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1.
In order to describe diffusive transport of solutes through a porous material, estimation of effective diffusion coefficients is required. It has been shown theoretically that in the case of uncharged porous materials the effective diffusion coefficient of solutes is a function of the pore morphology of the material and can be described by the tortuosity (tensor) (Bear, 1988 [1]). Given detailed information of the pore geometry at the micro-scale the tortuosity of different materials can be accurately estimated using homogenization procedures. However, many engineering materials (e.g., clays and shales) are characterized by electrical surface charges on particles of the porous material which strongly affect the (diffusive) transport properties of ions. For these type of materials, estimation of effective diffusion coefficients have been mostly based on phenomenological equations with no link to underlying micro-scale properties of these charged materials although a few recent studies have used alternative methods to obtain the diffusion parameters (Jougnot et al., 2009; Pivonka et al., 2009; Revil and Linde, 2006 2, 3 and 4). In this paper we employ a recently proposed up-scaled Poisson–Nernst–Planck type of equation (PNP) and its micro-scale counterpart to estimate effective ion diffusion coefficients in thin charged membranes. We investigate a variety of different pore geometries together with different surface charges on particles. Here, we show that independent of the charges on particles, a (generalized) tortuosity factor can be identified as function of the pore morphology only using the new PNP model. On the other hand, all electro-static interactions of ions and charges on particles can consistently be captured by the ratio of average concentration to effective intrinsic concentration in the macroscopic PNP equations. Using this formulation allows to consistently take into account electrochemical interactions of ions and charges on particles and so excludes any ambiguity generally encountered in phenomenological equations. 相似文献
2.
Upscaling electroosmosis in porous media is a challenge due to the complexity and scale-dependent nonlinearities of this coupled phenomenon. “Pore-network modeling” for upscaling electroosmosis from pore scale to Darcy scale can be considered as a promising approach. However, this method requires analytical solutions for flow and transport at pore scale. This study concentrates on the development of analytical solutions of flow and transport in a single rectangular channel under combined effects of electrohydrodynamic forces. These relations will be used in future works for pore-network modeling. The analytical solutions are valid for all regimes of overlapping electrical double layers and have the potential to be extended to nonlinear Boltzmann distribution. The innovative aspects of this study are (a) contribution of overlapping of electrical double layers to the Stokes flow as well as Nernst–Planck transport has been carefully included in the analytical solutions. (b) All important transport mechanisms including advection, diffusion, and electromigration have been included in the analytical solutions. (c) Fully algebraic relations developed in this study can be easily employed to upscale electroosmosis to Darcy scale using pore-network modeling. 相似文献
3.
Alan G. Jones 《Physics and Chemistry of Minerals》2016,43(4):237-265
Proton conduction in olivine is directly related to the diffusion rate of hydrogen by the Nernst–Einstein equation, but prior attempts to use this relationship have always invoked additional terms to try to reconcile laboratory measurements of proton conduction and hydrogen diffusion data. New diffusion experiments on olivine demonstrate that lattice diffusion associated with vacancies is indeed highly dependent on the defect site where hydrogen is bonded, but from none of the sites is diffusion fast enough to explain the observed laboratory proton conduction experiments. Hydrogen diffusion associated with polarons (redox-exchange) is significantly faster but still cannot explain the low activation energy typical of electrical conductivity measurements. A process of bulk diffusion, which combines lattice diffusion (either associated with redox-exchange or vacancies) with the far faster grain boundary diffusion, explains the laboratory results, but does not explain the field observations with an average grain size of 0.5–2 cm at 100 km below the Jagersfontein kimberlite field on the Kaapvaal craton. Either conduction is dominantly along well-interconnected grain boundaries of very fine-grained (0.01 mm) damp (80 wt ppm) olivine grains or fine-grained (0.05 mm), wet (400 wt ppm) pyroxene grains, or another conduction mechanism must be primarily responsible for the field observations. If diffusion is the correct explanation, the conductivity below the Gibeon kimberlite field in Namibia is too high to be explained by increased thermal state alone of a diffusion process, even for such fine-grained pyroxenes. 相似文献
4.
Using the available pressure–volume–temperature equation of state of sodium chloride, we show that the self-diffusion coefficients of sodium and chloride in sodium chloride as a function of temperature and pressure can be successfully reproduced in terms of bulk elastic and expansivity data. We use a thermodynamic model that interconnects point-defect parameters with bulk properties. Our calculated diffusion coefficients and point-defect parameters, including activation enthalpy, activation entropy, and activation volume, well agree with reported experimental results when uncertainties are considered. Furthermore, the ionic conductivity of sodium chloride inferred from our predicted diffusivities of sodium through the Nernst–Einstein equation is compared with previous experimental data. 相似文献
5.
Hydrogen and alkali ion diffusion in plagioclase feldspars is important to study the evolution of the crust and the kinetics of exsolution and ion-exchange reactions in feldspars. Using the available PVT equation of state of feldspars, we show that the diffusivities of H and alkali in plagioclase feldspars as a function of temperature can be successfully reproduced in terms of the bulk elastic and expansivity data through a thermodynamic model that interconnects point defect parameters with bulk properties. Our calculated diffusion coefficients of H, Na, and K well agree with experimental ones when uncertainties are considered. Additional point defect parameters such as activation enthalpy, activation entropy, and activation volume are also predicted. Furthermore, the electrical conductivity of feldspars inferred from our predicted diffusivities of H, Na, and K through the Nernst–Einstein equation is compared with previous experimental data. 相似文献
6.
Three-Dimensional Modeling of Mass Transfer in Porous Media Using the Mixed Hybrid Finite Elements and the Random-Walk Methods 总被引：2，自引：0，他引：2
A three-dimensional (3D) mass transport numerical model is presented. The code is based on a particle tracking technique: the random-walk method, which is based on the analogy between the advection–dispersion equation and the Fokker–Planck equation. The velocity field is calculated by the mixed hybrid finite element formulation of the flow equation. A new efficient method is developed to handle the dissimilarity between Fokker–Planck equation and advection–dispersion equation to avoid accumulation of particles in low dispersive regions. A comparison made on a layered aquifer example between this method and other algorithms commonly used, shows the efficiency of the new method. The code is validated by a simulation of a 3D tracer transport experiment performed on a laboratory model. It represents a heterogeneous aquifer of about 6-m length, 1-m width, and 1-m depth. The porous medium is made of three different sorts of sand. Sodium chloride is used as a tracer. Comparisons between simulated and measured values, with and without the presented method, also proves the accuracy of the new algorithm. 相似文献
7.
Determination of transport properties of geomaterials is an important issue in many fields of engineering analysis and design. For example, in petroleum engineering, in situ permeability of an oil reservoir may be crucial in establishing its viability for exploitation, whilst prevention of leakage from underground storage facilities for oil and gas, nuclear waste as well as viability of CO2 sequestration projects crucially depends on its long‐term values. Permeability is indirectly related to the porosity, pore‐size distribution and pore architecture of the porous media. These parameters evolve when a strain field is imposed. Physical measurement of permeability under a strain field in laboratory conditions is difficult, expensive and prone to a number of uncertainties. In the past, pore network models have been used to compute permeability of materials under stress/strain‐free conditions. In this paper, we propose an enhanced pore network model to compute permeability of rocks and rock‐like porous media under a stress/strain field. Data of pore‐size distribution obtained from mercury intrusion porosimetry are used to compute permeability of rock samples from various unspecified oilfields in the world. It is shown that the two permeabilities can be predicted from the model with sufficient accuracy. A hypothesis for change in porosity, pore‐size distribution and pore architecture as a result of imposed mechanical strains is then proposed. Based on this, permeability is computed again for one of the rock samples under uniaxial and triaxial compressive and tensile strain fields. It is shown that depending on the state of strain field imposed, permeability evolves in an anisotropic manner. Permeability under tensile strain field increases dramatically compared with the reduction that takes place under compressive strain field of the same magnitude. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
8.
This study aims at determining the macroscopic strength of porous materials having a Drucker–Prager solid phase at microscale and two populations of saturated pores with different pressures at both micro and meso scales. To this end, and taking account of the available results by Maghous et al. (2009), we first derive a closed‐form expression of approximate criterion for a dry porous medium whose matrix obeys to a general elliptic criterion. The methodology to formulate this criterion is based on limit analysis of a hollow sphere subjected to a uniform strain rate boundary conditions. The obtained results are then implemented in a two‐step homogenization procedure, which interestingly delivers analytical expression of the macroscopic criterion for dry double porous media whose solid phase at microscale obeys to a Drucker–Prager criterion. After a brief discussion of the results, we propose an extension to double porous saturated media, allowing therefore to quantify the simultaneous effects of the different pore pressures applied on each voids population. The results are discussed in terms of the existence or not of effective stresses. Finally, they are assessed by comparing them to recently available results. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
9.
Aline C. Rocha Marcio A. Murad Christian Moyne Saulo P. Oliveira Tien D. Le 《Computational Geosciences》2016,20(5):975-996
A new two-scale computational model is proposed to construct the constitutive law of the swelling pressure which appears in the modified form of the macroscopic effective stress principle for expansive clays saturated by an aqueous electrolyte solution containing multivalent ionic species. The microscopic non-local nanoscale model is constructed based on a coupled Poisson-Fredholm integral equation arising from the thermodynamics of inhomogeneous fluids in nanopores (Density Functional Theory), which governs the local electric double layer potential profile coupled with the ion-particle correlation function in an electrolytic solution of finite size ions. The local problem is discretized by invoking the eigenvalue expansion of the convolution kernel in conjunction with the Galerkin method for the Gauss-Poisson equation. The discretization of the Fredholm equation is accomplished by a collocation scheme employing eigenfunction basis. Numerical simulations of the local ionic profiles in rectangular cell geometries are obtained showing considerable discrepancies with those computed with Poisson-Boltzmann based models for point charges, particularly for divalent ions in calcium montmorillonite. The constitutive law for the disjoining pressure is reconstructed numerically by invoking the contact theorem within a post-processing approach. The resultant computational model is capable of capturing ranges of particle attraction characterized by negative values of the disjoining pressure overlooked by the classical electric double layer theory. Such results provide further insight in the role the swelling pressure plays in the modified macroscopic effective stress principle for expansive porous media. 相似文献
10.
The governing equation for steady flow in a homogeneous, partially saturated, porous medium can be written in a linear form if one adopts a hydraulic conductivity function which varies exponentially with capillary-pressure head. The resulting linear field equation is a steady Fokker–Planck equation and is well-suited to numerical solution by the boundary integral equation method (BIEM). The exponential conductivity function is often used in soil physics and is known to be a reasonable approximation over limited ranges of pressure head. A computer code based on the BIEM for obtaining numerical solutions is described and tested. The BIEM is found to exhibit quadratic convergence with element size reduction on smooth solutions and on singular problems, if mesh grading is used. Agreement between results from the BIEM code and a finite element code that solves the fully non-linear problem is excellent, and is achieved at a substantial advantage in computer processing time. As an illustrative example, the code is applied to determine the distribution of moisture in the vicinity of a tunnel. 相似文献
11.
Haiying Hu Lidong Dai Heping Li Jianjun Jiang Keshi Hui 《Mineralogy and Petrology》2014,108(5):609-618
Electrical conductivity measurements on dry polycrystalline K-feldspar were performed at 1.0 to 3.0 GPa and 873 to 1,173 K with a multi-anvil high-pressure apparatus and the Solartron-1260 Impedance/Gain Phase Analyzer in the frequency range of 10?1 to 106 Hz. At each temperature the complex impedance displays a perfect semi-circular arc that represents the grain-interior conduction. Under the experimental conditions, electrical conductivity exponentially increases with increasing temperature and slightly decreases with increasing pressure; however, the effect of pressure on the conductivity is less pronounced than that of temperature. The activation enthalpy decreases slightly from 0.99 to 1.02 eV with increasing pressure, and the activation energy and activation volume for K-feldspar are 0.98 eV and 1.46?±?0.17 cm3/mol, respectively. According to these Arrhenius parameters, ionic conduction is proposed to be the dominant conduction mechanism in K-feldspar at high temperatures and pressures, and potassium ions are the charge carriers transporting by an interstitial mechanism. The diffusion coefficient of potassium at high temperatures was calculated from our conductivity data on K-feldspar using Nernst–Einstein equation, and the results were compared with the previous experimental results. 相似文献
12.
P. M. Adler 《Mathematical Geology》2001,33(1):63-93
A general analysis of electroosmotic phenomena is given for random porous media through which an electrolyte flows. A dimensional analysis demonstrates the crucial importance of the dimensionless coupling parameter a, which is usually very small when compared to 1; this suggests an expansion in terms of a and a numerical scheme that avoids the instabilities occurring in the direct solution. For media whose properties such as permeability are lognormally distributed, an analytical expression of the macroscopic coupling coefficients can be obtained when the fluctuations are small. Various results are provided for laminated media, correlated media, and stratified or fractured media. The influence of some macroscopic geometrical parameters is illustrated. 相似文献
13.
D. W. Smith 《国际地质力学数值与分析法杂志》2000,24(8):693-722
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. 相似文献
14.
15.
基岩裂隙水运移模型评价 总被引：3，自引：0，他引：3
结合近几年的研究成果，按照建立模型时的能量方程不同，将基岩裂隙水运移模型划分为以Darcy定律为基础的模型和以Chezy公式为基础的模型；按照介质概化条件的差异，进一步划分为孔隙介质、裂隙介质和双重介质数学模型，并评价了各种模型的原理、适用条件及其优缺点。 相似文献
16.
深层渗滤效应普遍存在于多孔介质的渗透注浆过程中,并起着非常重要的作用。基于质量守恒方程、线性滤过定律、渗流连续性方程及Darcy定律,建立了水泥浆三维锋面的理论模型;通过现场试验,研究了水泥浆三维锋面扩散运移及沉积层渗透系数的变化规律,并将试验值与模型理论值进行了对比分析。结果表明,沉积层渗透系数随水泥浆锋面的扩散运移动态变化;当注浆压力恒定时,水灰比越小,深层渗滤效应越显著,浆液扩散距离相应越短;相同扩散距离时,受重力效应的影响,注浆点源之上的沉积层渗透系数大于注浆点源之下的沉积层渗透系数;浆液扩散距离及固定位置处的沉积层渗透系数均与水灰比呈正相关。研究成果可指导工程设计,具有一定的实际应用价值。 相似文献
17.
带吸附作用的煤层气运移规律一直是煤层气地质学界关注的焦点问题之一。为研究吸附-解吸状态下的煤层气运移机制,推导了气体吸附-解吸方程并分析了多孔介质扩散-渗流理论,开展了煤层气运移实验并对实验结果进行了分析。研究结果发现:煤体孔隙结构对煤层气运移具有"容阻效应","容储""阻降"二重特性并存构成了煤基质的基本功能;气体运移过程中煤体对CO2和CH4吸附能力的差异体现在吸附响应时间、吸附速率增长率、吸附平衡时间和最大吸附体积等4项指标;煤层气运移过程中扩散和渗流两种方式并存,当裂隙及大孔内气体压力较中-微孔隙系统气体压力高时,气体运移速率以渗流为主,否则以扩散为主。 相似文献
18.
Sidarta Araújo de Lima Márcio A. Murad Christian Moyne Didier Stemmelen 《Acta Geotechnica》2008,3(2):153-174
A new three-scale model to describe the coupling between electro-chemistry and hydrodynamics in non-swelling kaolinite clays
in steady-state conditions is proposed. The medium is characterized by three separate nano-micro and macroscopic length scales.
At the pore (micro)-scale the portrait of the clay consists of micro-pores saturated by an aqueous solution containing four
monovalent ions (Na+, H+, Cl−, OH−) and charged solid particles surrounded by thin electrical double layers. The movement of the ions is governed by the Nernst–Planck
equations and the influence of the double layers upon the hydrodynamics is modeled by a slip boundary condition in the tangential
velocity governed by the Stokes problem. To capture the correct form of the interface condition we invoke the nanoscopic modeling
of the thin electrical double layer based on Poisson–Boltzmann problem with varying surface charge density ruled by the protonation/deprotonation
reactions which occur at the surface of the particles. The two-scale nano/micro model is homogenized to the macroscale leading
to a precise derivation of effective governing equations. The macroscopic model is discretized by the finite volume method
and applied to numerically simulate desalination of a clay sample induced by an external electrical field generated by the
placement of electrodes. Numerical results indicate strong pH-dependence of the electrokinetics. 相似文献
19.
Macroscopic criteria for Green type porous materials with spheroidal voids: application to double porous materials 
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下载免费PDF全文 Combined effects of matrix plastic compressibility and void shape are investigated for ductile porous materials. To this end, a spheroidal volume containing a confocal spheroidal (prolate or oblate) void subjected to uniform strain rate boundary conditions has been first studied. A Green type matrix is chosen as a prototype for investigating effects of plastic compressibility. This is carried out by using a kinematics limit analysis theory from which a closed‐form expression of the macroscopic criterion is established for the considered class of materials. These results are then extended to ductile porous materials made up of a green matrix containing randomly oriented spheroidal voids. In the framework of a two‐step homogenization procedure, the obtained results are implemented to describe the macroscopic behavior of double porous materials involving spherical voids at the microscale and randomly oriented and distributed spheroidal voids at the mesoscale. For validation purpose, the new derived criteria are assessed and validated by comparing their predictions to available upper bounds and numerical data from literature. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
20.
In this paper, we present a numerical model for simulating two-phase (oil–water and air–water) incompressible and immiscible flow in porous media. The mathematical model which is based on a fractional flow formulation is formed of two nonlinear partial differential equations: a mean pressure equation and a water saturation equation. These two equations can be solved in a sequential manner. Two numerical methods are used to discretize the equations of the two-phase flow model: mixed hybrid finite elements are used to treat the pressure equation, h-based Richards' equation and the diffusion term in the saturation equation, the advection term in the saturation equation is treated with the discontinuous finite elements. We propose a better way to calculate the nonlinear coefficients contained in our equations on each element of the discretized domain. In heterogeneous porous media, the saturation becomes discontinuous at the interface between two porous media. We show in this paper how to use the capillary pressure–saturation relationship in order to handle the saturation jump in the mixed hybrid finite element method. The two-phase flow simulator is verified against analytical solutions for some flow problems treated by other authors. 相似文献