Model Calculations Research Articles

SELECTION OF A MRP SYSTEM FOR OIL AND GAS DEPOSITS

A number of serious problems arise in the development of sub-gas zones of oil and gas deposits due to the joint occurrence of oil and gas. The key problem is gas breakthrough from the gas cap to oil wells. This entails an increase in the gas factor (GOR), a rapid and intense decrease in pressure in the gas cap. If there is a reservoir pressure maintenance system or an active aquifer as a result of a decrease in reservoir pressure in the gas cap, oil may be pushed back into it, which leads to a rise in gas-oil contact, jamming of mobile oil in the «dry sandstones» of the gas cap, which in turn leads to a decrease in reserves of mobile oil and a decrease in the oil recovery factor (ORF). All this together allows us to consider oil in the sub-gas zones as hard-to-recover reserves.Preventing and combating the negative consequences of gas breakthrough from the gas cap to oil wells is a complex task and consists of several areas, such as selection of rational drilling of production and injection wells, selection of optimal operating modes for them, use of inflow control devices or performance of repair and isolation work to limit inflow from intervals with gas breakthrough, periodic shutdown of wells to disband gas cones. The ultimate goal of solving these problems is to increase the oil recovery factor and economic efficiency indicators for the development of sub-gas zones.Due to the variety of ways to optimize the development of oil and gas reservoirs, it is not possible to cover them all in one work, therefore, the tasks associated with optimizing the reservoir pressure maintenance system are considered. It is worth noting that in comparison with the development of oil reservoirs, the presence of a gas cap significantly complicates this task due to the lack of analytical solutions for three-phase filtration. For this reason, the selection of the optimal parameters of the reservoir pressure maintenance system is usually carried out either by multivariate calculations in the hydrodynamic model (HDM), or by the method of analogies or the implementation of pilot tests of various approaches.In this study, an approach based on multivariate numerical calculations using the sector model of the development element of the gas zone was used. As a result of calculations, it was shown that when choosing the optimal parameters of the reservoir pressure maintenance system, it is advisable to use a differentiated approach, which consists in the fact that these parameters must be set individually for zones with different ratios of oil-saturated and gas-saturated thicknesses.

Ab initio study of Z(N) = 6 magicity

Abstract The existence of magic numbers of protons and neutrons in nuclei is essential for understanding nuclear structure and fundamental nuclear forces. Over decades, researchers have conducted theoretical and experimental studies on the new magic number { $Z(N) = 6$}, focusing on observables such as radii, binding energy, electromagnetic transition, and nucleon separation energies. We perform the {\it ab initio} no-core shell model calculations for the occupation numbers of {the lowest} single particle states in {the ground states of} {$Z(N)=6$ and $Z(N)=8$ isotopes (isotones)}. Our calculations do not support {$Z(N)=6$} as a magic number over a span of atomic numbers. However, $^{14}$C and $^{14}$O exhibit the characteristics of double-magic nuclei.

The Application of the Particle Element Method in Tubular Propellant Charge Structure: Lumped Element Method and Multiple-Element Method

Due to the orderly arrangement of tubular propellant, the permeability of combustion gases is improved, which is beneficial for enhancing the safety of the combustion system. However, current internal ballistic gas-solid flow calculation methods adopt a quasi-fluid assumption, which cannot accurately account for the characteristics of long tube shapes. Additionally, tubular propellants exhibit both overall movement and parameter distribution characteristics, necessitating the decoupling of gas and solid phases. These two deficiencies in previous studies have limited the effectiveness of gas-solid flow simulations for tubular propellant. This paper proposes a numerical calculation model suitable for tubular propellant charging based on the particle element method for internal ballistic two-phase flow. Firstly, considering the overall movement characteristics of tubular propellants, the concept of blank particle elements is introduced to represent pure gas phase regions. Then, based on computational requirements, the tubular propellants are divided to form the lumped element method and the multiple-element method. The moving boundary method is used to calculate the movement process of the propellant bed particle group and is compared with experimental results to verify the applicability of the two methods in tubular propellant beds. Analysis results show that the particle element method can effectively capture changes in the flow field inside the chamber and the position of tubular propellants. The lumped element method can quickly obtain the flow field distribution characteristics inside the chamber, while the multiple-element method can capture parameter distribution characteristics at different positions of the tubular propellants while ensuring overall movement.

Ebullition drives high methane emissions from a eutrophic coastal basin

The production of methane in coastal sediments and its release to the water column is intensified by anthropogenic eutrophication and bottom water hypoxia, and it is still uncertain whether methane emissions to the atmosphere will be enhanced. Here, we assess seasonal variations in methane dynamics in a eutrophic, seasonally euxinic coastal basin (Scharendijke, Lake Grevelingen). In-situ benthic chamber incubations reveal high rates of methane release from the sediment to the water column (74 – 163 mmol m−2 d−1) during monthly measurements between March and October 2021. Comparison of these in-situ total benthic methane fluxes and calculated diffusive fluxes point towards a major role for ebullition. In spring and fall, when the water column was oxic, microbial removal of dissolved methane occurred aerobically in the bottom water. In summer, in contrast, dissolved methane accumulated to concentrations of up to 67 μmol L−1 below the oxycline. Shifts in δ13C–CH4 and δD-CH4 towards higher values and the abundant presence of methane oxidizing bacteria point towards removal of methane around the oxycline, likely through both aerobic and anaerobic pathways, with the latter possibly linked to iron oxide reduction. Shifts in δ13C–CH4 and δD-CH4 to lower values above the oxycline indicate that bubble dissolution contributed to dissolved methane. Methane emissions to the atmosphere were observed in all seasons with the highest, in-situ measured diffusive fluxes (1.2 mmol m−2 d−1) upon the onset of water column mixing at the end of summer. Methane release events during the measurement of in-situ water-air fluxes and model calculations point towards a flux of methane to the atmosphere in the form of bubbles, which bypass the microbial methane filter. The model calculations suggest a potential year-round ebullitive methane flux between 30 and 120 mmol m−2 d−1. We conclude that methane emissions from eutrophic coastal systems may be much higher than previously thought because of ebullition.

Lubrication Characteristics of Dry-Gas Seals with Spiral Grooves

To obtain an optimal range of structural parameters for dry-gas seals with good performance, this study employed advanced sensing technology to monitor and analyze the internal flow characteristics of dry-gas seals in real time. Additionally, the validity of the calculation program was verified through experimentation. Using steady-state performance parameters as evaluation indices, a calculation model with lubrication characteristics was developed. The results indicate that when there are 12 grooves, the gas film pressure distribution is uniform and has a high value. At pressures greater than 2 MPa, the opening force, leakage, and gas film stiffness change significantly due to enhanced dynamic pressure effects with high-pressure differences, which reduces the local contact forces and frictional forces. At a constant speed, decreasing the gas film thickness increases the pressure difference while increasing both the opening force and film stiffness; however, at higher rotational speeds where the gas flow becomes non-uniform, the stability of the gas film is affected, leading to increased frictional forces. When there are between 10 and 16 grooves with depths ranging from 5.0 to 6.0 μm, dynamic pressure effects caused by pressure gradients become apparent, resulting in good dry-gas sealing performance being achieved. This research provides a theoretical reference for optimizing the design of dry-gas seals, as well as their steady-state seal performance.

Dynamic response mechanisms of thin UHMWPE under high-speed impact

This study systematically explores the dynamic response mechanisms and energy dissipation mechanisms of ultra-high-molecular-weight polyethylene (UHMWPE) fiber laminated plates with thicknesses of 1.1 mm, 2.8 mm, and 5.4 mm under high-speed steel ball impacts through experimental, theoretical analysis, and dimensional analysis. By analyzing the damage mechanisms from experimental results, the main modes of energy absorption were identified, and a relatively accurate predictive model for ballistic limit speed was established. The results show that under high-speed steel ball impacts, the primary failure modes of UHMWPE fiber laminated plates are localized permanent bulging plastic deformation and perforation failure caused by compressive shear. The ballistic limit speeds for UHMWPE with thicknesses of 1.1 mm, 2.8 mm, and 5.4 mm are respectively 233.5 m/s, 415.7 m/s, and 602.9 m/s. The theoretical calculations of the energy model align well with the experimental results, indicating that as the speed increases, the proportion of tensile energy absorption gradually decreases, consistent with the observed phenomena. Near the ballistic limit, there are significant turning points in the level of energy absorption and the height of the rear bulge. The ballistic limit increases linearly with target thickness, and the unit area density energy absorption also increases continuously. Finally, this study established a dimensionless ballistic limit model considering the mechanical properties of fibers and the matrix, which through regression analysis, can accurately describe the ballistic limits of various strengths and types of fiber laminated plates, suitable for predicting the ballistic performance of various composite materials.

A Deep Learning Framework for IoT Lightweight TrafficMulti-classification: Smart-cities

Aim and Background: Increased traffic volume is a major challenge for effective network management in the wake of the proliferation of mobile computing and the Internet of Things (IoT). Earlier models surrender efficiency to achieve high-precision classification outcomes, which are no longer fitting for limited assets in edge network circumstances, making traffic classification a difficult task for network administrators everywhere. Given the nature of the problem, the current state of the art in traffic classification is characterized by extremely high computational complexity and large parameters. Methodology: To strike a clever balance between performance and size, we present a deep learning (DL)-based traffic classification model. We begin by decreasing the amount of model parameters and calculations by modifying the model's scale, width, and resolution. To further improve the capability of feature extraction at the traffic flow level, we secondly incorporate accurate geographical information on the attention mechanism. Thirdly, we get multiscale flow-level features by employing lightweight multiscale feature fusion. Results: The results of our experiments demonstrate that our model has high classification accuracy and efficient operation. Our study presents a traffic categorization model with an accuracy of over 99.82%, a parameter reduction of 0.26M, and a computation reduction of 5.26M. Conclusions: Therefore, this work offers a practical design used in a genuine IoT situation, where IoT traffic and tools' profiles are anticipated and classified while easing the data dispensation in the higher levels of an end-to-end communication strategy.

Determination of Chip Compression Ratio for the Orthogonal Cutting Process

The chip compression ratio is the most important characteristic of various machining processes with chip generation. This characteristic enables the determination of kinetic and other energy loads on the tool and the machined material. This provides an overall evaluation of the machining process and the possibility of its subsequent optimization. This paper presents the results of determining this cutting characteristic by experimental method, analytical calculation, and numerical modeling. For the analytical calculation of the chip compression ratio, an analytical cutting model developed based on the variational principle of the minimum potential energy was used. A finite element model of orthogonal cutting was used for the numerical simulation of the above process characteristic. Experimentally, the chip compression ratio was determined by the ratio of the chip thickness to the cutting depth (undeformed cutting thickness). The chip thickness was determined by direct measurement using chip slices obtained during the cutting process. The Johnson–Cook constitutive equation was used as the machined material model and the Coulomb model was used as the friction model. The generalized parameters’ determination of the constitutive equation was performed through a DOE (Design of Experiment) sensitivity analysis. The variation range of these parameters was chosen based on the analysis of the effect of individual parameters of the constitutive equation on the chip compression ratio value. The largest deviations between the experimental and analytically calculated values of the chip compression ratio did not exceed 21%. At the same time, the largest deviations of simulated values of the indicated cutting characteristic and its experimental values did not exceed 20%. When comparing the experimental values of the chip compression ratio with the corresponding calculated and simulated values, the deviations were within 22%.

Seepage-Heat Accumulation Characteristics and Hydrothermal Transport Calculation Model in Mining-Induced Fractured Rock Mass: Implications for Geothermal Water Control

Seepage-Heat Accumulation Characteristics and Hydrothermal Transport Calculation Model in Mining-Induced Fractured Rock Mass: Implications for Geothermal Water Control

Investigation on the multi-scale interactions in gas–liquid jet bubbling reactor

Due to the unreliability of the mechanical seal of the mechanical stirring reactor in traditional carbonyl synthesis reactions, a gas–liquid jet bubbling reactor has been developed that is a new type of hydraulic stirring. A cold model device was constructed to address the complex flow field characteristics of a gas–liquid jet bubbling reactor, and a gas–liquid phase testing method was established to obtain the gas–liquid phase flow parameters in the cold model device. A mathematical model of a cold model device was established based on computational fluid dynamics. The reliability and accuracy of the calculation model were verified by combining experimental data of the cold model device, and the gas–liquid two-phase flow characteristics of an industrial grade reactor were obtained. The multiscale characteristics of gas–liquid two-phase signals in industrial reactors and the multiscale gas–liquid two-phase interactions were analyzed by combining wavelet analysis, power spectrum analysis, and fractal analysis. Based on the multiscale gas–liquid interaction mechanism model of gas–liquid interaction, the liquid phase interaction in d1-d6 inside the reactor was increased. The gas–liquid mass transfer process was enhanced, and the liquid level fluctuation and temperature difference of industrial grade reactors were significantly reduced.

Accurate Measurement of Tower Grounding Resistance for Single-Tower and Multi-Tower Parallel Scenarios Based on the Clamp Meter Method: For the Sustainable Operation of Towers

Transmission tower grounding safety is a critical element that significantly impacts the reliability and sustainability of power grids. Tower grounding resistance is a significant grounding characteristic parameter. In order to accurately measure the grounding resistance of towers using the clamp meter method in both single-tower and multi-tower parallel scenarios, this paper establishes theoretical calculation models for measuring tower grounding resistance using the clamp meter method. Considering the interaction between the artificial grounding device and the tower foundation, this paper models and simulates transmission towers and lightning shield wires, analyzing the influencing factors on the grounding resistance measurement results using the clamp meter method in both single- and multi-tower parallel scenarios. The results show that for single towers, the clamp meter measurement results increase with decreasing foundation root spacing and increasing length of the artificial device’s extension lines, but the changes are relatively small. In multi-tower grounding scenarios, due to the shunting effect of the parallel branches formed by the towers and lightning shield wires, the value is smaller than in single-tower grounding scenarios. Changing the number of parallel towers and the type of lightning shield wire produces little effect on the measurement results. However, changes in soil resistivity have the most significant impact. Therefore, correction formulas for the impact of soil resistivity on clamp meter measurements are proposed and then verified by applying them to field tests.

Vertical Track–Bridge Interaction in Railway Bridges with Ballast Superstructure: Experimental Analysis of Dynamic Stiffness and Damping Behavior

Realistic vibration predictions of railway bridges during high-speed train crossings require reliable dynamic input parameters for the applied calculation model. In particular, the dynamic stiffness and damping properties of the ballast superstructure for the mathematical consideration of the vertical track–bridge interaction (TBI) significantly influence the generated calculation results. However, due to a striking scattering of model-related characteristic values available in the literature, adequate and realistic consideration of the dynamic properties of the vertical TBI in vibration predictions is associated with considerable uncertainties. This uncertainness illustrates the need to determine experimental-based and reliable characteristic values. For targeted and isolated research of dynamic characteristics of vertical TBI, a unique large-scale test facility was developed at the Institute of Structural Engineering at TU Wien, which replicates a section of ballast superstructure on a railway bridge on a scale of 1:1 and excited to vertical movements. This paper presents the essential results and findings from the experiments, focusing on determining the ballast superstructure’s dynamic stiffness and damping characteristics, which can subsequently be implemented in practical applications for vibration predictions. As a result of the experiments, model-related dynamic stiffness and damping parameters are provided to describe the vertical TBI. In addition, the experiments are used to identify destabilization processes occurring in the ballast superstructure as a result of vertical vibrations. The investigations include the vertical TBI’s displacement and acceleration behavior and the track’s settlement behavior due to the entire structure’s vertical movements. These investigations allow for assessing the currently valid, internationally, and nationally normatively prescribed permissible accelerations for railway bridges due to train crossings. The conclusion is that short-term excessive vertical accelerations of the ballast superstructure caused by train passage do not destabilize the ballast bed or considerably change the track position.

Multifractal Characteristics of Low-Field Nuclear Magnetic Resonance of Different Rank Coals and Its Permeability Predicting Method.

The permeability of methane in coal is a crucial factor in the production of coal-bed methane (CBM), which is dependent on the pore size distribution (PSD) of coal. The transverse relaxation time cutoff value (T2C) is a crucial parameter in nuclear magnetic resonance (NMR) techniques for converting NMR data into an absolute PSD. To investigate an appropriate approach for predicting the T2C and permeability of different rank coals, this study first revealed, through centrifuge experiments with a centrifugal force of 1.38 MPa, the T2C values of five coal samples: anthracite coal (3 ms), lean coal (8 ms), coking coal (12 ms), fat coal (11 ms), and lignite coal (13 ms). These T2C values were then employed to obtain the absolute PSD values of the coal samples. The results demonstrated that the pore structure characteristics of these coal samples are essentially identical, with micropores constituting the majority, varying between 63.47% and 93.74%. Subsequently, the multifractal analysis method was introduced to establish a new T2C value calculation model. A comparison of the model-calculated T2C values with those obtained from centrifugal experiments revealed an average deviation of only 5.26%. Finally, a new permeability model was developed by conducting multiple regressions on permeability and multifractal parameters. In comparison to classical models, such as the Timur-Coates (TC) model and the Schlumberger Dauer Research Center (SDR) model, the developed permeability model offers more accurate predictions. These results are applicable to pore structure characterization and methane permeability prediction in coal reservoirs of varying rank and other unconventional gas reservoirs.

Implementation of monitoring and certification with the developed China heavy-duty vehicle energy consumption and carbon emission calculation model

Owing to escalating concerns regarding global warming, there has been a heightened focus on greenhouse gases emitted by vehicles. To effectively monitor and certify the fuel consumption and CO2 emissions of heavy-duty vehicles, this study proposes a calculation model named the China Heavy-Duty Vehicle Energy Consumption and Carbon Emission Calculation Model (CHECM). The CHECM is a simulation tool based on longitudinal dynamics. A classification learner was utilised to obtain shifting strategies, achieving accuracies of 92.9% and 93.5% under regulated driving cycles. A fuel-consumption model was incorporated to predict the transient performance of the engine and transmission. In addition, the Sobol method was used to assess the sensitivities of rolling resistance, air drag and rotational mass conversion coefficients to the driving force and a method was proposed to obtain the road resistance correction factor. The test results of three China-6 heavy-duty vehicles over two regulatory test cycles were obtained and used for model accuracy evaluation. The results showed that the deviations between the measured and calculated fuel consumption were 1.25–3.57%, whereas those between the measured and calculated CO2 emissions using the Chinese World Transient Vehicle Cycle were 3.23–4.16%. The CHECM has the potential to accurately replicate various driving conditions and vehicle configurations, particularly when specific sources of uncertainty are constrained.

An efficient and lightweight banana detection and localization system based on deep CNNs for agricultural robots

Accurate detection and localization of fruits in natural environments is a key step for fruit picking robots to achieve precise harvesting. However, existing banana detection and positioning methods have two main limitations in practical applications: a large number of model parameters that make deployment difficult, and a need for performance improvement. To tackle the above issues, a high-precision and lightweight banana bunch recognition and localization method was proposed and deployed on edge devices for application. First, a Slim-Banana model was proposed based on the improvement of YOLOv8l. In order to reduce the model calculation amount and maintain high performance, GSConv was introduced in the Slim-Banana model to replace the standard convolution, and combined with grouped convolution and spatial convolution. At the same time, the cross-stage local network (GSCSP) module was designed to reduce the computational complexity and the complexity of the network structure through a single-stage aggregation method. Then, the RealSense depth sensor is combined with TOF technology to perform image registration and 3D localization of the banana. Finally, the pipeline is deployed on the Nvidia Orin NX edge device and its performance and resource consumption in actual work are deeply analyzed. Experimental results show that the detection precision, recall, mAP and inference time of our method are 0.947, 0.948, 0.98 and 113.6ms respectively, the network memory size required is 4449MiB, and the average localization errors in the X-axis, Y-axis and Z-axis directions are 13.47mm, 12.87mm and 13.87mm respectively. To our knowledge, this is the first work that implements banana detection and localization on edge devices. Experimental results show that compared with existing methods, our method achieves better performance in complex orchard environments, achieving efficient and lightweight banana recognition and localization.

Extraction of transhelicity worm-gear distributions and opportunities at the Electron-Ion Collider in China

We present a global analysis of the transhelicity worm-gear distribution function, g1T⊥, by fitting the longitudinal-transverse double-spin asymmetry data of the semi-inclusive deep inelastic scattering. The analysis is performed within the framework of transverse momentum dependent factorization and evolution. It is found that the u-quark favors a positive distribution and the d-quark favors a negative distribution, which is consistent with previous model calculations and phenomenological extractions. Based on the fit to existing world data, we also study the impact of the proposed Electron-Ion Collider in China and conclude that it can significantly improve the precision of the worm-gear distribution function and hence enhance our understanding of nucleon spin structures. Published by the American Physical Society 2024

Longitudinal Wave Defect Detection Technology Based on Ablation Mechanism

For laser ultrasound in the thermoelastic mechanism, excitation of ultrasonic body wave signal is weak, it is not easy to realize the detection of deep defects inside the workpiece. While the ablation mechanism produces a high and practical ultrasonic signal-to-noise ratio, this paper is based on the generation mechanism of laser ablation excitation of ultrasonic waves, the establishment of laser ultrasound in the ablation mechanism in the aluminum plate excitation and propagation of ultrasonic numerical model, through the solution, obtained the ultrasonic acoustic field map, discussed the ablation mechanism of the laser ultrasonic body wave acoustic field directionality. Additionally, the preliminary verification of the validity of the model is presented. Then, in order to explore the application potential of high signal-to-noise ratio longitudinal waves in defect detection, defects of different depths are preset in the model for simulation calculations, and waveform and acoustic field analyses are performed on the simulation results to study the ultrasonic propagation paths inside the member and the interaction with the defects, and the transverse position and depth of the internal defects are judged by using B-scan imaging. Finally, experimental validation is carried out. The experimental results are highly consistent with the simulation model, and the defect experiments can qualitatively determine the location of internal defects and verify the practicality and accuracy of the model.

Acetylene Semihydrogenation over Pd-Bi Intermetallic Compounds: A DFT Combined with Microkinetic Modeling Study.

Acetylene semihydrogenation is an important process both theoretically and experimentally. Pure Pd catalysts usually suffer from limited selectivity for ethylene products and poor stability. Pd-Bi bimetallic compounds are synthesized and show not only excellent catalytic performance but also remarkable long-term stability. However, the detailed mechanism is still unclear. In this paper, the acetylene semihydrogenation mechanism on Pd(100), Pd3Bi1(100), and Pd1Bi1(100) is studied by density functional theory (DFT) calculation and microkinetic modeling. Adding Bi causes the surface d-band center (εd) to move to a lower energy, and the adsorption strength of the intermediate becomes weaker. Besides, ethylidyne (CCH3) formation becomes more difficult on the Pd-Bi alloy due to the lack of continuous surface Pd atoms. As a spectator, CCH3 deactivates the Pd and Pd-Bi alloys by a steric effect. However, the selectivity for ethylene on the Pd-Bi alloy is still high because of the weakly bonded ethylene. We found the relationship between εd and the catalysts' activity and selectivity. This study may supply some clues for the design of selective hydrogenation catalysts.

Reproduction of single-to-double hysteresis transition of nuclear spin polarization in a single InAlAs quantum dot

We have observed a transition from single to double hysteresis of nuclear spin polarization (NSP) with increasing magnetic field in a single InAlAs self-assembled quantum dot, which means the birth of a third stable branch that depends on the field strength. This NSP transition behavior could not be reproduced by standard model calculations using a fixed electron–nuclear spin correlation time τc under different external field conditions. By introducing the field dependence of τc, we were able to successfully reproduce the observed NSP transition. This finding on the phenomenological description of the magnetic field dependence will be a future highlight of τc.

Model modification and influence of edge effect on effective area of giant electro-rheological polishing using plate electrodes

Abstract Giant electro-rheological polishing (GPRP) is recognized as an innovative ultra-precision machining technology with significant potential. However, the pronounced edge effect within the GPRP's polishing gap can introduce errors in calculating the effective area and designing the electrode structure. This, in turn, may lead to under-polishing and an increased risk of insulation breakdown. In this study, COMSOL was employed to investigate the electric field distribution characteristics within the polishing gap. This exploration aimed to refine the calculation model of the effective area, optimize the plate electrodes' structure and size, and diminish the likelihood of insulation breakdown. Through systematic finite element simulations, the impact of polishing voltage, inter-electrode gap, and plate length on the edge effect was thoroughly analyzed to ascertain its influence range. The simulation findings revealed that, while maintaining a constant inter-electrode gap for the tool electrode, variations in the polishing gap, polishing voltage, and plate length within specific ranges resulted in an edge effect influence range of approximately 1 mm. Moreover, when the machining gap, polishing voltage, and plate length remained unchanged, the edge effect influence range increased proportionally with the electrode gap within a specific range, approximately equivalent to the size of the electrode gap. Experimental validation of the giant electro-rheological effect confirmed the existence and influence range of the edge effect, aligning with the finite element simulation results. Ultimately, modifications to the calculation model of the effective area were proposed, along with a solution to optimize the electrode size and structure, with the objective of reducing the probability of insulation breakdown. In practical applications, this work can provide a valuable reference for electrode structure design, insulation breakdown improvement and parameter selection.