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.     

An Analytical Model for Simulating Step-Function Injection in a Radial Geometry

An analytical model is developed for analyzing underground injection of wastes that undergo advection, dispersion, sorption, and first-order degradation. The model uses a time-dependent, step-function source that simulates intermittent waste injection in a continuous fluid injection well. The governing equations for a cylindrically symmetrical system are cast in nondimensional form and then transformed and solved in Laplace space. The Laplace space solution is inverted with the Crump algorithm, which uses the real and imaginary parts of a Fourier series. The numerical solution is verified by replicating the step-function source at the point of injection, and the behavior of the model is demonstrated in a series of figures. The model is recommended for quick, scoping calculations in which there is little site-specific information and periods of discontinuous radial injection.     

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.     

Contaminant transport with non‐equilibrium processes in unsaturated soils and implicit characteristic Galerkin scheme

A non‐equilibrium sorption—advection—diffusion model to simulate miscible pollutant transport in saturated–unsaturated soils is presented. The governing phenomena modelled in the present simulation are: convection, molecular diffusion, mechanical dispersion, sorption, immobile water effect and degradation, including both physical and chemical non‐equilibrium processes. A finite element procedure, based on the characteristic Galerkin method with an implicit algorithm is developed to numerically solve the model equations. The implicit algorithm is formulated by means of a combination of both the precise and the traditional numerical integration procedures. The stability analysis of the algorithm shows that the unconditional stability of the present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results illustrate good performance of the present algorithm in stability and accuracy, and in simulating the effects of all the mentioned phenomena governing the contaminant transport and the concentration distribution. Copyright © 2000 John Wiley & Sons, Ltd.     

质量传输和同位素交换:流动几何学和交换机制

耦合的质量传输和动力学限制的同位素交换模型综合考虑了平流、扩散、热液弥散 ,以及岩石与水之间的不平衡同位素交换等项因素。把耦合模型应用于 2个构造环境下的古热液系统 ,进而解释稳定同位素数据。对于造成环绕浅成侵入岩体分布的18O亏损环带的流体的流动几何学 ,以及浅部正断层流体流动的几何学 ,耦合模型提供了不同于单一同位素交换模型的解释。耦合模型也提供了关于同位素相对交换速率和同位素交换机制的信息。结果表明 ,断层带的动态重结晶促进了表面反应 ,进而便利了同位素交换 ;在化学不反应性和未变形的矿物中 ,同位素交换可能受制于固态条件下的扩散。     

One-dimensional advective–dispersive transport into a deep layer having a variable surface concentration

Two analytic closed form solutions for the one-dimensional advection–dispersion equation are presented. These solutions take account of changes in surface concentration with time as mass is transported into the soil. The first solution is developed for the case of rapid landfill construction. The second solution considers a time-dependent mass input to the landfill. The use of these solutions is illustrated by a number of examples and it is shown that consideration of the finite mass of contaminant within the landfill can significantly affect the concentration profiles beneath the landfill.     

不流动水与非平衡吸附作用对溶质运移影响的数值模型-MIENESOR

不流动水与非平衡吸附作用对溶质在孔隙介质中的运移有很大影响,“两点-两区”模型是目前研究不流动水与非平衡吸附作用的较为完善和实用的模型。在溶质运移的“两点-两区”模型的基础上,同时考虑了土壤对溶质的平衡和非平衡吸附作用,开发了MIENESOR数值模型,并给出了基于有限差和有限元法联合的数值解,编制了相应的计算机程序。对MIENESOR数值模型的案例验算表明：该模型能很好地揭示溶质在包气带和含水层中运移的规律,所开发的计算机程序稳定性较强,可用于实际。     

A generalized advection dispersion equation

This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of the operator are presented. The operator is used to generalize the advection dispersion equation. The generalized equation differs from the standard equation in four properties. The generalized equation is solved via the variational iteration technique. Some illustrative figures are presented.     

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.     

A Subtidal Model of Temperature for a Well-Mixed Narrow Estuary: the Guadalquivir River Estuary (SW Spain)

This paper analyzes thermal energy transport in the narrow and tidally energetic Guadalquivir River Estuary (SW Spain). Measurements from a comprehensive monitoring campaign (2008–2011) reveal the forcing factors of the temperature field and its spatio-temporal variability. The along-channel thermal energy gradient reaches magnitudes of ～375 J/m⁴ near the mouth during the summer and winter. The water temperature is primarily controlled by shortwave radiation, latent heat transfer through the free surface, and tidal advection, whereas it depends less on freshwater discharge and longitudinal dispersion. The tidally averaged effective longitudinal thermal dispersion coefficient was evaluated at several stretches for each tidal cycle. The mean values of the coefficient tend to increase landward and are on the order of ～10³, larger than (but of the same order of magnitude as) the salinity coefficient values. Based on these analyses, a deterministic operational model for thermal energy transport was developed. The model solves the tidally and cross-sectionally averaged advection–dispersion equation for the thermal energy balance and obtains accurate fits of the subtidal temperature field at any location within the estuary. The modeled water temperatures agreed well with the observations at all the stations (coefficients of determination, R ² greater than 0.98), even after the seasonal oscillation in radiation was removed (R ²?>?0.77).     

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.     

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.     

Evaluation of Containment Performance from Viewpoints of Diffusion and Dispersion for Impervious Structures at Coastal Landfill Sites

The containment performance of impervious structures is considered the most important performance, which the toxic substances are enclosed in coastal landfill sites. The containment performance is evaluated generally by the hydraulic conductivity and the thickness of impervious structures to focus on an advection. However, the leakage of toxic substances is affected by a diffusion and a dispersion. The diffusion and the dispersion are considered to be easily distinguished on the impervious structure which has the low-hydraulic conductivity. Such phenomena should be considered due to evaluate the containment performance. This is because to improve the containment performance and comprehend leakage of the toxic substances. The containment performance is evaluated from the viewpoint of the diffusion and the dispersion in this research. Concretely, the influence which the toxic substances leaks from impervious structures on the diffusion and the dispersion is evaluated by the infiltration and advection–dispersion analysis on steel-made side impervious walls. In other word, The relation between the leaking amount of toxic substances and coefficient of molecular diffusion, the relation between the travel time or the flow velocity and the leaking amount and the change in the water-level difference are considered respectively. So, the leaking amount which is influenced by a diffusion and a dispersion is considered. Consideration about to secure the containment performance of impervious structure which is restrained leakage by a diffusion and a dispersion.     

Upscaling polydispersed particle transport in porous media using pore network model

Understanding particle transport in porous media is critical in the sustainability of many geotechnical and geoenvironmental infrastructure. To date, the determination of the first-order rate coefficients in the advection–dispersion equation for simulating attachment and detachment of particles in saturated porous media typically has been relied on the result of laboratory-scale experiments. However, to determine attachment and detachment coefficients under varied hydraulic and geochemical variables, this method requires a large experimental matrix because each test provides only one set of attachment and detachment coefficients. The work performed in this study developed a framework to upscale the results obtained in pore-scale modeling to the continuum scale through the use of a pore network model. The developed pore network model incorporated variables of mean particle size, the standard deviation of particle size distribution, and interparticle forces between particles and sand grains. The obtained retention profiles using the pore network model were converted into attachment coefficients in the advection–dispersion equation for long-term and large-scale simulation. Additionally, by tracking individual particles during and after the simulation, the pore network model introduced in this study can also be employed for modeling the clogging phenomenon, as well as fundamental investigation of the impact of particle size distribution on particle retention in the sand medium.

     

非饱和土中镉离子传输模型参数反演

使用自行设计的的真空实验装置,采用一维实验室土柱实验方法在不同实验条件下进行了15组实验,并基于实验所得的穿透曲线,使用梯度正则化方法反演得到了镉离子在8种葡萄牙土样和1种比利时土样中相应的传输模型参数。同时通过数值模拟实验验证了梯度正则化方法的有效性和可靠性,进而证明所得结果是有效的。     

潍河下游地区海咸水入侵动态三维数值模拟分析

文中以潍河下游的莱洲湾南岸地区为研究区 ,阐述了海咸水分布规律。针对海咸水运移过程中的水动力学特征和化学动力学特征 ,推导了水动力化学动力耦合的盐分运移对流弥散方程 ,水动力过程考虑了浓度变化对水流运动的影响 ,化学动力学过程考虑了含水介质表面吸附 (解吸 )作用对盐分运移的影响。采用改进的非线性特征有限元法 ,求解高浓度溶质运移三维模型。计算结果表明 ,该模型更真实地刻画了海咸水入侵系统。通过对海咸水入侵规律进行模拟 ,指出海咸水入侵的根本原因是过量开采地下淡水资源 ,要防止海咸水入侵 ,必须科学开采地下淡水资源。     

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.