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The distribution of the magnetic field generated by an electromagnetic device can provide insights into their operational condition. This paper focuses on diagnosing electrolyzers through magneto-tomography, a method which involves mapping the magnetic field generated by electrical devices. Since current density and magnetic field are directly linked, this study can characterize the normal and abnormal operation of an electrolyzer. To achieve this, a two-dimensional (2-D) Biot–Savart model in polar coordinates is developed. To validate this model for electrolyzer diagnostics, an experimental setup was established to replicate the electrolyzer operation. The purely analytical model was successfully validated, with the average difference between the analytical results and experimental measurements established. The model validation is performed by comparing the experimental data to the theoretical results, and it is observed that the difference does not exceed 5%. [ABSTRACT FROM AUTHOR]

Deep geothermal energy is a sustainable and renewable spacing heating source. Although many studies have discussed the design optimization of deep borehole systems, few have accomplished optimization and in-depth analysis of system operation control. In this study, an analytical model of the U-type deep borehole heat exchanger is proposed, and the average relative error between the simulated outlet temperatures and experimental data is −3.2%. Then, this paper presents an integrated model for the operation optimization study of the U-type deep-borehole ground source heat pump system. The optimal control of flow rate is adopted to match the variation in heating load. Compared with the constant-flow rate (110 m3/h) operation mode, the variable flow rate method reduces the power consumption of the heat pump and circulating pump by 22.1%, from 288,423 kW·h to 224,592 kW·h, during 2112 h of operation. In addition, the system has a larger RHS and COP when the thermal conductivity of the backfill material increases. When the borehole depth increases by 200 m from 2300 m, the energy consumption of the circulating pump will drop from 85,844 kW·h to 56,548 kW·h. The COP of the heat pump unit will decrease approximately linearly as the heating load increases, and the total power consumption will increase accordingly. This work can provide guidance for the design and optimization of U-shaped GSHP systems. [ABSTRACT FROM AUTHOR]

The determination of the critical ventilation flow rate is significant for risk control and standard development during accidental hydrogen leakage in a confined space with hydrogen-related equipment. This paper presents an analytical model for calculating the critical ventilation flow rate through the quantification and constraint solution of the ventilation effect and ventilation cost. The experimental method was used to investigate the effects of nozzle diameter and stagnation pressure on the diffusion and ventilation of horizontal hydrogen leakage in a cuboid chamber. Ventilations from 30 to 180 m3/h were carried out through the rectangular vent. It was shown that the peak concentration of the measuring point was positively correlated with the stagnation pressure and the nozzle diameter. The experimental data were used to verify the analytical model by calculating the effective ventilation time. This study demonstrates that the critical ventilation flow rate can be increased significantly at higher stagnation pressures and larger nozzle diameters. Furthermore, the discrepancy of critical ventilation flow rates under different nozzle diameters will be enhanced with the increase of stagnation pressure. For a stagnation pressure of 0.4 MPa, the critical ventilation flow rate under a 4 mm nozzle even increased by 52% relative to the 2 mm nozzle. [ABSTRACT FROM AUTHOR]

In this paper, the analytical determination of volumic eddy-current losses in rectangular-shaped conductive massive parts is presented with experimental validations. Eddy currents, as well as the resulting volumic losses, are generated by a sinusoidal spatially uniform applied magnetic field. A U-shaped electromagnetic device with a flat mobile armature (or adjustable air gap) is used to measure the eddy-current losses. The experimental device, its instrumentation, and the conductive massive parts are presented in detail in the paper. Thereafter, the magnetic field distribution applied on the conductive massive parts, which is the mean input data for the eddy-current loss model, is studied. A two-dimensional (2D) numerical model, under the FEMM software, for the magnetic field calculation was also developed. A comparative analysis between the experimental measurements and the numerical results allowed the distribution of the applied magnetic field to be accurately validated. In the final phase, the objective was to estimate the volumic eddy-current losses in rectangular-shaped aluminium conductive massive parts generated by the variation of this applied magnetic field. An analytical model, based on the Maxwell–Fourier method, for the accurate prediction of eddy-current losses has also been developed. An electromagnet with and without the conductive massive parts is characterized in terms of power consumption. By using the power conservation method (i.e., Boucherot's theorem), the eddy-current losses could be quantified experimentally. The influence of segmentation is also studied. The analytical results are compared to the experimental test results. [ABSTRACT FROM AUTHOR]

To achieve the goal of decarbonized energy and greenhouse gas reduction, underground gas storage (UGS) has proven to be an important source for energy storage and regulation of natural gas supply. The special working conditions in UGS cause offset vertical wells to easily interfere with target vertical wells. The current well testing methodology assumes that there is only one well, and the interference from offset wells is ignored. This paper proposes a solution and analysis method for the interference from adjacent vertical wells to target vertical wells by analytical theory. The model solution is obtained by the solution with a constant rate and the Laplace transform method. The pressure superposition is used to deal with the interference from adjacent vertical wells. The model reliability in the gas injection and production stages is verified by commercial software. Pressure analysis shows that the heterogeneity and interference in the gas storage are caused by long-term gas injection and production. As both the adjacent well and the target well are in the gas production stage, the pressure derivative value in radial flow is related to production rate, mobility ratio, and 0.5. Gas injection from offset wells will cause the pressure derivative to drop later. Multiple vertical wells from the Hutubi UGS are used to illustrate the properties of vertical wells and the formation. [ABSTRACT FROM AUTHOR]

There has been a large amount of experience in recent decades in the use of magnetic fields on reservoir fluids. This paper discusses the effect of a magnetic field on wax precipitation. An analytical model is developed to quantify the wax deposition rate on the tubing surface during the magnetic treatment of reservoir oil. It has been established that the passage of the oil flow through a non-uniform magnetic field causes a high-intensity electric field for a sufficiently long period of time, the effect of which decreases the solubility of wax in oil, increases the intensity of wax precipitation in oil, and reduces the wax deposition on the tubing surface. The model accounts for the fact that the wax deposits present on the tubing surface are a highly efficient heat insulator that changes the temperature regime of the flow and the temperature of the tubing wall. This circumstance changes the rate of deposits but does not make these deposits less harmful to wells' operation. A method for calculating the equilibrium wax concentration and changing the solubility of wax in oil under a constant electric field has been developed. We show that the effect of magnetic treatments on wax deposition rises with the increase in the concentration of asphaltenes in the oil and water cut. [ABSTRACT FROM AUTHOR]

The purpose of this study is to provide a holistic review of two decades of research advancement in the indoor environmental quality modelling and indexing field (IEQMI) using bibliometric analysis methods. The explicit objectives of the present study are: (1) identifying researchers, institutions, countries (territories), and journals with the most influence in the IEQMI topic; (2) investigating the hot topics in the IEQMI field; and (3) thematically analysing the keyword evolution in the IEQMI field. A scientometric review was conducted using the bibliometric data of 456 IEQMI research articles published in the past two decades. VOSviewer software was employed for bibliometric analysis, and the SciMAT tool was used to investigate the keywords' thematic evolution in three sub-periods (2004–2009; 2010–2015; 2016–2021). Results show that there is a continuous increment in the number of published papers in the field of IEQMI, and 60 out of 193 countries in the world have been involved in IEQMI studies. The IEQMI research mainly focuses on: (a) thermal comfort and energy efficiency; (b) occupant satisfaction and comfort; (c) IAQ and health issues; (d) methods and procedures. This field has undergone significant evolution. While 'indoor environmental quality was initially the only theme in the first period', 'occupant satisfaction', 'buildings', 'impact', 'building information modelling', and 'health' were added as the main thematic areas in the second period; 'occupant behaviour' and 'energy' were novel themes in IEQMI studies receiving much attention in the third period. [ABSTRACT FROM AUTHOR]

This paper presents some results from a computational fluid dynamics (CFD) model of a multi-megawatt crosswind kite spinning on a circular path in a straight downwind configuration. The unsteady Reynolds averaged Navier-Stokes equations closed by the k − ω SST turbulence model are solved in the three-dimensional space using ANSYS Fluent. The flow behaviour is examined at the rotation plane, and the overall (or global) induction factor is obtained by getting the weighted average of induction factors on multiple annuli over the swept area. The wake flow behaviour is also discussed in some details using velocity and pressure contour plots. In addition to the CFD model, an analytical model for calculating the average flow velocity and radii of the annular wake downstream of the kite is developed. The model is formulated based on the widely-used Jensen's model which was developed for conventional wind turbines, and thus has a simple form. Expressions for the dimensionless wake flow velocity and wake radii are obtained by assuming self-similarity of flow velocity and linear wake expansion. Comparisons are made between numerical results from the analytical model and those from the CFD simulation. The level of agreement was found to be reasonably good. Such computational and analytical models are indispensable for kite farm layout design and optimization, where aerodynamic interactions between kites should be considered. [ABSTRACT FROM AUTHOR]

Series connection is an attractive approach to increase the blocking voltage of SiC power MOSFETs. Currently, the voltage balancing design of the series connection of the SiC MOSFETs highly relies on offline calibration and is challenging in the complex field operation. In this paper, a quantitative model to assess the voltage balancing performance is proposed to achieve a clear mathematical interpretation of the dynamic response of the voltage imbalance control loop. To begin with, an analytical model of the drain-source voltage rising time during the turn-off transient concerning the non-constant Miller plateau is proposed. Based on the turn-off model of the single device, the voltage imbalance sensitivity (VIS) is proposed to describe the influence of the parameters on the gate driving signals on the voltage imbalance. The VIS parameter can be easily achieved from the behavior of single devices, abandoning the complex variables in series connection. Further, for the typical case, active time delay voltage balancing methods are selected to demonstrate the application of the VIS analysis method. Based on VIS, the accurate close-loop design is proposed for controlling the delayed time among the devices. The proposed analysis and method are verified in simulation and experiment. The paper offers a generalized approach to assess the performance and the design of the series connection of the SiC MOSFETs, which can be further applied in many other methods for parameter design and engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, an analytical model is proposed to analyze and predict the characteristics of a double stator linear and rotary permanent magnet machine (DSLRPMM). In order to simplify the magnetic field calculation, the DSLRPMM is cut along the axial direction (z direction) and transferred into a planar one. Hence, an analytical model of the machine considered the orthogonal effect (OE) is proposed based on the combined solution of Maxwell's equation, conformal mapping, and equivalent magnetic circuit model (EMCM). The magnetic field distributions of the DSLRPMM are calculated with and without considering the OE, and some important electromagnetic parameters, including the back electromotive force (EMF), detent force, cogging torque, and output torque and thrust, are also predicted and compared to the 3D finite element analysis (FEA). The results show that the errors between the proposed analytical model and the 3D FEA results are less than 0.2% and even less than 0.1% for certain parameters, that is, the results obtained from the proposed analytical model agree well with that of the FEA. Moreover, the analyzed and predicted results are also verified by the experimental results on the prototype of the DSLRPMM. [ABSTRACT FROM AUTHOR]

The aim of this paper is to calculate the static eccentricity (SE) of a double rotor axial flux permanent magnet (AFPM) machine by using a general analytical model. The flux density in the air gap under healthy conditions is calculated firstly, where the axial and circumferential magnetic flux densities are obtained using a coupled solution of Maxwell's equations and Schwarz-Christoffel (SC) mapping. The magnetic flux densities under SE conditions are calculated afterwards using a novel bilinear mapping. Some important electromagnetic parameters, e.g., back electromotive force (EMF), cogging torque and electromagnetic (EM) torque, are calculated for both SE and healthy conditions, and compared with the finite element (FE) model. As for the double rotor AFPM, SE does not contribute much effect on the back EMF and EM torque, while the cogging torque is increased. At each calculated section, FE models were built to validate the analytical model. The results show that the analytical predictions agree well with the FE results. Finally, the results of analytical model are verified via experimental results. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive analytical model for dual rotor radial flux wind generators based on the equivalent magnetic circuit method. This model is developed to predict the flux densities of the inner and outer air gaps, flux densities of the rotor and stator yokes, back electromotive force (EMF), electromagnetic torque, cogging torque, and some other characteristics important for generator design. The 2D finite element method (FEM) is employed to verify the presented analytical model, fine-tune it, and validate the prediction precision. The results show that the errors between the proposed analytical model and the FEM results are less than 5% and even less than 1% for certain parameters, that is, the results obtained from the proposed analytical model match well the ones obtained from FEM analysis. Meanwhile, the working points at different temperatures are confirmed to exceed the knee point of the BH curve, which means that irreversible demagnetization does not occur. Finally, the optimization by FEM with the objective of fully using the inner space of the generator, decreasing the cogging torque, and reducing the total harmonic distortion (THD) of back EMF is performed. [ABSTRACT FROM AUTHOR]

A physics-based explicit mathematical model for the external voltage-dependent forward dark current in bulk heterojunction (BHJ) organic solar cells is developed by considering Shockley-Read-Hall (SRH) recombination and solving the continuity equations for both electrons and holes. An analytical model for the external voltage-dependent photocurrent in BHJ organic solar cells is also proposed by incorporating exponential photon absorption, dissociation efficiency of bound electron-hole pairs (EHPs), carrier trapping, and carrier drift and diffusion in the photon absorption layer. Modified Braun's model is used to compute the electric field-dependent dissociation efficiency of the bound EHPs. The overall net current is calculated considering the actual solar spectrum. The mathematical models are verified by comparing the model calculations with various published experimental results. We analyze the effects of the contact properties, blend compositions, charge carrier transport properties (carrier mobility and lifetime), and cell design on the current-voltage characteristics. The power conversion efficiency of BHJ organic solar cells mostly depends on electron transport properties of the acceptor layer. The results of this paper indicate that improvement of charge carrier transport (both mobility and lifetime) and dissociation of bound EHPs in organic blend are critically important to increase the power conversion efficiency of the BHJ solar cells. [ABSTRACT FROM AUTHOR]

Requirements of modern process and power technologies for compact and highly efficient equipment for transferring large heat fluxes lead to designing these apparatuses as dense parallel flow systems, ranging from conventional to minichannel dimensions according to the specific industrial application. To avoid operating issues in such complex equipment, it is vital to identify not only the local distribution of heat flux in individual parts of the heat transfer surface but also the uniformity of fluid flow distribution inside individual parallel channels of the flow system. A composite modelling system is currently being developed for accurate design of such complex heat transfer equipment. The modeling approach requires a flow distribution model enabling to yield accurate-enough predictions in reasonable time frames. The paper presents the results of complex experimental and modeling investigation of fluid flow distribution in dividing headers of tubular-type equipment. Different modeling approaches were examined on a set of header geometries. Predictions obtained via analytical and numerical models were validated using data from the experiments conducted on additively manufactured header samples. Two case studies employing parallel flow systems (mini-scale systems and a conventional-size heat exchanger) demonstrated the applicability of the distribution model and the accuracy of the composite modelling system. [ABSTRACT FROM AUTHOR]

SiC MOSFETs have an excellent characteristic of high switching speed, which can improve the efficiency and power density of converters significantly. However, the fast switching processes of SiC MOSFETs cause serious crosstalk problems in bridge-arm configurations, which restricts the devices' performances. This paper presents a detailed and accurate improved crosstalk analytical model, which takes into account the nonlinear capacitances, the parasitic inductances, the reverse recovery characteristics of the anti-parallel diodes, and the nonlinear voltage switching and damping oscillation process. The novelty of the proposed model lies in the fact that under the condition of comprehensively considering all these non-ideal factors of the bridge-arm, the effects of multi-parasitic elements and multi-variables coupling to the crosstalk are hierarchically divided. The parasitic elements and their correlations are described in detail and the direct and indirect variables' impacts are clearly traced. Thus, according to the different variables switching stages, the influence processes of these parasitic elements and variables can be integrated and a complete equivalent analytical model of the crosstalk process can be derived. The simulation and experiment platforms are established and a series of experimental verifications and comparisons prove that the model can replicate experimental measurements of crosstalk with good accuracy and detail. [ABSTRACT FROM AUTHOR]

This paper presents the performance evaluation of a stator modular ring permanent-magnet generator to be embedded in a shrouded wind turbine. That is done to increase the power conversion for the same turbine area when compared to more conventional ones. An adapted structure allows the assembling of the prototype, aiming to verify its performance under controlled conditions. Aiming to verify the accuracy of an analytical subdomain model for a large diameter machine, the evaluation compares the results obtained by the electromagnetic finite element method and experimental measurements. The results of the components of the air-gap flux density, back EMF and electromagnetic torque obtained by the proposed analytical model and finite-element method are in good agreement with the experimental measurements. The experimental measurements of the iron loss and copper loss show that the prototype efficiency can reach 90% approximately. [ABSTRACT FROM AUTHOR]

The energy crisis and environmental concerns worldwide have helped usher in the age of electric vehicles (EVs) and hybrid EVs (HEVs). The interior permanent magnet motors (IPMMs) are widely used in these vehicles. The analysis of the armature reaction field is the most critical issue in the study of IPMMs since it determines the characters of torque, efficiency, vibration, and the radiated acoustic noise. This paper provides a calculation method of the armature reaction magnetic field (ARMF) of an IPMM. First, the formulas of ARMF without magnetic barrier are derived. Second, the relative permeance function of an IPMM is calculated. Third, the analytical solution of the ARMF of an IPMM is derived by applying the armature reaction magnetic field with unsaturated rotor multiplied by relative permeance function. Finally, several results of comparisons between the calculation method proposed in this paper and the finite element method are presented. Based on the calculation method proposed in this paper, the magnetic barrier's influence on the ARMF is studied. The spatial harmonic orders and time harmonic orders of the ARMF of IPMM are revealed respectively. [ABSTRACT FROM AUTHOR]

This paper proposes an analytical model for natural convection in a closed rectangular enclosure filled by a fluid, with imposed heat fluxes at the vertical walls and adiabatic horizontal walls. The analytical model offers a simplified, but easy to handle, description of the temperature and velocity fields. The predicted temperature, velocity, and pressure fields are shown to be in agreement with those obtained from a reliable numerical model. The Nusselt numbers for both the analytical and numerical solutions are then calculated and compared, varying both the aspect ratio of the enclosure and the Rayleigh number. Based on the comparisons, it is possible to assess the dependence of the reliability of the analytical model on the aspect ratio of the enclosure, showing that the prediction error rapidly decreases with the increase of the enclosure slenderness. [ABSTRACT FROM AUTHOR]

The increasing penetration of variable renewable energies (VRE) in the European electricity mix requires flexible energy storage systems (ESS), such as pumped storage hydropower (PSH). Disused mining voids from deep closed mines may be used as subsurface reservoirs of underground pumped-storage hydropower (UPSH) plants. Unlike conventional PSH plants, the air pressure in UPSH plants is variable and it differs from the atmospheric conditions. In this paper, the hydraulic transient process of an UPSH plant operating in pumping mode was investigated and a preliminary thermodynamic analysis of the closed surge tank was carried out. Analytical and CFD three-dimensional numerical simulations based on the volume of fluid (VOF) model with two-phase flow have been performed for analyzing the transient process. In the transient simulation, air and water are considered as ideal gas and compressible liquid, respectively. Different guide vanes closing schemes have been simulated. The obtained results show that the dimensioning of underground reservoir, surge tank, and air ducts is essential for ensuring the hydraulic performance and optimizing the operation of UPSH plants. The static pressure in the air duct, surge tank and lower reservoir reaches −1.6, 112.8 and −4 kPa, respectively, while a heat flux of −80 W was obtained through the surge tank walls. [ABSTRACT FROM AUTHOR]

This paper presents an inner-type of magnetic gears for non-contact driving, based on the nutation gearing principle. An improved three-dimensional analytical model, based on the magnetic vector potential of rectangular permanent magnets, via the equivalent current, is deduced for the proposed nutation magnetic gears. The transformation of coordinates is applied for a global field solution. The analytical model and the finite element model have analyzed the output torque of the nutation magnetic drive, respectively. The results show that the values calculated by the two models are consistent. The proposed analytical model can provide a reference for the design and optimization of nutation magnetic gears and other permanent magnetic mechanisms with rectangular magnets. [ABSTRACT FROM AUTHOR]

In recent years, the zero-mode inrush current of high-impedance transformer with built-in high-voltage winding (T-Hin), which has large amplitude and decays slowly, causes the misoperation of zero-sequence overcurrent protection. Compared with magnetizing inrush current, the waveform of zero-mode inrush current is inconsistent and irregular, and few researches have proposed the mathematical analysis as well as the improved protection using waveform characteristics. In this paper, the mathematical expression of transformer zero-mode inrush current is derived. Further considering the parameter differences, the zero-mode inrush current of T-Hin is larger, which tends to cause the misoperation. The mathematical waveforms fit well with the recorded waveforms. Both recorded waveforms and mathematical waveforms in various conditions prove that the second harmonic ratio (the ratio between the second harmonic and first harmonic) of zero-mode inrush current is significant. Based on the above analysis, a criterion based on the second harmonic ratio restraint of zero-mode inrush current is proposed. If the second harmonic ratio exceeds the setting value, it is considered that the inrush current is generated and sends a signal to restrain the protection. The theoretical setting value of the proposed criterion and the practical engineering method for determining the setting value are obtained. [ABSTRACT FROM AUTHOR]

This paper proposes a demagnetization fault detection, mode recognition, magnetic pole positioning, and degree evaluation method for permanent magnet synchronous motors. First, the analytical model of the single-coil no-load back electromotive force (EMF) of demagnetization fault for Permanent magnet synchronous motor (PMSM) arbitrary magnetic poles is established. In the analytical model, the single-coil no-load back EMF residual of the health state and the single magnetic pole sequential demagnetization fault are calculated and normalized. Model results are used as the fault sample database. Second, the energy interval database of the single-coil no-load back EMF residual with different numbers of magnetic pole demagnetization is established. Demagnetization fault detection and degree evaluation are performed by the real-time acquired amplitudes of the single-coil no-load back EMF residual. The number of demagnetization poles is determined by comparing the energy of the single-coil no-load back EMF residual with the energy interval database. Demagnetization mode recognition and magnetic pole positioning are realized by analyzing the correlation coefficients between normalized the single-coil no-load back EMF residual and the fault sample database. Finally, results of analysis of the finite element simulation validate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The significant decreased wellbore temperature and increased casing pressure during fracturing fluid injection present a big challenge for the mechanical integrity of cement sheath in fracturing wells. Based on the theories of elastic mechanics, thermodynamics, and a multi-layer composed thick-wall cylinder, this paper proposed a new mechanical model of cement sheath for fracturing wells, coupling pressure, and thermal loads, which consider the failure modes of de-bonding, radial cracking, disking, and shear failure. The radial nonuniform temperature change and the continuous radial stress and radial displacement at two interfaces have been considered. With the proposed model, the radial distributions of failure stress and the corresponding safety factor for cement sheath during fracturing fluid injection have been analyzed and compared under four failure modes. Results show that the decreased wellbore temperature will produce significant tri-axial tensile stress and induce cement failure of de-bonding, radial cracking, and disking. The increased casing pressure will significantly lower the risk of de-bonding but also aggravate radial cracking and shear failure. For integrity protection of cement sheath, increasing the injected fluid temperature, maintaining higher circulation pumping pressures, and adopting cement sheath with a low elasticity modulus have been suggested for fracturing wells. [ABSTRACT FROM AUTHOR]

Geothermal energy development has increasingly been studied in recently decades because of its renewable and sustainable features. It can be divided into two categories: traditional geothermal (hydrothermal) systems and enhanced geothermal systems (EGS) based on the type of exploitation. The hot dry rock (HDR) in the EGS incorporates about 80% of all thermal energy, and its value is about 100–1000 times that of fossil energy. It is pivotal for geothermal wells to improve the flow conductivity of the HDR mass, enhance the communication area of natural fractures, and constitute the fracture network between injection and production wells by hydraulic treatments. While the wellbore temperature significantly decreases because of fracturing, fluid injection will induce additional thermal stresses in the cement sheath, which will aggravate its failure. Considering the radial nonuniform temperature change, this paper proposes a new thermal stress model for a casing-cement sheath-formation combined system for geothermal wells during fracturing based on elastic mechanics and thermodynamics theory. This model is solved by the Gaussian main elimination method. Based on the analytical model, the thermal stresses of cement sheath have been analyzed. The effects of the main influencing parameters on thermal stresses have also been investigated. Results show that the radial and axial tensile thermal stresses are both obviously larger than tangential tensile thermal stress. The maximum radial and axial thermal stresses always occur at the casing interface while the location of the maximum tangential thermal stress varies. Generally, thermal stresses are more likely to induce radial and axial micro cracks in the cement sheath, and the cement sheath will fail more easily at the casing interface in fracturing geothermal wells. For integrity protection of the cement sheath, a proper decrease of casing wall thickness, casing linear thermal expansion coefficient, cement sheath elasticity modulus, and an increase of the fracturing fluid temperature has been suggested. [ABSTRACT FROM AUTHOR]

Square and circular coils are two typical topologies for coupling coils and are applied to wireless charging. However, most of the research on coupling coils is based on the finite element model (FEM), which is a time-consuming process for 3-D structure coils. In this paper, on the basis of Fourier–Bessel transformation and Dual Fourier transformation, two theoretical models of square and circular coils between two multilayer media are proposed. With the proposed models, we consider several important parameters such as the size of the coils, thickness, and permeability of each layer. Thus, both the self-inductance and mutual inductance of two planar coils can be calculated without much computational time. Additionally, these theoretical models can help designers figure out the different trends of self-inductance and mutual inductance, which has plenty of benefits for the preliminary pad design. Lastly, a prototype with a size of 600 mm × 600 mm and a 200 mm air gap was built in order to verify the proposed models. [ABSTRACT FROM AUTHOR]