الفهرس 
A REVIEW OF THE LOW FREQUENCY ELECTRICAL SPECTROSCOPY OF ROCKSOnly 14 pages are availabe for public view
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Abstract
The last twenty years witness intensive amount of studies aiming to discover the relationships between hydraulic and electrical properties of porous media. Besides, more sophisticated models by incorporating charge storage (complex resistivity) with petrophysical characteristics of porous matrix were produced, result in even more appropriate relationships between the electrical spectra and some hydrogeological parameters. This is may be due to the influence of the complex resistivity by the characteristics of the pore/ grain interface. Still, there are no universal models explaining such relationships. Moreover, the majority of the previous work was focusing on a specific sandstone aquifer, or on a specific soils or soil mixtures, where published works that cover SIP response on a range of sandstones are scarce, and almost all the proposed correlations are the resultant of studying very similar samples, with even different of saturating fluids with different chemical composition and electrical conductivity. Besides, previous studies applied different models to analyze the observed spectra response causing non-comparable different calculations of the parameters characterizing observed electrical spectra.
Moreover, as illustrated earlier in this thesis, there is no agreement on the origin of the observed polarization phenomenon of porous materials and the accompanied dominant physical and chemical processes are not clearly understood. Generally, the low frequency conductivity response of porous material is believed to be a result of combination of two processes. The first process attributed to the polarization of mineral/water interface at the electrical double or triple layer when the grains are submitted to an alternating electric field. This process is called electrochemical polarization (EC polarization) of the medium where a relaxation of charge is occurring, peaking at a mean relaxation time. The second process corresponds to the Maxwell-Wagner polarization associated with the accumulation of the electric charges in the pore space of the composite medium.
All of these theories clarify the importance of the current study aiming to extract much greater information about the intrinsic structure of the porous rock from the low frequency electrical spectrometry. In other words, the electrical spectroscopy measurements, and its rapidly developing theory, make the SIP of a potential value for the characterization of porous media, especially sandstones. This study aims to approach a better understanding of the polarisation processes occurring in sandstone, and establish the potential value of SIP for characterising the physical and hydraulic properties of unsaturated sandstones. In order to avoid all of these limitations of the previously mentioned results and their accompanied suggested hypotheses in this current study, the laboratory electrical spectra response of samples from ten different types of sandstone; Berea, Coconino, Tennessee, Arizona Chocolate, Elb, Gravenhoster, Obernkirchner, Pennsylvania Blue, Taref and Sabya have been examined against several measured physical and petrophysical parameters of sandstones included in order to assess the universality of any correlations between the spectral IP response and hydrological characteristics that are important in any hydrogeological and environmental investigations. Besides, in order to be able to evaluate the potential generality of the previously proposed relationships between the electrical spectra response and the petrophysical properties under study, this study applies the same empirical models for all sandstone samples to determine the parameters describing their electrical dispersion behaviour. Moreover, although there is a growing interest in the application of the induced polarization (IP) method in environmental investigations, especially in vadose zone, the published studies considering the dependence of IP parameters on saturation are sparse, and models for IP mechanisms in Earth material primarily focus on water-saturated materials. Therefore, knowing the dependence of SIP parameters on saturation is obviously necessary in order to reliably interpret SIP response in terms of lithologic parameters such as grain size, specific surface area, and hydraulic conductivity when the survey is wholly or partly conducted in the vadose zone.
Eight different types of sandstone; Berea, Coconino, Tennessee, Arizona Chocolate, Elb, Graven Hoster, Obernkirchner and Pennsylvania Blue were used in this study (for details, see table 5.1, in the chapter 5). In order to be able to define the relationship(s), if any, between SIP response and the physical and chemical characteristics of sandstones, a range of other non-electrical characteristics is necessary in order to make comparisons or correlations with the electrical spectra response of the sandstones and their internal structure. For this purpose, the following measurements were carried out for certain sandstone samples involved in this project:
A clear specific characterization of the studies sandstones is necessary in order to make comparisons or correlations with the electrical spectra response of the sandstones and their internal structure. For this purpose, several petrophysical measurements were carried out for certain sandstone samples involved in this study. On the other hand, an intensive laboratory programme measurements was applied to measure the SIP response of the different types of sandstone involved in the current study. The SIP-Fuchs system used to measure the electrical spectrometry of the fully and partially saturated sandstone samples in the form of the resistivity magnitude and phase spectra over the range of mHz to kHz. Measurements have been made using the arrangement outlined by Binley et al. (2005) performed in the same laboratory at Lancaster University. Several checks have been performed in order to make sure that the sample preparation procedures have not influence the sample structure, and detailed procedures and cautions have been applied to obtain accurate SIP measurements in the laboratory.
The results of SIP measurements of the sandstone samples under this study show capacitive phase angle errors ranging from 0.2 to 0.5 mrad, and resistance errors of around 1 to 3 % within the frequency range 0.01 Hz to 100 Hz. These errors are than 5% of the expected phase angles in sandstones samples of the type considered here. On the other hand, capacitive coupling becomes more significant above 100 Hz, with errors around 3 mrad or more, and these high frequency parts of the measurements were mainly excluded during modelling the spectra.
The resultant spectra results displayed here have been expressed in both Polar and Cartesian form. In the Polar form, the complex conductivity is expressed in terms of a magnitude (|σ|) and a phase (φ). On the other hand, in the Cartesian form, the complex conductivity is expressed by the in-phase or real (σ’) and the quadrature or imaginary (σ’’) components.
All over the study, samples with clearly flat, constant phase spectra were not observed at all. In contrast, the phase spectra of the all samples implied in this study display truly relaxation type phenomena. In fact, this study shows that, it is common for sandstones to exhibit clear electrical relaxation response over the measured frequency range used in this current study (mHz to kHz), so, it is very obvious from the shape of the resultant spectra of studied sandstones that, the Constant Phase Angle (CPA) model (constant quadrature conductivity) is totally not suitable for modelling these spectra with clear quadrature conductivity peaks.
In general, the SIP response of a polarized porous material is characterized by a decrease in resistivity magnitude as the frequency increased throughout the spectrum. On the other hand, a peak is shown in the phase spectra at the lower end of the spectrum and a rise in phase at higher frequencies which is attributed to coupling effects. similarly in the Cartesian form, a positive peak in the quadrature conductivity spectra is noticed, which is also associated with a decrease in the in-phase conductivity over the measure frequency range, where the frequency at which the maximum rate of decrease of the in-phase conductivity occurs is at the same frequency as the quadrature conductivity peak.
Although the main origin of the relaxation phenomena is not completely understood, and even some of these models are empirical and lack to theoretical physical justification, they still more practicable via their ability to relate descriptive petrophysical parameters of rocks to measurable spectral quantities. The Cole-Cole family models, which considered the most popular model for electrical relaxations in rocks, provide a symmetrical distribution of the relaxation around a central relaxation time.
The frequency dependence of saturated sandstones SIP response could be explained if we regard the saturated geological materials as a mixture of grains and fluids, each with different electrical conductivity. As the phenomenon of induced polarization firstly recognized as a delayed voltage response in earth materials or earth materials have the ability to store a charge similar to a common capacitor, it is always believed that the low frequency spectra response is strongly related to integrated ions diffusive polarization mechanisms.
If a saturated porous material is applied to DC voltage, the resultant current will flow via the diffusion or migration of ions across the bulk fluid saturation, grain/fluid interface and interconnected pores distribution. After the removal of the applied electric field, ions will migrate back to their equilibrium distribution. As each ion has different diffusion velocity depending upon their effective mobility and the different distances over which the ion are polarized, there will be different associated time period required for each individual ion to be fully charged.
By applying an AC voltage across saturated porous media, it is expected that the required time period associated with every ion to be fully charged will be frequency dependent. When a high frequency (short period time) AC voltage is applied across a porous media, there will not be enough time for ions to travel over their length scale. Therefore, these ions will store only small proportion of their potential charge. As the frequency of the applied AC voltage is reduced (time period is increased), greater length will be travelled by ion, a proportion of the ions will travel the full distance of their length scale, and a greater proportion of their potential charge will be stored, meaning that the stored charge increases as frequency decreases. This charge is a resistance to current flow, so reduction in the real conductivity and an increase in imaginary conductivity of the sample are expected with reducing frequency. This can be conceptualized as a capacitor in which the current flow into the capacity reduces with increasing charge. As the frequency is reduced further, more ions will become fully charged. At a specific frequency, the time period of the applied AC voltage will be long enough for every ion to be fully charged (the capacitor is fully charged), where the phase spectra peak is observed. At very low frequency (long period time), ions with shorter charge length will begin to charge and discharge where the phase spectra start to decrease again.
Generally, the real part of the conductivity (σ’) depends mainly on the saturating fluid conductivity and porosity of a porous medium, where the characteristics of the electrical double layer at the matrix-fluid interface has the major influence on the imaginary part (σ’’), which explains why the quadrature conductivity is considered a more meaningful measure of the polarization magnitude than the phase angle.
Assuming that the diffusion of the electrical polarization occurs in porous earth materials is mainly controlled by pore-size distribution, then larger pores will cause slower relaxation than smaller pores. As a result, smaller pores will polarize at higher frequencies and larger pores will polarize at increasingly lower frequencies. Moreover, the critical frequency, fc, where a downward inflection in the quadrature conductivity is noticed, can be contributed to the largest length scale (pore-size). For fairly porous sandstone types (Berea, Coconino, Elb and Obernkirchner), a clear peak is noticed on both the phase and quadrature spectra that can be attributed to the existence of an effective length scale dominating the electrical polarization diffusion process. On the other hand, the more broadly and flat spectra correspond to less permeable and porous sandstones (Tennessee, Arizona Chocolate and Pennsylvania Blue) can be a result of a more broad distribution of pore-sizes, resulting in a more broad distribution of length scales. This is may be due to the existence of fine-grain materials inter-laying between the coarse-grains, which led to a wider mixture of pore-sizes.
These structures can be related to increase in surface roughness. Moreover, in the absence of clear difference between the geometric parameters of active (narrow) and passive (wide) zones, the measured polarization effect become minimal, and the phase peak can be disappeared as in the case of Graven Hoster sandstone. Moreover, the SIP response of each of the all different sandstone types implied in this study (each with different chemical and petrophysical characteristics) display truly distinguish spectra from each other. This is very promising to our target of linking the Spectral Induced Polarization (SIP) response of a formation to it is intrinsic internal characteristics.
In this study, the Solver tool in Microsoft® Excel had been used to optimize the fit the electrical spectra for each sample with the 6 parameters generalized Cole-Cole model. With the generalized Cole-Cole model, an extra parameter had been added in order to allow for the asymmetric spread of the relaxation spectra. However, due to the observed encountered asymmetry of the measured spectra with changing water saturation, fitting of the Cole-Cole model to the current spectra makes the fitted parameters highly uncertain and errors in the overall fit considerably higher than the experimental measurement errors, especially in moderate and low saturation levels.
Moreover, for the formulation of an electrical dispersion model in terms of a distribution of relaxation times and associated chargeabilities, the Keery et al., (2012) approach has been applied for the estimation of distributed Debye relaxations in Spectral Induced Polarization measurements. A spectral model based on a distribution of polarizations was formulated in order to cast the model in a stochastic manner and solve it using a Markov-chain Monte Carlo (McMC) sampler, thus allowing the computation of model-parameter uncertainties. The model applied to synthetic data and demonstrates that the stochastic method can provide posterior distributions of model parameters with narrow bounds around the true values when little or no noise is added to the synthetic data, with posterior distributions that broaden with increasing noise. Besides, the model applied to experimental measurements of six sandstone samples from this study, and compare physical properties of a number of samples of porous media with stochastic estimates of characteristic relaxation times. Our results suggest the utility of this method on electrical spectra with different response characteristics and show that a single metric of relaxation time for the SIP response is not always sufficient to provide clear insight into the physical characteristics of a sample. Multiple salinity measurements were carried out on samples from different eight sandstone types implied in this study. Samples were saturated with three different strength NaCl solutions; 0.002M, 0.005M, and 0.01M, in order to find the effect of salinity variation upon the phase spectra produced over fresh-water range. A decrease in resistivity magnitude and a reduction in the phase peak are noticed as the salinity increase. The position of the phase peak is shifted on the frequency scale with an increase in frequency apparent for a decrease in salinity, while increasing the salinity increases the magnitude of the quadrature conductivity. However, sandstones with lower porosity, such as Tennessee sandstone (porosity ≈ 4%); do not exhibit clear change in response with changing the salinity of the saturation fluid over this range of salinity. However, the effect of changing the saturated fluid conductivity over the specified chemistry range seems of minor importance, and even smaller for low permeability sandstones. This is very promising to our target of linking the (SIP) response of a formation to it is intrinsic internal characteristics.
The laboratory electrical spectra response is examined against several measured physical and petrophysical parameters of sandstones included in this study in order to assess the generality of observed or proposed relationships between the spectral IP response and hydrological characteristics that are important in any hydrogeological and environmental investigations. In fact, several attempts or approaches have been suggested in the last decades to link some intrinsic properties of porous rock samples such as specific surface, cation exchange capacity (CEC) to parameters extracted or determined from the shape of the electrical spectra. However, despite the intensive work performed in the last three decades that reveal the possibility or potentiality to use the spectral induced polarization (SIP) for the estimation of key hydrogeologic parameters, the universality and nonuniqueness of these relationships have not been explored (Kruschwitz et al., 2010). Here, this study aims to assess the generalization of the previously proposed relationships between the shape of the electrical spectra and different petrophysical and hydrological characteristics over different types of sandstone with different physical intrinsic properties.
The initial examination of the proposed relationships exhibits no strong correlation between the electrical spectra response parameters extracted from different applied analytical models, and the petrophysical properties of all studied sandstone types, which show wide range of petroohysical characteristics. That’s why; the different sandstone types used in this study have been classified into two categories. The first category will represent the permeable sandstones, where the other category will include the less permeable sandstones.
The previously mentioned petrophysical characteristics were tested also against the other SIP parameters including τpeak ,τGCC, τmean ,the exponent of the GCC model and the Debye Distribution parameters. No clear relationships were found. In fact, the only two parameters that found to have a direct relationship with the internal physical characteristics of sandstones were the quadrature conductivity σ’’ and the chargeability\total chargeability of the recorded SIP response.
A relationship between the quadrature electrical conductivity σ’’ and the surface area per unit volume Spor can be considered intuitive, where the polarisable surface area increases, an increase in the overall polarization is also expected, and even had been documented before. However, no significant relationship between the quadrature electrical conductivity σ’’ at 1.4 Hz and the surface area per unit volume Spor was found. This is may be because the spectra response of the sandstone samples used in these previous studies were analysed by a constant phase angle model, and do not account for the frequency dependence of σ’’, where all samples used in this study show clear different dispersion behaviour in their spectra. However, excluding samples of the second category, which are characterized by relatively high surface area, a fair similar trend will be observed (r2=0.68). On the other hand, as illustrated before, a more robust measure of polarization is required than a single frequency measurement to account for the dispersion in the electrical spectra, and hence, a strong positive relationship (r2=0.97) between the Spor and the total chargeability extracted from the Debye Distribution technique was found. This means that as the specific surface area increases the total chargeability is expected to increase. On the other hand, a strong positive relationship (r2=0.9) between the Spor and the chargeability calculated from the Generalized Cole-Cole GCC model have been found.
Spor has been used to represent the inverse hydraulic radius measurement required to predict K from popular Kozeny– Carman type equations which suggest the potentiality that the total chargeability, mt, would appear to provide a measure of some effective grain (or pore) length scale. These findings provide further evidence of this relationship, and give it a significant level of universality, which raises the possibility to predict K from the spectral IP measurements.
Although a relationship between some intrinsic length scale (e.g. pore throat size) and the time constant of a relaxation model seems intuitive, as the electrical polarization in porous material such as sandstones is thought to be a result of a diffusive relaxation process, to date, there is no evidence of any universality in such a relationship. In fact, the few studied that have explored this relationship reveals contradictory results.
Excluding samples of the second category, a weak positive relationship (r2=0.48) between the dominant pore throat size, D0 and the generalized C-C model time constant can be observed. On the other hand, a more significant negative relationship (r2=0.8) was found between the dominant pore-throat size and the quadrature conductivity, meaning that as the pore throat size D0 reduces, the length scale of the diffusion process expects to increase. Moreover, excluding the Graven Hoster samples will lead to even a more significant relationship. Indeed, the pore-throat distribution sizes curve of this sandstone is characterized by a clear wide and flat behaviour, which is also observed in its SIP spectrum (no clear peak) suggesting a wide distribution band of individual electrical relaxation lengths integrated together to introduce this gentle flat spectra without single effective length scale. Again, excluding the Graven Hoster samples will result in a significant relationship between the product of porosity and electrical formation factor as a reflect of the magnitude of tortuosity, and both the quadrature conductivity and total chargeability.
We previously tried to link the SIP response of sandstones to several intrinsic internal characteristics which can be related to permeability or hydraulic conductivity. Here, we test the SIP response of the different sandstone types included in this study against permeability. A strong negative relationship (r2=0.9) between the quadrature conductivity σ’’ and log-permeability, proving that both electrical current and groundwater flow are channelled through the interconnected pore space and the parameters describing this transport are function of parameters describing some measure of interconnected pore volumes, and/or interconnected pore surfaces.
Although the dependence of SIP measured parameters on water saturation is documented in the literature, there is no universal behavior of such impact. Moreover, even contrary relationships have been observed. According to the findings of this study, SIP relaxation curve is strongly controlled by the distribution of pore throat sizes in saturated samples, so a reduction in the relaxation curve is expected as saturation decreases. On contrary, a shift towards higher frequency and phase angle as well as quadrature conductivity for all samples with deceasing saturation to a specific point acts as reflection point, then both phase angle and quadrature conductivity start to decrease again. Moreover, the non-linear behavior of both phase angle as well as quadrature conductivity with saturation is clearly observed. Moreover, the previously observed water saturation reflection point in Figures (7.9:7.1) is even more obvious here (≈70%). Another reflection point could be observer (≥ 40%).
This observed behavior could be explained as for fully saturated samples, a clear peak is noticed on both the phase and quadrature spectra that can be attributed to the existence of an effective length scale dominating the electrical polarization diffusion process. On the other hand, in the case of reducing saturation, the smaller pore throats become more and more the main dominant path controlling the relaxation process as relatively larger pores dewater faster, causing a shift in the SIP curve. That’s why; a significant increase in polarization-relaxation behavior is noticed due to bulk resistivity increase as saturation decrease. Moreover, expected further variation in the relaxation spectrum at very low saturation level will be vanished due to the major reduction in the role of large pores throats (and its effective length scale) due to dewater mechanism.
On the other hand, the current study clarifies the strong dependence of SIP parameters on water saturation. Moreover, our results shows that, even small reduction in water saturation away from the fully saturated statues causes result in huge difference in SIP spectra, and it’s parameters. These results raise the importance and future potentiality of applying SIP measurements in studying, monitoring and modeling the vadose zone. Current study have confirmed the potential value of SIP method for groundwater modeling as well as groundwater contamination studies due to pore throat sizes and distribution influence on relaxation behavior.
Considerable interest has recently been shown in the development of detailed physical descriptions of polarization mechanisms at the microscopic scales at which electrical charges are stored and released within porous media, with attempts to provide mathematical relationships between electrical and hydraulic properties. Studies linking the overall SIP response to a distribution of relaxations have suggested possible direct links to a distribution of physical properties such as pore size, or surface roughness, and this approach has recently been applied in an investigation of the effects of different cations on the SIP response in laboratory measurements of saturated sands. Leroy et al. Moreover, ambitious attempts to suggest that the overall SIP response could be modelled as a convolution of the particle size distribution, and the relaxation characteristics of each single grain size.
Finally, due to its sensitivity to several intrinsic characteristics of sandstones (e.g. surface area, grain/pore size distribution, saturating fluid chemistry; and clay content), spectral induced polarization SIP has a potentiality in addition to limitation during applying to evaluate or study physical properties of sandstone. The large numbers of physical and chemical parameters that have direct or indirect influence on the spectra response of sandstone make it very difficult to generalize many of the observed relationships between the electrical spectra response of the sandstone and the studies physical parameters.
In contrast, it is sensitivity to the same intrinsic parameters present a potential value of applying the spectral induced polarization SIP for a lot of hydrogeological studies. Moreover, greater advances would be reached by using this method to map or monitor any facies changes, solute transport or even assess the spatial variability inside one formation through surface or well-logging surveys.
Further intensive work need to be done on different sandstone types towards the optimum aim of categorizing the sandstone types depending on their physical and chemical characteristics such as clay ratio, saturating fluid conductivity, matrix and chemical composition; and pore throat size distribution, where an increase in the significance of the studied physical/petrophysical relationships could be observed.
Moreover, upscaling such proposed electrical- petrophysical correlations from laboratory into field-scale is always the optimum goal towards non-invasive estimation of aquifer geometries. Besides, multi-disciplinary geophysical approach as well as joint inversion algorisms and Time-lapse monitoring are of preferred value for subsurface characterization, in the field of hydrogeophysics and the rising biogeophysics fields.