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 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%.

Pore-Scale Joint Evaluation of Dielectric Permittivity and Electrical Resistivity for Assessment of Hydrocarbon Saturation Using Numerical Simulations

SPE Journal ◽  
2016 ◽  
Vol 21 (06) ◽  
pp. 1930-1942 ◽  
Author(s):  
Huangye Chen ◽  
Zoya Heidari
Keyword(s):  
Electrical Resistivity ◽  
Spatial Distribution ◽  
Dielectric Permittivity ◽  
Pore Structure ◽  
Maximum Error ◽  
New Method ◽  
Pore Scale ◽  
Resistivity Measurements ◽  
Hydrocarbon Saturation ◽  
Permittivity Measurements

Summary Complex pore geometry and composition, as well as anisotropic behavior and heterogeneity, can affect physical properties of rocks such as electrical resistivity and dielectric permittivity. The aforementioned physical properties are used to estimate in-situ petrophysical properties of the formation such as hydrocarbon saturation. In the application of conventional methods for interpretation of electrical-resistivity (e.g., Archie's equation and the dual-water model) and dielectric-permittivity measurements [e.g., complex refractive index model (CRIM)], the impacts of complex pore structure (e.g., kerogen porosity and intergranular pores), pyrite, and conductive mature kerogen have not been taken into account. These limitations cause significant uncertainty in estimates of water saturation. In this paper, we introduce a new method that combines interpretation of dielectric-permittivity and electrical-resistivity measurements to improve assessment of hydrocarbon saturation. The combined interpretation of dielectric-permittivity and electrical-resistivity measurements enables assimilating spatial distribution of rock components (e.g., pore, kerogen, and pyrite networks) in conventional models. We start with pore-scale numerical simulations of electrical resistivity and dielectric permittivity of fluid-bearing porous media to investigate the structure of pore and matrix constituents in these measurements. The inputs to these simulators are 3D pore-scale images. We then introduce an analytical model that combines resistivity and permittivity measurements to assess water-filled porosity and hydrocarbon saturation. We apply the new method to actual digital sandstones and synthetic digital organic-rich mudrock samples. The relative errors (compared with actual values estimated from image processing) in the estimate of water-filled porosity through our new method are all within the 10% range. In the case of digital sandstone samples, CRIM provided reasonable estimates of water-filled porosity, with only four out of twenty-one estimates beyond 10% relative error, with the maximum error of 30%. However, in the case of synthetic digital organic-rich mudrocks, six out of ten estimates for water-filled porosity were beyond 10% with CRIM, with the maximum error of 40%. Therefore, the improvement was more significant in the case of organic-rich mudrocks with complex pore structure. In the case of synthetic digital organic-rich mudrock samples, our simulation results confirm that not only the pore structure but also spatial distribution and tortuosity of water, kerogen, and pyrite networks affect the measurements of dielectric permittivity and electrical resistivity. Taking into account these parameters through the joint interpretation of dielectric-permittivity and electrical-resistivity measurements significantly improves assessment of hydrocarbon saturation.

National Primary Standard for the Units of Complex Dielectric Permittivity in the Frequency Range from 1 to 178.4 Ghz

2014 ◽  
Vol 57 (1) ◽  
pp. 1-7 ◽  
Author(s):  
V. N. Egorov ◽  
M. V. Kashchenko ◽  
V. L. Masalov ◽  
E. Yu. Tokareva ◽  
Nong Quoc Quang
Keyword(s):  
Dielectric Permittivity ◽  
Primary Standard ◽  
Complex Dielectric Permittivity ◽  
Frequency Range ◽  
National Primary Standard

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.

The Arctic soils dielectric characteristics

2021 ◽  
pp. 127-134
Author(s):  
K.N. Suslov ◽  
A.S. Yashchenko ◽  
S.V. Krivaltsevich
Keyword(s):  
Dielectric Permittivity ◽  
Arctic Region ◽  
The State ◽  
The Arctic ◽  
Underlying Surface ◽  
Complex Dielectric Permittivity ◽  
Frequency Range ◽  
Near Surface ◽  
Laboratory Conditions ◽  
The Arctic Region

The state of the underlying surface has a noticeable effect on the process of emission and propagation of radio waves. The state of the underlying surface is dependent on the value of the complex dielectric permittivity. Usually, the underlying surface is understood as soil or ground medium. The Dobson model is recommended by the International Telecommunication Union (ITU) for calculating the dielectric permittivity of moist soils over a wide frequency range. However, this model was developed based on experimental data obtained at frequencies above 1 GHz for soils of the temperate climatic zone. This paper presents the results of measuring the complex dielectric permittivity of the Arctic region soils sample at the frequency range from 1 MHz to 8 GHz. Also, we compared the dielectric permittivity data measured in laboratory conditions and calculated by the Dobson model. It was found that the Arctic soil dielectric permittivity data measured under laboratory conditions and calculated using the Dobson model differ markedly from each other, which indicates the impossibility of using the Dobson model for calculating soil dielectric permittivity of the Arctic region. The data obtained in the laboratories case may be used to estimate the directional characteristics of near-surface emissivity systems, as well as of the ground wave propagation prediction in the Arctic region.

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