Solute transport through a deforming porous medium

Solute transport through a porous medium is typically modelled assuming the porous medium is rigid. However, many applications exist where the porous medium is deforming, including, municipal landfill liners, mine tailings dams, and land subsidence. In this paper, mass balance laws are used to derive the flow and transport equations for a deforming porous medium. The equations are derived in both spatial and material co‐ordinate systems. Solute transport through an engineered landfill liner is used as an illustrative example to show the differences between the theory for a rigid porous medium, and small and large deformation analysis of a deforming porous medium. It is found that the large deformation model produces shorter solute breakthrough times, followed by the small deformation model, and then the rigid porous medium model. It is also found that it is important to include spatial and temporal void ratio variations in the large deformation analysis. It is shown that a non‐linear large deformation model may greatly reduce the solute breakthrough time, compared to a standard transport analysis typically employed by environmental engineers. Copyright © 2002 John Wiley & Sons, Ltd.     

砂岩含水介质中铀的吸附和迁移行为研究

地浸铀矿山退役后,含水层中残留的含铀浸出液随着地下水的运动向下游迁移扩散,存在对周边地下水污染的风险。本文设计了若干组批实验和柱实验,研究铀在北方某地浸铀矿山砂岩含水介质中的吸附和迁移行为。实验结果表明,砂岩对铀的吸附在12 h以内达到平衡,铀初始浓度越高,砂岩的铀吸附容量越大;砂岩对铀的吸附为吸热反应,温度升高有利于吸附反应的进行。溶液pH值和共存 {\mathrm{HCO}}_3^{-}浓度会对铀的吸附作用产生强烈的影响:pH值在7左右时,铀的吸附量最高; {\mathrm{HCO}}_3^{-}浓度越高,铀的吸附量越低。这些影响是通过改变溶液中铀的络合形态和砂岩矿物表面的电荷性质实现的。柱实验表明,pH值、铀浓度、流速和 {\mathrm{HCO}}_3^{-}浓度是影响铀在饱和砂岩含水介质中迁移的重要因素。pH值≤7时,pH值越高,砂岩柱越不易被铀穿透;而铀浓度、流速、 {\mathrm{HCO}}_3^{-}浓度越高,砂岩柱越易被铀穿透。两点非平衡模型可以很好地拟合不同条件下铀在砂岩柱中的迁移过程。批实验获得的分配系数是柱实验的1.16.6倍。通过对比实验条件、含水层特性和地下水化学特征,确定分配系数为48.1 mL/g时,较适合描述研究区内砂岩含水层中的铀迁移。上述认识为地浸铀矿山地下水铀的反应运移过程和天然自净化机理提供了理论依据。     

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。     

Multidimensional upstream weighting for multiphase transport in porous media

Truly multidimensional methods for hyperbolic equations use flow-based information to determine the computational stencil, as opposed to applying one-dimensional methods dimension by dimension. By doing this, the numerical errors are less correlated with the underlying computational grid. This can be important for reducing bias in flow problems that are inherently unstable at simulation scale, such as in certain porous media problems. In this work, a monotone, multi-D framework for multiphase flow and transport in porous media is developed. A local coupling of the fluxes is introduced through the use of interaction regions, resulting in a compact stencil. A relaxed volume formulation of the coupled hyperbolic–elliptic system is used that allows for nonzero residuals in the pressure equation to be handled robustly. This formulation ensures nonnegative masses and saturations (volume fractions) that sum to one (Acs et al., SPE J 25(4):543–553, 1985). Though the focus of the paper is on immiscible flow, an extension of the methods to a class of more general scalar hyperbolic equations is also presented. Several test problems demonstrate that the truly multi-D schemes reduce biasing due to the computational grid.     

A general reduction scheme for reactive transport in porous media

We present a method to transform the governing equations of multispecies reactive transport in porous media. The reformulation leads to a smaller problem size by decoupling of equations and by elimination of unknowns, which increases the efficiency of numerical simulations. The reformulation presented here is a generalization of earlier works. In fact, a whole class of transformations is now presented. This class is parametrized by the choice of certain transformation matrices. For specific choices, some known formulations of reactive transport can be retrieved. Hence, the software based on the presented transformation can be used to obtain efficiency comparisons of different solution approaches. For our efficiency tests, we use the MoMaS benchmark problem on reactive transport.     

Multibody approach for reactive transport modeling in discontinuous-heterogeneous porous media

Computational Geosciences - In the context of long-term degradation of porous media, the coupling between fracture mechanics and reactive transport is investigated. A reactive transport model in a...     

Boundary element analysis of contaminant transport in fractured porous media

A two-dimensional boundary integral method to analyse the flow of contaminant in fractured media having a two- or three-dimensional orthogonal fracture network is presented. The method assumes that the fractures provide the paths of least resistance for transport of contaminants while the matrix, because of its low permeability, acts as ‘storage blocks’ into which the contaminant diffuses. Laplace transform is used to eliminate the time variable in the governing equation in order to facilitate the formulation of a boundary integral equation in the Laplace transform space. Conventional boundary element techniques are applied to solve for the contaminant concentrations at specified locations in the spatial domain. The concentration in the time domain is then obtained by using an efficient inversion technique developed by Talbot. The method is able to analyse the behaviour of waste repositories which have diminishing concentration due to the mass transport of the contaminant into the surrounding fractured media.     

Adaptive POD model reduction for solute transport in heterogeneous porous media

We study the applicability of a model order reduction technique to the solution of transport of passive scalars in homogeneous and heterogeneous porous media. Transport dynamics are modeled through the advection-dispersion equation (ADE) and we employ Proper Orthogonal Decomposition (POD) as a strategy to reduce the computational burden associated with the numerical solution of the ADE. Our application of POD relies on solving the governing ADE for selected times, termed snapshots. The latter are then employed to achieve the desired model order reduction. We introduce a new technique, termed Snapshot Splitting Technique (SST), which allows enriching the dimension of the POD subspace and damping the temporal increase of the modeling error. Coupling SST with a modeling strategy based on alternating over diverse time scales the solution of the full numerical transport model to its reduced counterpart allows extending the benefit of POD over a prolonged temporal window so that the salient features of the process can be captured at a reduced computational cost. The selection of the time scales across which the solution of the full and reduced model are alternated is linked to the Péclet number (P e), representing the interplay between advective and dispersive processes taking place in the system. Thus, the method is adaptive in space and time across the heterogenous structure of the domain through the combined use of POD and SST and by way of alternating the solution of the full and reduced models. We find that the width of the time scale within which the POD-based reduced model solution provides accurate results tends to increase with decreasing P e. This suggests that the effects of local-scale dispersive processes facilitate the POD method to capture the salient features of the system dynamics embedded in the selected snapshots. Since the dimension of the reduced model is much lower than that of the full numerical model, the methodology we propose enables one to accurately simulate transport at a markedly reduced computational cost.     

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.

     

Clarification of nonlinear retardation factors for colloid-enhanced transport in porous media

There have been a couple of contaminant retardation factors reported for the three-phase (aqueous, solid, and colloid) groundwater system. However, the retardation factor has often been presented by itself and not incorporated into the relevant transport equation, particularly when derived from the mass fraction approach. This may cause a misunderstanding of the retardation factor especially for the systems where multi-phases exist due to the presence of colloids and/or nonlinear sorption processes are involved. It is, therefore, necessary to clarify the form of the nonlinear retardation factor along with the relevant transport equation in the multi-phase system. Alternative forms of the retardation factor and relevant transport equation for specific conditions are presented in various combinations of the nonlinearity of involved sorption mechanisms. The retardation factors for specific conditions are compared with the ones available in the literature. The results indicate that more caution should be given in applying the retardation factor in order to explore contaminant transport in the multi-phase system where any nonlinear sorption is involved. Finally, presentation of the retardation factor along with the relevant transport equation in this study would help prevent possible misuse of the retardation factor in investigating contaminant transport in the multi-phase system.     

Influence of temporal fluctuations and spatial heterogeneity on pollution transport in porous media

The combined influence of temporal fluctuations and spatial heterogeneity on non-reactive solute transport mechanisms in porous media can be understood by performing simulations of steady and unsteady flow and transport in heterogeneous media. The study focuses on issues such as the degree of heterogeneity, correlation length, separation of the combined effects of temporal and spatial variations, and ergodicity conditions under unsteady flow conditions. It is shown that the effect of temporal variations on solute transport is masked by the strong effect of spatial heterogeneity. There is no obvious difference in plume shape between steady and unsteady flow conditions; the first and the second spatial moments of the plume of the unsteady-state flow condition fluctuate around the steady-state flow condition with the same period of oscillations as the input signal at small storage coefficient (S????0.001). At a relatively high standard deviation in hydraulic conductivity and a small storage coefficient, the unsteady flow condition sharpens the temporal variations in macrodispersion coefficients. The magnitude of the longitudinal macrodispersion coefficient under unsteady flow condition is almost doubled at the maximum values. However, the transverse macrodispersion coefficient fluctuates around zero. The Kubo number and Peclet number ranges are 1.2?C64 and 10?C250, respectively.     

Numerical modeling of the flow and transport of radionuclides in heterogeneous porous media

This paper is concerned with numerical methods for the modeling of flow and transport of contaminant in porous media. The numerical methods feature the mixed finite element method over triangles as a solver to the Darcy flow equation and a conservative finite volume scheme for the concentration equation. The convective term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion–dispersion term is discretized by piecewise linear conforming triangular finite elements. It is shown that the scheme satisfies a discrete maximum principle. Numerical examples demonstrate the effectiveness of the methodology for a coupled system that includes an elliptic equation and a diffusion–convection–reaction equation arising when modeling flow and transport in heterogeneous porous media. The proposed scheme is robust, conservative, efficient, and stable, as confirmed by numerical simulations.      

非饱和介质中热能传输及水分迁移的数值积分解

在给出非饱和介质热能-水分传输的耦合质量控制方程和基于Fourier热传导定律的热能平衡方程的基础上,对热能传输及水分迁移的基本特征和机理进行了分析。其中,考虑了温度势、吸力势和重力势的耦合作用影响。给出有热源时控制方程的简化形式,并对半无限体自由表面作用平面热源条件下介质内非稳态温度场、体积含水率分布场进行数值积分求解。利用这些解答给出常热源强度和变热源强度两种情况下,温度场随时间的变化特征以及水分迁移的演化过程,并分析了重力项对计算结果的影响。     

Remediation of colloid-facilitated contaminant transport in saturated porous media treated by nanoparticles

Facilitation of contaminant transport in porous media due to the effect of indigenous colloidal fine materials has been widely observed in laboratory and field studies. It has been explained by the increase in the apparent solubility of low soluble contaminants as a result of their adsorption on the surface of fine particles. Attachment of colloidal fine particles onto the rock surface could be a promising remedy for this challenge. In this experimental study, the effect of five types of metal oxide nanoparticles, γ-Al₂O₃, ZnO, CuO, MgO, and SiO_2, on suspension transport was investigated. In several core flooding tests, different nanofluids were used to saturate the synthetic porous media. Subsequently, after sufficient soaking time, the suspension was injected into the treated porous media. Analysis of the effluent samples’ concentration by Turbidimeter apparatus demonstrated that the presence of nanoparticles on the rock surface resulted in a significant reduction in fine concentrations in the effluent samples compared with non-treated media; ZnO and γ-Al₂O₃ demonstrated the best scenarios among the tests performed in this study. In order to characterize the surface properties of the treated porous media, the zeta potential of the surface was measured. Results showed that the treated porous media acts as a strong adsorbent of fine particles, which are the main carrier of contaminants in porous media. These findings were quantitatively confirmed by calculation of the total energy of interaction between the fine particles and rock surface using the Derjaguin–Landau–Verwey–Overbeek theory.     

A global method for coupling transport with chemistry in heterogeneous porous media

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection–diffusion PDEs coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper, a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton–Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that one be able to solve chemical equilibrium problems (and compute derivatives) without having to know the solution method. An additional advantage of the Newton–Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.     

基于图像法的多孔介质双分子反应溶质运移模拟

采用图像分析法确定溶质浓度,以硫酸铜和EDTA二钠作为双分子反应物,在多孔介质模型中开展了不同粒径(1.52.0,2.53.0,3.54.0 mm)和流量(1.0,1.5,2.0 mL/s)下反应性溶质运移实验,探讨了应用不完全混合的对流弥散模型(IM-ADRE)对双分子反应溶质运移的模拟和预测,并进行了参数敏感性分析。结果表明:图像分析法可准确获取多孔介质中显色反应性溶质的浓度,灰度值与浓度的决定系数R²大于0.96;用IM-ADRE模型能够准确预测双分子反应性溶质硫酸铜和EDTA二钠在3种不同多孔介质中的运移过程,误差低于3.71%;实验条件的改变对IM-ADRE模型参数D、m和β₀的影响显著,说明模型参数依赖于环境条件,其变化规律需要根据实际环境条件进一步率定,便于IM-ADRE模型的进一步推广应用。     

悬浮颗粒形状对其在多孔介质中迁移和沉积特性的影响

悬浮颗粒在多孔介质中迁移的研究在地下水回灌、地下污染物扩散、核废料处置、石油开采等领域有重要的理论意义和应用价值。为了研究形状对颗粒迁移的影响,对1组球状颗粒（10 ?m中位粒径）和2组杆状颗粒（长径比为3:1和6:1）进行了三阶段室内土柱试验,得到了不同形状颗粒在多种溶液离子强度条件下的穿透曲线。结合DLVO理论分析了悬浮颗粒沉积和释放机制,阐释了形状对颗粒迁移行为的影响。试验结果表明,颗粒形状对迁移特性有重要影响,当离子强度较低时（6 mmol/L）,DLVO势能曲线展现较高能量壁垒,各种形状颗粒沉积主要为次级势阱沉积;当离子强度较高时（150 mmol/L）,球状颗粒因能量壁垒较高,其滞留机制仍以次级势阱沉积为主,但长径比为6:1的杆状颗粒在次级势阱和初级势阱都有沉积,这和杆状颗粒的静电性能和优先方向有关。对于杆状颗粒,边位沉积比端位沉积具有更深的次级势阱和更大的影响距离,边位沉积是更加稳定的沉积方式和沉积的优先方向。基于Derjaguin近似方法的DLVO理论计算显示,DLVO理论预测结果和土柱试验结果吻合较好。