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.     

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.     

Numerical modeling of two-phase fluid flow and oil slick transport in estuarine water

Oil spills is one of the most important hazards in the estuarine and coastal water. In recent decades, engineers try to predict the status of oil slick to manage the pollution spreading. The prediction of oil slick transport is carried out mainly by means of numerical models. In the current study, the development and application of a two-phase fluid flow model to simulate oil transport in the marine environment are presented. Different transport and fate processes are included in the developed model. The model consists of the Lagrangian method for the advection process, the Random Walk technique for horizontal diffusion process and the empirical equations for the fate processes. The major forces for driving oil particles are fluid current, wind speed and turbulent flow. Therefore, the multi-component hydrocarbon method has been included to the developed model in order to predict fate processes. As prediction of particle velocity components is of major importance for oil slick advection, therefore the binomial interpolation procedure has been chosen for the particle velocity components computations. In addition, shoreline boundary condition is included in the developed model to simulate shore response to oil slick transport near the beaches. The results of the model applications are compared with the analytical solutions, experimental measurements and other numerical models cited in literature. Comparisons of different sets of results represent the capability of developed model to predict the oil slick transport. In addition, the developed model is tested for two oil spill cases in the Persian Gulf.     

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.     

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。     

Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion

Quantification of mass and heat transport in fractured porous rocks is important to areas such as contaminant transport, storage and release in fractured rock aquifers, the migration and sorption of radioactive nuclides from waste depositories, and the characterization of engineered heat exchangers in the context of enhanced geothermal systems. The large difference between flow and transport characteristics in fractures and in the surrounding matrix rock means models of such systems are forced to make a number of simplifications. Analytical approaches assume a homogeneous system, numerical approaches address the scale at which a process is operating, but may lose individual important processes due to averaging considerations. Numerical stability criteria limit the contrasts possible in defining material properties. Here, a hybrid analytical–numerical method for transport modeling in fractured media is presented. This method combines a numerical model for flow and transport in a heterogeneous fracture and an analytical solution for matrix diffusion. By linking the two types of model, the advantages of both methods can be combined. The methodology as well as the mathematical background are developed, verified for simple geometries, and applied to fractures representing experimental field conditions in the Grimsel rock laboratory.     

双重介质中的一类核素迁移数学模型及其反演

探讨了孔隙与单裂隙双重介质中的一类核素迁移数学模型及其反演问题。该核素迁移模型是一个耦合的抛物型方程组定解问题。若已知排污点的核素浓度变化规律,利用Laplace变换及其逆变换方法,求得了核素迁移模型正问题的解析解;反之,由下游裂隙中某个点的实测核素浓度,利用偏微分方程的叠加原理和反问题的拟解法,反求出核素迁移模型反问题的解,即排污点的核素状态。最后,给出核素迁移模型的正问题和反问题的数值模拟。数值结果表明,正问题的解析解能够刻画核素的迁移规律,也显示出所提反问题方法能有效地反演核素污染源。     

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。     

MT3D-通用的三维地下水污染物运移数值模型

定量研究污染物在地下水中的运移过程通常采用数值模拟方法。MT3D是一套基于有限差分方法的污染物运移模拟软件，近年来在国外水文地质和水环境模拟等领域的研究中已经得到较为广泛的认可。MT3D比较全面地考虑了污染物在地下水中的对流、弥散和化学反应等过程，可以灵活处理各种复杂的源汇项和边界条件，能够准确模拟承压、无压和越流含水层中的污染物运移过程。MT3D具有模块化的程序结构、灵活的求解方法以及全面的模拟功能，非常适合实际问题的研究，值得在国内推广使用。     

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。     

A particle tracking transport method for the simulation of resident and flux-averaged concentration of solute plumes in groundwater models

A new numerical technique called the convolution-based particle tracking (CBPT) method is developed to simulate resident or flux-averaged solute concentrations in groundwater models. The method is valid for steady-state flow and linear transport processes such as sorption with a linear sorption isotherm and first-order decay. The CBPT method uses particle tracking to take advantage of the ability of particle-based approaches to maintain sharp fronts for advection-dominated transport problems common in groundwater modeling and because of the flexibility of the random walk method to simulate a wide range of possible forms of the dispersion tensor. Furthermore, the algorithm for carrying out the convolution and superposition calculation from particle tracking results is very efficient. We show that from a single particle tracking run, source term variability, sorption, and decay can all be simulated rapidly without rerunning the underlying transport model unless the flow field or dispersion parameters are changed. A series of verification simulations are presented to demonstrate the accuracy and efficiency of the CBPT method compared to more conventional particle tracking approaches.     

Modeling the hydrogeochemical evolution of brine in saline systems: Case study of the Sabkha of Oum El Khialate in South East Tunisia

We studied the effects of evaporation and groundwater flow on the formation of salt minerals in the Sabkha of Oum El Khialate in South East Tunisia, which contains large amounts of sulfate sodium mineral deposits. Due to the fact that there are no important surface water bodies present in this sabkha, transport of solutes is dominated by advection rather than mixing in lakes. For our study we used both analytical conservative and numerical reactive transport models. Results showed that salinity varies with distance and may reach very high levels near a watershed where the groundwater flux is zero. As a consequence, reactive transport simulations results showed that more minerals precipitate and water activity decreases values near this watershed. Model results also showed that a sequence of precipitating minerals could be deduced after 140,000 years. From the boundary of the sabkha towards the watershed the mineral sequence was dolomite, gypsum, magnesite, bloedite, halite and mirabilite. It was found that the amounts as well as the mineral precipitation distribution strongly depend on salinity and rates of inflowing water.     

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.     

Analytical solution of advection–diffusion equation in heterogeneous infinite medium using Green’s function method

Some analytical solutions of one-dimensional advection–diffusion equation (ADE) with variable dispersion coefficient and velocity are obtained using Green’s function method (GFM). The variability attributes to the heterogeneity of hydro-geological media like river bed or aquifer in more general ways than that in the previous works. Dispersion coefficient is considered temporally dependent, while velocity is considered spatially and temporally dependent. The spatial dependence is considered to be linear and temporal dependence is considered to be of linear, exponential and asymptotic. The spatio-temporal dependence of velocity is considered in three ways. Results of previous works are also derived validating the results of the present work. To use GFM, a moving coordinate transformation is developed through which this ADE is reduced into a form, whose analytical solution is already known. Analytical solutions are obtained for the pollutant’s mass dispersion from an instantaneous point source as well as from a continuous point source in a heterogeneous medium. The effect of such dependence on the mass transport is explained through the illustrations of the analytical solutions.     

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.     

Modeling and assessment of polychlorinated biphenyls contamination in soil at a burial site of power capacitors

Numerous industrial or burial sites contaminated by persistent organic pollutants such as polychlorinated biphenyls (PCBs) and pesticides were discovered in China recently. Due to improper choice of technology, many remediation cases had cost too much; however, failed to attain expected goals. In this study, the distribution and transport of PCBs at a burial site were investigated using tested PCBs concentration in order to support the choice of remediation technology and estimate the remediation results. Site characterization was carried out in order to investigate the hydrogeological condition and PCBs pollution nearby the capacitor burial site located in Shanxi, China. Results of PCBs measurement indicated that the proportion of contaminated soil with concentration above 500 mg/kg is 7.8 % and the value for soil with concentration between 50 and 500 mg/kg is 18.0 %. Considering adsorption and biodegradation, the two-dimensional PCBs transport model was established based on advection–dispersion equation. The model calibration showed a good agreement between measured and computed values, indicating the feasibility of this model used for predicting the transport and disappearance of PCBs in soil. Results of 100 years’ simulation demonstrated the slow migration and biodegradation of PCBs. Simulations were conducted for before and after remediation scenarios. Comparison of the results indicates that the remediation alternatives of excavation–incineration and thermal desorption have successfully removed most of the organics and thus reduced the environmental risk to a low level.     

Study on numerical simulation of organic pollutant transport in groundwater northwest of Laixi

The construction and hydrogeological area in the low hill, which is northwest of Laixi City and in the east of Shandong Province more precisely, is one of Dagu River’s groundwater source. Regarding COD as the typical pollutant according to general situation of groundwater pollution in aforementioned area, a three-dimensional advection-dispersion model was established to simulate the transport of organic pollutants under two accident conditions. In addition, the effect of corresponding dispersity was analyzed. The results show that COD transport is mainly in accordance with the direction of groundwater flow, pollutant concentration and its gradient as well as the rule of narrower pollution range in deeper stratum. Moreover, COD is mainly transported and diffused in groundwater of sandy soil in the first and second layers. However, under accident condition II, the pollutant concentration begins to decay gradually after its transport and diffusion tends to be stable. Besides, in terms of dominance, dispersion is to transverse transport of pollutants what advection is to longitudinal transport. If considering random dispersion, the final results see higher peak concentration of COD and longer transverse distance from pollution center compared to transport route. What’s more, the pollution plume changes and concentration isocline becomes slightly irregular.     

非均匀土壤中溶质运移的两区模型及其解析解

给出了非均匀土壤中考虑水动力弥散尺度效应的一维溶质运移两区模型。然后在初始浓度为零,半无限一维空间内常数通量边界条件下,推导出了可动区和不动区溶质浓度分布的解析表达式。并用Mathematica软件包作了数值计算。计算结果表明,该模型的模拟结果符合溶质运移的一般规律,因而该模型在土壤溶质运移的研究和应用中有一定的价值。