Well-developed pores and cracks in coal reservoirs are the main venues for gas storage and migration.To investigate the multi-scale pore fractal characteristics,six coal samples of different rankings were studied usin...Well-developed pores and cracks in coal reservoirs are the main venues for gas storage and migration.To investigate the multi-scale pore fractal characteristics,six coal samples of different rankings were studied using high-pressure mercury injection(HPMI),low-pressure nitrogen adsorption(LPGA-N2),and scanning electron microscopy(SEM)test methods.Based on the Frankel,Halsey and Hill(FHH)fractal theory,the Menger sponge model,Pores and Cracks Analysis System(PCAS),pore volume complexity(D_(v)),coal surface irregularity(Ds)and pore distribution heterogeneity(D_(p))were studied and evaluated,respectively.The effect of three fractal dimensions on the gas adsorption ability was also analyzed with high-pressure isothermal gas adsorption experiments.Results show that pore structures within these coal samples have obvious fractal characteristics.A noticeable segmentation effect appears in the Dv1and Dv2fitting process,with the boundary size ranging from 36.00 to 182.95 nm,which helps differentiate diffusion pores and seepage fractures.The D values show an asymmetric U-shaped trend as the coal metamorphism increases,demonstrating that coalification greatly affects the pore fractal dimensions.The three fractal dimensions can characterize the difference in coal microstructure and reflect their influence on gas adsorption ability.Langmuir volume(V_(L))has an evident and positive correlation with Dsvalues,whereas Langmuir pressure(P_(L))is mainly affected by the combined action of Dvand Dp.This study will provide valuable knowledge for the appraisal of coal seam gas reservoirs of differently ranked coals.展开更多
Chemical solvents instead of pure water being as hydraulic fracturing fluid could effectively increase permeability and improve clean methane extraction efficiency.However,pore-fracture variation features of lean coal...Chemical solvents instead of pure water being as hydraulic fracturing fluid could effectively increase permeability and improve clean methane extraction efficiency.However,pore-fracture variation features of lean coal synergistically affected by solvents have not been fully understood.Ultrasonic testing,nuclear magnetic resonance analysis,liquid phase mass spectrometry was adopted to comprehensively analyze pore-fracture change characteristics of lean coal treated by combined solvent(NMP and CS_(2)).Meanwhile,quantitative characterization of above changing properties was conducted using geometric fractal theory.Relationship model between permeability,fractal dimension and porosity were established.Results indicate that the end face fractures of coal are well developed after CS2and combined solvent treatments,of which,end face box-counting fractal dimensions range from 1.1227 to 1.4767.Maximum decreases in ultrasonic longitudinal wave velocity of coal affected by NMP,CS_(2)and combined solvent are 2.700%,20.521%,22.454%,respectively.Solvent treatments could lead to increasing amount of both mesopores and macropores.Decrease ratio of fractal dimension Dsis 0.259%–2.159%,while permeability increases ratio of NMR ranges from 0.1904 to 6.4486.Meanwhile,combined solvent could dissolve coal polar and non-polar small molecules and expand flow space.Results could provide reference for solvent selection and parameter optimization of permeability-enhancement technology.展开更多
Accurate and quantitative investigation of the physical structure and fractal geometry of coal has important theoretical and practical signifcance for coal bed methane(CBM)development and the prevention of dynamic dis...Accurate and quantitative investigation of the physical structure and fractal geometry of coal has important theoretical and practical signifcance for coal bed methane(CBM)development and the prevention of dynamic disasters such as coal and gas outbursts.This study investigates the pore structure and fractal characteristics of soft and hard coals using nitrogen and carbon dioxide(N_(2)/CO_(2))adsorption.Coal samples from Pingdingshan Mine in Henan province of China were collected and pulverized to the required size(0.20–0.25 mm).N_(2)/CO_(2)adsorption tests were performed to evaluate the specifc surface area(SSA),pore size distribution(PSD),and pore volume(PV)using Braunuer-Emmett-Teller(BET),Barrett-Joyner-Halenda(BJH),and Density Functional Theory(DFT).The pore structure was characterized based on the theory of fractal dimensions.The results unveiled that the strength of coal has a signifcant infuence on pore structure and fractal dimensions.There are signifcant diferences in SSA and PV between both coals.The BJH-PV and BET-SSA obtained by N_(2)-adsorption for soft coal are 0.029–0.032 cm^(3)/g and 3.523–4.783 m^(2)/g.While the values of PV and SSA obtained by CO_(2)-adsorption are 0.037–0.039 cm^(3)/g and 106.016–111.870 m^(2)/g.Soft coal shows greater SSA and PV than hard coal,which is consistent with the adsorption capacity(VL).The fractal dimensions of soft and hard coal are respectively diferent.The Ding coal exhibits larger D1 and smaller D_(2),and the reverse for the Wu coal seam is observed.The greater the value of D1(complexity of pore surface)of soft coal is,the larger the pore surface roughness and gas adsorption capacity is.The results enable us to conclude that the characterization of pores and fractal dimensions of soft and hard coals is diferent,tending to diferent adsorption/desorption characteristics.In this regard,the results provide a reference for formulating corresponding coal and gas outburst prevention and control measures.展开更多
A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. T...A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing.展开更多
Fractal characteristics are introduced into solving lubrication problems. Based on the analysis of the relationship between roughness and engineering surfaces' fractal characteristics and by introducing fractal pa...Fractal characteristics are introduced into solving lubrication problems. Based on the analysis of the relationship between roughness and engineering surfaces' fractal characteristics and by introducing fractal parameters into the mixed lubrication equation, the relationship between flow factors and fractal dimensions is analyzed. The results show that the pressure flow factors' values increase, while the shear flow factor decreases, with the increasing length to width ratio of a representative asperity γ at the same fractal dimension. It can be also found that these factors experience more irregular and significant variations and show the higher resolution and the local optimal and the worst fractal dimensions, by a fractal dimension D , compared with the oil film thickness to roughness ratio h/R q . As an example of application of the model to solve the lubrication of the piston skirt in an engine, the frictional force and the load capacity of the oil film in a cylinder were analyzed. The results reveal that the oil film frictional force and the load capacity fluctuate with increasing fractal dimension, showing big values at the small D and smaller ones and slightly variable in the range of bigger one, at the same crank angle.展开更多
Fish feces affect the structure and function of aquatic ecosystems,and they are affected by the functional fish organizations.In this research,Ctenopharyngodon idellus,Hypophthalmichthys molitrix,and Cyprinus carpio w...Fish feces affect the structure and function of aquatic ecosystems,and they are affected by the functional fish organizations.In this research,Ctenopharyngodon idellus,Hypophthalmichthys molitrix,and Cyprinus carpio were selected to study the effects of different functional fish organizations on the fractal characteristics of fecal micro-structure by scanning electron microscopes(SEM),particles(pores)and cracks analysis system(PCAS).The results showed that fish feces pores mainly consisted of medium pores(cumulative pore number,97%)classified by the International Union of Pure and Applied Chemistry(IUPAC).The grain area fractal dimension D_(1) and the pore-number and pore-size fractal dimension D_(2) were 1.94-1.96 and 2.07-2.19,respectively.The distribution of fish feces pores was very close to the Sierpinski carpet structure,which is the basic fractal construction methods widely used to describe the fractal of pore surface distribution.D_(1)(1.96)and D_(2)(2.19)of Hypophthalmichthys molitrix were the maximum values of the three functional organizations.Combining with the habit of fish,it is inferred that the feces of H.molitrix,the finer the feed and the faster the swimming of fish,the higher the content of feces clay,the larger the fractal dimension of feces,the easier it is to decompose feces,and the high the content of nutrients and organic matter to release into the water.It is demined that fish functional organizations affected the fractal characteristics and the stability of fish feces in water.This study is helpful for further research on water quality prediction and the impact of functional fish organizations on the structure and function of the ecosystem.展开更多
To investigate the influence of dynamic loading and freeze-thaw cycles(F-T)on the energy evolution and damage characteristics of multi-walled carbon nanotubes(MWCNTs)reinforced concrete specimens,impact compression te...To investigate the influence of dynamic loading and freeze-thaw cycles(F-T)on the energy evolution and damage characteristics of multi-walled carbon nanotubes(MWCNTs)reinforced concrete specimens,impact compression tests were conducted.These tests used a split-Hopkinson pressure bar(SHPB)apparatus with a diameter of 50 mm and were performed on MWCNTs concrete samples that had undergone different numbers of F-T cycles.The impact pressures applied were 0.40,0.50,and 0.60 MPa,respectively.The effects of impact pressure and F-T number on the fractal dimension(D_(f))of the fractured blocks and absorbed energy(W_s)of MWCNTs concrete were investigated.The results indicate that the D_(f) of the fractured blocks in MWCNTs concrete increases with the increase of impact pressure and F-T number,and under the same experimental conditions,the D_(f) of MWCNTs concrete is lower than that of ordinary concrete.The variation in W_s is different:the W_s of MWCNTs concrete under impact load increases with increasing impact pressure but decreases with increasing F-T number.Additionally,under the same experimental conditions,the W_s of MWCNTs concrete is greater than that of ordinary concrete.The incorporation of MWCNTs significantly enhances the impact resistance of the concrete.展开更多
The primary wind of a low-NO_x coaxial swirling burner was visualized byusing glycol as smog tracer. The information of the visual flow field was input into a computerthrough image-capturing card with CCD camera as th...The primary wind of a low-NO_x coaxial swirling burner was visualized byusing glycol as smog tracer. The information of the visual flow field was input into a computerthrough image-capturing card with CCD camera as the image-capturing element. The boundary of thevisual zone, i. e. , the interface of the primary wind and secondary wind was obtained by imageprocessing. The fractal dimension (FD) of the boundary was examined and found to vary from 1. 10 to1. 40 with S_1, S_2 and ζ_1 . It is concluded that when FD is small, the complex level of theinterface is low, and mixture between the primary and secondary wind is weak near the exit of theburner at the initial phase of combustion resulting in stratified flow; when FD is big, mixturebecomes strong near the exit of the burner. It is showed that the flow with FD ranging from 1.10 to1. 20 is stratified flow, which is benefical to reduce NO_x yield and the flow with FD from 1. 25 to1. 40 is mixed flow, producing much NO_x. The mechanism of the forming of stratified flow and mixedflow was theoretically analyzed. The corresponding S_1 , S_2 and ζ_1 of these flows were given.展开更多
To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based...To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based on adaptive fractal dimension characterization.By analyzing the nonlinear characteristics of gas concentration data,an adaptive window fractal analysis method is introduced.Combined with boxcounting dimension and variation of box dimension metrics,a cross-scale dynamic warning model for disaster prevention is established.The implementation involves three key phases:First,wavelet denoising and interpolation methods are employed for raw data preprocessing,followed by validation of fractal characteristics.Second,an adaptive window cross-scale fractal dimension method is proposed to calculate the box-counting dimension of gas concentration,enabling effective capture of multi-scale complex features.Finally,dynamic threshold partitioning is achieved through membership functions and the 3σprinciple,establishing a graded classification standard for the mine gas disaster(MGD)index.Validated through engineering applications at Shoushan#1 Coal Mine in Henan Province,the results demonstrate that the adaptive window fractal dimension curve exhibits significantly enhanced fluctuation characteristics compared to fixed window methods,with local feature detection capability improved and warning accuracy reaching 86.9%.The research reveals that this model effectively resolves the limitations of traditional methods in capturing local features and dependency on subjective thresholds through multiindicator fusion and threshold optimization,providing both theoretical foundation and practical tool for coal mine gas outburst early warning.展开更多
In this study, differences of signal characteristics between mine shocks and coal and gas outbursts in coal mines were examined with the micro-seismic monitoring technique and time-frequency analysis. The duration of ...In this study, differences of signal characteristics between mine shocks and coal and gas outbursts in coal mines were examined with the micro-seismic monitoring technique and time-frequency analysis. The duration of the mine shock is short while the coal and gas outburst lasts longer. The outburst consists of three stages： the pre-shock, secondary shock and main shock stage, respectively. The velocity amplitude of the mine shock is between 10 s and 10-3 m/s, which is higher than that of the outburst with the same energy level. In addition, in both cases, the correlation between the velocity amplitude and energy is positive while the correlation between the signal frequency band distribution and energy is negative. The signal frequency band of the high energy mine shock is distributed between 0 and 50 Hz, and the low energy mine shock is between 50 and 100 Hz. The fractal characteristics of mine shocks were studied based on a fractal theory. The box dimensions of high energy mine shocks are lower than the low energy ones, however, the box dimensions of outbursts are higher than that of mine shocks with the same energy level. The higher box dimensions indicate more dangerous dynamic events.展开更多
Several sets of Paleozoic tight reservoirs are developed in the Central Uplift of the South Yellow Sea Basin.A qualitative analysis of the microscopic pore structure of the tight reservoir rocks was carried out throug...Several sets of Paleozoic tight reservoirs are developed in the Central Uplift of the South Yellow Sea Basin.A qualitative analysis of the microscopic pore structure of the tight reservoir rocks was carried out through cast thin slice and scanning electron microscopic image observation.Based on reservoir pet-rophysical properties,thirty core samples in the Central Uplift of the South Yellow Sea Basin were selected for high-pressure mercury intrusion(HPMI)analysis,which was then combined with fractal calculation to classify and evaluate the tight reservoirs.The analysis of the HPMI curves and related parameters shows that the Paleozoic tight reservoirs can be divided into three types:Type-A,Type-B and Type-C.Type-A sandstone reservoirs contain pores with size mostly ranging between 0.01 and 0.1 mm,followed by pores with size range of 0.001-0.01 m m,and relatively fewer pores larger than 0.1 m m.The Type-B reservoirs are carbonate rocks with extremely heterogeneous pore size distribution,which is closely related to the development of dissolution pores and microfractures.Type-C sandstone reservoirs are dominated by nanopores and submicron pores that distribute more heterogeneously than pores in Type-A reservoirs.The pore distribution in sandstone reservoirs shows significant fractal characteristics and is closely related to the pore size.The heterogeneity of nanopore distribution has a negative cor-relation with porosity and median pressure and a relatively weak correlation with permeability.Our study has important implications for petroleum exploration in the South Yellow Sea Basin.展开更多
The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-har...The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.展开更多
To investigate the instability mechanisms of heterogeneous geological structures in goaf area roofs,three-point bending tests(TPBT)and numerical simulations are performed on composite coal-rock(CCR).Acoustic emission(...To investigate the instability mechanisms of heterogeneous geological structures in goaf area roofs,three-point bending tests(TPBT)and numerical simulations are performed on composite coal-rock(CCR).Acoustic emission(AE)monitoring is employed to analyze key parameters,establishing a multiparameter quantitative system for CCR fracture processes.The impact of lithological homogeneity on fracture evolution and energy migration is examined.Results show that CCR exhibits a three-stage mechanical response:weak contact,strong contact,and post-peak stages,each with distinct crack evolution patterns.A positive correlation is found between lithological homogeneity and tensile crack proportion.No significant correlation is observed between AE average frequency(AF)and AE counts across different lithological CCR;however,peak frequency(PF)displays clear lithology-dependent characteristics.The regulatory effect of the rock homogeneity coefficient(φ)on crack deriva tion mechanisms is quantfied,yielding mathematical relationships between fracture strength(f),crack propagation path angle(β),crack fractal dimension(D),andφ.The study highlights how different fracture modes alter energy migration pathways,confirming the coupling effect of grain distribution on mechanical response and crack propagation,and the influence of parameterφon critical energy release zones.These findings offer new insights into CCR failure mechanisms for mining safety.展开更多
Hydrophilic characteristics of rocks are affected by their microscopic pore structures,which clearly change after water absorption.Water absorption tests and scanning electron microscopic（SEM） experiments on rock sa...Hydrophilic characteristics of rocks are affected by their microscopic pore structures,which clearly change after water absorption.Water absorption tests and scanning electron microscopic（SEM） experiments on rock samples,located at a site in Tibet,China,were carried out Changes of rock pore structures before and after water absorption were studied with the distribution of pore sizes and fractal characteristics of pores.The results show that surface porosities,fractal dimensions of pores and the complexity of pore structures increased because the number of new small pores produced increased or the original macropore flow channels were expanded after rocks absorbed water.There were points of inflection on their water absorption curves.After water absorption of other rocks,surface porosities and fractal dimensions of pores and complexity of pore structures decreased as the original pore flow channels became filled.Water absorption curves did not change.Surface porosity and the pore fractal dimensions of rocks have good linear relationships before and after water absorption.展开更多
The mechanical behavior of coal is the key factor affecting underground coal mining and coalbed methane extraction.In this study,triaxial compression and seepage tests were carried out on coal at different gas pressur...The mechanical behavior of coal is the key factor affecting underground coal mining and coalbed methane extraction.In this study,triaxial compression and seepage tests were carried out on coal at different gas pressures.The mechanical properties and failure process of coal were studied,as well as the acoustic emission(AE)and strain energy.The influence of gas pressure on the mechanical parameters of this coal was analyzed.Based on the conventional energy calculation formula,the pore pressure was introduced through the effective stress formula,and each energy component of coal containing gas was refined innovatively.The contribution of gas pressure to the total energy input and dissipation during loading was quantitatively described.Finally,the influence of gas pressure on coal strength was theo-retically analyzed from the perspectives of MohreCoulomb criterion and fracture mechanics.The results show that the total absorbed energy comprises the absorbed energy in the axial pressure direction(positive)and in the confining pressure direction(negative),as well as that induced by the pore pressure(initially negative and then positive).The absorbed energy in the axial pressure direction accounts for the main proportion of the total energy absorbed by coal.The quiet period of AE in the initial stage shortens,and AE activity increases during the pre-peak stage under high gas pressure.The fractal characteristics of AE in three stages are studied using the correlation dimension.The AE process has different forms of self-similarity in various deformation stages.展开更多
Since the fracture property of corn stalk determines the difficulty for corn to fall off,it is of great significance to study the fracture law of the corn stalk with high water content and explore the corn threshing m...Since the fracture property of corn stalk determines the difficulty for corn to fall off,it is of great significance to study the fracture law of the corn stalk with high water content and explore the corn threshing method without causing great damage.Taking two varieties of corn as the research object,this study carried out single and multi-angle corn stalk fracture tests to explore the changes in the linkage between stalk and corn kernel at different positions as well as under different application modes and angles.The results showed that the force required for radial stretching was the greatest.Moreover,the fracture mechanics model of corn stalk was established to measure the fracture toughness of corn stalk.The peak value of critical load P_(Q) load displacement curve(F_(MAX))was indicated.Based on the fractal theory,the fractal characteristics of the fracture surface of the stalk at different positions of the ear were analyzed,and the fractal dimension was calculated using the islet method.The findings indicated that the larger the fractal dimension of the fracture surface on the corn stalk,the more energy consumed in the fracture of corn stalk.These findings can be further utilized to explore the performance of corn kernel and reveal the fracture rule of corn kernel and stalk to identify the optimal form of force to make corn kernels fall off the corn cob and provide the theoretical basis for reducing the loss caused in the falling process of corn kernel.展开更多
Global positioning system(GPS)common-view observation data were processed by using the multi-scale Kalman algorithm based on a correlative structure of the discrete wavelet coefficients.Suppose that the GPS commonview...Global positioning system(GPS)common-view observation data were processed by using the multi-scale Kalman algorithm based on a correlative structure of the discrete wavelet coefficients.Suppose that the GPS commonview observation data has the 1/f fractal characteristic,the algorithm of wavelet transform was used to estimate the Hurst parameter H of GPS clock difference data.When 0<H<1,the 1/f fractal characteristic of the GPS clock difference data is a Gaussian zero-mean and non-stationary stochastic process.Thus,the discrete wavelet coefficients can be discussed in the process of estimating multi-scale Kalman coefficients.Furthermore,the discrete clock difference can be estimated.The single-channel and multi-channel common-view observation data were processed respectively.Comparisons were made between the results obtained and the Circular T data.Simulation results show that the algorithm discussed in this paper is both feasible and effective.展开更多
基金The first author would like to express sincere appreciation for the scholarship provided by China Scholarship Council(No.202006430006)and University of Wollongongfinancially supported by the ACARP Project C28006+1 种基金the National Key Research and Development Program of China(No.2018YFC0808301)the Natural Science Foundation of Beijing Municipality,China(No.8192036)。
文摘Well-developed pores and cracks in coal reservoirs are the main venues for gas storage and migration.To investigate the multi-scale pore fractal characteristics,six coal samples of different rankings were studied using high-pressure mercury injection(HPMI),low-pressure nitrogen adsorption(LPGA-N2),and scanning electron microscopy(SEM)test methods.Based on the Frankel,Halsey and Hill(FHH)fractal theory,the Menger sponge model,Pores and Cracks Analysis System(PCAS),pore volume complexity(D_(v)),coal surface irregularity(Ds)and pore distribution heterogeneity(D_(p))were studied and evaluated,respectively.The effect of three fractal dimensions on the gas adsorption ability was also analyzed with high-pressure isothermal gas adsorption experiments.Results show that pore structures within these coal samples have obvious fractal characteristics.A noticeable segmentation effect appears in the Dv1and Dv2fitting process,with the boundary size ranging from 36.00 to 182.95 nm,which helps differentiate diffusion pores and seepage fractures.The D values show an asymmetric U-shaped trend as the coal metamorphism increases,demonstrating that coalification greatly affects the pore fractal dimensions.The three fractal dimensions can characterize the difference in coal microstructure and reflect their influence on gas adsorption ability.Langmuir volume(V_(L))has an evident and positive correlation with Dsvalues,whereas Langmuir pressure(P_(L))is mainly affected by the combined action of Dvand Dp.This study will provide valuable knowledge for the appraisal of coal seam gas reservoirs of differently ranked coals.
基金financially supported by National Natural Science Foundation of China(No.52274171)Joint National-Local Engineering Research Centre for Safe and Precise Coal Mining Fund(No.EC2023015)+1 种基金Excellent Youth Project of Universities in Anhui Province(No.2023AH030042)Unveiled List of Bidding Projects of Shanxi Province(No.20201101001)。
文摘Chemical solvents instead of pure water being as hydraulic fracturing fluid could effectively increase permeability and improve clean methane extraction efficiency.However,pore-fracture variation features of lean coal synergistically affected by solvents have not been fully understood.Ultrasonic testing,nuclear magnetic resonance analysis,liquid phase mass spectrometry was adopted to comprehensively analyze pore-fracture change characteristics of lean coal treated by combined solvent(NMP and CS_(2)).Meanwhile,quantitative characterization of above changing properties was conducted using geometric fractal theory.Relationship model between permeability,fractal dimension and porosity were established.Results indicate that the end face fractures of coal are well developed after CS2and combined solvent treatments,of which,end face box-counting fractal dimensions range from 1.1227 to 1.4767.Maximum decreases in ultrasonic longitudinal wave velocity of coal affected by NMP,CS_(2)and combined solvent are 2.700%,20.521%,22.454%,respectively.Solvent treatments could lead to increasing amount of both mesopores and macropores.Decrease ratio of fractal dimension Dsis 0.259%–2.159%,while permeability increases ratio of NMR ranges from 0.1904 to 6.4486.Meanwhile,combined solvent could dissolve coal polar and non-polar small molecules and expand flow space.Results could provide reference for solvent selection and parameter optimization of permeability-enhancement technology.
基金supported by the National Natural Science Foundation of China(No.51874294,No.51974300,and No.52034008)the Fundamental Research Funds for the Central Universities(No.2017XKZD01 and No.2020ZDPY0224)the Six Talent Peaks Project in Jiangsu Province(GDZB-027).
文摘Accurate and quantitative investigation of the physical structure and fractal geometry of coal has important theoretical and practical signifcance for coal bed methane(CBM)development and the prevention of dynamic disasters such as coal and gas outbursts.This study investigates the pore structure and fractal characteristics of soft and hard coals using nitrogen and carbon dioxide(N_(2)/CO_(2))adsorption.Coal samples from Pingdingshan Mine in Henan province of China were collected and pulverized to the required size(0.20–0.25 mm).N_(2)/CO_(2)adsorption tests were performed to evaluate the specifc surface area(SSA),pore size distribution(PSD),and pore volume(PV)using Braunuer-Emmett-Teller(BET),Barrett-Joyner-Halenda(BJH),and Density Functional Theory(DFT).The pore structure was characterized based on the theory of fractal dimensions.The results unveiled that the strength of coal has a signifcant infuence on pore structure and fractal dimensions.There are signifcant diferences in SSA and PV between both coals.The BJH-PV and BET-SSA obtained by N_(2)-adsorption for soft coal are 0.029–0.032 cm^(3)/g and 3.523–4.783 m^(2)/g.While the values of PV and SSA obtained by CO_(2)-adsorption are 0.037–0.039 cm^(3)/g and 106.016–111.870 m^(2)/g.Soft coal shows greater SSA and PV than hard coal,which is consistent with the adsorption capacity(VL).The fractal dimensions of soft and hard coal are respectively diferent.The Ding coal exhibits larger D1 and smaller D_(2),and the reverse for the Wu coal seam is observed.The greater the value of D1(complexity of pore surface)of soft coal is,the larger the pore surface roughness and gas adsorption capacity is.The results enable us to conclude that the characterization of pores and fractal dimensions of soft and hard coals is diferent,tending to diferent adsorption/desorption characteristics.In this regard,the results provide a reference for formulating corresponding coal and gas outburst prevention and control measures.
基金supported by the National Natural Science Foundation of China (Grant No 60571058)Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No 20070701010)
文摘A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing.
基金ThisresearchwassupportedbytheNationalNaturalScienceFoundationofChina (No .5 9990 472 )
文摘Fractal characteristics are introduced into solving lubrication problems. Based on the analysis of the relationship between roughness and engineering surfaces' fractal characteristics and by introducing fractal parameters into the mixed lubrication equation, the relationship between flow factors and fractal dimensions is analyzed. The results show that the pressure flow factors' values increase, while the shear flow factor decreases, with the increasing length to width ratio of a representative asperity γ at the same fractal dimension. It can be also found that these factors experience more irregular and significant variations and show the higher resolution and the local optimal and the worst fractal dimensions, by a fractal dimension D , compared with the oil film thickness to roughness ratio h/R q . As an example of application of the model to solve the lubrication of the piston skirt in an engine, the frictional force and the load capacity of the oil film in a cylinder were analyzed. The results reveal that the oil film frictional force and the load capacity fluctuate with increasing fractal dimension, showing big values at the small D and smaller ones and slightly variable in the range of bigger one, at the same crank angle.
基金financial support from the National Natural Science Youth Foundation of China(No.32002443)the Natural Science Foundation of Shandong Province(No.ZR2021QD 149)。
文摘Fish feces affect the structure and function of aquatic ecosystems,and they are affected by the functional fish organizations.In this research,Ctenopharyngodon idellus,Hypophthalmichthys molitrix,and Cyprinus carpio were selected to study the effects of different functional fish organizations on the fractal characteristics of fecal micro-structure by scanning electron microscopes(SEM),particles(pores)and cracks analysis system(PCAS).The results showed that fish feces pores mainly consisted of medium pores(cumulative pore number,97%)classified by the International Union of Pure and Applied Chemistry(IUPAC).The grain area fractal dimension D_(1) and the pore-number and pore-size fractal dimension D_(2) were 1.94-1.96 and 2.07-2.19,respectively.The distribution of fish feces pores was very close to the Sierpinski carpet structure,which is the basic fractal construction methods widely used to describe the fractal of pore surface distribution.D_(1)(1.96)and D_(2)(2.19)of Hypophthalmichthys molitrix were the maximum values of the three functional organizations.Combining with the habit of fish,it is inferred that the feces of H.molitrix,the finer the feed and the faster the swimming of fish,the higher the content of feces clay,the larger the fractal dimension of feces,the easier it is to decompose feces,and the high the content of nutrients and organic matter to release into the water.It is demined that fish functional organizations affected the fractal characteristics and the stability of fish feces in water.This study is helpful for further research on water quality prediction and the impact of functional fish organizations on the structure and function of the ecosystem.
基金Funded by the Gansu Provincial Key Research and Development Plan-Industrial Project(No.25YFGA029)。
文摘To investigate the influence of dynamic loading and freeze-thaw cycles(F-T)on the energy evolution and damage characteristics of multi-walled carbon nanotubes(MWCNTs)reinforced concrete specimens,impact compression tests were conducted.These tests used a split-Hopkinson pressure bar(SHPB)apparatus with a diameter of 50 mm and were performed on MWCNTs concrete samples that had undergone different numbers of F-T cycles.The impact pressures applied were 0.40,0.50,and 0.60 MPa,respectively.The effects of impact pressure and F-T number on the fractal dimension(D_(f))of the fractured blocks and absorbed energy(W_s)of MWCNTs concrete were investigated.The results indicate that the D_(f) of the fractured blocks in MWCNTs concrete increases with the increase of impact pressure and F-T number,and under the same experimental conditions,the D_(f) of MWCNTs concrete is lower than that of ordinary concrete.The variation in W_s is different:the W_s of MWCNTs concrete under impact load increases with increasing impact pressure but decreases with increasing F-T number.Additionally,under the same experimental conditions,the W_s of MWCNTs concrete is greater than that of ordinary concrete.The incorporation of MWCNTs significantly enhances the impact resistance of the concrete.
文摘The primary wind of a low-NO_x coaxial swirling burner was visualized byusing glycol as smog tracer. The information of the visual flow field was input into a computerthrough image-capturing card with CCD camera as the image-capturing element. The boundary of thevisual zone, i. e. , the interface of the primary wind and secondary wind was obtained by imageprocessing. The fractal dimension (FD) of the boundary was examined and found to vary from 1. 10 to1. 40 with S_1, S_2 and ζ_1 . It is concluded that when FD is small, the complex level of theinterface is low, and mixture between the primary and secondary wind is weak near the exit of theburner at the initial phase of combustion resulting in stratified flow; when FD is big, mixturebecomes strong near the exit of the burner. It is showed that the flow with FD ranging from 1.10 to1. 20 is stratified flow, which is benefical to reduce NO_x yield and the flow with FD from 1. 25 to1. 40 is mixed flow, producing much NO_x. The mechanism of the forming of stratified flow and mixedflow was theoretically analyzed. The corresponding S_1 , S_2 and ζ_1 of these flows were given.
基金funded by the National Key Research and Development ProgramFund for Young Scientists(No.2021YFC2900400)+5 种基金the National Natural Science Foundation of China(No.52304123)Fundamental Research Funds for the Central Universities(No.2024CDJXY025)Sichuan-Chongqing Science and Technology Innovation Cooperation Program Project(No.CSTB2024TIAD-CYKJCXX0016)Postdoctoral Research Foundation of China(No.2023M730412)Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(No.GZB20230914)Chongqing Outstanding Youth Science Foundation Program(No.CSTB2023NSCQ-JQX0027)。
文摘To address the issues of single warning indicators,fixed thresholds,and insufficient adaptability in coal and gas outburst early warning models,this study proposes a dynamic early warning model for gas outbursts based on adaptive fractal dimension characterization.By analyzing the nonlinear characteristics of gas concentration data,an adaptive window fractal analysis method is introduced.Combined with boxcounting dimension and variation of box dimension metrics,a cross-scale dynamic warning model for disaster prevention is established.The implementation involves three key phases:First,wavelet denoising and interpolation methods are employed for raw data preprocessing,followed by validation of fractal characteristics.Second,an adaptive window cross-scale fractal dimension method is proposed to calculate the box-counting dimension of gas concentration,enabling effective capture of multi-scale complex features.Finally,dynamic threshold partitioning is achieved through membership functions and the 3σprinciple,establishing a graded classification standard for the mine gas disaster(MGD)index.Validated through engineering applications at Shoushan#1 Coal Mine in Henan Province,the results demonstrate that the adaptive window fractal dimension curve exhibits significantly enhanced fluctuation characteristics compared to fixed window methods,with local feature detection capability improved and warning accuracy reaching 86.9%.The research reveals that this model effectively resolves the limitations of traditional methods in capturing local features and dependency on subjective thresholds through multiindicator fusion and threshold optimization,providing both theoretical foundation and practical tool for coal mine gas outburst early warning.
基金the Key Research Development Program of Jiangsu Province (No.BE2015040)the Priority Academic Program Development of Jiangsu Higher Education Institutions and the Graduate Student Research Innovation Project of Jiangsu Province (No.KYLX_1403)
文摘In this study, differences of signal characteristics between mine shocks and coal and gas outbursts in coal mines were examined with the micro-seismic monitoring technique and time-frequency analysis. The duration of the mine shock is short while the coal and gas outburst lasts longer. The outburst consists of three stages： the pre-shock, secondary shock and main shock stage, respectively. The velocity amplitude of the mine shock is between 10 s and 10-3 m/s, which is higher than that of the outburst with the same energy level. In addition, in both cases, the correlation between the velocity amplitude and energy is positive while the correlation between the signal frequency band distribution and energy is negative. The signal frequency band of the high energy mine shock is distributed between 0 and 50 Hz, and the low energy mine shock is between 50 and 100 Hz. The fractal characteristics of mine shocks were studied based on a fractal theory. The box dimensions of high energy mine shocks are lower than the low energy ones, however, the box dimensions of outbursts are higher than that of mine shocks with the same energy level. The higher box dimensions indicate more dangerous dynamic events.
基金This study is supported by the National Natural Science Foun-dation of China(41806057)the Shandong Provincial Natural Science Foundation,China(ZR2018BD026).
文摘Several sets of Paleozoic tight reservoirs are developed in the Central Uplift of the South Yellow Sea Basin.A qualitative analysis of the microscopic pore structure of the tight reservoir rocks was carried out through cast thin slice and scanning electron microscopic image observation.Based on reservoir pet-rophysical properties,thirty core samples in the Central Uplift of the South Yellow Sea Basin were selected for high-pressure mercury intrusion(HPMI)analysis,which was then combined with fractal calculation to classify and evaluate the tight reservoirs.The analysis of the HPMI curves and related parameters shows that the Paleozoic tight reservoirs can be divided into three types:Type-A,Type-B and Type-C.Type-A sandstone reservoirs contain pores with size mostly ranging between 0.01 and 0.1 mm,followed by pores with size range of 0.001-0.01 m m,and relatively fewer pores larger than 0.1 m m.The Type-B reservoirs are carbonate rocks with extremely heterogeneous pore size distribution,which is closely related to the development of dissolution pores and microfractures.Type-C sandstone reservoirs are dominated by nanopores and submicron pores that distribute more heterogeneously than pores in Type-A reservoirs.The pore distribution in sandstone reservoirs shows significant fractal characteristics and is closely related to the pore size.The heterogeneity of nanopore distribution has a negative cor-relation with porosity and median pressure and a relatively weak correlation with permeability.Our study has important implications for petroleum exploration in the South Yellow Sea Basin.
基金Project supported by the National Natural Science Foundation of China (No.50275024)
文摘The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.
基金support from the National Key Research and Development Plan Project(No.2022YFC3004700)the National Natural Science Foundation of China(No.52374241)+1 种基金Postgraduate Research&Practice Innovation Program of Jiangsu Province(No.KYCX24_2924)Graduate Innovation Program of China University of Mining and Technology(No.2024WLKXJ151).
文摘To investigate the instability mechanisms of heterogeneous geological structures in goaf area roofs,three-point bending tests(TPBT)and numerical simulations are performed on composite coal-rock(CCR).Acoustic emission(AE)monitoring is employed to analyze key parameters,establishing a multiparameter quantitative system for CCR fracture processes.The impact of lithological homogeneity on fracture evolution and energy migration is examined.Results show that CCR exhibits a three-stage mechanical response:weak contact,strong contact,and post-peak stages,each with distinct crack evolution patterns.A positive correlation is found between lithological homogeneity and tensile crack proportion.No significant correlation is observed between AE average frequency(AF)and AE counts across different lithological CCR;however,peak frequency(PF)displays clear lithology-dependent characteristics.The regulatory effect of the rock homogeneity coefficient(φ)on crack deriva tion mechanisms is quantfied,yielding mathematical relationships between fracture strength(f),crack propagation path angle(β),crack fractal dimension(D),andφ.The study highlights how different fracture modes alter energy migration pathways,confirming the coupling effect of grain distribution on mechanical response and crack propagation,and the influence of parameterφon critical energy release zones.These findings offer new insights into CCR failure mechanisms for mining safety.
基金Financial support for this work,provided by the Key Basic Research Program of China(Nos.2010CB226800 and 2007CB202200)National Natural Science Foundation of China(No. 50490270)the Innovation Team Development Program of the Ministry of Education of China(No.IRT0656)
文摘Hydrophilic characteristics of rocks are affected by their microscopic pore structures,which clearly change after water absorption.Water absorption tests and scanning electron microscopic（SEM） experiments on rock samples,located at a site in Tibet,China,were carried out Changes of rock pore structures before and after water absorption were studied with the distribution of pore sizes and fractal characteristics of pores.The results show that surface porosities,fractal dimensions of pores and the complexity of pore structures increased because the number of new small pores produced increased or the original macropore flow channels were expanded after rocks absorbed water.There were points of inflection on their water absorption curves.After water absorption of other rocks,surface porosities and fractal dimensions of pores and complexity of pore structures decreased as the original pore flow channels became filled.Water absorption curves did not change.Surface porosity and the pore fractal dimensions of rocks have good linear relationships before and after water absorption.
基金This study is sponsored by the National Natural Science Foun-dation of China(Grant No.12002270)the China Postdoctoral Science Foundation(Grant Nos.2021T140553 and 2021M692600).
文摘The mechanical behavior of coal is the key factor affecting underground coal mining and coalbed methane extraction.In this study,triaxial compression and seepage tests were carried out on coal at different gas pressures.The mechanical properties and failure process of coal were studied,as well as the acoustic emission(AE)and strain energy.The influence of gas pressure on the mechanical parameters of this coal was analyzed.Based on the conventional energy calculation formula,the pore pressure was introduced through the effective stress formula,and each energy component of coal containing gas was refined innovatively.The contribution of gas pressure to the total energy input and dissipation during loading was quantitatively described.Finally,the influence of gas pressure on coal strength was theo-retically analyzed from the perspectives of MohreCoulomb criterion and fracture mechanics.The results show that the total absorbed energy comprises the absorbed energy in the axial pressure direction(positive)and in the confining pressure direction(negative),as well as that induced by the pore pressure(initially negative and then positive).The absorbed energy in the axial pressure direction accounts for the main proportion of the total energy absorbed by coal.The quiet period of AE in the initial stage shortens,and AE activity increases during the pre-peak stage under high gas pressure.The fractal characteristics of AE in three stages are studied using the correlation dimension.The AE process has different forms of self-similarity in various deformation stages.
基金supported by the National Natural Science Foundation of China(Grant No.52275245)Henan Science and Technology Research Program(Grant No.222103810041).
文摘Since the fracture property of corn stalk determines the difficulty for corn to fall off,it is of great significance to study the fracture law of the corn stalk with high water content and explore the corn threshing method without causing great damage.Taking two varieties of corn as the research object,this study carried out single and multi-angle corn stalk fracture tests to explore the changes in the linkage between stalk and corn kernel at different positions as well as under different application modes and angles.The results showed that the force required for radial stretching was the greatest.Moreover,the fracture mechanics model of corn stalk was established to measure the fracture toughness of corn stalk.The peak value of critical load P_(Q) load displacement curve(F_(MAX))was indicated.Based on the fractal theory,the fractal characteristics of the fracture surface of the stalk at different positions of the ear were analyzed,and the fractal dimension was calculated using the islet method.The findings indicated that the larger the fractal dimension of the fracture surface on the corn stalk,the more energy consumed in the fracture of corn stalk.These findings can be further utilized to explore the performance of corn kernel and reveal the fracture rule of corn kernel and stalk to identify the optimal form of force to make corn kernels fall off the corn cob and provide the theoretical basis for reducing the loss caused in the falling process of corn kernel.
基金supported by the National Natural Science Foundation of China (Grant No.60571060).
文摘Global positioning system(GPS)common-view observation data were processed by using the multi-scale Kalman algorithm based on a correlative structure of the discrete wavelet coefficients.Suppose that the GPS commonview observation data has the 1/f fractal characteristic,the algorithm of wavelet transform was used to estimate the Hurst parameter H of GPS clock difference data.When 0<H<1,the 1/f fractal characteristic of the GPS clock difference data is a Gaussian zero-mean and non-stationary stochastic process.Thus,the discrete wavelet coefficients can be discussed in the process of estimating multi-scale Kalman coefficients.Furthermore,the discrete clock difference can be estimated.The single-channel and multi-channel common-view observation data were processed respectively.Comparisons were made between the results obtained and the Circular T data.Simulation results show that the algorithm discussed in this paper is both feasible and effective.
