An experimental study on diffusion characteristics of hardened liner materials to inorganic chemicals

For materials of very low hydraulic conductivity used in the landfill liner systems, e.g., natural clay liners, soil-cement liners, etc., diffusion characteristics should be evaluated, as the transport mechanism of contaminant through them is diffusion controlled. Studies on the diffusion characteristics of the hardened liner materials, such as the soil cement, are relatively few compared with those of clayey soils. In this paper, diffusive characteristics of hardened liner materials (HLMs) applied to the liner system of Sudokwon Metropolitan Landfill in Korea, were studied. Laboratory pure diffusion column tests in the pure- and the advection-diffusion status were performed for the chemicals, NaCl, KCl, and CaCl₂. To evaluate the diffusion coefficient of a HLMs system, a one-dimensional numerical transport program was developed for use in a multi-layered HLMs system. The range of dispersion coefficients of advection diffusion column tests was a little narrower than that of diffusion coefficients of pure diffusion tests, although the two coefficients were quite close. The effective diffusion coefficients of chloride ions of a HLMs were about a half of those in clayey soil due to the high density by compaction and curing. Diffusion coefficients of chloride ions in this study were correlated closely with hydraulic conductivities of the materials tested and were consistent with work in the literature.     

多孔介质中溶质有效扩散系数预测的分形模型

依据分形理论和方法,探索溶质在多孔介质中的有效扩散系数的替代预测方法。在多孔介质溶质扩散的弯曲毛细管束模型的基础上,以分形维数作为介质的基本几何特性参数,建立了多孔介质中溶质扩散的分形毛细管束模型,推导出了溶质有效扩散系数与介质孔隙度之间的幂定律关系式,幂指数是介质孔隙分维和表面分维的函数,反映了介质孔隙体积的层次分布与孔隙通道曲折程度对扩散的影响。对粘性土的分形维数测定数据和有效扩散系数试验测定数据的分析表明,利用该关系式预测多孔介质中溶质的有效扩散系数是较为准确可靠的。     

Upscaling of Navier–Stokes equations in porous media: Theoretical, numerical and experimental approach

The accurate estimation of hydraulic conductivity is important for many geotechnical engineering applications, as the presence of fluids affects all aspects of soil behaviour, including its strength. Darcy’s law is the key experimental (or phenomenological) equation employed to model ground water flow. Yet, this phenomenological equation can be linked to a more fundamental microscale model of flow through the pore spaces of the porous material. This paper provides an experimental verification of the relationships between Darcy’s law (macroscale) and the Navier–Stokes equations (microscale) for actual complex pore geometries of a granular material. The pore geometries are experimentally obtained through state-of-the-art X-ray computer assisted micro-tomography. From the numerical modelling of the microscale flow based on actual pore geometries, it is possible to quantify and visualize the development of pore-scale fluid preferential flow-paths through the porous material, and to assess the importance of pore connectivity in soil transport properties.     

一种适用于孔隙体积应变的有效应力方程

土力学奠基石Terzaghi有效应力原理被广泛应用于油藏孔隙和渗透率应力敏感研究中,然而其对于岩石孔隙体积应变的适用性存在争议。对颗粒不可压缩和颗粒可压缩的多孔介质分别进行了受力分析,推导了总体积、颗粒骨架、孔隙体积的有效应力表达式,与Biot、Skepmton有效应力方程对比,建立了适用于孔隙体积应变的新型有效应力方程,并进行了试验论证和应用举例。研究表明:在颗粒不可压缩多孔介质中,有效应力为超出平衡孔隙流压之外的颗粒间宏观等效应力;在颗粒可压缩变形多孔介质中,有效应力为其相同应变下的等效应力,有3种有效应力分别适用于总体积应变、颗粒体积应变、孔隙体积应变;新提出的孔隙体积有效应力方程与孔隙度、岩石总体积压缩系数、颗粒压缩系数、总应力和流压相关,4个理论计算式计算结果在3种多孔介质试验测试结果中的偏差均在5%以内;孔隙体积有效应力系数解决了如何定量增总应力来等效模拟储层降流压生产过程这一关键问题,3个压缩系数关系式理论计算准确方便。     

Implications of pore space characteristics on diffusive transport in basalts and granites

A detailed characterization of the pore space is crucial for understanding of transport and element transfer in rocks. Here, the effect of differences in texture and content of secondary minerals on transport in pore systems was determined for two rocks of widespread occurrence, mid-ocean ridge basalts (MORB) and granites. Pore space characteristics were analyzed by Hg-porosimetry, intrusion of a molten alloy, and synchrotron-based X-ray tomographic microscopy. For evaluating the role of pore space characteristics for the prediction of diffusive transport, data on porosity, and the effective diffusion coefficient (D _eff) were compared. Extended connective pore systems due to cracks and mineral dissolution are present in samples of both rocks, indicating high internal specific surface area. Uneven pore size distributions in altered MORB samples can be assigned to secondary minerals. Pore spaces determined by X-ray tomography, used to determine main direction of pores in the 3-D orthogonal system, suggest a slight anisotropy. In log–log plots, both rocks show roughly a linear dependence of D _eff for H₂O and compounds with comparable diffusivities (D₂O, monovalent cations, and anions) on porosity, but at same porosity D _eff is clearly higher in granitic than in basaltic samples. This difference is increasing with decreasing porosity, indicating that at low porosities the efficiency of element transport in basaltic samples is diminished, mainly inherited by the presence of small pores slowing down diffusion. The fact that diffusive transport in basaltic rocks is stronger dependent on porosity than in granitic rocks shows that also other rock characteristics such as pore size distribution and tortuosity of the pore network, highly affected by the alteration degree, can markedly affect transport and reactivity of pore solution.     

水溶液中溶质的扩散同位素分馏研究

稳定同位素分析是判定水溶液中溶质的组成、来源、迁移和转化过程与规律的重要工具,在自由扩散等物理化学作用下,对溶质的同位素分馏研究是稳定同位素技术应用的重要基础.本研究介绍了溶质的扩散过程与其同位素分馏效应之间的联系,论述了研究溶质扩散过程中引入的稳定同位素分馏现象的意义,描述了水溶液中溶质扩散的不同模拟实验方法及相关研...     

Diffusive transport of water in porous feldspars from granitic saprolites: In situ experiments using FTIR spectroscopy

A novel experimental cell was developed for in situ measurements of transport phenomena in porous media using Fourier-Transform Infrared (FTIR) Spectroscopy. The technique was employed at ambient pressure in the temperatures range of 11–44 °C to study the H₂O → D₂O exchange between water-saturated weathered feldspars (bulk porosity of 5–19 vol% for feldspar) from granitic saprolites and a surrounding aqueous liquid. Such measurements are an important step for understanding internal weathering reactions of feldspars in soils and aquifers. Effective diffusion coefficients D_eff for water in water-saturated porous feldspars were determined assuming one-dimensional diffusion in a quasi-homogeneous medium. The values of D_eff vary from 7.2 × 10⁻¹⁰ to 1.9 × 10⁻¹¹ m²/s and are 1–2 orders of magnitude lower than the diffusion coefficients (D) of protons and molecular H₂O in liquid water. The activation energy for the H₂O → D₂O exchange process in porous feldspars ranges from 7.8 to 18.8 kJ/mol.The results imply that the effective diffusivity of water is mainly controlled by physical properties of the feldspars like porosity, pore connectivity, pore geometry and distribution. Perthitic feldspars with homogeneous pore distribution in the albitic lamellas have diffusional tortuosity factors X = D/D_eff between 3 and 10 while alkali feldspars with inhomogeneously distributed and disconnected pores have much higher X values up to 129. Diffusion anisotropy has been verified for a vein perthite with diffusion perpendicular to the lamellas being faster by 0.3–0.5 log units than within the lamellas. It has to be emphasized that the study is based only on few selected feldspars, including perthitic feldspar, and additional work on samples with different weathering stages is needed to test the importance of the different parameters controlling diffusive transport in the pore system.     

Multi‐species diffusion analysis in porous media under various dry density and temperature conditions: molecular dynamics simulation,homogenization analysis,and finite element method

In porous media, chemical species that dissolve in pore water can be transported via diffusion mechanisms or advective fluxes, close to or far away from where precipitation occurs. In the case of a high‐level radioactive waste disposal system, compacted bentonite is used in a buffer material in an engineering barrier system to minimize the amount of specific nuclides that breach into the surrounding host rock. To minimize breaching, it is very important to understand the transport mechanism of multiple chemical species in porous media. In the following research, we introduced FEM analysis methods using the results of the molecular dynamics simulation and homogenization analysis (MD/HA) method. First, the diffusion coefficients of ions (Cl^?, I^?, and Na⁺) in different water layers of Na‐beidellite were calculated using the MD/HA procedure under various dry density (1.2, 1.6, and 2.0 Mg/m³) and temperature (293, 323, and 363 K) conditions. Next, using FEM analysis that used the MD/HA results as input parameters, the diffusion behaviors of ions in porous media were calculated. The results indicate that the diffusion coefficients of the interlayer water in Na‐beidellite are different from the diffusion coefficients under dry density conditions. Further, the concentration profiles (C_t/C₀) of iodine and chloride are proportional to temperature but inversely proportional to dry density. Copyright © 2014 John Wiley & Sons, Ltd.     

非饱和土中热弹性波的传播特性分析

基于非饱和多孔介质的研究成果,考虑热效应和孔隙流体迂曲度的影响,研究了非饱和土中热弹性波的传播特性。利用非饱和土中耦合热的固-液-气三相介质的质量平衡方程、渗流连续方程、动量平衡方程和广义非Fourier热传导定律,建立了问题的热弹性波动方程。通过引入势函数,经过理论推导给出了非饱和土中热弹性波的弥散特征方程。结合数值算例,分析了几类热弹性波的波速和衰减系数随迂曲度、热膨胀系数和介质温度等热物理参数的变化规律。结果表明：孔隙水迂曲度的增大将引起P1波、P3波和S波的波速增大,而孔隙气体迂曲度的增大仅使得P2波的波速增大;热膨胀系数的增大将造成P1波波速的增大和热（T）波波速的减小;介质温度的升高将引起各类热弹性波波速的增大;频率、热膨胀系数和介质温度的变化对各类热弹性波的衰减系数均有较大影响,不可忽视。     

Effect of the formation of EDTA complexes on the diffusion of metal ions in water

The diffusion coefficients of aquo metal ions (M^z+) and their EDTA complexes (M-EDTA^(z−4)+) were compared to understand the effect of EDTA complexation on the diffusion of metal ions by the diffusion cell method for Co²⁺, Ga³⁺, Rb⁺, Sr²⁺, Ag⁺, Cd²⁺, Cs⁺, Th⁴⁺, , and trivalent lanthanides. Most studies about ionic diffusion in water have dealt with free ion (hydrated ion). In many cases, however, polyvalent ions are dissolved as complexed species in natural waters. Hence, we need to study the diffusion behavior of complexes in order to understand the diffusion phenomenon in natural aquifer and to measure speciation by diffusive gradient in thin films (DGT), which requires the diffusion coefficients of the species examined. For many ions, the diffusion coefficients of M-EDTA^(z−4)+ are smaller than those of hydrated ions, but the diffusion coefficients of M-EDTA^(z−4)+ are larger than those of hydrated ions for ions with high ionic potentials (Ga³⁺ and Th⁴⁺). As a result, the diffusion coefficients of EDTA complexes are similar among various metal ions. In other words, the diffusion of each ion loses its characteristics by the complexation with EDTA. Although the difference is subtle, it was also found that the diffusion coefficients of EDTA complexes increase as the ionic potential increases, which can be explained by the size of the EDTA complex of each metal ion.     

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。     

The influence of tortuosity on molecular diffusion in freshwater sediments of high porosity

In sediments, diffusive transport of ions and molecules is basically influenced by two sediment characteristics: tortuosity and porosity. For the first time, the formation factor F, which combines the effect of tortuosity and porosity on diffusion, was quantified in freshwater sediments at submillimeter resolution. Sediment cores were treated with KCl and F was determined using a resistivity sensor and K⁺ selective electrodes.F was determined in sediments from different water depths of the eutrophic Lake Zug (Switzerland): In sandy sediments from a shallow site (12 m depth), F increased by approximately 50% within a few millimeters below the sediment surface. In clayey and silty sediments from the oxic (<80 m depth) and seasonally anoxic (80-120 m depth) zones of the lake, the initial increase in F was only 20%. In the permanent anoxic zone (>160 m depth), F increased by only 10% just below the sediment surface. Values of F were correlated with the porosity at each depth. We found close correlations of F = 1.02 · φ^−1.81 for clay-silt sediments, and F = 1.04 · φ^−1.21 for sandy sediments. The exponents are considerably smaller in Lake Zug than found for marine sediments, thus, diffusive transport seems to be less affected by tortuosity in this freshwater system.     

A micromechanics model for molecular diffusion in materials with complex pore structure

Molecular diffusion in fully saturated porous materials is strongly influenced by the pore space, which, in general, is characterized by a complex topological structure. Hence, information on macroscopic diffusion properties requires up‐scaling of transport processes within nano‐pores and micro‐pores over several spatial scales. A new model in the framework of continuum micromechanics is proposed for predicting the effective molecular diffusivity in porous materials. Considering a representative volume element, characterizing a porous material without any information about the pore space microstructure complexity, the uniform flux is perturbed by recursively embedding shape information hierarchically in the form of the ESHELBY matrix‐inclusion morphology to obtain the effective diffusivity as a function of the recurrence level and the porosity. The model predicts a threshold value for the porosity, below which no molecular diffusion can occur because of the presence of isolated pore clusters that are not connected and unavailable for transport. The maximum porosity, below which no molecular transport is possible, is predicted as one‐third for spherical inclusions. The model allows for extensions to more complex morphologies of the inclusions. We also identify, that the effects of the micro‐structure on molecular transport are characterized by porosity dependent long‐range and short‐range interactions. The developed framework is extended to incorporate realistic pore size distributions across several spatial scales by means of a distribution function within the hierarchical homogenization scheme. Available experimental results assert the model predictions. Copyright © 2015 John Wiley & Sons, Ltd.     

Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients

In this work, we undertake a numerical study of the effective coefficients arising in the upscaling of a system of partial differential equations describing transport of a dilute N-component electrolyte in a Newtonian solvent through a rigid porous medium. The motion is governed by a small static electric field and a small hydrodynamic force, around a nonlinear Poisson–Boltzmann equilibrium with given surface charges of arbitrary size. This approach allows us to calculate the linear response regime in a way initially proposed by O’Brien. The O’Brien linearization requires a fast and accurate solution of the underlying Poisson–Boltzmann equation. We present an analysis of it, with the discussion of the boundary layer appearing as the Debye–Hückel parameter becomes large. Next, we briefly discuss the corresponding two-scale asymptotic expansion and reduce the obtained two-scale equations to a coarse scale model. Our previous rigorous study proves that the homogenized coefficients satisfy Onsager properties, namely they are symmetric positive definite tensors. We illustrate with numerical simulations several characteristic situations and discuss the behavior of the effective coefficients when the Debye–Hückel parameter is large. Simulated qualitative behavior differs significantly from the situation when the surface potential is given (instead of the surface charges). In particular, we observe the Donnan effect (exclusion of co-ions for small pores).     

Isotopic effects in fracture-dominated reactive fluid-rock systems

A mathematical model is presented that describes the effects of pore fluid aqueous diffusion and reaction rate on the isotopic exchange between fluids and rocks in reactive geo-hydrological systems where flow is primarily through fractures. The model describes a simple system with parallel equidistant fractures, and chemical transport in the matrix slabs between fractures by aqueous diffusion through a stagnant pore fluid. The solid matrix exchanges isotopes with pore fluid by solution-precipitation at a rate characterized by a time constant, R (yr⁻¹), which is an adjustable parameter. The effects of reaction on the isotopes of a particular element in the fracture fluid are shown to depend on the ratio of the diffusive reaction length for that element (L) to the fracture spacing (b). The reaction length depends on the solid-fluid exchange rate within the matrix, the partitioning of the element between the matrix pore fluid and the matrix solid phase, the porosity and density of the matrix, and the aqueous diffusivity. For L/b < 0.3, fluid-rock isotopic exchange is effectively reduced by a factor of 2L/b relative to a standard porous flow (single porosity) model. For L/b > 1, the parallel fracture model is no different from a porous flow model. If isotopic data are available for two or more elements with different L values, it may be possible to use the model with appropriate isotopic measurements to estimate the spacing of the primary fluid-carrying fractures in natural fluid-rock systems. Examples are given using Sr and O isotopic data from mid-ocean ridge (MOR) hydrothermal vent fluids and Sr isotopes in groundwater aquifers hosted by fractured basalt. The available data for MOR systems are consistent with average fracture spacing of 1-4 m. The groundwater data suggest larger effective fracture spacing, in the range 50-500 m. In general, for fractured rock systems, the effects of fracture-matrix diffusive exchange must be considered when comparing isotopic exchange effects for different elements, as well as for estimating water age using radioactive and cosmogenic isotopes.     

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。     

天然矿物材料的多孔结构、结构组装和光催化性能

自然界存在丰富的多孔矿物资源,其孔隙结构使其具有良好的吸附性能,能够吸附聚集水体中的污染物(特别是有机污染物)。在分析天然多孔矿物的孔结构基础上,文中提出了结构组装的概念,即在多孔矿物中进行功能粒子组装,对多孔矿物进行表面修饰、微结构组装(如层状结构矿物的插层)。通过结构组装,在多孔矿物中引进功能粒子(如有光催化性能的TiO2 颗粒)。组装在天然矿物中的功能粒子能够降解聚集在其中的污染物,大幅度提高功能粒子的效果,提高光催化降解的功效,获得性能优异、成本低廉的天然矿物型有机污染物降解材料。此外,在同一矿物材料中复合小孔、中孔、大孔不同大小的孔结构,实现不同大小的孔径组装,也能够扩大光催化剂TiO2 的承载面积,提高吸附性能。经过结构组装的天然多孔矿物材料复合了吸附、光催化等性能,在环境治理特别是有机物污染降解方面有很好的应用价值。     

An integrated modelling approach to reconstruct complex solute transport mechanisms - Cl and δCl in pore water of sediments from a former brackish lagoon in The Netherlands

A one-dimensional transport model was developed to reconstruct historical conservative transport of chloride and δ³⁷Cl in pore water of sediments from a former brackish lagoon in The Netherlands, an area now covered by the freshwater Lakes IJssel and Marken. Knowledge of the mechanism of historical solute transport in the sediments and environmental conditions during transport is critical in understanding observed pore water chemistry and will form a basis for simulating effects of changing environmental (climate change) conditions. The model synthesizes present knowledge of geology and historical information on storm surges in the area and takes into account processes such as erosion of sediments, mixing of pore water, sedimentation, and diffusion (EMSD). The chemistry of pore water from one particular boring in the area was found to be mainly controlled by alternating seawater and freshwater diffusion. Models with a constant (averaged) porosity (? = 0.55) and tortuosity factor (τ = 0.3) showed similar results as models incorporating the measured bulk porosity variations (? = 0.4-0.8) and variable tortuosity factors calculated with Archie’s law, τ = ?. The relatively small tortuosity factor either results from anion exclusion or from the heterogeneous build-up of the profile in which a peaty layer in the middle part may obstruct diffusion. Diffusion of ³⁵Cl⁻ was found to be 1.0017 times faster than of ³⁷Cl⁻. Seawater diffusion into the sediments started at least 400 years ago and refreshening took place since the lagoon was isolated from the sea by a dam in 1932.     

Modelling of chloride ingress into concrete through a single‐ion approach. Application to an idealized surface crack pattern

The paper examines ion (chloride) transport equations in porous media (concrete) integrated over a representative elementary volume, that is to say, averaging over the macroscopic level the phenomena that occur really at the pore scale. There are three basic variables to be used: chloride concentration, moisture and temperature. The diffusion process is examined, in addition to other phenomena such as convection (the motion of dissolved substances caused by flow of water in a pore solution of partially saturated media) or chloride binding (the capacity of free chloride of being chemically bound, particularly with C₃A to form Friedel salts). Contrary to other approaches, such effects are not considered by means of apparent diffusion coefficients but by developing the complete set of time‐dependent equations for both the chloride concentration within the pore solution and the moisture content within the pore space. Once the general model is described, the system of equations can be solved numerically by means of a two‐dimensional finite element formulation. The main objective is to reproduce results of experimental tests by means of a priori parameter estimation, according to the characteristics of materials and external environment conditions, thereby superseding the well‐known best fit a posteriori through Fick's second equation. While the introduction of hygrometric conditions and convection phenomena appears to be of high significance, other factors like temperature, surface concentration, chloride binding or equivalent hydration time are analysed too. The proposed model can reproduce bidimensional complex geometries, for example, cracked concrete cover, as well as variable surface condition. An application case is developed through a realistic model of the geometry of a crack. Copyright © 2014 John Wiley & Sons, Ltd.     

Modelling of bentonite–granite solutes transfer from an in situ full-scale experiment to simulate a deep geological repository (Grimsel Test Site, Switzerland)

The FEBEX experiment is a 1:1 simulation of a high level waste disposal facility in crystalline rock according to the Spanish radwaste disposal concept. This experiment has been performed in a gallery drilled in the underground laboratory Grimsel Test Site (Switzerland). Two boreholes parallel to the FEBEX drift were drilled 20 and 60 cm away from the granite–bentonite interface to provide data on potential bentonite–granite solutes transfer. Periodic sampling and analysis of the major ions showed: (a) the existence of solutes transfer from the bentonite porewater towards the granite groundwater, explaining the Cl⁻ and Na⁺ contents of the latter; (b) that the concentration of the natural tracers coming into the granite groundwater from the bentonite porewater increased over time. This bentonite–granite solutes transfer was modelled in order to predict the increase in the Cl⁻ and Na⁺ concentrations of the granite groundwater. The modelled results seem to confirm that the mechanism of solute migration in this scenario is that of diffusive transport. An effective diffusion coefficient of D_e = 5 × 10⁻¹¹ m²/s was that which best fitted the data obtained.