A three-scale model for ionic solute transport in swelling clays incorporating ion–ion correlation effects

A new three-scale model is proposed to describe the movement of ionic species of different valences in swelling clays characterized by three separate length scales (nano, micro, and macro) and two levels of porosity (nano- and micropores). At the finest (nano) scale the medium is treated as charged clay particles saturated by aqueous electrolyte solution containing monovalent and divalent ions forming the electrical double layer. A new constitutive law is constructed for the disjoining pressure based on the numerical resolution of non-local problem at the nanoscale which, in contrast to the Poisson–Boltzmann theory for point charge ions, is capable of capturing the short-range interactions between the ions due to their finite size. At the intermediate scale (microscale), the two-phase homogenized particle/electrolyte solution system is represented by swollen clay clusters (or aggregates) with the nanoscale disjoining pressure incorporated in a modified form of Terzaghi’s effective principle. At the macroscale, the electro-chemical–mechanical couplings within clay clusters is homogenized with the ion transport in the bulk fluid lying in the micro pores. The resultant macroscopic picture is governed by a three-scale model wherein ion transport takes place in the bulk solution strongly coupled with the mechanics of the clay clusters which play the role of sources/sinks of mass to the bulk fluid associated with ion adsorption/desorption in the electrical double layer at the nanoscale. Within the context of the quasi-steady version of the multiscale model, wherein the electrolyte solution in the nanopores is assumed at instantaneous thermodynamic equilibrium with the bulk fluid in the micropores, we build-up numerically the ion-adsorption isotherms along with the constitutive law of the retardation coefficients of monovalent and divalent ions. In addition, the constitutive law for the macroscopic swelling pressure is reconstructed numerically showing patterns of attractive forces between particles for bivalent ions for particular ranges of bulk concentrations. The three-scale model is applied to numerically simulate ion diffusion in a compacted clay liner underneath a sanitary landfill. Owing to the distinct constitutive behavior of the swelling pressure and partition coefficient for each ionic species, different compaction regimes and diffusion/adsorption patterns, with totally different characteristic time scales, are observed for sodium and calcium migration in the clay liner.     

Permeability dependence of streaming potential coefficient in porous media

In theory, the streaming potential coefficient depends not only on the zeta potential but also on the permeability of the rocks that partially determines the surface conductivity of the rocks. However, in practice, it is hard to show the permeability dependence of streaming potential coefficients because of the variation of zeta potential from sample to sample. To study permeability dependence of streaming potential, including the effects of the variation of the zeta potential and surface conductance due to the difference in mineral compositions between samples, we perform measurements on 12 consolidated samples, including natural and artificial samples saturated with 7 different NaCl solutions to determine the streaming potential coefficients. The results have shown that the streaming potential coefficients strongly depend on the permeability of the samples for low fluid conductivity. When the fluid conductivity is larger than than 0.50 S/m for the natural samples or 0.25 S/m for the artificial ceramic samples, the streaming potential coefficient is independent of permeability. This behavior is quantitatively explained by a theoretical model.     

A fractal model for streaming potential coefficient in porous media

Streaming potential is the result of coupling between a fluid flow and an electric current in porous rocks. The modified Helmholtz–Smoluchowski equation derived for capillary tubes is mostly used to determine the streaming potential coefficient of porous media. However, to the best of our knowledge, the fractal geometry theory is not yet applied to analyse the streaming potential in porous media. In this article, a fractal model for the streaming potential coefficient in porous media is developed based on the fractal theory of porous media and on the streaming potential in a capillary. The proposed model is expressed in terms of the zeta potential at the solid?liquid interface, the minimum and maximum pore/capillary radii, the fractal dimension, and the porosity of porous media. The model is also examined by using another capillary size distribution available in published articles. The results obtained from the model using two different capillary size distributions are in good agreement with each other. The model predictions are then compared with experimental data in the literature and those based on the modified Helmholtz–Smoluchowski equation. It is shown that the predictions from the proposed fractal model are in good agreement with experimental data. In addition, the proposed model is able to reproduce the same result as the Helmholtz–Smoluchowski equation, particularly for high fluid conductivity or large grain diameters. Other factors influencing the streaming potential coefficient in porous media are also analysed.     

低频交变压差作用下岩心流动电流和zeta电势实验测量

实验测量岩样zeta电势,对于认识地震诱导的电磁场现象以及探索利用动电效应的测井方法具有重要意义.本文介绍了专门设计的岩样流动电流和流动电势实验测量系统及一种获得岩样zeta电势的测量方法——流动电势和流动电流综合测量法.实验采用交流锁相放大技术,测量了3～100 Hz频率范围内交变压差作用下岩样的流动电势系数和流动电...     

Estimation of clay content in soil based on resistivity modelling and laboratory measurements

The determination of clay content in near‐surface formations is crucial for geotechnical, hydrogeological and oil‐contamination studies. We have developed a technique for estimating clay content that consists of the minimization of the difference between the theoretically calculated and measured soil resistivities as a function of water salinity. To calculate the resistivity, we used a model that takes into account the electrochemical processes in the clay micropores. The experimental measurements of soil resistivity were performed on soil samples, completely saturated by brines at different concentrations of NaCl salt in the range 0.6–100 g/l, to obtain the resistivity versus salinity curve. The parameters obtained with this curve inversion are the clay content, the total porosity and the cation exchange capacity. To verify the new technique, we determined clay concentrations of artificial mixtures of calibrated sand and clay. The relative mean error in the clay content does not exceed 20% for a 5% fitting error of the resistivity versus salinity curves. Such evaluations allow the correct separation of the main lithological groups (sand, sandy loam, loam, and light, medium and heavy clay). We applied this technique to estimate the petrophysical parameters of soils (clay content, porosity and cation exchange capacity) at various sites in Mexico. The results improved the interpretation of the vertical electrical soundings, the lithological soil characterization and the delineation of oil‐contaminated areas.     

Experimental measurements of the streaming potential and seismoelectric conversion in Berea sandstone

The streaming potential across a porous medium is induced by a fluid flow due to an electric double layer between a solid and a fluid. When an acoustic wave propagates through a porous medium, the wave pressure generates a relative movement between the solid and the fluid. The moving charge in the fluid induces an electric field and seismoelectric conversion. In order to investigate the streaming potential and the seismoelectric conversion in the same rock sample, we conduct measurements with Berea sandstone saturated by NaCl solutions with different conductivities. We measure the electric voltage (streaming potential) across a cylindrical sample in NaCl solutions with different conductivities and under different pressures to determine the DC coupling coefficients. We also measure the seismoelectric signals induced by acoustic waves with a Berea sandstone plate at different frequencies and solution conductivities. The pressures of the acoustic waves are calibrated with a standard hydrophone (Brüel & 8103) at different frequencies (15–120 kHz). We calculate the quantitative coupling coefficients of the seismoelectric conversion at DC and at high frequencies with samples saturated by solutions with different conductivities. When the Berea sandstone sample is saturated by the NaCl solution with 0.32 mS/m in conductivity, for example, the DC and seismoelectric coupling coefficients at 15 kHz are 0.024 μV/Pa and 0.019 μV/Pa, respectively. The seismoelectric coupling coefficient is an important and helpful parameter for designing a seismoelectric tool. More experimental measurements of seismoelectric coupling coefficients in the frequency range of 100 Hz to 15 kHz are needed in the future.     

孔隙岩样动电特性的实验研究

本文针对流体饱和孔隙介质的动电效应,在实验室内进行了小岩样的动电实验(流动电势实验)测量,获得了10块岩样在6种不同饱和浓度下的流动电势系数,进而分析了饱和溶液浓度、岩样渗透率和泥质含量对流动电势系数的影响,探讨了流动电势系数对上述参数的敏感性,并进一步给出了流动电势系数随这些参数的变化规律.实验结果表明:前人流动电势系数频响曲线中的凹点现象是由实验装置的共振引起,并非岩样动电效应的自身特性.实验还发现:孔隙介质的动电耦合能力与溶液浓度有关,流动电势系数随溶液浓度增大而减小,但在很高浓度溶液中,动电现象依然存在,流动电势系数趋于常数.此外,流动电势系数对地层参数(渗透率和泥质含量)的敏感性受溶液浓度影响较大,随着溶液浓度增大,敏感性降低.因此,可在低浓度饱和情况下(低于0.4mol/L),利用流动电势系数的幅度对地层渗透率进行直接评价.本文结果对动电测井的可行性及应用条件给出了实验说明.     

引潮力作用下饱和地质岩体的力学响应

本文应用孔隙弹性理论,探讨了引潮力作用下饱和地质岩体的力学响应.首先通过引潮力作用下饱和岩体的自由能表达式,得到岩体孔压与应力、应力与应变之间的关系;然后从引潮力作用下饱和岩体的平衡微分方程出发,结合流-固耦合理论,分析了饱水岩体应变与引潮位之间的关系;最后推导出饱和岩体的两大力学物理量--孔压和潮汐应力(平均应力)与引潮位之间的物理关系.模型表明:饱和岩体孔压与引潮位成反比,平均潮汐应力与引潮位成正比;比例系数不仅与岩体骨架的Lame系数有关,而且与Biot模量有关.将模型应用于会理川-18井水位变化分析,估计出水位响应系数D,并以此为基础,求得岩体孔压、潮汐应力与引潮位的相关系数(A和C)及Skempton系数B.最后对比分析了耦合条件下与不考虑耦合时得到的各参数之间的差异,分析表明:对饱和地质岩体而言,应力、孔压对引潮力的响应是流-固耦合作用的产物;研究其力学响应时必须充分考虑耦合效应.模型的建立,为研究引潮力作用下井-承压含水层系统力学、水动力学、与地震有关的断层力学以及引潮力触发机制的定量研究提供了基础.     

Multicomponent competitive monovalent cation exchange in hierarchical porous media with multimodal reactive mineral facies

This paper presents a stochastic model for multicomponent competitive monovalent cation exchange in hierarchical porous media. Reactive transport in porous media is highly sensitive to heterogeneities in physical and chemical properties, such as hydraulic conductivity (K), and cation exchange capacity (CEC). We use a conceptual model for multimodal reactive mineral facies and develop a Eulerian-based stochastic theory to analyze the transport of multiple cations in heterogeneous media with a hierarchical organization of reactive minerals. Numerical examples investigate the retardation factors and dispersivities in a chemical system made of three monovalent cations (Na⁺, K⁺, and Cs⁺). The results demonstrate how heterogeneity influences the transport of competitive monovalent cations, and highlight the importance of correlations between K and CEC. Further sensitivity analyses are presented investigating how the dispersion and retardation of each cation are affected by the means, variances, and integral scales of K and CEC. The volume fraction of organic matter is shown to be another important parameter. The Eulerian stochastic framework presented in this work clarifies the importance of each system parameters on the migration of cation plumes in formations with hierarchical organization of facies types. Our stochastic approach could be used as an alternative to numerical simulations for 3D reactive transport in hierarchical porous media, which become prohibitively expensive for the multicomponent applications considered in this work.     

Study of swelling-shrinkage regularity of montmorillonite crystal and its relation with matric suction

The swell-shrinking mineral of saturated and unsaturated expansive soil has important effect on engineering mechanical behavior. Based on the swelling-shrinkage change regularity of montmorillonite crystal in this paper, the actions between various interlayers of montmorillonite crystal are generally summarized as two kinds of action potentials-shrinkage potential and swelling potential. Moreover, through the experimental research and analysis, the expression formula for variations of the swelling potential and shrinkage potential with interlayer distance is presented, and the regularity of matric suction variations with interlayer distance is also obtained for unsaturated expansive soil. It may provide a new theoretical basis and research path for further research on the swelling-shrinkage mechanism of expansive soil and matric suction potential of unsaturated soil.     

利用毛管模型研究泥质砂岩电化学测井响应机理

自然电位和激发极化电位测井响应所涉及的离子导体激发极化电位的微观机理解释,主要依据双电层形变假说和浓差极化假说,缺少定量描述的数学模型和理论体系.本文利用孔隙介质的微观毛管模型,给出了毛管模型中双电层理论和阳离子交换量与Zeta电位的关系,推导出毛管中离子流量和电流强度表达式.由电荷守恒定律和物质守恒定律,推导出毛管中离子浓度分布的解析表达式,建立了描述含水泥质砂岩激发极化电位和自然电位的数学模型.从而系统地严格证明了含水泥质砂岩激发极化现象是在电流场和浓度梯度场的共同作用下,由孔隙中离子浓度浓差极化电位和双电层形变电位形成的.并且证明了描述泥质砂岩自然电位的数学方程和描述激发极化电位的数学方程及形成机理是一致的.计算结果表明：激发极化极化率随孔隙度和渗透率的增大而减小;极化率随溶液浓度的增加而减小,随阳离子交换量的增加而增加;证明了地层水浓度、阳离子交换量是影响自然电位大小的主要因素.     

频率域有限差分数值模拟地震波衰减和震电效应特征

地震波在地下含流体孔隙介质中传播时,会引起中观尺度的"局域流",进而产生地震波震电效应.基于Biot(1941)固结理论的准静态方程,在频率域中采用空间有限差分方法,正演模拟虚岩石物理岩样的地震波衰减和震电效应.与时间域虚岩石物理方法相比,该方法既可以直接求取任一频率下的地震波衰减和电势,便于应用于实际岩样的预测分析,也避免了讨论岩样外表面施加的力源函数表达式及时间剖分稳定性条件等问题.首先利用周期性层状介质模型验证了本文所描述方法的有效性,并进一步求取分析了周期性层状介质两种不同特征单元的渗流电流密度及电势,数值模拟结果表明由中观尺度"局域流"引起的震电效应电势振幅数量级在实验室测量范围之内,随后,分析研究了四种不同高渗介质占比值的地震衰减及震电效应特征.最后,将本文提出的震电效应数值计算方法推广至二维,并求取了二维斑块饱和模型的地震波衰减、速度频散、电势的振幅和相位角数值结果.     

Mechanical Response of Saturated Geological Rock Mass under Tidal Force

In this paper,the mechanical response of saturated geological rock under tidal force is explored by poroelastic theory.First,we use the free energy formula of saturated rock under a tidal force to study the relationships of pore pressure with stress,and stress with strain.Then we analyze the relationship between rock strain and tidal potential by the equilibrium differential equations of saturated rock under tidal force.Finally,we derive the physical relationship between the two parameters (pore pressure and tidal mean stress) of saturated rock and tidal potential.The relationship shows that:pore pressure is directly proportional with tidal potential,but tidal mean stress of saturated rock is inversely proportional with tidal potential.The ratio coefficient is related not only to the Lame coefficients of rock skeletons,but also to the Biot modulus.By using this model to analyze observational well water level of C-18 well which locates in Huili,Sichuan Province,the well level response coefficient (D) was estimated.This way,we derive the Skempton coefficient (B),the coefficient A and C which refer to the response coefficients of pore pressure and tidal stress to tidal potential respectively.Then we compare the differences among each coefficient in coupling and uncoupling conditions.It shows that for saturated rocks,the response of stress and pore pressure to earth tides is a product of coupling,and it is necessary to take into account the coupling effect when we study the mechanical response.The model will provide the basis not only for the study of mechanics and hydrodynamics of well-confined aquifer systems,and the mechanics of faulting under tidal force,but also for quantitative research of the triggering mechanism of tidal forces.     

Fully coupled finite element model for dynamics of partially saturated soils

Understanding the response of partially saturated earth structures under various static and dynamic loads is important for the design and construction of economical and safe geotechnical engineering structures. In this study, the numerical approach is used to understand the dynamics of partially saturated soils. The mathematical equations governing the dynamics of partially saturated soils are derived based on the theory of mixtures and implemented within a finite element framework. The stress–strain behavior of the soil is represented by an elasto-plastic constitutive model for unsaturated soil based on bounding surface concept and the moisture-suction behavior is modeled using van Genuchten model. Fully coupled finite element simulations are performed to study the response of partially saturated soil embankment under earthquake loading and validated with centrifuge test results available in the literature. The predicted displacement responses are in good agreement with the measured responses. The pore water pressure, pore air pressure, matric suction, the degree of saturation in various elements and the response of the embankment under different initial moisture content are also discussed.     

Electrokinetic phenomena associated with a water injection experiment at the Nojima fault on Awaji Island, Japan

Abstract Self-potential variations were measured to estimate the magnitude of electrokinetic and hydrological parameters (zeta potential and permeability) of the Nojima Fault zone in Awaji, Japan. The study observed self-potential variations that seemed to be associated with water flow from the injection well to the fracture zone, which were induced by turning the injection on and off. Amplitudes of the variations were a few to 0.03 V across 320–450 m dipoles. These variations can be explained well with an electrokinetic model. The quantity k/ζ (permeability/zeta potential) is in the range 1.6 × 10⁻¹³− 5.4 × 10⁻¹³ m²/V. Permeability of the Nojima fault zone can be estimated as approximately 10⁻¹⁶–10⁻¹⁵ m² on the assumption that the zeta potential is in the range –0.01 to –0.001 V.     

饱和南京细砂永久应变势模型的试验研究

土单元永久应变势的预测模型是土动力学的重要研究内容之一。现有的土单元永久应变势模型没有反映振动孔压增长的影响,难以合理解释地震动作用引起的饱和砂土地基永久变形一般是由土层软化或再固结变形所致的机理。基于饱和南京细砂永久变形动三轴试验结果的有效应力状态分析,研究了试样的永久变形与振动孔压增长的关系,建立了一个能反映振动孔压增长影响的土单元永久应变势模型,给出了土单元永久应变势的数学表达式,分析了土单元永久应变势模型参数的影响因素。初步的验证性试验表明:模型预测与试验测得的试样永久应变势与振动孔压增长曲线比较接近,说明该模型具有一定的合理性。     

Effect of pH on Adsorption Equilibria for Dissolved Weak Organic Electrolytes on Activated Carbon

The influence of pH on the adsorption equilibria of a-picolin and phenol from aqueous solution on activated carbon is studied experimentally for the single solutes and their mixtures. For these weak bases and weak acids the effect of pH on adsorption capacity is contrary, thus allowing an efficient separation by adsorption. A model based on the concept of competitive adsorption of ionic and molecular forms of the organic electrolytes represents the experimental data qualitatively. Deviations between theoretical and experimental results are discussed on the basis of possible interactions of the organic solutes and the activated carbon with components of the buffer used in the experiments.     

Classification of self-potential anomalies on volcanoes and possible interpretations for their subsurface structure

Self-potential (SP) surveys were conducted on 10 island-arc-type volcanoes in Japan. Large-scale SP anomalies that covered entire volcanic edifices and had simple shapes were observed. Neglecting the local fluctuations, we named the SP anomaly that shows voltage gradients anywhere on the flank a long spatial wavelength (LSW) SP anomaly. We first classified these anomalies into three types: 1) no anomaly (SP profile is flat): 2) “W”-shaped profile: and 3) “V”-shaped profile. In some volcanoes, one flank with a flat SP profile and another with half of the W-shaped SP profile coexist. Next, we compared LSW-SP anomalies with various factors that may be related to SP generation and found that the SP profile is approximately flat on the flank where geothermal manifestations exist. This relationship, which is new aspect of the SP data on volcanoes, is important because it can impose a constraint on the model for SP generation and the subsurface structure. Based on the discussion that SP is generated by an electrokinetic mechanism, we propose that resistivity, zeta potential, and hydraulic radius are the possible parameters that control the existence of LSW-SP anomalies. The new relationship between SP and geothermal manifestation are understood in terms of the presence of hydrothermal system. Although the structure of volcanic edifice is probably spatially complicated, the insight into the SP data presented in this study implies that the flanks with flat SP profiles are relatively weak and have high potential for sector collapse.     

Velocity–porosity relationships: Predictive velocity model for cemented sands composed of multiple mineral phases

Computer simulations are used to calculate the elastic properties of model cemented sandstones composed of two or more mineral phases. Two idealized models are considered – a grain‐overlap clay/quartz mix and a pore‐lining clay/quartz mix. Unlike experimental data, the numerical data exhibit little noise yet cover a wide range of quartz/cement ratios and porosities. The results of the computations are in good agreement with experimental data for clay‐bearing consolidated sandstones. The effective modulus of solid mineral mixtures is found to be relatively insensitive to microstructural detail. It is shown that the Hashin–Shtrikman average is a good estimate for the modulus of the solid mineral mixtures. The distribution of the cement phase is found to have little effect on the computed modulus–porosity relationships. Numerical data for dry and saturated states confirm that Gassmann's equations remain valid for porous materials composed of multiple solid constituents. As noted previously, the Krief relationship successfully describes the porosity dependence of the dry shear modulus, and a recent empirical relationship provides a good estimate for the dry‐rock Poisson's ratio. From the numerical computations, a new empirical model, which requires only a knowledge of system mineralogy, is proposed for the modulus–porosity relationship of isotropic dry or fluid‐saturated porous materials composed of multiple solid constituents. Comparisons with experimental data for clean and shaly sandstones and computations for more complex, three‐mineral (quartz/dolomite/clay) systems show good agreement with the proposed model over a very wide range of porosities.     

Porosity of bimodal and trimodal sediment mixtures

This study focuses on the prediction of the porosity of nonuniform sediment mixtures,considering the effects of particle packing.A random particle packing model has been developed for the porosity of bimodal mixtures by extending the existing random particle filling theory.Coefficients in the developed model are calibrated by fitting the model to measured data for a variety of bimodal mixtures,including spherical glass particles,rounded quarry grains,and natural sediments.The model coefficients ...