Equivalent Permeability Research Articles

Experimental study on characteristics of gas seepage in broken coal and rock

AbstractThe characteristics of gas seepage in broken coal and rock composed of different particle sizes and grades were investigated in this study. On the basis of Darcy's law and non‐Darcy seepage theory, equations of gas permeability in the nonlinear seepage of broken coal and rock, as well as the porosity of broken coal and rock, under triaxial compression were determined. The stress loading path of gas seepage in broken coal and rock was developed. The characteristics of gas seepage in broken coal and rock composed of different particle sizes and grades were analyzed, and the results showed that the gas permeability after compression was proportional to the particle size of the broken coal and rock. Under triaxial compression, the gas permeability of the broken coal and rock composed of graded‐particle sizes was lower than that of the broken coal and rock composed of different single‐particle sizes. The gas permeability of the broken coal was lower than that of the broken rock mass, and the gas permeability and porosity of the broken coal and rock can be described by the exponential decay function. At a constant porosity, the gas permeability of the broken coal and rock was proportional to the size grading index under triaxial compression. The coefficient of viscosity and gravity of the flow are key factors influencing the flow permeability in broken coal and rock. This study provides a reference for on‐site practice such as the efficient extraction of gas in goafs.

A New model of gas-water two-phase seepage based on Newton's law of motion

The pore throat size, structure distribution, and lithology of porous media in gas reservoirs are varied, and the gas-water two-phase seepage law is complex, making it difficult to describe the seepage model. Newton's law of motion is a basic law of motion in classical mechanics, and its application in gas-water two-phase seepage modeling is an innovative practice of classical mechanics in seepage mechanics systems. Based on Newton's three laws of motion, a gas-water two-phase seepage model was established from the force analysis of fluid, and the relationship between velocity and pressure difference, pipe radius, water film thickness, viscosity, etc. was derived under the condition that the model reached a stable state, i.e., force balance. The relationship is referred to as the steady-state model. Subsequently. the equivalent permeability representation model was derived based on the steady-state model to calculate the permeability of rock samples with different channel distribution characteristics. The results were consistent with the measured values, and there is a good correspondence between channel distribution characteristics and permeability. The relative permeability calculation method was established based on the steady-state model and capillary pressure curve. The obtained relative permeability curve aligned with the two-phase seepage law and coincides with the relative permeability curve obtained by Poiseuille's law. Finally, a new productivity equation was derived based on the steady-state model, and the Inflow Performance Relationship (IPR) curve calculated by the gas well example was consistent with the traditional equation. The research results were based on the force analysis of fluid in porous media and fundamentally explored the law of fluid flow. The derived seepage model can be used to calculate reservoir permeability, the gas-water relative permeability curve, and gas well productivity analysis and to effectively guide gas reservoir development. The study was a successful application of the basic theory of mechanics in gas-water two-phase seepage in gas reservoirs.

REV and Three-Dimensional Permeability Tensor of Fractured Rock Masses with Heterogeneous Aperture Distributions

This study performed a representative elementary volume (REV) and 3D equivalent continuum study of rock fractures based on fluid simulations of 3D discrete fracture networks (DFNs). A series of 3D DFNs with heterogeneous aperture distributions (the DFN-H model) and uniform apertures (the DFN-I model) were established, in which the fractures were oriented according to the geological field mapping of a high-level radioactive waste candidate site in China. The 3D DFNs of the different model sizes were extracted and rotated in a number of directions to check whether there was a tensor quality of the permeability at a certain scale. The results show that aperture heterogeneity increases the REV size and results in a necessarily larger model size to reach an equivalent continuum behavior, and this effect is more obvious when the fracture density is smaller. The shape of the 2D permeability contour is irregular, with some breaks when the model size is small. As the model size increases, its shape gradually tends to become smooth and approaches an ellipse. The shape of the permeability contours of the DFN-H model is slender compared to the DFN-I model, indicating a larger difference between the minimum and maximum values of the permeability. For the DFN-H model, there is no appropriate approximation for the equivalent permeability tensor over the studied model size range, whereas a good fit of the permeability ellipsoid is obtained for the DFN-I model, and the 3D directional permeability is calculated at this model scale. The corresponding magnitude and direction of the principal permeability are obtained, which can be viewed as the equivalent permeability tensor for the approximated continuum medium.

Multiscale discrete fracture network modelling of shallow-water carbonates: East Agri Valley Basin, Southern Italy

We investigate the multiscale geometrical and dimensional properties of fracture and fault networks crosscutting Lower Jurassic to Cretaceous shallow-water carbonate rocks. The carbonates are exposed along the flanks of the Viggiano Mt., on the eastern side of the High Agri Valley Basin of southern Italy. Furthermore, we employ the results of field and digital structural analyses to derive the input parameters for subsequent Discrete Fracture Network modelling (DFN) of geocellular volumes whose dimension and architecture resemble those of the investigated sites. DFN modelling is carried out for geocellular volumes representing the studied bed packages (5m-side volumes), outcrops (50m-side volumes), and reservoir-scale carbonate cliffs (500m-side volumes). Notably, modelling is obtained considering the minimum mechanical aperture value obtained in the field for porosity computations and theoretical values of fracture hydraulic aperture for permeability computations. This is because the mechanical aperture values and roughness profiles collected in the field along single fractures are unreliable due to weathering and localized karst-related dissolution. Our findings reveal that a scale-dependent geometry characterizes the Cretaceous carbonates over three orders of magnitude. These results support previously published data, and contrast with those obtained for the Lower Jurassic carbonates, which suffer of some bias due to the quality of the exposures. After DFN modelling, we show that the amount of computed fracture porosity is mainly due to the SB and NSB fractures, and that equivalent permeability is greater within faulted rock volumes. In terms of horizontal permeability, which is the most reliable result after DFN modelling, we document near isotropic horizontal permeability ellipses at all scales of observations. At individual outcrops, we note that the permeability ellipses are elongated parallel to the dominant fault sets that denotes how localized strain affects the directionality of fluid flow. Finally, we summarize the original data in a conceptual model illustrating the modalities of meteoric fluid infiltration through the vadose zone, and then subsequent horizontal flow in the phreatic zone present within the fracture carbonates at shallow depths.

Soil pores in preferential flow terminology and permeability equations

AbstractLinkages between the micro‐scale of soil water and landscape scale of hydrological data could be improved with the analysis of soil factors in preferential flow rates. This rearrangement of the terminology on soil pore size from published literature focused on the relationship between aggregate and pore size. In the range of pore size relevant to water flow (>0.005 mm), a 2:1 ratio of aggregate to pore diameter approximated the mean of proposed pore size categories. Major functional change points in soil pore size were identified where water becomes mobile in soil (0.005 mm), where preferential flow among aggregate surfaces begins (0.3 mm), and where water flows without soil interaction (bypass flow ∼1.0 mm). A number of published equations supported the application of soil pore size in permeability estimation for modeling hydraulic conductivity. Common understanding of soil pore terminology would support water flow estimation from soil to landscape scales.

Combined effects of the roughness, aperture, and fractal features on the equivalent permeability and nonlinear flow behavior of rock fracture networks

The hydraulic properties of a fractured rock mass are largely controlled by connected fracture networks. A thorough understanding of the physical flow processes in fracture networks is essential for assessing the transport capacity of the rock mass. However, the fracture surface roughness morphology, fracture distribution characteristics, and fluid flow regimes strongly influence the flow capacity of a fracture network. To this end, the rough topographic characteristics of fracture surfaces were quantified using fractal theory, and then the effective permeability model and nonlinear seepage effect assessment model of the rough fracture network for different flow regimes were developed based on the possible occurrence of laminar and turbulent flows in a single fracture. Finally, the influences of the geometric parameters of the fracture network on the effective permeability and nonlinear flow characteristics were analyzed. The results show that the prediction results of the proposed models are in good agreement with the field test data and can effectively reveal the seepage influence mechanisms under different flow regimes. Additionally, the results show that the effective permeability is closely related to the fractal dimension, relative roughness, aperture scale, distribution characteristics, and hydraulic gradient of the fractures. The nonlinear behavior of fluid flow significantly reduces the effective permeability of the rock mass. The proposed models can provide a reference for evaluating the transport capacity of rock masses under different fracture distributions and flow regimes.

An exploratory study on bamboo permeability for evaluation of treatability with chemical solutions

The rapid and uniform impregnation of resins and preservative fluids is critical to improving the quality and durability of wood-based materials. Permeability coefficients obtained in laboratory experiments aid in the development of optimal conditions for uniform resin filling on an industrial scale. However, due to the shape and orientation of pores in the bulk structure of bamboo, simplified permeability equations may not be sufficient to provide realistic resin impregnation predictions. In this study, the permeability coefficients for Dendrocalamus asper bamboo were determined using air flow measurements and Forchheimer's equation in the x, y, and z directions, and they were correlated to the bamboo microstructure, providing a detailed perspective on how to further investigate this property for real-world applications, such as pressure treatments with chemical solutions. Porosity was measured using mercury intrusion porosimetry (MIP) and water immersion methods to aid in the permeability analysis. The results showed that the longitudinal direction had 1000 to 10,000 times higher permeability coefficients than the radial and tangential directions. This finding is consistent with the alignment of transport vessels as well as the limited pore network in the transversal bamboo section. The outer region of bamboo had higher radial permeability than the middle and inner layers, despite having lower porosity. It is hypothesized that the greater number of vessels, albeit smaller, provides a more direct path for air to flow. The Darcian permeability coefficients of bamboo were found to be comparable to those reported in the literature for wood. This exploratory study provided insights into a novel approach for assessing the treatability of bamboo species.

A complex-network-based estimation of the representative elementary volume and equivalent permeability coefficient for fractured rock masses

The determination of the representative elementary volume (REV) and equivalent permeability coefficient (EPC) of fractured rock masses is crucial for studying the hydraulic behaviors of engineering rock masses. The complex network originated from graph theory and represents a rapidly developing interdisciplinary field in the 21st century. In this paper, we propose a novel method that utilizes complex-network-based metrics to estimate the REV and EPC of fractured rock masses. In this method, fractures and their intersections are treated as nodes and edges of a complex network, respectively. We propose a transformation procedure of a discrete fracture network (DFN) into a complex network, and the corresponding algorithms are conducted in MATLAB. Subsequently, we obtain a complex network, and several complex-network-based metrics, such as average degree, average clustering coefficient, and graph density, are calculated using Gephi software. We employ the average degree to estimate the REV size of DFN models, while the coefficient of variation is used to quantitatively assess changes in the average degree of multiple random models. Furthermore, we establish an empirical formula utilizing the average degree, average clustering coefficient, and graph density to estimate the EPC of a large-scale DFN model based on the EPC of a small-scale DFN model. To verify the developed method, we conduct numerical experiments using the MAFIC (Matrix/Fracture Interaction Code) solver within the FracMan software. This enabled us to calculate the EPC, which was then used to determine the REV. The results demonstrate that: (a) the REV size estimated by the average degree aligns with the REV size obtained through numerical simulations for both isotropic and anisotropic DFN models, and (b) the error rates between the average EPC calculated by the empirical formula and that obtained by numerical simulations are within 10%. Thus, the proposed seepage parameter estimation methods are deemed valid.

Research on high-power and high-efficiency emission of crosswell electromagnetic logging

Crosswell electromagnetic (EM) logging has useful applications in oil, gas, and water monitoring as well as carbon sequestration estimation. Difficulties in the efficient propagation of EM waves through a steel casing inhibit crosswell EM logging at distances greater than 300 m. This study investigates whether high-power transmission and high-efficiency transmitting antennas can resolve the challenges of long-distance crosswell EM logging through steel casings. Theoretical analysis indicates that the emission moment should be at least 12,000 A·m2. By calculating the equivalent relative permeability and selecting the appropriate coil materials and magnetic cores, the maximum emission magnetic moment can create a high-power transmission. Based on series and parallel resonant circuits and the alternating current/direct current cable core multiplexing power supply method, the effective transmission bandwidth is broadened and the transmission efficiency increases by three times. The emission unit is fabricated and tested using single, double, and fiberglass casing. We observe that the crosswell EM technology performs better for nonmetal casing wells than that for metal casing wells. The amplitude and phase curves between two fiberglass casing wells in the range of 425 m are quite smooth. However, the receiving signals in the double-layer steel casing decrease to only a few tenths of the value in the fiberglass casing wells, highlighting the difficulty of long-distance EM wave transmission when using steel casings. Thus, studies on EM transmission through four or more layers of steel casings should be conducted in the future.

0.16BaFeO3-0.84MgFe2O4 hexa-spinel composited ferrites with enhanced magneto-dielectric properties for miniaturized high-frequency antennas

we deeply dived multi-phase-based 0.16BaFeO3-0.84MgFe2O4 ferrite for VHF antennas. The structural and magneto-dielectric properties synthesized at various temperatures (1100 °C, 1125 °C, 1150 °C and 1175 °C) were investigated. The results demonstrated the coexistence of hexagonal and cubic spinel phases. Microstructure analysis indicated higher temperature induced lager grain size and denser structure. Meanwhile, both the saturation magnetization (from 28 to 25 emu/g) and coercivity (19–5 Oe) decreased. In addition, real permeability (μ′) and permittivity (ε′) arose at higher temperature, promising equivalent permeability and permittivity. What's more, relatively low magnetic and dielectric losses (tanδμ ∼10−2 to 10−3 and tanδε ∼10−3 to 10−4) promote low energy loss. Finally, a miniaturized antenna with relative bandwidth of 14.6 %, peak gain of 0.98 dB, and radiation efficiency of 74.6 % was simulated based on the processed ferrites. In conclusion, the presented investigation greatly improves the magneto-dielectric response, which paves the way to realize high performance in VHF antenna application.

Electromagnetic characteristics analysis of dual-frequency magnetic single negative metamaterials

Abstract With the development of multi-frequency wireless transmission technology, it is necessary to expand the research of single-frequency metamaterials in the multi-frequency field. The dual-frequency metamaterial studied adopts a nested square spiral structure, which can resonate at two frequencies, and the real part of the equivalent permeability of metamaterial changes dramatically at the resonance frequency, and the equivalent electromagnetic parameter exhibits anomalous characteristics in the two frequency bands. Firstly, the effects of the number of turns, the width of the copper wire, the spacing of the copper wire, and the length of the outermost edge of inner and outer helical coils are investigated, respectively, using the HFSS software on the resonance frequency of dual-frequency metamaterials, which improves the study of dual-frequency metamaterials with nested square spiral structure. Then, based on the results of the change rule of resonance frequency with the four types of influencing factors, the dual-frequency metamaterials with the real part of the equivalent permeability close to -1 at 6.78 MHz and 13.56 MHz are designed, which is of certain reference significance for the subsequent practical design of dual-frequency metamaterials to satisfy the needs of the project.

Slope stability considering multi-fissure seepage under rainfall conditions

Fissures form the channel for rainwater infiltration, which accelerate the infiltration of rainwater into slope bodies, hence its important impact on the seepage field and stability of the slope. In this paper, taking one landslide of Liang-Wan freeway as the research object, firstly, the equivalent permeability coefficient method is used to homogenize the fissured soil. Then considering the boundary conditions of rainfall infiltration and groundwater level, a fluid–structure coupling model is established based on saturated–unsaturated seepage theory, and evolution characteristics of seepage, displacement and stress of the slope are studied. Based on these, the slope stability coefficient is determined. The results show that the rising rate of pore water pressure and volume water content of topsoil increases when multi-fissure seepage is considered, and the pore water velocity is larger in the local seepage range of fissures. With the increase of buried depth, the closer to groundwater level, the influence of multi-fissure seepage gradually weakens. The theoretical calculation results of slope displacement are more consistent with the field monitoring results. With the increase of rainfall time, the stability coefficient of slope decreases gradually, and the rate and range of decrease are greater.

On quantification of equivalent permeability tensor in sparsely fractured rock masses

The work presented in this paper is focused on the assessment of hydraulic conductivity in sparsely fractured rocks. Different simplified methodologies are used, including Oda's notion of permeability tensor as well as pipe network models, and the results are compared with those generated by a more accurate approach, which incorporates a constitutive law with embedded discontinuity (CLED). Several numerical examples involving fluid flow in the presence of discrete fracture networks are provided, and the estimates of principal values as well as eigenvectors of the equivalent conductivity tensor are compared for all methodologies employed. It is demonstrated that the predictions corresponding to pipe-network model, enhanced by the graph theory algorithm, are fairly consistent with CLED approach, particularly in terms of assessing the orientation of principal directions of permeability. A simple pragmatic procedure is therefore suggested for defining the anisotropic equivalent hydraulic conductivity operator.

Analysis of Soil Improvement Through PVD and Vacuum Preloading with Several Equivalent Permeability Methods

Vacuum preloading combined with prefabricated vertical drain (PVD) is one of the common soft soil improvement methods. Soft soils often pose significant problems in construction projects due to their low shear strength and high compressibility, leading to settlement issues and potential structural instability. The PVD combined with vacuum preloading method addresses these problems by accelerating the consolidation process and minimizing settlement during service period. The acceleration occurs due to the presence of PVD, allowing dissipation of excess pore water in horizontal direction towards the PVD. Thereafter, the water in the PVD is drained to the surface. When modelled in 2D, PVD behaves as a continuous drain in the plane strain direction, causing the flow conditions to deviate from the actual conditions. To address this issue, equivalent soil permeability values is required, allowing the 2D model to produce results closely resembling the actual conditions. This research explores the improvement of PVD vacuum preloading through three equivalent permeability approaches. Utilizing field monitoring data, which includes settlement measurements from settlement plates, changes in pore water pressure recorded by piezometers, and lateral deformation data captured by inclinometers, the study evaluates the effectiveness of these approaches. Comparative analyses with field monitoring data reveal that Indraratna equivalent permeability method has the best fit. The integration of PVD and vacuum preloading, coupled with the refinement of equivalent permeability methodologies, offers a promising solution for addressing soft soil problems in geotechnical engineering. This research contributes to the practical application of these methods in construction projects, emphasizing their potential to enhance soil stabilization and reduce settlement-related risks.

Experimental Study of the Effect of Molecular Collision Frequency and Adsorption Capacity on Gas Seepage Flux in Coal

Summary The differences in the transport behavior and adsorption capacity of different gases in coal play crucial roles in the evolution of coal permeability. Previous studies of coreflooding experiments failed to explain the mechanism of gas flow and have attributed the variation in gas seepage flux (flow rate) at the beginning of the experiment to the change in effective stress, while the differences in the microscopic properties of different gases, such as molar mass, molecular diameter, mean molecular free path, and molecular collision frequency, were ignored. To research the effect of these gas properties on seepage flux while circumventing the effective stress, coreflooding experiments with helium (He), argon (Ar), nitrogen (N2), methane (CH4), and carbon dioxide (CO2) were designed. The results show that the gas transport velocity in coal is affected by the combination of molecular collision frequency and dynamic viscosity, and the transport velocities follow the order of ν (CH4) > ν (He) > ν (N2) > ν (CO2) > ν (Ar). A permeability equation corrected by the molecular collision frequency is proposed to eliminate differences in the permeabilities measured with different gases. The adsorption of different gases on the coal matrix causes different degrees of swelling, and the adsorption-induced swelling strains follow the order of ε (CO2) > ε (CH4) > ε (N2) > ε (Ar) > ε (He). The reduction in seepage flux and irreversible alterations in pore structure caused by adsorption-induced swelling are positively correlated with their adsorption capacities. The gas seepage fluxes after adsorption equilibrium of coal follow the order of Q (He) > Q (CH4) >Q (N2) > Q (Ar) > Q (CO2). Like supercritical CO2 (ScCO2), conventional CO2 can also dissolve the organic matter in coal. The organic molecules close to the walls of the cleats along the direction of gas flow are preferentially dissolved by CO2, and the gas seepage flux increases when the dissolution effect on the cleat width is greater than that on adsorption swelling.

Experimental study on the impact of effective stress and cyclic loading on permeability of methane hydrate clayey sediments

Permeability evolution directly determine gas production and its efficiency of gas hydrates in the South China Sea. Due to existence of submarine overlying rocks and change of soil internal mechanics during the hydrate exploitation, permeability evolution is significantly affected. Therefore, in this paper, influence of effective stress on the porosity and permeability of sediment with different hydrate saturation was studied, and functional relationship between them was revealed. Effect of cyclic loading and unloading stress on the permeability recovery and damage degree was also discussed. The results show that when hydrate saturation increases, the relation of permeability and effective stress are power function rules, while porosity and effective stress are exponential function rules in clayey sediments. An empirical prediction equation for gas permeability of clay sediments with effective stress was presented, which takes into account hydrate saturation and porosity. In addition, during cyclic loading experiments, the results showed a linear increase in permeability during unloading. The permeability recovery rate and permeability damage rate are completely opposite with change of hydrate saturation. Permeability damage rate of kaolin is different from that of other two kinds of sediment. With the increase of cycle times, the proportion of plastic deformation of sediment decreases gradually.

Quantitative Evaluation Method and Response Mechanism of Shallow Groundwater in Multi-Mine Mining of “Soil–Rock” Composite Water-Resisting Strata

The sustainability of shallow groundwater systems, pivotal to maintaining ecosystem equilibrium and facilitating the sustainable development of mine sites, is the core of various dynamic indicators in response to mining activity and mining area planning. This study quantitatively evaluates the impact of mining activities on shallow groundwater systems at the orefield scale, taking the equivalent permeability coefficient (EPC) of “Soil–Rock” composite water-resisting strata and the response mechanism of shallow groundwater in multi-mine mining as the entry points. A modified six-step evaluation method for the response mechanism of shallow groundwater in multi-mine mining is proposed using mathematical statistics, numerical simulation, and theoretical analysis methods. The method is used to evaluate the sustainability of the shallow water system in the Yushen mining area, to study the distribution characteristics of the water resource carrying capacity (WRCC) in different mining areas of the Yushen area, and to analyze the number of mines allowed to be mined under geological conditions with a WRCC of more than moderate bearing capacity. The results show that when the mining area of a mine in the Yushen area is set to 1 × 108, 7.5 × 107, 5 × 107, and 2.5 × 107 m2, as the mining area of the designed mine decreases, the area bearing surplus gradually increases, with values of 1.70 × 109, 1.98 × 109, 2.28 × 109, and 2.58 × 109 m2. The number of mines allowed to be mined under geological conditions with a WRCC above moderate capacity is 20, 31, 51, and 112, respectively.

A Semi‐Analytical Solution for the Equivalent Permeability Coefficient of the Multilayered Porous Medium With Continuous Fracture

AbstractFractures significantly alter the permeability characteristics of the natural porous media, especially for the multilayered porous medium system. The most direct and effective approach to assess the hydraulic conductivity of a multilayered porous medium with continuous fracture is to determine its equivalent permeability coefficient (EPC). A mathematical model with second‐order accuracy is established to analysis the permeability characteristics of the multilayered porous medium incorporating a continuous fracture. The Navier‒Stokes equation is used to govern the clear fluid motion in the continuous fracture, and the seepage fluid motion in the multilayered porous matrix is governed by the Brinkman‒Darcy equation. The semi‐analytical solutions for the velocity profile and EPC of the present model are derived under the conditions of the jumping stress at the fracture‐matrix interface and the continuous velocity at the matrix(i)‐matrix(i +1) interface. The Lattice Boltzmann method, finite element method, and one domain method simulations are conducted to verify the deduced semi‐analytical solutions of the velocity profile. Furthermore, the calculated EPC of the present multilayered model is in good agreement with that of the existing classic models (i.e., one region: fracture, two regions: fracture‐matrix, three regions: fracture‐matrix1‐matrix2, and multilayered porous medium without fracture). Parameter sensitivity reveals that increasing the thickness, dip angle, and porosity of the fractured porous media increases the flow velocity, while an increase in the stress jump coefficient can result in the opposite effect. This implies that porous layers containing fracture are more susceptible to erosion, particularly under conditions of steep dip angle and strong permeability.

Simulation Analysis of the Characteristics of Layered Cores during Pulse Decay Tests

The permeability of low-permeability cores is generally measured using a pulse decay method. The core of low-permeability rocks, such as shale, often has a layered structure. The applicability of pulse decay testing for layered cores is not clear. In this study, the performance of the pulse decay method on layered cores was comprehensively investigated. Numerical simulations were conducted to investigate the influence of the interlayer permeability ratio, storativity ratio, layer thickness, interlayer location, and number of layers on the pulse decay pressure and pressure derivative curves, as well as the permeability obtained from pulse decay testing. The results revealed that the pressure curves of layered cores exhibit distinct differences from those of homogeneous cores if the upstream permeability is larger than the downstream one. The pressure derivative curve shows more inclined or horizontal straight-line segments than in the homogeneous case. The shapes of the pressure and pressure derivative curves are affected by the upstream and downstream positions of the core, but the tested permeability is not affected. The tested permeability differs from the equivalent model permeability, with an error of up to 22%. If the number of layers is not less than 10, the permeability obtained from the pulse decay test is consistent with that of the equivalent model. These differences are influenced by the interlayer permeability ratio, storativity ratio, layer thickness, interlayer location, and number of layers. To improve the accuracy of permeability analysis in pulse decay testing for layered cores, curve fitting using the characteristics of the pressure derivative curve can be employed.

High frequency modeling of dry type detuned reactor for transient studies: Simulation and experimental analyses

Dry-type detuned reactor (DDR) is a key component for power quality management. Improper design of DDR may result in insulation failure during power system transient events. This can be avoided by developing a proper DDR high frequency model that can accurately capture the behavior of the reactor during transients and provide better insight into its performance under various operating conditions. One of the main challenges of proper DDR modeling is the shape of the leakage flux, which is strongly dependent on the shielding effect of the foil conductors and hence affecting the winding frequency response at high frequencies. This paper proposes a high-frequency lumped equivalent circuit model for DDR with frequency-dependent parameters. The frequency-dependent inductances and resistances are calculated using anisotropic equivalent complex permeability to represent the damping effects in the core and winding. A combined analytical-finite element modelling approach is employed to calculate the winding capacitances. The accuracy of the proposed model is verified by comparing its frequency response with the experimental results obtained from a laboratory prototype. Furthermore, the impulse voltage distribution within the windings is obtained through simulation and measurement analyses to attest the robustness of the proposed model. The proposed model is expected to aid in the proper design and optimization of DDR to improve its insulation withstand capability and enhance its performance during transient events within power grids.