Electrical Properties Of Rocks Research Articles

New insights into how temperature affects the electrical conductivity of clay-free porous rocks

Summary Geothermal energy is increasingly important for the global environment and for the sustainable development of our society. Electrical surveys are widely employed for the exploration of geothermal energy, because the electrical geophysical properties provide useful information about the fluids at depth. However, although quantitative interpretation of electrical survey data relies on the knowledge about the effects of temperature on the electrical properties of fluid-bearing rocks, it remains poorly understood about how temperature affects the electrical conductivity of clay-free porous rocks. We bridge this knowledge gap by measuring the electrical conductivity and porosity of five brine saturated clean Berea sandstones with temperature ranging between 25° C and 140° C, and analysing all the factors that impact the rock conductivity. We showed that the effects of surface conductivity on the temperature dependent electrical conductivity can be negligible, whereas the temperature induced variation in the porosity and pore structure quantitatively characterized in terms of cementation exponent can be more significant. We also found that temperature affects the electrical conductivity of brine saturated Berea sandstones by impacting the brine conductivity, and the pore structure and porosity of the samples, with their importance in a descending order. The results have provided new insights into how temperature affects the electrical conductivity of clay-free porous rocks, and will help to improve the quantitative interpretation of electrical survey data for the exploration of geothermal energy.

Effect of microvariability on electrical rock properties

SUMMARY In petrophysics, physical rock properties are typically established through laboratory measurements of individual samples. These measurements predominantly relate to the specific sample and can be challenging to associate with the rock as a whole since the physical attributes are heavily reliant on the microstructure, which can vary significantly in different areas. Thus, the obtained values have limited applicability to the entirety of the original rock mass. To examine the dependence of petrophysical measurements based on the variable microstructure, we generate sets of random 2-D microstructure representations for a sample, taking into account macroscopic parameters such as porosity and mean grain size. For each microstructure produced, we assess the electrical conductivity and evaluate how it is dependent on the microstructure’s variability. The developed workflow including microstructure modelling, finite-element simulation of electrical conductivity as well as statistical and petrophysical evaluation of the results is presented. We show that the methodology can adequately mimic the physical behaviour of real rocks, showing consistent emulation of the dependence of electrical conductivity on connected porosity according to Archie’s law across different types of pore space (microfracture, intergranular and vuggy, oomoldic pore space). Furthermore, properties such as the internal surface area and its fractal dimension as well as the electrical tortuosity are accessible for the random microstructures and show reasonable behaviour. Finally, the possibilities, challenges and meshing strategies for extending the methodology to 3-D microstructures are discussed.

Slopes of the pressure-dependent elastic–electrical correlations in artificial sandstones

SUMMARY Seismic and electromagnetic explorations are two of the most successful geophysical applications for understanding the subsurface earth, and the joint interpretation of seismic and electromagnetic survey data can help to better characterize the rocks because they contain independent and complementary information about the rocks. However, the success of the joint interpretation depends on the understanding of the correlations between the elastic and electrical rock properties and their influencing factors. Confining pressure is an important geological parameter that has been found to give rise to linear elastic–electrical correlations in sandstones. However, it is still poorly known what controls the slopes of the pressure-dependent linear correlations, even though slope is one of the most important parameters determining the linear correlation. We make artificial sandstones with controlled porosity and permeability, respectively, and measure their pressure-dependent elastic (electrical resistivity) and electrical (P-wave velocity) properties simultaneously, as well as porosity. We show that the slopes of the measured electrical resistivity versus P-wave velocity as an implicit function of confining pressure correlate positively with the compliant porosity in all the samples. The results not only reveal the petrophysical parameter that controls the slopes of the pressure-dependent linear elastic–electrical correlations in sandstones, but also provide a basis for the discrimination of the slope-controlling parameter from the simultaneously measured elastic and electrical properties.

Design of Three-Dimensional Electrical Impedance Tomography System for Rock Samples

Research on the electrical properties of rocks and ores plays a crucial role in the development of geophysical electromagnetism methods. However, currently available instruments suffer from high power consumption, a limited number of electrodes, inaccurate measurements, poor portability, and a limited ability to measure the electrical parameters of rocks and ores. To address these issues, this paper presents a three-dimensional electrical impedance tomography system for rock samples with high-density microelectrodes based on an Android system and STM32 microcontroller. The system features high observation accuracy, dense electrode arrays (with 384 current and potential electrodes), flexible electrode selection, user-friendly human–computer interaction, good stability, and real-time performance. Powered by a single power bank, the entire instrument can be controlled and monitored wirelessly via Bluetooth and Wi-Fi technology using an Android smartphone. Additionally, the system not only enables accurate measurement of electrical parameters, but also facilitates the generation of three-dimensional impedance imaging of specimens via inversion algorithms after data export, allowing for a comprehensive understanding of the electrical properties of rocks and ores. This system holds great potential for future research in this field.

An Improved Rock Resistivity Model Based on Multi-Fractal Characterization Method for Sandstone Micro-Pore Structure Using Capillary Pressure

Micro-pore structures are an essential factor for the electrical properties of porous rock. Theoretical electrical conductivity models considering pore structure can highly improve the accuracy of reservoir estimation. In this study, a pore structure characterization method based on a multi-fractal theory using capillary pressure is developed. Next, a theoretical electrical conductivity equation is derived based on the new pore structure characterization method. Furthermore, a distinct interrelationship between fractal dimensions of capillary pressure curves (Dv) and of resistivity index curves (Dt and Dr) is obtained. The experimental data of 7 sandstone samples verify that the fitting result by the new pore structure characterization method is highly identical to the experimental capillary pressure curves, and the accuracy of the improved rock resistivity model is higher than the Archie model. In addition, capillary pressure curves can be directly converted to resistivity index curves according to the relationship model between fractal dimensions of capillary pressure curves (Dv) and resistivity index curves (Dt and Dr). This study provides new ideas to improve the accuracy of pore structure characterization and oil saturation calculation; it has good application prospects and guiding significance in reservoir evaluation and rock physical characteristics research.

Extracting crucial microstructures to characterize the elastic wave velocity and resistivity of Berea sandstone using convolutional neural networks

To reveal the internal structure of the earth, rock physical models are insightful for interpreting geophysical observation data and are often used for estimating subsurface structures. However, as the estimated value of each model significantly depends on the assumed microstructure, the obtained subsurface structure may be biased. Despite the innovations of high-resolution imaging technologies and their application to digital rock physics (DRP) and machine learning (ML), the characteristic microstructure controlling rock physical properties remains unclear. We apply ML and extraction of regression activation mapping (RAM) and learned filters to visualize the characteristic microstructure underlying the elastic and electrical properties of rock (P-wave velocity [Formula: see text], S-wave velocity [Formula: see text], [Formula: see text]/[Formula: see text] ratio, and electrical resistivity). This regression task is implemented using convolutional neural networks (CNNs) that are trained on these properties and calculated with the DRP approach using Berea sandstone images as samples. Although the calculated geophysical properties show perturbations even among digital rocks that have the same porosity, the results predicted using the best-performing CNN model exhibit a relative error of 2%–7% with respect to elastic properties. The visualized RAM revealed that the machine focuses on larger grains for predicting P-wave and S-wave velocities, whereas their ratio ([Formula: see text]/[Formula: see text]) takes into account the pore space. In contrast, electrical properties consider grain edges and surrounding pores, which may be related to the tortuosity of the pore space. Moreover, filter visualizations demonstrated that the geometric characteristics of Berea sandstone could be representative of circular or elliptical shapes for determining elastic properties, whereas tube-like shapes were extracted for electrical resistivity. These findings shed new light on the crucial internal structures used for defining each rock property.

High-resolution geoelectrical characterization and monitoring of natural fluids emission systems to understand possible gas leakages from geological carbon storage reservoirs

Gas leakage from deep geologic storage formations to the Earth’s surface is one of the main hazards in geological carbon sequestration and storage. Permeable sediment covers together with natural pathways, such as faults and/or fracture systems, are the main factors controlling surface leakages. Therefore, the characterization of natural systems, where large amounts of natural gases are released, can be helpful for understanding the effects of potential gas leaks from carbon dioxide storage systems. In this framework, we propose a combined use of high-resolution geoelectrical investigations (i.e. resistivity tomography and self-potential surveys) for reconstructing shallow buried fracture networks in the caprock and detecting preferential gas migration pathways before it enters the atmosphere. Such methodologies appear to be among the most suitable for the research purposes because of the strong dependence of the electrical properties of water-bearing permeable rock, or unconsolidated materials, on many factors relevant to CO2 storage (i.e. porosity, fracturing, water saturation, etc.). The effectiveness of the suggested geoelectrical approach is tested in an area of natural gas degassing (mainly CH4) located in the active fault zone of the Bolle della Malvizza (Southern Apennines, Italy), which could represent a natural analogue of gas storage sites due to the significant thicknesses (hundreds of meters) of impermeable rock (caprock) that is generally required to prevent carbon dioxide stored at depth from rising to the surface. The obtained 3D geophysical model, validated by the good correlation with geochemical data acquired in the study area and the available geological information, provided a structural and physical characterization of the investigated subsurface volume. Moreover, the time variations of the observed geophysical parameters allowed the identification of possible migration pathways of fluids to the surface.

Improved geoelectrical resistivity monitoring for earthquake precursors near the Xinfengjiang reservoir of southern China, with a fixed Wenner array of downhole electrodes in four separated boreholes

Over the past five decades, a geoelectrical resistivity monitoring experiment using fixed electrode arrays has been conducted at Heyuan in the Guangdong Province of China for detecting possible earthquake precursors near the Xinfengjiang reservoir. A pair of surface quasi-Wenner arrays designed to monitor temporal resistivity variations have been used in two oblique directions of N27°E and N80°W with electrode spacings AB/MN of 997 m/315 m and 1032 m/328 m, respectively. To reduce the effects of near-surface environmental changes, an improved experiment has been introduced in August 1992, using a subsurface Wenner array in the direction of N80°W with electrode spacings AB/MN of 54 m/18 m, consisting of downhole electrodes in four horizontally separated boreholes at the same depth of 65 m. During the experimental period of August 1992 to December 1996, a continuously downward trend in apparent resistivity with the improved downhole array and a peculiar annual variation with the conventional surface arrays have been observed. For the same period, no notable earthquakes occur in and around the Xinfengjiang reservoir. The field tests indicate that the downward trend of apparent resistivity was due to the aging of one of the current electrodes. By using simple layered models, we develop a sensitivity analysis to design a monitoring array with minimum environmental effects and to explain the observed resistivity variations, such as a paradoxical resistivity behavior related with negative sensitivity. No significant resistivity variations, which could be attributed to earthquake activity of magnitude 3.4 or less in the study area, are detected. We prove that the two monitoring methods with the modified subsurface Wenner and the conventional surface quasi-Wenner arrangements can complement each other to efficiently estimate a change in the electrical properties of rocks and reduce the ambiguity in the interpretation of apparent resistivity data.

Pore pressure effects on the anisotropic joint elastic-electrical properties of artificial porous sandstones with aligned fractures

Fractures widely exist in rocks and joint interpretation of elastic and electrical survey data can improve the characterization of fractured rocks. However, the cross-property relationship between the elastic and electrical rock properties, which is the key to the successful joint elastic-electrical interpretation, remains poorly understood in fractured rocks with varying pore pressure. This knowledge gap was by developing a method for making calcite-cemented sandstones with penny-shaped fractures and by simultaneously measuring the anisotropic elastic and electrical properties of the artificial sandstones with and without fractures as a function of pore pressure through the development of an anisotropic joint elastic-electrical measurement system. We find that elastic velocities and electrical resistivities of the intact and fractured samples reduce with increasing pore pressure, and the reduction in the physical properties of the fractured rock is less significant than that of the intact sample. We also find that elastic and electrical anisotropic parameters decrease in the sample without fractures but decrease first and then increase with increasing pore pressure in the sample with fractures. Most interestingly, the anisotropic elastic and electrical properties are found to exhibit a strong linear correlation in the intact and fractured samples with varying pore pressure and a difference exists in the slopes between the samples with and without fractures. The experimental data are explained and interpreted through the contrary contributions of the dilation of the random microcracks and the aligned fractures with increasing pore pressure to the anisotropic elastic and electrical properties. The results reveal the pore pressure effects on the anisotropic joint elastic-electrical properties of sandstones with fractures and provide a potential for the detection of overpressure in fractured rocks through integrated elastic and electrical surveys.

Spectral characteristics analysis of rocks and ores based on the generalized effective medium theory of induced polarization

To study the electrical characteristics of rocks and ores, two- and three-phase medium models with different mineral contents, attenuation coefficients, relaxation times, and ellipticities were established based on the generalized effective medium theory of induced polarization (GEMTIP) model and the Debye decomposition method. Furthermore, the corresponding program was written for numerical simulation, and the complex resistivity (CR) spectral characteristics and relaxation time distribution (RTD) characteristics were analyzed. At the same time, seven representative ore samples from different mining areas were selected, their structural compositions were observed, and their complex resistivity was measured to obtain the variation characteristics and Nyquist curves of ore phase spectra. The differential evolution (DE) algorithm was employed to write a curve parameter fitting program based on which parameter fitting was performed for the theoretical model and the measured curves of ore samples. The physical and electrical parameters of the curves were obtained, and the variation characteristics of each parameter were analyzed. The generalized effective medium theory of induced polarization model could be adopted to further study the induced polarization (IP) anomaly from the structural and electrical properties of rocks and ores, which has important guiding significance for energy resource exploration, deep prospecting beyond 500 m, and environmental investigation by electrical (magnetic) methods.

Simulation of Rock Electrical Properties in Deep Reservoirs Based on Digital Rock Technology

Deep reservoirs are in a high-pressure and high-temperature (HPHT) environment, while the experimental conditions for rock electrical properties that meet the deep reservoir conditions are harsh and costly. Although digital rock technology can simulate the electrical properties of rocks, it is limited to electrical simulation studies under normal temperature and pressure conditions (NPT), which limits their ability to capture the electrical characteristics of deep hydrocarbon reservoirs. This limitation affects the accuracy of saturation prediction based on resistivity logging. To simulate the rock electrical properties under HPHT conditions, we proposed a low-cost and high-efficiency HPHT digital rock electrical simulation workflow. Firstly, samples from deep formations were CT-scanned and used to construct multi-component digital rocks that reflect the real microstructure of the samples. Then, mathematical morphology was used to simulate the overburden correction under high-pressure conditions, and the changes in the conductivity of formation water and clay minerals at different temperatures were used to simulate the conductivity changes of rock components under high-temperature conditions. To carry out the electrical simulation of digital rock in deep reservoirs, a numerical simulation condition for HPHT in deep layers was established, and the finite element method (FEM) was used. Finally, based on the equivalent changes in the conductivity of different components, the effects of clay minerals and formation water under HPHT conditions on rock electrical properties were studied and applied to predict the water saturation based on well logging data. We found that considering the influence of temperature, salinity, and clay type, the saturation index (n) of the rock depends on the ratio of the clay conductivity to the formation water conductivity. The larger the ratio is, the smaller the value of n. In addition, the average relative error between the predicted water saturation under HPHT conditions and the sealed coring analysis was 6.8%, which proved the accuracy of the proposed method. Overall, this method can effectively simulate the pressure and temperature environment of deep formations, reveal the electrical conductivity mechanisms of rocks under formation pressure and temperature conditions, and has promising prospects for the study of rock physical properties and reservoir evaluation in deep formations.

Electrical Tortuosity Index: A New Approach for Identifying Rock Typing to Enhance Reservoir Characterization Using Well-Log Data of Uncored Wells.

The world is gradually moving toward a severe energy crisis, with an ever-increasing demand for energy overstepping its supply. Therefore, the energy crisis in the world has shed important light on the need for enhanced oil recovery to provide an affordable energy supply. Inaccurate reservoir characterization may lead to the failure of enhanced oil recovery projects. Thus, the accurate establishment of reservoir characterization techniques is required to successfully plan and execute the enhanced oil recovery projects. The main objective of this research is to obtain an accurate approach that can be used to estimate rock types, flow zone indicators, permeability, tortuosity, and irreducible water saturation for uncored wells based on electrical rock properties that were obtained from only logging tools. The new technique is obtained by modifying the Resistivity Zone Index (RZI) equation that was presented by Shahat et al. by taking the tortuosity factor into consideration. When true formation resistivity (Rt) and inverse porosity (1/Φ) are correlated on a log-log scale, unit slope parallel straight lines are produced, where each line represents a distinct electrical flow unit (EFU). Each line's intercept with the y-axis at 1/Φ = 1 yields a unique parameter specified as the Electrical Tortuosity Index (ETI). The proposed approach was validated successfully by testing it on log data from 21 logged wells and comparing it to the Amaefule technique, which was applied to 1135 core samples taken from the same reservoir. Electrical Tortuosity Index (ETI) values show marked accuracy for representing reservoir compared with Flow Zone Indicator (FZI) values obtained by the Amaefule technique and Resistivity Zone Index (RZI) values obtained by the Shahat et al. technique, with correlation coefficients of determination (R2) values equal to 0.98 and 0.99, respectively. Hence, by using the new technique, the Flow Zone Indicator, permeability, tortuosity, and irreducible water saturation were estimated and then compared with the obtained results from the core analysis, which showed a great match with the R2-values of 0.98, 0.96, 0.98, and 0.99, respectively.

Crosshole radio electromagnetic tomography using apparent source intensity and logarithmic barrier

Crosshole radio-frequency (typically from 1 to 36 MHz) electromagnetic methods are powerful tools for locating conductive ores and distribution of electric properties of rocks between boreholes. In the range of these frequencies, electromagnetic field can be approximated by the wave field. Usually, crosshole radio-frequency electromagnetic inversion requires exact source intensity but it is difficult to determine that.We present a ray-based inversion method of crosshole radio electromagnetic data which does not require exact source intensity. We introduce a concept of apparent source intensity, establish the method of determining that and realize absorption coefficient and conductivity imaging of crosshole radio electromagnetic data using that. And then we improve accuracy and reliability of tomographic inversion of crosshole radio electromagnetic data using positive constraints for absorption and conductivities. Inversion is based on simultaneous iterative reconstruction technique or adaptive control gradient method.Tests of synthetic and field data show that the method we propose has high reliability.

Electrical rock typing using Gaussian mixture model to determine cementation factor

Many studies have worked on the estimation of fluid saturation as an important petrophysical property in hydrocarbon reservoirs. Based on Archie's law, proper determination of cementation factor (m) can lead to accurate values of water saturation. Given that the m is mainly affected by electrical properties of rock, electrical quality index (EQI) can be used to estimate m through a novel rock typing technique. Despite the efficient applicability of EQI for the classification of rocks, with similar electrical behaviors, into distinct electrical rock types (ERTs), manual implementation of this method is time-consuming and gets excessively more difficult for larger datasets. In this work, a fast automated version of EQI methodology was presented. As a fuzzy clustering algorithm, Gaussian mixture model (GMM) was implemented on a large quantity of carbonate and sandstone samples to cluster them into distinct ERTs based on EQI values. To this end, 100 data points were randomly selected for testing purposes, and the remaining data points were used as training subsets for carbonate and sandstone samples. An innovative hybrid EQI-GMM approach was developed to determine the optimum number of clusters. Furthermore, results of two commonly-used criteria, namely Schwarz's Bayesian Criterion (BIC) and Akaike Information Criterion (AIC), showed that they fail to specify ERTs properly. The predicted values for m by the hybrid EQI-GMM approach were more accurate (RMSE is 0.0167 and 0.0056 for carbonate and sandstone samples, respectively) than outputs of the traditional Archie’s law (RMSE is 1.6697 and 0.1850 for carbonate and sandstone samples, respectively).

Cementation factor in clayey rock samples: investigating the role of clay content and determination using electrical rock classification

Accurate determination of cementation factor (m) has a significant role in the petrophysical characterization of underground reservoirs. For clean sandstones, the application of this parameter in Archie's Equation provides a basic framework for estimating water saturation. However, the presence of clay minerals in the rock texture could affect the evaluation process. There are different correlations from which the cementation factor can be estimated. In addition, applying rock classification techniques revealed an excellent prospect for better estimating this parameter. However, in most of the mentioned approaches, the effect of clay minerals is missed. In this study, a newly developed modified form of electrical rock typing technique (i.e. classification of rock samples according to their electrical properties) incorporating the effect of clay minerals for improving the prediction of cementation factor in clay-bearing rocks is proposed. In doing so, a new form of electrical quality index is defined based on which the modified formation resistivity factor versus porosity data for 204 clayey rock samples are classified into nine distinct rock types. Comparative studies demonstrated the priority of the suggested methodology rather than classic hydraulic flow unit-based methods such as flow zone indicator and discrete rock type. The latter showed a high degree of scattering in the classification stage. For each rock type, developed based on the proposed scheme, the equations were proposed in which the modified form of formation resistivity factor and cementation factor versus porosity were correlated. Linear relationships with reasonable values of coefficient of determination were then demonstrated for the developed equations. In addition, the effect of clay minerals on the rock's electrical quality and electrical properties (i.e., rock conductivity and cementation factor) is discussed. The results of this study offer a better framework to incorporate the effect of clay constituents in the prediction of cementation factor, as compared to classical rock typing approaches.

Comparative Study on Hydraulic and Electrical Transport Properties of Carbonate Rocks Based on Rock Typing

The permeability (k) and electrical resistivity of carbonate rocks with similar porosity (ϕ) may exhibit multiple orders of magnitude differences due to the diversity of pore types and the multiscale characteristics of pore size. As a result, traditional permeability-porosity and resistivity-porosity models usually have strong limitations when applied to carbonate reservoirs, let alone evaluate permeability from electrical resistivity. In this study, a new rock typing parameter named relative transport quality index (RTQI) is proposed to categorize rock samples using permeability and formation resistivity factor (F). Samples with similar RTQI values tend to have similar relative capacities of hydraulic and electrical transport. Subsequently, the classification performance and microscopic differences between RTQI and other rock typing indices including flow zone indicator (FZI), current zone indicator (CZI), and electrical quality index (EQI) were compared and discussed based on the reported petrophysical data of 316 carbonate rock samples. The results indicate that the RTQI method significantly reduces the scattering of k and F by dividing the samples into distinct groups, and each RTQI group corresponds to a special k–F correlation with a high determination coefficient. However, the number of rock types identified by different rock typing indices is different, meaning that samples belonging to the same rock type in the k–F plot of the RTQI method may be classified into different rock types in the k–ϕ plot of the FZI method and the F–ϕ plots of the CZI and EQI methods, which may be caused by the microscopic differences of rock typing parameters. Different from the strong dependence of FZI on hydraulic tortuosity and CZI/EQI on electrical tortuosity, RTQI is mainly dominated by the ratio of electrical tortuosity to hydraulic tortuosity. Additionally, in view of the good correlation between petrophysical data after rock typing, two workflows are proposed to estimate the hydraulic and electrical parameters of carbonate rocks from log data.

Elastic and electrical properties of calcite-cemented artificial sandstones based on a new manufacturing method

Calcite cement is widely existing in sandstones and can significantly affect the elastic and electrical properties of sandstones. Accordingly, understanding the effects of calcite cement on the elastic and electrical rock properties is of key importance for the accurate characterization of sandstone reservoirs through seismic and electromagnetic surveys. To obtain such knowledge, we design and implement dedicated laboratory experiments to investigate the effects of calcite cement and porosity on the P- and S-wave velocities and electrical resistivity of synthetic calcite-cemented sandstones made using a new recipe. The experimental results show that elastic velocities and electrical resistivity generally decrease with increasing porosity when the content of the calcite cement keeps constant, whereas the elastic and electrical rock properties exhibit complex variation with cement content in sandstones with approximately the same porosity. Analyses and interpretation of the experimental data indicate that the elastic and electrical rock properties are affected jointly by porosity, the content and distribution of the calcite cement, as well as the microstructure of the pore space resulting from the different axial stress employed for the consolidation of the rock samples. The results have revealed the mechanisms of how porosity and calcite cement affect the elastic and electrical properties of calcite-cemented sandstones, and provided a theoretical basis for the accurate characterization of sandstone reservoirs through seismic and electromagnetic surveys.

ЕЛЕКТРИЧНІІ ПРУЖНІ ПАРАМЕТРИ УЩІЛЬНЕНИХ ТЕРИГЕННИХ ПОРІД КЕМБРІЮ СХІДНОГО СХИЛУ ЛЬВІВСЬКОГО ПАЛЕОЗОЙСЬКОГО ПРОГИНУ

Paper concerned the research of elastic and electric properties of consolidated terrigenous rocks of Cambrian period of the southern slope of the Lviv Palaeozoic trough. The purpose of the research was to study the petrophysical parameters of the consolidated reservoir rocks (siltstones and sandstones), as the basis of the integrated analysis of their physical properties. The research looked at electric and elastic parameters of terrigenous rock samples, resistivity and formation resistivity factor, formation resistivity enlargement factor, velocities of the P-waves and interval (transit) time in atmospheric and reservoir conditions. Correlations between resistivity and formation resistivity factor, and between porosity and formation resistivity factor of consolidated rocks were established in atmospheric and reservoir conditions. The correlation between the resistivity and formation resistivity factor manifest itself in linear function. Physical modeling of reservoir conditions allows adapting the values of electrical parameters obtained in atmospheric conditions to parameters of rocks in reservoir conditions. Laboratory acoustic study of rock samples managed to establish correlations of: velocities of the P-waves and interval (transit) time with density and porosity in atmospheric conditions; velocities of the P-waves in atmospheric and reservoir conditions; velocities with porosity in reservoir conditions. The correlations between velocities of the P-waves in atmospheric and reservoir conditions for the studied rocks manifested itself in linear function. Physical modeling of reservoir conditions allows adapting the values of elastic parameters obtained in atmospheric conditions to parameters of rocks in reservoir conditions. The correlations between the electric and elastic properties and reservoir properties of siltstones and consolidated sandstones should be at the basis of preliminary interpretation of geophysical well logging on prospective areas of the southern slope of the Lviv Palaeozoic trough.

PREDICTING THE ELECTRICAL CONDUCTIVITY OF DUAL-POROSITY MEDIA WITH FRACTAL THEORY

The microspatial structure of porous media affects the electrical properties of reservoir rocks significantly. In this work, a dual-porosity model is established to investigate the electrical properties of porous media, in which tree-like networks and capillary channels represent fractures and pores. By using fractal theory, we established an analytical equation for the conductivity of water-saturated dual-porosity media. The analytical equation, devoid of any empirical constants, expresses the electrical properties of the porous media as a function of some structural parameters ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. We also examine the impact of various matrix structural parameters on conductivity. It is found that increasing the length of mother channel ([Formula: see text], length ratio ([Formula: see text], the number of branching layers ([Formula: see text], and tortuosity fractal dimension ([Formula: see text] leads to a decrease in conductivity, whereas increasing the diameter of mother channel ([Formula: see text], diameter ratio ([Formula: see text], the cross-sectional porosity ([Formula: see text], [Formula: see text], and the channel bifurcation number ([Formula: see text] enhances conductivity. Furthermore, we validated this analytical model by comparing it with the experimental data available, and the results demonstrate good agreement. This research has proposed an advanced conductivity model that enables us to better understand the underlying physical mechanisms of the electrical properties in porous media.

All Solid-State Electrode With Low Contact Resistance and Low Polarization for Measuring the Electrical Properties of Rocks

All Solid-State Electrode With Low Contact Resistance and Low Polarization for Measuring the Electrical Properties of Rocks