Predicting the cation exchange capacity of reservoir rocks from complex dielectric permittivity measurements

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. MR1-MR14 ◽  
Author(s):  
Ali A. Garrouch
Keyword(s):  
Dielectric Permittivity ◽  
Dimensional Analysis ◽  
High Frequency ◽  
Exchange Capacity ◽  
Reservoir Rocks ◽  
Dimensionless Groups ◽  
Number Formula ◽  
Water Saturated ◽  
Permittivity Measurements ◽  
Prediction Capability

Dimensional analysis was performed to understand the physics of ionic dispersion in reservoir rocks and to identify the factors influencing the cation exchange capacity (CEC) of these rocks. Dimensional analysis revealed the existence of a general relation independent of the unit system between two dimensionless groups denoted as the cationic dispersion number [Formula: see text] and the conductivity number [Formula: see text]. The former group [Formula: see text] stands for the ratio of the CEC to the electrical double-layer dispersion. The latter group [Formula: see text] represents the ratio of the low-frequency ionic conductivity to the high-frequency electronic polarization. Complex dielectric permittivity measurements on 121 water-saturated sandstone and carbonate rock samples were used to validate the dimensionless groups. In retrospect, dimensional analysis was useful in identifying variables influencing the CEC of hydrocarbon rocks. In particular, these variables consist of rock porosity [Formula: see text], specific surface area, and five other parameters of the Cole-Cole function, which describes the frequency dependence of the complex permittivity of rock samples in the range 10–1300 MHz. The Cole-Cole function parameters are [Formula: see text], which is a characteristic relaxation time; [Formula: see text] is the so-called spread parameter; [Formula: see text] is the real DC conductivity of water-saturated rocks; and [Formula: see text] and [Formula: see text], which are the real numbers representing the static and the high-frequency dielectric permittivities of the water-saturated rock, respectively. A general regression neural network (GRNN) model was developed to predict the CEC of shaly sandstones and carbonate rocks as a function of the variables identified by the dimensional analysis as essential in predicting the CEC. The CEC prediction capability of the GRNN model has been tested with a blind data set, and it has been compared with the CEC prediction capability using a nonlinear regression model developed in this study and using a linear regression model available in the literature. The GRNN model outperformed both of these empirical models. With the GRNN model, it is possible to obtain reliable quantitative estimates of the CEC of shaly sandstone and carbonate rocks using nondestructive frequency-dependent dielectric permittivity measurements that are rapid, economic, and accurate. In return, accurate and fast estimates of the CEC are useful in many petroleum engineering applications. They can be used to identify clay types and can also be used to quantify the volume of hydrocarbon in shaly sands using well-log resistivity data. The results of this study represent a major advantage for formation evaluation, wellbore stability analysis, and designing stimulation jobs.

Numerical Modeling of Multi-Frequency Complex Dielectric Permittivity Dispersion of Clay-Rich Rocks

Geophysics ◽  
2021 ◽  
pp. 1-70
Author(s):  
Artur Posenato Garcia ◽  
Zoya Heidari
Keyword(s):  
Spatial Distribution ◽  
Dielectric Permittivity ◽  
Mineralogical Composition ◽  
Exchange Capacity ◽  
Complex Dielectric Permittivity ◽  
Frequency Range ◽  
Volumetric Concentration ◽  
New Equation ◽  
Permittivity Measurements ◽  
The Impact

Interpretation of complex dielectric permittivity measurements is challenging in clay-rich rocks, such as shaly sands and organic-rich mudrocks, due to complex rock fabric and mineralogical composition, which are overlooked by conventional interpretation models. For instance, the impact of fabric features (e.g., laminations, structural/dispersed shale) and diverse constitution (e.g., clay, kerogen, pyrite, brine) to the broadband complex permittivity is not well understood. Therefore, the main objective of this work is to develop a framework capable of reliably quantifying the impact of different minerals and their corresponding spatial distribution on the multi-frequency complex dielectric permittivity measurements in clay-rich rocks.To achieve the aforementioned objective, we introduce a numerical algorithm to compute the dielectric dispersion in 3D pore-scale images of clay-rich rocks. We numerically solve the quasi-electrostatic approximation to Maxwell's equations in the frequency domain through the finite volume method. The clay particles are often sub-resolution in most imaging methods. Therefore, we introduce a workflow to calculate the effective admittance of the clay network. Furthermore, we derive a new equation to incorporate the induced polarization effect into the effective admittance of pyrite particles. Finally, we perform a sensitivity analysis of the complex dielectric permittivity of clay-rich rocks in the frequency range from 100 Hz to 1 GHz to the volumetric concentration and spatial distribution of clays, cation exchange capacity (CEC), volumetric concentration of pyrite, and the orientation of the electric field. Results showed that clays can enhance or diminish electrical conductivity values at different frequencies depending on their intrinsic properties and spatial distribution. Laminations, for instance, significantly enhance dielectric permittivity in the sub-MHz frequency range, but their effect is imperceptible at 1 GHz. Furthermore, the impact of the variation of CEC on permittivity is approximately proportional at 100Hz but negligible at 1 GHz.

scholarly journals Sintering, Microstructure, and Dielectric Properties of Copper Borates for High Frequency LTCC Applications

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4017
Author(s):  
Dorota Szwagierczak ◽  
Beata Synkiewicz-Musialska ◽  
Jan Kulawik ◽  
Norbert Pałka
Keyword(s):  
Dielectric Properties ◽  
Dielectric Permittivity ◽  
High Frequency ◽  
Ceramic Materials ◽  
Sintering Behavior ◽  
Terahertz Time Domain Spectroscopy ◽  
Very High Frequency ◽  
X Ray ◽  
Low Dielectric ◽  
Very High

New ceramic materials based on two copper borates, CuB2O4 and Cu3B2O6, were prepared via solid state synthesis and sintering, and characterized as promising candidates for low dielectric permittivity substrates for very high frequency circuits. The sintering behavior, composition, microstructure, and dielectric properties of the ceramics were investigated using a heating microscope, X-ray diffractometry, scanning electron microscopy, energy dispersive spectroscopy, and terahertz time domain spectroscopy. The studies revealed a low dielectric permittivity of 5.1–6.7 and low dielectric loss in the frequency range 0.14–0.7 THz. The copper borate-based materials, owing to a low sintering temperature of 900–960 °C, are suitable for LTCC (low temperature cofired ceramics) applications.

scholarly journals Polytetrafluoroethylene Films in Rigid Polyurethane Foams’ Dielectric Permittivity Measurements with a One-Side Access Capacitive Sensor

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1173
Author(s):  
Ilze Beverte ◽  
Ugis Cabulis ◽  
Sergejs Gaidukovs
Keyword(s):  
Dielectric Properties ◽  
Dielectric Permittivity ◽  
Low Frequency ◽  
Capacitive Sensor ◽  
Polyurethane Foams ◽  
Active Area ◽  
Ptfe Film ◽  
Practical Applications ◽  
Permittivity Measurements ◽  
The Impact

As a non-metallic composite material, widely applied in industry, rigid polyurethane (PUR) foams require knowledge of their dielectric properties. In experimental determination of PUR foams’ dielectric properties protection of one-side capacitive sensor’s active area from adverse effects caused by the PUR foams’ test objects has to be ensured. In the given study, the impact of polytetrafluoroethylene (PTFE) films, thickness 0.20 mm and 0.04 mm, in covering or simulated coating the active area of one-side access capacitive sensor’ electrodes on the experimentally determined true dielectric permittivity spectra of rigid PUR foams is estimated. Penetration depth of the low frequency excitation field into PTFE and PUR foams is determined experimentally. Experiments are made in order to evaluate the difference between measurements on single PUR foams’ samples and on complex samples “PUR foams + PTFE film” with two calibration modes. A modification factor and a small modification criterion are defined and values of modifications are estimated in numerical calculations. Conclusions about possible practical applications of PTFE films in dielectric permittivity measurements of rigid PUR foams with one-side access capacitive sensor are made.

Numerical Modeling of Multi-Frequency Complex Dielectric Permittivity Dispersion of Sedimentary Rocks

Geophysics ◽  
2021 ◽  
pp. 1-69
Author(s):  
Artur Posenato Garcia ◽  
Zoya Heidari
Keyword(s):  
Numerical Simulation ◽  
Dielectric Permittivity ◽  
Numerical Simulations ◽  
Dielectric Response ◽  
Water Saturation ◽  
Pore Scale ◽  
Simulation Results ◽  
Wet Rocks ◽  
Permittivity Measurements ◽  
The Impact

The dielectric response of rocks results from electric double layer (EDL), Maxwell-Wagner (MW), and dipolar polarizations. The EDL polarization is a function of solid-fluid interfaces, pore water, and pore geometry. MW and dipolar polarizations are functions of charge accumulation at the interface between materials with contrasting impedances and the volumetric concentration of its constituents, respectively. However, conventional interpretation of dielectric measurements only accounts for volumetric concentrations of rock components and their permittivities, not interfacial properties such as wettability. Numerical simulations of dielectric response of rocks provides an ideal framework to quantify the impact of wettability and water saturation ( Sw) on electric polarization mechanisms. Therefore, in this paper we introduce a numerical simulation method to compute pore-scale dielectric dispersion effects in the interval from 100 Hz to 1 GHz including impacts of pore structure, Sw, and wettability on permittivity measurements. We solve the quasi-electrostatic Maxwell's equations in three-dimensional (3D) pore-scale rock images in the frequency domain using the finite volume method. Then, we verify simulation results for a spherical material by comparing with the corresponding analytical solution. Additionally, we introduce a technique to incorporate α-polarization to the simulation and we verify it by comparing pore-scale simulation results to experimental measurements on a Berea sandstone sample. Finally, we quantify the impact of Sw and wettability on broadband dielectric permittivity measurements through pore-scale numerical simulations. The numerical simulation results show that mixed-wet rocks are more sensitive than water-wet rocks to changes in Sw at sub-MHz frequencies. Furthermore, permittivity and conductivity of mixed-wet rocks have weaker and stronger dispersive behaviors, respectively, when compared to water-wet rocks. Finally, numerical simulations indicate that conductivity of mixed-wet rocks can vary by three orders of magnitude from 100 Hz to 1 GHz. Therefore, Archie’s equation calibrated at the wrong frequency could lead to water saturation errors of 73%.

scholarly journals Dimensional analysis on forest fuel bed fire spread

2018 ◽  
Vol 48 (1) ◽  
pp. 105-110
Author(s):  
Jiann C. Yang
Keyword(s):  
Dimensional Analysis ◽  
Fire Spread ◽  
Fuel Particle ◽  
Wind Condition ◽  
Spread Rate ◽  
Fuel Loading ◽  
Rate Of Spread ◽  
Dimensionless Groups ◽  
Dimensionless Correlations ◽  
Fuel Moisture Content

A dimensional analysis was performed to correlate the fuel bed fire rate of spread data previously reported in the literature. Under wind condition, six pertinent dimensionless groups were identified, namely dimensionless fire spread rate, dimensionless fuel particle size, fuel moisture content, dimensionless fuel bed depth or dimensionless fuel loading density, dimensionless wind speed, and angle of inclination of fuel bed. Under no-wind condition, five similar dimensionless groups resulted. Given the uncertainties associated with some of the parameters used to estimate the dimensionless groups, the dimensionless correlations using the resulting dimensionless groups correlate the fire rates of spread reasonably well under wind and no-wind conditions.

Shallow subsurface mapping by electromagnetic sounding in the 300 kHz to 30 MHz range: Model studies and prototype system assessment

Geophysics ◽  
1994 ◽  
Vol 59 (8) ◽  
pp. 1201-1210 ◽  
Author(s):  
Duff C. Stewart ◽  
Walter L. Anderson ◽  
Thomas P. Grover ◽  
Victor F. Labson
Keyword(s):  
Dielectric Permittivity ◽  
High Frequency ◽  
Low Frequency ◽  
Computer Programs ◽  
Thin Layers ◽  
Depth Range ◽  
Frequency Range ◽  
Model Studies ◽  
New Instrument ◽  
Displacement Currents

A new instrument designed for frequency‐domain sounding in the depth range 0–10 m uses short coil spacings of 5 m or less and a frequency range of 300 kHz to 30 MHz. In this frequency range, both conduction currents (controlled by electrical conductivity) and displacement currents (controlled by dielectric permittivity) are important. Several surface electromagnetic survey systems commonly used (generally with frequencies less than 60 kHz) are unsuitable for detailed investigation of the upper 5 m of the earth or, as with ground‐penetrating radar, are most effective in relatively resistive environments. Most computer programs written for interpretation of data acquired with the low‐frequency systems neglect displacement currents, and are thus unsuited for accurate high‐frequency modeling and interpretation. New forward and inverse computer programs are described that include displacement currents in layered‐earth models. The computer programs and this new instrument are used to evaluate the effectiveness of shallow high‐frequency soundings based on measurement of the tilt angle and the ellipticity of magnetic fields. Forward model studies indicate that the influence of dielectric permittivity provides the ability to resolve thin layers, especially if the instrument frequency range can be extended to 50 MHz. Field tests of the instrument and the inversion program demonstrate the potential for detailed shallow mapping wherein both the resistivity and the dielectric permittivity of layers are determined. Although data collection and inversion are much slower than for low‐frequency methods, additional information is obtained inasmuch as there usually is a permittivity contrast as well as a resistivity contrast at boundaries between different materials. Determination of dielectric permittivity is particularly important for hazardous waste site characterization because the presence of some contaminants may have little effect on observed resistivity but a large effect on observed permittivity.

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