Scale aspects of groundwater flow and transport systems

Flow-system analysis is based on the concept of hierarchical groundwater flow systems. The topography of the water table, which is strongly related to the topography of the land surface, is a major factor in the hierarchical nesting of gravity-driven groundwater flow, resulting in flow systems of different orders of magnitude in lateral extent and depth of penetration. The concept of flow systems is extremely useful in the analysis of spatial and temporal scales and their mutual relationships. Basic equations on the laboratory scale are extended to larger, regional scales. Making use of Fourier analysis further develops Tóth's original idea of topography-driven flow systems. In this way, the different spatial scales of the water table are separated in a natural way, leading to a simple expression for the penetration depth of a flow system. This decomposition leads also to the relationship between spatial and temporal scales. Analogous to flow systems, water bodies with different water quality may be called 'transport systems.' Field studies, numerical micro-scale modeling over macro-scale domains, and stochastic dispersion theory indicate that between systems with steady transport, the interfaces are relatively thin. The interfaces are much thinner than the relatively large mixing zones predicted by the conventional engineering approach to macrodispersion, in which relatively large, time-independent macrodispersion lengths are applied. A relatively simple alternative engineering approach is presented. For macrodispersion of propagating solute plumes, the alternative dispersion term gives the same results as the conventional engineering approach and gives correct results for steady-state transport.     

Transverse Dispersion of a Kinetically Sorbing Solute

A recursion formulation for the transverse spreading of a solute is developed, and under conditions of steady flow in a stratified aquifer, the transport of a linearly sorbing solute undergoing nonequilibrium sorption is studied. The effect of spatial variability in the velocity field and the sorption kinetics are modeled to see the combined effect of the two processes on the spreading of the solute injected at a point in the aquifer. The main result of this work is a transport model based on a discrete formulation that includes local dispersion and leads to nonasymptotic behavior in the spreading of the plume in a direction normal to the mean flow velocity.     

Numerical modeling of contaminant transport in a stratified heterogeneous aquifer with dipping anisotropy

The combined influence of dip angle and adsorption heterogeneity on solute transport mechanisms in heterogeneous media can be understood by performing simulations of steady-state flow and transient transport in a heterogeneous aquifer with dipping anisotropy. Reactive and non-reactive contaminant transport in various types of heterogeneous aquifer is studied by simulations. The hydraulic conductivity (K) of the heterogeneous aquifer is generated by HYDRO_GEN with a Gaussian correlation spectrum. By considering the heterogeneity of the adsorption distribution coefficient (K _d), a perfect negative correlation between lnK and lnK _d is obtained by using the spherical grains model. The generated K and K _d are used as input to groundwater flow and transport models to investigate the effects of dipping sedimentary heterogeneity on contaminant plume evolution. Simulation results showed that the magnitude of the dip angle strongly controls the plume evolution in the studied anisotropic and heterogeneous aquifer. The retarded average pore-water velocity (v/R) of the adsorption model significantly controls the horizontal spreading of the plume. The bottom plume is intensively retarded in the zones between the dipping lenses of lower hydraulic conductivity and the no-flow bottom boundary. The implications of these findings are very important for the management of contaminated heterogeneous aquifers.     

孔隙尺度多孔介质流体流动与溶质运移高性能模拟

深入探究孔隙尺度下的流体流动特性和溶质运移规律对石油开采、农田养分管理、地下水污染修复有着重要意义。以人工构建的多孔介质结构和同步辐射X射线显微CT扫描的土壤团聚体(分辨率3.7μm)为研究对象,在空间节点数多达64 000 000的情况下,基于格子Boltzmann模型和GPU并行技术计算得到多孔介质流体运动和溶质运移过程的关键参数,并据此探究多孔介质空间异质性对水力学特性的影响。通过对3组不同结构的多孔介质比较发现,结构复杂程度最高的土壤样品和不规则堆叠的圆球结构的渗透率在100 mD(即10^-13m^2)量级,远低于规则堆叠的圆球结构(>20 000 mD);土壤的迂曲度为1.40~1.60,明显高于规则堆叠的圆球结构。研究结果表明,渗透率大的样品具有较小的迂曲度,这与结构的空间异质性有较强的关系;土壤的渗透率和迂曲度呈现各向异性;在水力梯度一定的前提下,渗透率较大的样品,纵向弥散系数也较大;同时,结构的异质性也会影响溶质的穿透曲线。本研究提出的模拟方法可在土壤结构中进行高效的水流运动和溶质运移模拟,可用于土壤多孔介质在孔隙尺度下的水力学特性研究。     

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.     

孔隙尺度多孔介质流体流动与溶质运移高性能模拟

深入探究孔隙尺度下的流体流动特性和溶质运移规律对石油开采、农田养分管理、地下水污染修复有着重要意义。以人工构建的多孔介质结构和同步辐射X射线显微CT扫描的土壤团聚体（分辨率3.7 μm）为研究对象，在空间节点数多达64 000 000的情况下，基于格子Boltzmann模型和GPU并行技术计算得到多孔介质流体运动和溶质运移过程的关键参数，并据此探究多孔介质空间异质性对水力学特性的影响。通过对3组不同结构的多孔介质比较发现，结构复杂程度最高的土壤样品和不规则堆叠的圆球结构的渗透率在100 mD（即10^-13m²）量级，远低于规则堆叠的圆球结构（>20 000 mD）；土壤的迂曲度为1.40~1.60，明显高于规则堆叠的圆球结构。研究结果表明，渗透率大的样品具有较小的迂曲度，这与结构的空间异质性有较强的关系；土壤的渗透率和迂曲度呈现各向异性；在水力梯度一定的前提下，渗透率较大的样品，纵向弥散系数也较大；同时，结构的异质性也会影响溶质的穿透曲线。本研究提出的模拟方法可在土壤结构中进行高效的水流运动和溶质运移模拟，可用于土壤多孔介质在孔隙尺度下的水力学特性研究。     

宏观各向异性多孔介质中流体变形及溶质运移

为深入探究含水层中多孔介质的不规则形态和分布对于地下水流场及溶质运移的作用,根据沉积环境中已被发现的倾斜交叉分层地质单元结构,人为构造多孔介质双层交叉鱼骨结构,使其形成宏观各向异性水力传导特征,通过数值模拟研究该结构及其空间位置对于流场和溶质运移的影响。研究发现:宏观各向异性多孔介质引发了螺旋状流动,导致流线的拉伸和折叠,使得溶质羽发生不规则变形,显著提升了非反应性溶质的稀释程度;宏观各向异性结构和溶质羽在三维空间中的垂向相对位置对于溶质运移具有显著影响。     

非均质介质中重非水相污染物运移受泄漏速率影响数值分析

重非水相污染物(DNAPL)在地下介质中运移和分布受多种因素控制,包括DNAPL本身的物理化学性质,土的性质,泄漏条件等等。由于介质的非均质性,使得多相流运移行为更为复杂。基于地下水随机理论构建渗透率随机场,采用蒙特卡罗方法探讨泄漏速率对非均质饱和介质中DNAPL运移的影响。数值结果表明,在泄漏总量一定的情况下,泄漏速率越低,介质非均质性对DNAPL运移的影响程度越高。反之,DNAPL的渗漏速率越高,小尺度地层的非均质性影响越低。由于DNAPL运移过程中在垂直方向受重力的影响,污染羽在空间上的质心位置(一阶矩)以及展布范围(二阶矩)在垂直方向上的变异程度要高于水平方向。     

Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium)

Sedimentological processes often result in complex three-dimensional subsurface heterogeneity of hydrogeological parameter values. Variogram-based stochastic approaches are often not able to describe heterogeneity in such complex geological environments. This work shows how multiple-point geostatistics can be applied in a realistic hydrogeological application to determine the impact of complex geological heterogeneity on groundwater flow and transport. The approach is applied to a real aquifer in Belgium that exhibits a complex sedimentary heterogeneity and anisotropy. A training image is constructed based on geological and hydrogeological field data. Multiple-point statistics are borrowed from this training image to simulate hydrofacies occurrence, while intrafacies permeability variability is simulated using conventional variogram-based geostatistical methods. The simulated hydraulic conductivity realizations are used as input to a groundwater flow and transport model to investigate the effect of small-scale sedimentary heterogeneity on contaminant plume migration. Results show that small-scale sedimentary heterogeneity has a significant effect on contaminant transport in the studied aquifer. The uncertainty on the spatial facies distribution and intrafacies hydraulic conductivity distribution results in a significant uncertainty on the calculated concentration distribution. Comparison with standard variogram-based techniques shows that multiple-point geostatistics allow better reproduction of irregularly shaped low-permeability clay drapes that influence solute transport.     

弥散系数在非均质多相岩层中的尺度效应

根据渗透系数在多相岩层中的协方差函数,文中首先推导了用以描述溶质在三维模型中运移特征的宏观弥散系数方程,然后导出了纵向弥散系数用来表达该参数的尺度效应。利用一个例子,讨论了宏观弥散随时间的变化趋势,以及同一岩相内转移项和越相转移项对弥散的相对贡献。灵敏度分析指出纵向弥散系数是与岩相平均长度正相关,也与不同岩相的渗透系数的差值正相关,其取值随渗透系数的总方差的增加而增大。     

The effect of heterogeneity of diffusion parameters on chloride transport in low-permeability argillites

Understanding flow and transport in low-permeability media is very important in the context of nuclear waste disposal, oil and gas reservoirs and long term evolution of groundwater systems. In low-permeability media, transport by diffusion is often the most important mass transport process. This study investigates the effect of the heterogeneity of diffusion parameters on mass transport in low-permeability media. A geostatistical approach for integrating heterogeneity of diffusion parameters in groundwater flow and transport models is proposed and applied to the Toarcian argillites in France which are studied in the framework of feasibility of storing radioactive waste in deep clayey massifs. Stochastic fields of the diffusion parameters of the Toarcian argillites (France) are generated based on 64 measured values of diffusion coefficient and diffusion accessible porosity and used as input for a 3D local-scale groundwater flow and transport model. The chloride concentrations computed by these heterogeneous models are compared to the measured chloride concentrations and to concentrations calculated with a model in which the Toarcian argillites are subdivided into several homogeneous zones. The heterogeneous simulations result in a slightly better correspondence between measured and calculated values and have the additional advantage that the measured diffusion coefficient values in the Toarcian are perfectly honored in the model. This study shows that small-scale variability of diffusion parameters has a significant effect on solute concentrations and omitting this heterogeneity may be a problem in transport calculations in low-permeability media, depending on the specific setting and objectives of the study.     

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.     

The use of laboratory experiments for the study of conservative solute transport in heterogeneous porous media

 Laboratory experiments on heterogeneous porous media (otherwise known as intermediate scale experiments, or ISEs) have been increasingly relied upon by hydrogeologists for the study of saturated and unsaturated groundwater systems. Among the many ongoing applications of ISEs is the study of fluid flow and the transport of conservative solutes in correlated permeability fields. Recent advances in ISE design have provided the capability of creating correlated permeability fields in the laboratory. This capability is important in the application of ISEs for the assessment of recent stochastic theories. In addition, pressure-transducer technology and visualization methods have provided the potential for ISEs to be used in characterizing the spatial distributions of both hydraulic head and local water velocity within correlated permeability fields. Finally, various methods are available for characterizing temporal variations in the spatial distribution (and, thereby, the spatial moments) of solute concentrations within ISEs. It is concluded, therefore, that recent developments in experimental techniques have provided an opportunity to use ISEs as important tools in the continuing study of fluid flow and the transport of conservative solutes in heterogeneous, saturated porous media. Received, December 1996 · Revised, July 1997 · Accepted, August 1997     

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.     

含水层非均质性不同刻画方法对地下水流和溶质运移预测的影响

为探讨含水层非均质性不同刻画方法对地下水流和溶质运移预测的影响,基于非均质含水层砂箱实验,分别用传统等效均质模型、克立金插值和水力层析刻画含水层渗透系数场,并探讨了先验信息对水力层析结果的影响.将不同方法估算的渗透系数场用以预测地下水流和溶质运移过程,以此判断不同方法估算结果的优劣,分析含水层非均质性对地下水流和溶质运移的影响.结果表明:与克立金插值法相比,水力层析法可以更好地刻画含水层非均质性,较准确地预测地下水流和溶质运移过程;钻孔岩心渗透系数样本值作为先验信息可以提高水力层析法估算结果的精度;传统等效均质模型无法准确预测地下水流和溶质运移过程.含水层非均质性的增强将导致溶质污染羽分布形态和运移路径的空间变异性增强,并且优势通道直接决定溶质的分布及运移路径.      

多个相关随机参数的空间变异性对溶质运移的影响

根据给定渗透系数、孔隙度以及吸附系数的概率分布,采用顺序高斯模拟生成相关的多参数随机场的实现,作为地下水流和溶质运移模型的输入参数,对污染物浓度进行随机分析。研究结果表明,与仅考虑渗透系数空间变异性相比,考虑相关的多参数空间变异性导致污染羽的扩散程度有显著不同。当孔隙度与渗透系数呈正相关关系时,会减少污染羽的扩散程度,反之,当孔隙度与渗透系数为负相关关系时,会加剧污染羽的扩散程度。吸附系数也是如此。在考虑吸附系数的空间变异性之后,污染羽的分布表现出拖尾现象。同时考虑渗透系数、孔隙度以及吸附系数空间变异性时,孔隙度非均质性对溶质运移的影响较吸附系数非均质性的影响更大。     

河道一维非恒定流微分结构摩阻公式及其试验论证

传统的恒定流经验摩阻公式作为对恒定流状态下摩阻的总结,建立在摩阻、流速、水深存在单一关系的基础之上。而非恒定流条件下,水文要素的涨落存在先后顺序,各水文要素之间不再是单一关系。为提高一维非恒定流摩阻的模拟精度,考虑水文要素的时空变化对摩阻的影响,运用量纲分析整理出以微分结构表达的摩阻改进公式。并设计实验模拟单峰水流过程,验证公式改进的有效性。结果表明,相对于谢才公式,改进公式提高了对一维非恒定摩阻的模拟精度,有一定的实用价值。     

弯曲岩溶管道溶质运移的尺度效应研究

岩溶管道溶质运移的尺度效应研究对穿透曲线的正确解译非常重要,但目前针对单一弯曲管道中溶质运移尺度效应的研究仍比较缺乏。文章将岩溶管道和溶潭分别概化为透明软管和水箱,基于前期建立的水箱-管道系统(简称“管道系统”),在水箱下游设置不同长度的弯曲管道,通过示踪试验研究管道运移尺度对穿透曲线的影响,并采用暂时存储模型模拟试验曲线。结果表明：(1)随着水箱下游管道长度的增加,峰值质量浓度逐渐缓慢降低,穿透曲线上升段斜率无明显变化,穿透曲线拖尾逐渐缩短,表明运移管道长度增加对溶质运移的影响大于下游管道弯曲;(2)穿透曲线偏度系数、后段溶质羽穿透时间和溶质羽穿透时间与管道系统长度呈良好的负线性相关关系(R²>0.96);(3)当对称和不对称水箱管道系统长度分别增加至154.5 m和164.3 m时,偏度系数接近0,穿透曲线分布接近对称;(4)弥散系数、存储区截面积和交换系数与管道系统长度呈良好的负线性相关关系,当对称和不对称水箱管道系统长度分别增加至159.9 m和178.1 m时,存储区截面积接近0,水箱导致的溶质运移滞后效应基本消失。研究结果对野外岩溶管道穿透曲线的...     

A note on transport of a pulse of nonlinearly reactive solute in a heterogeneous formation

Saturated flow takes place in geological formations of spatially variable permeability which is regarded as a stationary random space function of given statistical moments. The flow is assumed to be uniform in the mean and the Eulerian velocity field has stationary fluctuations. Water carries solutes that react according to the nonlinear equilibrium Freundlich isotherm. Neglecting pore scale dispersion (high Peclet number), we study the behavior of an initially finite pulse injection of constant concentration. Mean flux-averaged concentration is derived in a simple manner by using the previously determined solution of transport in a homogeneous one-dimensional medium and the Lagrangian methodology developed by Cvetkovic and Dagan [5] to model reactive transport in a three-dimensional flow field. The mean breakthrough curves are computed and the combined effect of reactive parameters and heterogeneity upon reduction of the concentration peak is investigated. Furthermore, with the aid of temporal moments, we determine equivalent reaction and macrodispersion coefficients pertinent to a homogeneous medium. This revised version was published online in July 2006 with corrections to the Cover Date.