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.     

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.     

Seismoelectric measurements in a porous quartz‐sand sample with anisotropic permeability

Seismoelectric coupling coefficients are difficult to predict theoretically because they depend on a large numbers of rock properties, including porosity, permeability, tortuosity, etc. The dependence of the coupling coefficient on rock properties such as permeability requires experimental data. In this study, we carry out a set of laboratory measurements to determine the dependence of seismoelectric coupling coefficient on permeability. We use both an artificial porous “sandstone” sample, with cracks, built using quartz‐sand and Berea sandstone samples. The artificial sample is a cube with 39% porosity. Its permeability levels are anisotropic: 14.7 D, 13.8 D, and 8.3 D in the x‐, y‐, and z‐directions, respectively. Seismoelectric measurements are performed in a water tank in the frequency range of 20 kHz–90 kHz. A piezoelectric P‐wave source is used to generate an acoustic wave that propagates through the sample from the three different (x, y, and z) directions. The amplitudes of the seismoelectric signal induced by the acoustic waves vary with the direction. The highest signal is in the direction of the highest permeability, and the lowest signal is in the direction of the lowest permeability. Since the porosity of the sample is constant, the results directly show the dependence of seismoelectric coefficients on permeability. Seismoelectric measurements with natural rocks are performed using Berea sandstone 500 and 100 samples. Because the Berea samples are nearly isotropic in permeability, the amplitudes of the seismoelectric signals induced in the different directions are the same within the measurement error. Because the permeability of Berea 500 is higher than that of Berea 100, the amplitude of the seismoelectric signals induced in Berea 500 is higher than those in Berea 100. To determine the relative contributions of porosity and permeability on seismoelectric conversion, we carried out an analysis, using Pride (1994) formulation and Kozeny–Carman relationship; the normalized amplitudes of seismoelectric coupling coefficients in three directions are calculated and compared with the experimental results. The results show that the seismoelectric conversion is related to permeability in the frequency range of measurements. This is an encouraging result since it opens the possibility of determining the permeability of a formation from seismoelectric measurements.     

基于动电效应的岩芯渗透率实验测量

根据孔隙介质的动电耦合理论设计了一套岩芯渗透率测量系统.实验采用交流锁相放大技术,在低频12~42 Hz范围内完成了砂岩岩样流动电势和电渗实验,得到了流动电势系数K_S和电渗压力系数K_E,进而计算出岩样动电渗透率,对于中、高渗透率岩样,测量得出的动电渗透率与常规气测渗透率差异较小,两者具有很好的相关性.实验表明,动电测量可作为岩样渗透率测量的一种方法,同时揭示了利用地层动电测井信号反演地层参数的可能性,实验结果对于分析天然地震动电效应也有参考意义.     

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.     

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...     

储层岩石流动电位频散特性的数学模拟

利用储层岩石流动电位的频散特性评价复杂储层已经成为勘探地球物理领域关注的热点,但是目前还没有形成基于储层岩石储渗特性及电化学性质的具有普遍指导意义的理论方法和数学模型.本文利用微观毛管理论,通过随时间谐变条件下渗流场和电流场的耦合模型,建立了描述储层岩石流动电位频散特性的数学方法,定量分析了频率域储层岩石动态渗透率、动电耦合系数和流动电位耦合系数随储层岩石孔隙度、溶液浓度和阳离子交换量的变化规律.研究结果表明:储层岩石流动电位频散特性是储层流体惯性力与流体黏滞力相互作用的结果.储层岩石孔隙度越大,储层维持流体原有运动状态的能力越大,临界频率越小;储层岩石的溶液浓度和阳离子交换量对临界频率没有影响.储层岩石的孔隙度越大,流体流动能力越强,流动电位各耦合系数的数值越大;溶液浓度越小或阳离子交换量越大,孔隙固液界面的双电层作用越强,各耦合系数的数值越大.     

Artificial neural network forward modelling and inversion of electrokinetic logging data

An artificial neural network method is proposed as a computationally economic alternative to numerical simulation by the Biot theory for predicting borehole seismoelectric measurements given a set of formation properties. Borehole seismoelectric measurements are simulated using a finite element forward model, which solves the Biot equations together with an equation for the streaming potential. The results show that the neural network method successfully predicts the streaming potentials at each detector, even when the input pressures are contaminated with 10% Gaussian noise. A fast inversion methodology is subsequently developed in order to predict subsurface material properties such as porosity and permeability from streaming potential measurements. The predicted permeability and porosity results indicate that the method predictions are more accurate for the permeability predictions, with the inverted permeabilities being in excellent agreement with the actual permeabilities. This approach was finally verified by using data from a field experiment. The predicted permeability results seem to predict the basic trends in permeabilities from a packer test. As expected from synthetic results, the predicted porosity is less accurate. Investigations are also carried out to predict the zeta potential. The predicted zeta potentials are in agreement with values obtained through experimental self potential measurements.     

围压对低渗砂岩渗透率有效应力系数的影响

多孔岩石渗透率有效应力系数的取值至今仍没有一致的认识,影响取值的因素较为复杂.为了探索围压对低渗砂岩渗透率有效应力系数的影响,实验上采用较大的围压范围(10MPa～50MPa),选取两块低渗致密砂岩岩样,进行渗透率测试,并利用二元线性回归方法,计算了不同围压组合下的渗透率有效应力系数值,获取了该系数随围压的变化趋势.实验中,两块岩样的渗透率有效应力系数随围压的增加而减小,但各自的减小趋势略有不同.利用Bernabé和Berryman提出的模型,理论上解释了围压对渗透率有效应力系数的影响,并得到渗透率有效应力系数的下限值为岩样孔隙度.尽管渗透率有效应力系数不是一个常数,但可以表示为压差的函数,进而起到简化分析的作用.     

In-Situ Electrical Conductivity and Permeability of Mid-Crustal Rocks from the Ktb Drilling: Consequences for High Conductive Layers in the Earth Crust

Freshly cored samples from a microprofile (7011–7013m in depth) of the German Continental Deep Drilling Project (KTB) were taken to measure the complex electrical conductivity (1 kHz up to 1 MHz), porosity, BET-surface, permeability and density. The porosity ranged about 1 vol%, while the permeability k varied from 16.05 µD to > 0.01 µD for in-situ pressure conditions. The permeability decreased about 2 orders in magnitude up to pressures of 200 MPa. Conductivity was measured in the same pressure range on 1 M NaCl saturated samples. Thin sections and SEM analysis revealed an enrichment of carbon and ilmenite (about 1 vol%) on inner cleavage cracks of mica, thus causing an unusual high (ranging from 4.2 × 10^-3 S/m to 67 × 10^-3 S/m) being orders of magnitude higher than normally measured on such types of rocks (about 300 × 10^-6 S/m). An inverse pressure dependence of was detected on some of the samples. Electronic conduction was confirmed by least-squares-fits of model data to the frequency dispersion of the conductivity and by measuring the time dependence of the volume conductivity and its frequency dispersion. Thus the dominating role of the reconnected network of carbon and ilmenite on the enhanced volume conductivity was proved. An increase of the conductivity due to hydrofracturing by high pore fluid pressures plays a less important role.     

Numerical Simulation of the Effect of a DC Electric Field on Seismic Wave Propagation with the Pseudospectral Time Domain Method

We have modeled the effect of a direct current (DC) electric field on the propagation of seismic waves by the pseudospectral time domain (PSTD) method, based on a set of governing equations for the poroelastic media. This study belongs to the more general term of the seismoelectric coupling effect. The set of physical equations consists of the poroelastodynamic equations for the seismic waves and the Maxwell's equations for the electromagnetic waves; the magnitude of the seismoelectric coupling effect is characterized by the charge density, the electric conductivity, the Onsager coefficient, a function of the dielectric permittivity, the fluid viscosity, and the zeta potential. The poroelastodynamic vibration of a solid matrix generates an electric oscillation with the form of streaming current via the fluctuation of pore pressure. Meanwhile, fluctuating pore pressure also causes oscillatory variation of the electric resistivity of the solid matrix. The simulated poroelastic wave propagation and electric field variation with an existing background DC electric field are compared with the results of a physical experiment carried out in an oilfield. The results show that the DC electric field can significantly affect the propagating elastic energy through the seismoelectric coupling in a wide range of the seismic frequency band.     

Zeta potential of porous rocks in contact with mixtures of monovalent and divalent electrolytes

The zeta potential is one of the most important parameters influencing the electrokinetic coupling. Most reservoir rocks are saturated or partially saturated by natural water containing various types of ions (mostly monovalent and divalent ions). Therefore, understanding how the zeta potential behaves for mixtures of electrolytes is very important. In this work, measurements of the zeta potential for four different silica-based samples saturated by seven different mixtures of monovalent and divalent electrolytes are then carried out at a fixed ionic strength. It is seen that the magnitude of the measured zeta potential decreases with increasing divalent cation fraction. The experimental results are then explained by a model developed for mixtures of monovalent and divalent electrolytes. The result shows that the theoretical model is able to reproduce the main trend of the variation of the zeta potential with divalent cation fractions. Additionally, the model can fit the experimental data reported in literature well for reasonable values of the input parameters.     

不同围压和流体饱和状态下致密砂岩弹性各向异性特征

为研究致密砂岩声波速度及其各向异性随围压的变化规律以及不同流体饱和状态下的弹性各向异性特征,钻取了不同方向的岩心并在实验室超声波频率下对致密砂岩的声学特性进行了测量,分别给出干燥和饱和水状态下,不同方向样品纵横波速度、刚性系数以及各向异性系数随围压的变化规律,并对实验结果进行了分析讨论.实验结果表明致密砂岩纵横波速度、纵横波速度比以及刚性系数均随围压增加而增加,但其在不同饱和状态下的变化率却截然不同;纵横波速度比、各向异性系数在饱和水状态下变化规律不明显,表明孔隙流体的存在对于岩石物理性质有着非常重要的影响.这方面的实验工作不但对于考察不同流体性质对致密岩石弹性各向异性影响是必要的,而且有助于致密砂岩油水和气层的识别.     

基于二维图像的数字岩心电导率计算方法研究

电导率是表征岩石电学性质的重要物理参数,在地质资源勘查和测井解释等领域发挥着巨大作用.快速、准确地确定岩石电导率具有重要的理论和实践意义.作为近年来发展的一种岩石物理数值模拟工具,数字岩心技术在定量计算电导率等物性参数方面应用广泛.三维微观结构的准确获取是数字岩心技术计算岩石电导率的关键,但传统获取岩石三维微观结构的方法较为复杂费时.为了方便快速地通过数字岩心技术计算岩石的电导率,本文研究了岩石二维与三维数字岩心的电导率联系.我们基于微米级X射线CT扫描得到的三个砂岩样品的微观结构信息建立了三维数字岩心,并通过有限元法计算的三维数字岩心电导率与实验数据的对比验证数值计算方法的有效性.随后我们数字地扩展了岩石的孔隙,产生了较大孔隙度的三维数字岩心样本,在此基础上,计算了三维数字岩心和相应二维数字岩心的电导率,并通过Archie公式分别拟合了电导率与孔隙度之间的关系,得到了相应的胶结系数.结果表明,三维数字岩心的胶结系数小于二维数字岩心的胶结系数,且二者的比值与岩石实测孔隙度呈线性负相关关系.以该联系为纽带,通过二维图像快速计算得到的电导率与孔隙度关系,确定了三维数字岩心的电导率与孔隙度关系,并进一步通过三维数字岩心的孔隙度计算其电导率.该方法计算得到的人工砂岩样品的电导率与其三维数字岩心电导率相关系数高于96%,验证了基于二维图像的数字岩心电导率计算方法的有效性.本文的研究结果为快速、准确地计算岩石电导率提供了新的思路,在油气勘探开发中有广阔的应用前景.     

Changes in geophysical properties caused by fluid injection into porous rocks: analytical models

Analytical models are provided that describe how the elastic compliance, electrical conductivity, and fluid‐flow permeability of rocks depend on stress and fluid pressure. In order to explain published laboratory data on how seismic velocities and electrical conductivity vary in sandstones and granites, the models require a population of cracks to be present in a possibly porous host phase. The central objective is to obtain a consistent mean‐field analytical model that shows how each modeled rock property depends on the nature of the crack population. The crack populations are described by a crack density, a probability distribution for the crack apertures and radii, and the averaged orientation of the cracks. The possibly anisotropic nature of the elasticity, conductivity, and permeability tensors is allowed for; however, only the isotropic limit is used when comparing to laboratory data. For the transport properties of conductivity and permeability, the percolation effect of the crack population linking up to form a connected path across a sample is modeled. However, this effect is important only in crystalline rock where the host phase has very small conductivity and permeability. In general, the importance of the crack population to the transport properties increases as the host phase becomes less conductive and less permeable.     

密度对非饱和粘土渗透系数的影响研究

取三峡库区某滑坡滑带土制备不同干密度的重塑土样进行饱和渗透试验和非饱和土水特征曲线试验,得到不同干密度重塑土样的土水特征曲线,通过理论公式预测出相应的非饱和渗透系数,进而得到不同干密度重塑土样渗透系数与基质吸力的关系.结果显示:渗透系数随着基质吸力的增大而呈非线性减小,当基质吸力较高时,渗透系数随基质吸力的变化比较小;...     

1.2千巴围压下岩样破裂和摩擦滑动过程中电阻率变化h

在1.2千巴围压下进行了三种初始饱和岩样(辉长岩、花岗岩Ⅰ和Ⅱ,各以淡水和盐水饱和)的压缩实验直至破裂并继续到摩擦滑动,所有实验中测定了岩样电阻率。 以Brace等人研究表面电导的方法为基础,我们引入给定含水岩样的体电阻系数和面电导系数两个专用术语以分析实验结果。发现一旦岩样开始膨胀,其面电导系数随差应力增加都增大。结果表明:含水岩样体膨胀后电阻率下降主要是由于表面电导作用的增强。 和前人的结果不同,不同岩样摩擦滑动时电阻率变化各异。作者提出:这种差异可能与岩石中所含矿物颗粒大小有关。含大颗粒的岩石滑动时电阻率下降,而含小颗粒的岩石滑动时电阻率上升。      

Influence of water pressure dynamics and fluid flow on the streaming‐potential response for unsaturated conditions

Streaming‐potentials are produced by electrokinetic effects in relation to fluid flow and are used for geophysical prospecting. The aim of this study is to model streaming potential measurements for unsaturated conditions using an empirical approach. A conceptual model is applied to streaming potential measurements obtained from two drainage experiments in sand. The streaming potential data presented here show a non‐monotonous behaviour with increasing water saturation, following a pattern that cannot be predicted by existing models. A model involving quasi‐static and dynamic components is proposed to reproduce the streaming potential measurements. The dynamic component is based on the first time derivative of the driving pore pressure. The influence of this component is investigated with respect to fluid velocity, which is very different between the two experiments. The results demonstrate that the dynamic component is predominant at the onset of drainage in experiments with the slowest water flow. On the other hand, its influence appears to vanish with increasing drainage velocity. Our results suggest that fluid flow and water distribution at the pore scale have an important influence on the streaming potential response for unsaturated conditions. We propose to explain this specific streaming potential response in terms of the behaviour of both rock/water interface and water/air interfaces created during desaturation processes. The water/air interfaces are negatively charged, as also observed in the case of water/rock interfaces. Both the surface area and the flow velocity across these interfaces are thought to contribute to the non‐monotonous behaviour of the streaming potential coefficient as well as the variations in its amplitude. The non‐monotonous behaviour of air/water interfaces created during the flow was highlighted as it was measured and modelled by studies published in the literature. The streaming potential coefficient can increase to about 10 to 40 when water saturation decreases. Such an increase is possible if the amount of water/air interfaces is increased in sufficient amount, which can be the case.     

Thermal effect of magma intrusion on the electrical properties of magnetic rocks from Hammamat sediments, Cairo, Egypt

The thermal effects of magmatic intrusion on the conductivity and dielectric constant of magnetic rocks from Hammamat sediments, NE desert, Cairo, Egypt (latitude ∼27° and longitude ∼33°) were investigated experimentally in the laboratory using nonpolarizing electrodes. Granitic magma was intruded into the Hammamat sediments, which are a mixture of mainly magnetite with sandstone and due to the thermal effect the area around was extensively heated and altered to different degrees. Due to this magma intrusion, magnetite was transformed (by heating) to hematite to different degrees according to its location from the intrusion. Complex impedance measurements were performed in the frequency range of 10 Hz to 100 KHz at normal temperature (∼20°C) and at a relative humidity of ∼50% RH. Samples were collected at different locations perpendicular to the core of the magma intrusion. Experimental data indicate that the electrical properties vary strongly as we move away (with distance) from the magma intrusion. The conductivity of hematite is ∼10⁻² S/m and that of magnetite is ∼10⁴ S/m. As we move from magnetite to hematite (to the core of the magma intrusion) it is supposed that the conductivity will decrease but it was found that the conductivity increases (which is supposed to be abnormal). The conductivity increases with increasing frequency from ∼10⁻⁸ S/m to ∼10⁻⁵ S/m with almost power‐law dependence on frequency. The conductivity increases in the order of one decade due to the variation from magnetite to hematite. The increase of conductivity, as we move from magnetite to hematite, was argued to be due to the heating that partially or completely melts the samples, thus the porosity of the samples was decreased and accordingly the conductivity and dielectric constant increased. It was also supposed that the grains of the conductor in the samples are coated or isolated with insulator material. A percolation behaviour for the conductivity and dielectric constant, characteristic of random conductor‐insulator mixtures, was found with distance, where continuous paths of the conductive material occur accompanied by peaking of the dielectric constant. Complex impedance plots show that as we move in the direction of altered samples (towards hematite) the relation between real and imaginary impedance changes from a linear form to an arc of a depressed semicircle and increases in depression as we move in the direction of the altered samples, which is consistent with the above interpretation.     

Interrelations Between Thermal Conductivity and Other Physical Properties of Rocks: Experimental Data

— A new non-contact and non-destructive optical scanning instrument provided a large number of high-precision measurements of thermal conductivity tensor components in samples of sedimentary and impact rocks, as well as new insights into interrelations between thermal conductivity and other physical properties. More than 800 core samples (dry and fluid-saturated) of sedimentary rocks from different Russian oil-gas deposits and impact rocks from the well “Nördlingen 1973” drilled in the Ries impact structure (Germany) were studied using optical scanning technology. It was established that the thermal conductivity parallel to the stratification is more informative for petrophysical investigations than the thermal conductivity perpendicular to the layering. Different approaches were developed to estimate porosity, permeability, pore space geometry, and matrix thermal conductivity with a combination of thermal conductivity measurements in dry and fluid-saturated samples and mathematical modelling. These approaches allow prediction of the rock porosity and permeability and their spatial distribution along a well using thermal conductivity measurements performed with the optical scanning instrument directly applied to cores. Conditions and constraints for using Lichtenecker-Asaad's theoretical model for the estimation of porosity and thermal conductivity of sedimentary rocks were determined. A correlation between thermal conductivity and acoustic velocity, porosity, density, and electric resistivity of impact rocks was found for different rock types. New relationships between permeability, electrical and thermal conductivity found for sedimentary rocks are described.