     

西宁市贵德县河滨公园林场第四系含水层弥散试验研究

地下水污染问题日益严重,研究溶质运移的弥散理论开始应用于实际问题。建立地下水溶质运移模型,对地下水中污染物的运移及发展趋势进行准确预测,是对地下水进行保护、对地下水污染进行控制的基础。而弥散参数的确定则是地下水溶质运移模型建立的关键环节之一,直接影响着模型预测结果的精度和准确性。 对西宁市贵德县地下水污染的水质运移规律进行分析,在贵德县河滨公园林场采用径向收敛流水动力弥散理论方法进行了第四系含水层现场弥散试验,计算了试验场地潜水含水层的弥散度,获得纵向弥散度(a_L)为0.843~0.998 cm,横向弥散度(a_T)经验推断值为0.17~0.20 cm,为进一步建立该地区的地下水溶质运移模型、预测地下水污染的发展趋势和评价该地区地下水环境质量提供了数据参考。     

Comparison Between Analytical and Numerical Methods in Evaluating the Pollution Transport in Porous Media

Contaminant transport modelling in environmental engineering is generally conducted to evaluate the potential impact of contaminant migration on the subsurface environment or for interpreting tracer tests or groundwater quality data. In the past few decades a number of mathematical models have been established for evaluating the migration of pollution as indicated in the literature. This paper presents a comparison between a number of analytical and numerical models in evaluating pollution transport in soils. Three analytical models and a finite element model developed in this research are used for comparing four numerical examples under different conditions. Four cases of advection dominated problem with line source boundary, advection dominated problem with semi-line source boundary, advection–dispersion–sorption problem with line source boundary and advection–dispersion–sorption problem with semi-line source are considered. Based on the results the best analytical model that has a higher accuracy is recommended for practical applications.     

The transport of heat and matter by fluids during metamorphism

Non-dimensional solutions to the equations for the combined advective and diffusive one-dimensional transport of heat and solute in a layer are derived for fixed temperature/concentration on the boundaries and initial conditions of a linear gradient across the layer or a step function at the lower boundary. The solutions allow distinction of regimes in which advective or diffusive transport of either heat or solute predominate as a function of fluid flux, time and a length scale. The much lower diffusive coefficients for solute than heat results in a significant range of length scales and fluid flux rates characterised by advection of matter and diffusion of heat. The advective velocity of a component is a function of its fluid:rock partition coefficient. The most rapidly transported tracers which partition largely into the fluid phase, such as He, will travel orders of magnitude faster than heat or compatible solutes such as oxygen. Geochemical profiles in boundary layer regions where both advective and diffusive transport are significant are shown to be particularly informative as to properties of the rocks related to fluid flow such as porosity, permeability, time scales and fluid flux rates. The importance of advection can be directly estimated from the asymmetry of the geochemical profiles across individual layers.