Mechanism of internal thermal runaway propagation in blade batteries

Blade batteries are extensively used in electric vehicles,but unavoidable thermal runaway is an inherent threat to their safe use.This study experimentally investigated the mechanism underlying thermal runaway propagation within a blade battery by using a nail to trigger thermal runaway and thermocouples to track its propagation inside a cell.The results showed that the internal thermal runaway could propagate for up to 272 s,which is comparable to that of a traditional battery module.The velocity of the thermal runaway propagation fluctuated between 1 and 8 mm s^(-1),depending on both the electrolyte content and high-temperature gas diffusion.In the early stages of thermal runaway,the electrolyte participated in the reaction,which intensified the thermal runaway and accelerated its propagation.As the battery temperature increased,the electrolyte evaporated,which attenuated the acceleration effect.Gas diffusion affected thermal runaway propagation through both heat transfer and mass transfer.The experimental results indicated that gas diffusion accelerated the velocity of thermal runaway propagation by 36.84%.We used a 1D mathematical model and confirmed that convective heat transfer induced by gas diffusion increased the velocity of thermal runaway propagation by 5.46%-17.06%.Finally,the temperature rate curve was analyzed,and a three-stage mechanism for internal thermal runaway propagation was proposed.In Stage I,convective heat transfer from electrolyte evaporation locally increased the temperature to 100℃.In Stage II,solid heat transfer locally increases the temperature to trigger thermal runaway.In StageⅢ,thermal runaway sharply increases the local temperature.The proposed mechanism sheds light on the internal thermal runaway propagation of blade batteries and offers valuable insights into safety considerations for future design.

Heat transfer enhanced inorganic phase change material compositing carbon nanotubes for battery thermal management and thermal runaway propagation mitigation

Developing technologies that can be applied simultaneously in battery thermal management(BTM)and thermal runaway(TR)mitigation is significant to improving the safety of lithium-ion battery systems.Inorganic phase change material(PCM)with nonflammability has the potential to achieve this dual function.This study proposed an encapsulated inorganic phase change material(EPCM)with a heat transfer enhancement for battery systems,where Na_(2)HPO_(4)·12H_(2)O was used as the core PCM encapsulated by silica and the additive of carbon nanotube(CNT)was applied to enhance the thermal conductivity.The microstructure and thermal properties of the EPCM/CNT were analyzed by a series of characterization tests.Two different incorporating methods of CNT were compared and the proper CNT adding amount was also studied.After preparation,the battery thermal management performance and TR propagation mitigation effects of EPCM/CNT were further investigated on the battery modules.The experimental results of thermal management tests showed that EPCM/CNT not only slowed down the temperature rising of the module but also improved the temperature uniformity during normal operation.The peak battery temperature decreased from 76℃to 61.2℃at 2 C discharge rate and the temperature difference was controlled below 3℃.Moreover,the results of TR propagation tests demonstrated that nonflammable EPCM/CNT with good heat absorption could work as a TR barrier,which exhibited effective mitigation on TR and TR propagation.The trigger time of three cells was successfully delayed by 129,474 and 551 s,respectively and the propagation intervals were greatly extended as well.

Robust autofocusing propagation in turbulence

Turbulence in complex environments such as the atmosphere and biological media has always been a great challenge to the application of beam propagation in optical communication, optical trapping and manipulation. To overcome this challenge, this study comprehensively investigates the robust propagation of traditional Gaussian and autofocusing beams in turbulent environments. In order to select stable beams that exhibit high intensity and high field gradient at the focal position in complex environments, Kolmogorov turbulence theory is used to simulate the propagation of beams in atmospheric turbulence based on the multi-phase screen method. We systematically analyze the intensity fluctuations, the variation of the coherence factor and the change in the scintillation index with propagation distance. The analysis reveals that the intensity fluctuations of autofocusing beams are significantly smaller than those of Gaussian beams, and the coherence of autofocusing beams is better than that of Gaussian beams under turbulence. Moreover, autofocusing beams exhibit less oscillation than Gaussian beams, indicating that autofocusing beams propagate in complex environments with less distortion and intensity fluctuation. Overall, this work clearly demonstrates that autofocusing beams exhibit higher stability in propagation compared with Gaussian beams, showing great promise for applications such as optical trapping and manipulation in complex environments.

Numerical modeling of fracture propagation of supercritical CO_(2)compound fracturing

The exploitation of shale gas is promising due to depletion of the conventional energy and intensification of the greenhouse effect.In this paper,we proposed a heat-fluid-solid coupling damage model of supercritical CO_(2)(SC-CO_(2))compound fracturing which is expected to be an efficient and environmentally friendly way to develop shale gas.The coupling model is solved by the finite element method,and the results are in good agreement with the analytical solutions and fracturing experiments.Based on this model,the fracture propagation characteristics at the two stages of compound fracturing are studied and the influence of pressurization rate,in situ stress,bedding angle,and other factors are considered.The results show that at the SC-CO_(2)fracturing stage,a lower pressurization rate is conducive to formation of the branches around main fractures,while a higher pressurization rate inhibits formation of the branches around main fractures and promotes formation of the main fractures.Both bedding and in situ stress play a dominant role in the fracture propagation.When the in situ stress ratio(sx/sy)is 1,the presence of bedding can reduce the initiation pressure and failure pressure.Nevertheless,it will cause the fracture to propagate along the bedding direction,reducing the fracture complexity.In rocks without bedding,hydraulic fracturing has the lengthening and widening effects for SC-CO_(2)induced fracture.In shale,fractures induced at the hydraulic fracturing stage are more likely to be dominated by in situ stresses and have a shorter reorientation radius.Therefore,fracture branches propagating along the maximum principal stress direction may be generated around the main fractures induced by SC-CO_(2)at the hydraulic fracturing stage.When the branches converge with the main fractures,fracture zones are easily formed,and thus the fracture complexity and damage area can be significantly increased.The results are instructive for the design and application of SC-CO_(2)compound fracturing.

Non-dimensional analysis on blast wave propagation in foam concrete:Minimum thickness to avoid stress enhancement

Foam concrete is a prospective material in defense engineering to protect structures due to its high energy absorption capability resulted from the long plateau stage.However,stress enhancement rather than stress mitigation may happen when foam concrete is used as sacrificial claddings placed in the path of an incoming blast load.To investigate this interesting phenomenon,a one-dimensional difference model for blast wave propagation in foam concrete is firstly proposed and numerically solved by improving the second-order Godunov method.The difference model and numerical algorithm are validated against experimental results including both the stress mitigation and the stress enhancement.The difference model is then used to numerically analyze the blast wave propagation and deformation of material in which the effects of blast loads,stress-strain relation and length of foam concrete are considered.In particular,the concept of minimum thickness of foam concrete to avoid stress enhancement is proposed.Finally,non-dimensional analysis on the minimum thickness is conducted and an empirical formula is proposed by curve-fitting the numerical data,which can provide a reference for the application of foam concrete in defense engineering.

Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

Modelling of debris-flow susceptibility and propagation: a case study from Northwest Himalaya

The geological and geographical position of the Northwest Himalayas makes it a vulnerable area for mass movements particularly landslides and debris flows. Mass movements have had a substantial impact on the study area which is extending along Karakorum Highway(KKH) from Besham to Chilas. Intense seismicity, deep gorges, steep terrain and extreme climatic events trigger multiple mountain hazards along the KKH, among which debris flow is recognized as the most destructive geohazard. This study aims to prepare a field-based debris flow inventory map at a regional scale along a 200 km stretch from Besham to Chilas. A total of 117 debris flows were identified in the field, and subsequently, a point-based debris-flow inventory and catchment delineation were performed through Arc GIS analysis. Regional scale debris flow susceptibility and propagation maps were prepared using Weighted Overlay Method(WOM) and Flow-R technique sequentially. Predisposing factors include slope, slope aspect, elevation, Topographic Roughness Index(TRI), Topographic Wetness Index(TWI), stream buffer, distance to faults, lithology rainfall, curvature, and collapsed material layer. The dataset was randomly divided into training data(75%) and validation data(25%). Results were validated through the Receiver Operator Characteristics(ROC) curve. Results show that Area Under the Curve(AUC) using WOM model is 79.2%. Flow-R propagation of debris flow shows that the 13.15%, 22.94%, and 63.91% areas are very high, high, and low susceptible to debris flow respectively. The propagation predicated by Flow-R validates the naturally occurring debris flow propagation as observed in the field surveys. The output of this research will provide valuable input to the decision makers for the site selection, designing of the prevention system, and for the protection of current infrastructure.

Improved Segmented Belief Propagation List Decoding for Polar Codes with Bit-Flipping

Belief propagation list(BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL(CA-SCL) decoding.In this work, an improved segmented belief propagation list decoding based on bit flipping(SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the errorcorrection performance of BPL decoding for medium and long codes. It is more than 0.25 d B better than the state-of-the-art BPL decoding at a block error rate(BLER) of 10^(-5), and outperforms CA-SCL decoding in the low signal-to-noise(SNR) region for(1024, 0.5)polar codes.

Effect of Blasting Stress Wave on Dynamic Crack Propagation

Stress waves affect the stress field at the crack tip and dominate the dynamic crack propagation.Therefore,evaluating the influence of blasting stress waves on the crack propagation behavior and the mechanical characteristics of crack propagation is of great significance for engineering blasting.In this study,ANSYS/LS-DYNA was used for blasting numerical simulation,in which the propagation characteristics of blasting stress waves and stress field distribution at the crack tip were closely observed.Moreover,ABAQUS was applied for simulating the crack propagation path and calculating dynamic stress intensity factors(DSIFs).The universal function was calculated by the fractalmethod.The results show that:the compressive wave causes the crack to close and the reflected tensile wave drives the crack to initiate and propagate,and failure mode is mainly tensile failure.The crack propagation velocity varies with time,which increases at first and then decreases,and the crack arrest occurs due to the attenuation of stress waves and dissipation of the blasting energy.In addition,crack arrest toughness is smaller than the crack initiation toughness,applied pressure waveforms(such as the peak pressure,duration,waveforms,wavelengths and loading rates)have a great influence on DSIFs.It is conducive to our deep understanding or the study of blasting stress waves dominated fracture,suggesting a broad reference for the further development of rock blasting in engineering practice.

Fatigue Crack Propagation Law of Corroded Steel Box Girders in Long Span Bridges

In order to investigate the fatigue performance of orthotropic anisotropic steel bridge decks,this study realizes the simulation of the welding process through elastic-plastic finite element theory,thermal-structural sequential coupling,and the birth-death element method.The simulated welding residual stresses are introduced into the multiscale finite element model of the bridge as the initial stress.Furthermore,the study explores the impact of residual stress on crack propagation in the fatigue-vulnerable components of the corroded steel box girder.The results indicate that fatigue cracks at the weld toe of the top deck,the weld root of the top deck,and the opening of the transverse diaphragm will not propagate under the action of a standard vehicle load.However,the inclusion of residual stress leads to the propagation of these cracks.When considering residual stress,the fatigue crack propagation paths at the weld toe of the transverse diaphragm and the U-rib weld toe align with those observed in actual bridges.In the absence of residual stress,the cracks at the toe of the transverse diaphragm with a 15%mass loss rate are categorized as type I cracks.Conversely,when residual stress is considered,these cracks become I-II composite cracks.Residual stress significantly alters the cumulative energy release rate of the three fracturemodes.Therefore,incorporating the influence of residual stress is essential when assessing the fatigue performance of corroded steel box girders in long-span bridges.

In Vitro Propagation and Artificial Seed Production of Fritillaria cirrhosa D. Don, an Endangered Medicinal Plant

Fritillaria cirrhosa D.Don(Liliaceae)is an endangered perennial bulbous plant and its dry bulb is a valuable med-icinal material with antitussive and expectorant effects.Nevertheless,lack of resources and expensive prices make it difficult to meet clinical needs.This study presents a regeneration system aimed at overcoming the challenge of inadequate supply in F.cirrhosa,focusing on:(1)callus induction,(2)bulblets and adventitious bud induction,and(3)artificial seed production.Callus development was achieved in 84.93%on Murashige and Skoog(MS)medium fortified with 1.0 mg·L^(-1) picloram.The optimal medium for callus differentiation into regenerated bulb-lets was MS medium supplemented with 1.0 mg·L^(-1)6-benzyladenine(6-BA)and 0.2 mg·L^(-1)α-naphthaleneacetic acid(NAA).Subsequently,bulblets and adventitious buds were induced from regenerated bulblet sections cul-tured on MS medium fortified with 0.3 mg·L^(-1)6-BA+1.0 mg·L^(-1)2,4-dichlorophenoxyacetic acid(2,4-D),2.0 mg·L^(-1)6-BA+0.5 mg·L^(-1),and the induction rates were 88.17%and 84.24%,respectively.The regenerated bulblets were transplanted into a substrate of humus soil,river sand,and pearlite(1:1:1)after low-temperature treatment.The germination rate was 42.80%after culture for 30 days.Regenerated bulblets were used for encap-sulations in liquid MS medium containing 3%sucrose(w/v)+0.5 mg·L^(-1) NAA+2.0 mg·L^(-1)6-BA+3%sodium alginate(w/v)with a 10 min exposure to 2%CaCl_(2).Under non-aseptic conditions,the germination rate reached 81.67%,while the rooting rate was 20.56%after 45 days.The capsule added 1.0 g·L^(-1) carbendazim and 1.0 g·L^(-1) activated carbon was the best component of artificial seeds.This study successfully established an efficient regen-eration system for the rapid propagation of F.cirrhosa,involving in vitro bulblet regeneration and artificial seed production.This method introduces a novel approach for efficient breeding and germplasm preservation,making it suitable for large-scale industrial resource production.

Cutting Propagation Technique of Pennisetum purpureum Schum

[Objectives]The paper was to study the cutting propagation technique of Pennisetum purpureum Schum and to provide a technical reference for establishing an efficient cutting propagation method.[Methods]Six treatments were set up using P.purpureum cv.Guiminyin and P.purpureum cv.Guimu-1 as test materials,including 1-node oblique insertion,1-node oblique insertion+rooting powder,1-node transverse burial,2-node oblique insertion,2-node oblique insertion+rooting powder and 2-node transverse burial.The following indices were observed and determined for P.purpureum cuttings:emergence rate,rooting rate,root number,longest root length,fresh root weight,plant height,number of tillers,number of leaves,and fresh stem and leaf weight.[Results]In the 2-node cutting+rooting powder treatment,Guiminyin and Guimu-1 exhibited the highest survival rate,root growth indices,and stem and leaf growth indices,with the emergence rates of 94.29%and 90.26%,respectively.The 2-node cutting treatment followed closely behind,while the 1-node cutting treatment had the lowest indices.Under the same treatment,Guimuyin exhibited higher mean values for plant height,number of leaves,fresh stem and leaf weight,longest root length,and fresh root weight compared to Guimu-1.However,it had lower mean number of tillers,and emergence rate and rooting rate of the 1-node cutting treatment compared to Guimu-1.[Conclusions]The P.purpureum cuttings thrived in the 2-node cutting+rooting powder treatment,and the overall cutting effect of Guiminyin was superior to that of Guimu-1.

Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.

Impact Analysis of Microscopic Defect Types on the Macroscopic Crack Propagation in Sintered Silver Nanoparticles

Sintered silver nanoparticles(AgNPs)arewidely used in high-power electronics due to their exceptional properties.However,the material reliability is significantly affected by various microscopic defects.In this work,the three primary micro-defect types at potential stress concentrations in sintered AgNPs are identified,categorized,and quantified.Molecular dynamics(MD)simulations are employed to observe the failure evolution of different microscopic defects.The dominant mechanisms responsible for this evolution are dislocation nucleation and dislocation motion.At the same time,this paper clarifies the quantitative relationship between the tensile strain amount and the failure mechanism transitions of the three defect types by defining key strain points.The impact of defect types on the failure process is also discussed.Furthermore,traction-separation curves extracted from microscopic defect evolutions serve as a bridge to connect the macro-scale model.The validity of the crack propagation model is confirmed through tensile tests.Finally,we thoroughly analyze how micro-defect types influence macro-crack propagation and attempt to find supporting evidence from the MD model.Our findings provide a multi-perspective reference for the reliability analysis of sintered AgNPs.

Fracture propagation law of temporary plugging and diversion fracturing in shale reservoirs under completion experiments of horizontal well with multi-cluster sand jetting perforation

This study conducted temporary plugging and diversion fracturing(TPDF)experiments using a true triaxial fracturing simulation system within a laboratory setting that replicated a lab-based horizontal well completion with multi-cluster sand jetting perforation.The effects of temporary plugging agent(TPA)particle size,TPA concentration,single-cluster perforation number and cluster number on plugging pressure,multi-fracture diversion pattern and distribution of TPAs were investigated.A combination of TPAs with small particle sizes within the fracture and large particle sizes within the segment is conducive to increasing the plugging pressure and promoting the diversion of multi-fractures.The addition of fibers can quickly achieve ultra-high pressure,but it may lead to longitudinal fractures extending along the wellbore.The temporary plugging peak pressure increases with an increase in the concentration of the TPA,reaching a peak at a certain concentration,and further increases do not significantly improve the temporary plugging peak pressure.The breaking pressure and temporary plugging peak pressure show a decreasing trend with an increase in single-cluster perforation number.A lower number of single-cluster perforations is beneficial for increasing the breaking pressure and temporary plugging peak pressure,and it has a more significant control on the propagation of multi-cluster fractures.A lower number of clusters is not conducive to increasing the total number and complexity of artificial fractures,while a higher number of clusters makes it difficult to achieve effective plugging.The TPAs within the fracture is mainly concentrated in the complex fracture areas,especially at the intersections of fractures.Meanwhile,the TPAs within the segment are primarily distributed near the perforation cluster apertures which initiated complex fractures.

Development of a Post Quantum Encryption Key Generation Algorithm Using Electromagnetic Wave Propagation Theory

In today’s rapid widespread of digital technologies into all live aspects to enhance efficiency and productivity on the one hand and on the other hand ensure customer engagement, personal data counterfeiting has become a major concern for businesses and end-users. One solution to ensure data security is encryption, where keys are central. There is therefore a need to find robusts key generation implementation that is effective, inexpensive and non-invasive for protecting and preventing data counterfeiting. In this paper, we use the theory of electromagnetic wave propagation to generate encryption keys.

基于不同算法优化的back propagation神经网络在三元乙丙橡胶混炼胶门尼黏度预测中的应用

分别采用遗传算法(GA)和粒子群算法(PSO)优化的back propagation(BP)神经网络建立了三元乙丙橡胶(EPDM)混炼胶门尼黏度的预测模型,并对预测结果的误差进行了对比分析。结果表明,两种算法优化后的BP神经网络模型的预测值与实测值均保持较高的拟合度和相关性;相比单一的BP神经网络,GA优化后BP神经网络模型的精度提高了58.9%,PSO优化后BP神经网络模型的精度提高了3.57%,说明两种算法优化后的预测模型,特别是GA优化的BP神经网络预测模型对EPDM混炼胶门尼黏度的预测精度改善明显。

Comparison on crack propagation under tension at 150℃ of Mg-2Zn-1.5Mn alloy sheets with and without crack notch

Generally,edge crack of rolled magnesium alloy sheets initiates in the RD(rolling direction)-ND(normal direction)plane and then propagate in the RD-TD(transverse direction)plane.Hence,the Mg-2Zn-1.5Mn(ZM21)alloy sheets with and without crack notch were designed to carry out in-situ tensile experiments under 150℃(the same temperature of rolling),with the aim to understand their crack propagation mechanism.The scanning electron microscopy(SEM)and electron backscattered diffraction(EBSD)techniques were utilized to reveal microstructural evolution in real time at designated displacements.The results show that the prismatic slip,basal slip,and extension twining play synergistic role in coordinating strain during the tensile process in ZM21 alloy sheet at 150℃.In both tensile samples with and without crack notch,localized strain is mainly concentrated at relatively fine grain area and the grain boundaries or triple junctions of the grains with large basal Schmid factor(SF)difference,which eventually leads to severe surface roughening and subsequent crack initiation.Compared with the sample without crack notch,the pre-cracked sample exhibits severer deformation at the crack tip due to strain concentration.Strain gradient distribution is observed at the crack tip region in the pre-cracked sample.The crack propagation path of the sample with pre-crack is identified and the underlying mechanism is also discussed.

Fatigue crack propagation of 7050 aluminum alloy FSW joints after surface peening

The surface composite modification of the 7050 aluminum alloy friction stir-welded joints was performed by shot peening(SP)/multiple rotation rolling(MRR)and MRR/SP,and the fatigue performance of the nugget zone(NZ)was investigated.The results demonstrated that the fatigue life of SP/MRR samples is longer than that of MRR/SP.On the plane 150μm below the surface.The grains with high angle grain boundary account for 71.5%and 34.3%for MRR/SP and SP/MRR samples,respectively.The crack propagation path of the MRR/SP is transgranular and intergranular,and it is intergranular for the MRR/SP.Multitudinous fatigue striations and some voids appeared at the fracture during the stable crack propagation stage.However,fatigue striations for SP/MRR are with smaller spacing,fewer holes,and smaller size under SP/MRR compared with fatigue fracture of MRR/SP.The differences in fatigue properties and fracture characteristics of the NZ are related to the microstructure after the two combined surface modifications.

Analysis of fracture propagation and shale gas production by intensive volume fracturing

This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing.The fracture propagation model takes into account the interaction between hydraulic fracture and natural fracture by means of the displacement discontinuity method(DDM)and the Picard iterative method.The shale gas flow considers multiple transport mechanisms,and the flow in the fracture network is handled by the embedded discrete fracture model(EDFM).A series of numerical simulations are conducted to analyze the effects of the cluster number,stage spacing,stress difference coefficient,and natural fracture distribution on the stimulated fracture area,fractal dimension,and cumulative gas production,and their correlation coefficients are obtained.The results show that the most influential factors to the stimulated fracture area are the stress difference ratio,stage spacing,and natural fracture density,while those to the cumulative gas production are the stress difference ratio,natural fracture density,and cluster number.This indicates that the stress condition dominates the gas production,and employing intensive volume fracturing(by properly increasing the cluster number)is beneficial for improving the final cumulative gas production.