Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on R^d. Denote by D the Hausdorff dimension, by H^D(E) the Hausdorff measu...Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on R^d. Denote by D the Hausdorff dimension, by H^D(E) the Hausdorff measure and by diam(E) the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the Hausdorff dimension is smaller than one and H^O(E) = diam(E)^D if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover, we present a parametrised UIFS, where ω depends on c and show the inequatily H^D(E) 〈 diam(E)^D, if c is small enough.展开更多
A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes...A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.展开更多
Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media withi...Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.展开更多
The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the...The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the degree of deformation and fractal dimension.The zone between the Main Boundary Thrust(MBT)and the Main Central Thrust(MCT)in the Himalayan Mountain Range(HMR)experienced large variations in earthquake magnitude,which were identified by Number-Size(NS)fractal modeling.The central IGP zone experienced only moderate to low mainshock levels.Fractal analysis of earthquake epicenters reveals a large scattering of earthquake epicenters in the HMR and central IGP zones.Similarly,the fault fractal analysis identifies the HMR,central IGP,and south-western IGP zones as having more faults.Overall,the seismicity of the study region is strong in the central IGP,south-western IGP,and HMR zones,moderate in the western and southern IGP,and low in the northern,eastern,and south-eastern IGP zones.展开更多
After exposure to freeze-thaw cycles, scanning electron microscopy(SEM) and nuclear magnetic resonance(NMR) were used to test the four mixtures. The microstructure is qualitatively analyzed from the 2D SEM image and t...After exposure to freeze-thaw cycles, scanning electron microscopy(SEM) and nuclear magnetic resonance(NMR) were used to test the four mixtures. The microstructure is qualitatively analyzed from the 2D SEM image and the 3D pore distribution curve before and after freezing and thawing. The fractal dimension is utilized to characterize the two-dimensional topography image and the three-dimensional pore distribution, quantitatively. The results reveal that the surface porosity and volume porosity increase as the freeze-thaw action increases. Self-similarity characteristics exist in micro-damage inside the concrete. In the fractal dimension, it is possible to characterize pore evolution quantitatively. The fractal dimension correlates with pore damage evolution. The fractal dimension effectively quantitatively characterizes micro-damage features at various scales from the local to the global level.展开更多
After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organiz...After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.展开更多
Spontaneous imbibition(SI)is an important mechanism for enhancing oil recovery in low-permeability reservoirs.Due to the strong heterogeneity,and the non-Darcy flow,the construction of SI model for lowpermeability res...Spontaneous imbibition(SI)is an important mechanism for enhancing oil recovery in low-permeability reservoirs.Due to the strong heterogeneity,and the non-Darcy flow,the construction of SI model for lowpermeability reservoirs is extremely challenging.Commonly,traditional SI models based on single or averaged capillary tortuosity ignore the influence of heterogeneity of pore seepage channels and the threshold pressure(TP)on imbibition.Therefore,in this work,based on capillary model and fractal theory,a mathematical model of characterizing SI considering heterogeneity of pore seepage channels is established.On this basis,the threshold pressure was introduced to determine the pore radius at which the wetted phase can displace oil.The proposed new SI model was verified by imbibition experimental data.The study shows that for weakly heterogeneous cores with permeability of 0-1 m D,the traditional SI model can characterize the imbibition process relatively accurately,and the new imbibition model can increase the coefficient of determination by 1.05 times.However,traditional model has serious deviations in predicting the imbibition recovery for cores with permeability of 10-50 m D.The new SI model coupling with heterogeneity of pore seepage channels and threshold pressure effectively solves this problem,and the determination coefficient is increased from 0.344 to 0.922,which is increased by2.68 times.For low-permeability reservoirs,the production of the oil in transitional pores(0.01-0.1μm)and mesopores(0.1-1μm)significantly affects the imbibition recovery,as the research shows that when the heterogeneity of pore seepage channels is ignored,the oil recovery in transitional pores and mesopores decreases by 7.54%and 4.26%,respectively.Sensitivity analysis shows that increasing interfacial tension,decreasing contact angle,oil-water viscosity ratio and threshold pressure will increase imbibition recovery.In addition,there are critical values for the influence of these factors on the imbibition recovery,which provides theoretical support for surfactant optimization.展开更多
Natural creatures and ancient cultures are full of potential sources to provide inspiration for applied sciences.Inspired by the fractal geometry in nature and the fretwork frame in ancient culture,here we design the ...Natural creatures and ancient cultures are full of potential sources to provide inspiration for applied sciences.Inspired by the fractal geometry in nature and the fretwork frame in ancient culture,here we design the acoustic metasurface to realize sound anomalous modulation,which manifests itself as an incident-dependent propagation behavior:sound wave propagating in the forward direction is allowed to transmit with high efficiency while in the backward direction is obviously suppressed.We quantitatively investigate the dependences of asymmetric transmission on the propagation direction,incident angle and operating frequency by calculating sound transmittance and energy contrast.This compact fractal fretwork metasurface for acoustic anomalous modulation would promote the development of integrated acoustic devices and expand versatile applications in acoustic communication and information encryption.展开更多
To study the damage and failure of shale with different fracture inclination angles under uniaxial compression loading,in this work,RFPA2D-Thermal,a two-dimensional real failure process analysis software,was used for ...To study the damage and failure of shale with different fracture inclination angles under uniaxial compression loading,in this work,RFPA2D-Thermal,a two-dimensional real failure process analysis software,was used for numerical simulation.Numerical simulation results show that quartz in shale mainly affects the tensile and compressive strength of shale by increasing rock brittleness.The coupling of temperature and pressure will cause lateral and volume destruction of shale,which enables the shale body to be more easily broken.Fracture inclination is the key factor affecting shale damage patterns.The failure mode of shale with low-and high-angle fractures is mainly shear failure,and the compressive strength does not vary with crack inclination.The damage mode of obliquely intersecting fractured shale is slip damage along the fracture face,the compressive strength decreases and then increases with the fracture inclination,and a minimum value exists.The acoustic emission simulation results of the damage process effectively reflect the accumulated internal damage and macroscopic crack appearance until fracture instability when the prefabricated fractured shale is subjected to uniaxial compressive loading.The crack inclinations of 0°and 120℃ corresponds to the most complex"N"shape damage mode.The crack inclinations of 30°and 60°,and the damage mode is an inverted"λ"shape.展开更多
The microscopic characterization of isolated bubbles in gassy soil plays an important role in the macroscopic physical properties of sediments and is a key factor in the study of geological hazards in gas-bearing stra...The microscopic characterization of isolated bubbles in gassy soil plays an important role in the macroscopic physical properties of sediments and is a key factor in the study of geological hazards in gas-bearing strata.Based on the box-counting method and the pore fractal features in porous media,a fractal model of bubble microstructure parameters in gassy soil under different gas con-tents and vertical load conditions is established by using an industrial X-ray CT scanning system.The results show that the fractal di-mension of bubbles in the sample is correlated with the volume fraction of bubbles,and it is also restricted by the vertical load.The three-dimensional fractal dimension of the sample is about 1 larger than the average two-dimensional fractal dimension of all the slices from the same sample.The uniform porous media fractal model is used to test the equivalent diameter,and the results show that the variation of the measured pore diameter ratio is jointly restricted by the volume fraction and the vertical load.In addition,the measured self-similarity interval of the bubble area distribution is tested by the porous media fractal capillary bundle model,and the fitting curve of measured pore area ratio in a small loading range is obtained in this paper.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
Efforts to protect electric power systems from faults have commonly relied on the use of ultra-high frequency(UHF)antennas for detecting partial discharge(PD)as a common precursor to faults.However,the effectiveness o...Efforts to protect electric power systems from faults have commonly relied on the use of ultra-high frequency(UHF)antennas for detecting partial discharge(PD)as a common precursor to faults.However,the effectiveness of existing UHF antennas suffers from a number of challenges such as limited bandwidth,relatively large physical size,and low detection sensitivity.The present study addresses these issues by proposing a compact microstrip patch antenna with fixed dimensions of 100 mm×100 mm×1.6 mm.The results of computations yield an optimized antenna design consisting of 2nd-order Hilbert fractal units positioned within a four-layer serpentine arrangement with a fractal unit connection distance of 3.0 mm.Specifically,the optimized antenna design achieves a detection bandwidth for which the voltage standing wave ratio is less than 2 that is approximately 97.3%of the UHF frequency range(0.3–3 GHz).Finally,a prototype antenna is fabricated using standard printed circuit board technology,and the results of experiments demonstrate that the proposed antenna is capable of detecting PD signals at a distance of 8 m from the discharge source.展开更多
Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short w...Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short when evaluating actual geographic features. In our study, we took a novel approach by analyzing map projection distortion from a geometric perspective. We computed the fractal dimensions of different stretches of coastline before and after projection using the divide-and-conquer algorithm and image processing. Our findings revealed that map projections, even when preserving basic shapes, inevitably stretch and compress coastlines in diverse directions. This analysis method provides a more realistic and practical way to measure map-induced distortions, with significant implications for cartography, geographic information systems (GIS), and geomorphology. By bridging the gap between theoretical analysis and real-world features, this method greatly enhances accuracy and practicality when evaluating map projections.展开更多
The study of the hydrate formation process in porous media is of great significance for hydrate application.In this work,the formation process of methane hydrate in porous media was monitored in situ by a low-field ma...The study of the hydrate formation process in porous media is of great significance for hydrate application.In this work,the formation process of methane hydrate in porous media was monitored in situ by a low-field magnetic resonance imaging(MRI)system.The formation characteristics of methane hydrate in porous media and the change of fractal dimension of pore space were studied through the change of residual water saturation and T2 relaxation time distribution.The experimental results show that the hydrate formation process is divided into two stages:fast and slow.During the formation process,the water in the pores is continuously consumed and transformed into hydrate,and the overall T2 distribution gradually shifts to the left.In the formation process of hydrate,the pore space becomes more complex,the change of fractal dimension from top to bottom of the reactor gradually increases,and the hydrate formation rate also gradually increases.展开更多
This paper studies the self-similar fractals with overlaps from an algorithmic point of view.A decidable problem is a question such that there is an algorithm to answer"yes"or"no"to the question fo...This paper studies the self-similar fractals with overlaps from an algorithmic point of view.A decidable problem is a question such that there is an algorithm to answer"yes"or"no"to the question for every possible input.For a classical class of self-similar sets{E b.d}b,d where E b.d=Sn i=1(E b,d/d+b i)with b=(b1,...,b n)∈Qn and d∈N∩[n,∞),we prove that the following problems on the class are decidable:To test if the Hausdorff dimension of a given self-similar set is equal to its similarity dimension,and to test if a given self-similar set satisfies the open set condition(or the strong separation condition).In fact,based on graph algorithm,there are polynomial time algorithms for the above decidable problem.展开更多
The main contents in this note are: 1. introduction; 2. locally compact groups and local fields; 3. calculus on fractals based upon local fields; 4. fractional calculus and fractals; 5. fractal function spaces and PDE...The main contents in this note are: 1. introduction; 2. locally compact groups and local fields; 3. calculus on fractals based upon local fields; 4. fractional calculus and fractals; 5. fractal function spaces and PDE on fractals.展开更多
At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynam...At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynamics i.e. deterministic chaos and fractal geometry is the best mathematical theory to apply to the problems of high energy particle physics and cosmology. In the present work we give a short survey of some recent achievements of applying nonlinear dynamics to notoriously difficult subjects such as quantum entanglement as well as the origin and true nature of dark energy, negative absolute temperature and the fractal meaning of the constancy of the speed of light.展开更多
A new model of multirange fractals is proposed to explain the experimental results observed on the fractal dimensions of the fractured surfaces in materials. A new explanation to the Williford's multifractal curve...A new model of multirange fractals is proposed to explain the experimental results observed on the fractal dimensions of the fractured surfaces in materials. A new explanation to the Williford's multifractal curve on the relationship of fractal dimension with fracture properties in materials has been given. It shows the importance of fractorizing out the effect of fractal structure from other physical causes and separating the appropriate range of scale from multirange fractals. Mechanical alloying process under ball milling as a non-equilibrium dynamical system has been also analyzed.展开更多
文摘Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on R^d. Denote by D the Hausdorff dimension, by H^D(E) the Hausdorff measure and by diam(E) the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the Hausdorff dimension is smaller than one and H^O(E) = diam(E)^D if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover, we present a parametrised UIFS, where ω depends on c and show the inequatily H^D(E) 〈 diam(E)^D, if c is small enough.
基金This study was supported by the National Natural Science Foundation of China(U22B2075,52274056,51974356).
文摘A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.
基金supported by the National Natural Science Foundation of China (Nos.52374078 and 52074043)the Fundamental Research Funds for the Central Universities (No.2023CDJKYJH021)。
文摘Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.
文摘The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the degree of deformation and fractal dimension.The zone between the Main Boundary Thrust(MBT)and the Main Central Thrust(MCT)in the Himalayan Mountain Range(HMR)experienced large variations in earthquake magnitude,which were identified by Number-Size(NS)fractal modeling.The central IGP zone experienced only moderate to low mainshock levels.Fractal analysis of earthquake epicenters reveals a large scattering of earthquake epicenters in the HMR and central IGP zones.Similarly,the fault fractal analysis identifies the HMR,central IGP,and south-western IGP zones as having more faults.Overall,the seismicity of the study region is strong in the central IGP,south-western IGP,and HMR zones,moderate in the western and southern IGP,and low in the northern,eastern,and south-eastern IGP zones.
基金Funded by the Key Project of Science and Technology Research in Higher Educational Institutions of Inner Mongolia Autonomous Region (No.NJZZ22518)Inner Mongolia Natural Science Foundation Project (No.2022MS05043)Inner Mongolia Autonomous Region Water Conservancy Research Special Project(No.NSK2016-S11)。
文摘After exposure to freeze-thaw cycles, scanning electron microscopy(SEM) and nuclear magnetic resonance(NMR) were used to test the four mixtures. The microstructure is qualitatively analyzed from the 2D SEM image and the 3D pore distribution curve before and after freezing and thawing. The fractal dimension is utilized to characterize the two-dimensional topography image and the three-dimensional pore distribution, quantitatively. The results reveal that the surface porosity and volume porosity increase as the freeze-thaw action increases. Self-similarity characteristics exist in micro-damage inside the concrete. In the fractal dimension, it is possible to characterize pore evolution quantitatively. The fractal dimension correlates with pore damage evolution. The fractal dimension effectively quantitatively characterizes micro-damage features at various scales from the local to the global level.
文摘After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.
基金supported by China Natural Science Foundation(Grant No.52274053)Beijing Natural Science Foundation(Grant No.3232028)Open Fund of State Key Laboratory of Offshore Oil Exploitation(Grant No.CCL2021RCPS0515KQN)。
文摘Spontaneous imbibition(SI)is an important mechanism for enhancing oil recovery in low-permeability reservoirs.Due to the strong heterogeneity,and the non-Darcy flow,the construction of SI model for lowpermeability reservoirs is extremely challenging.Commonly,traditional SI models based on single or averaged capillary tortuosity ignore the influence of heterogeneity of pore seepage channels and the threshold pressure(TP)on imbibition.Therefore,in this work,based on capillary model and fractal theory,a mathematical model of characterizing SI considering heterogeneity of pore seepage channels is established.On this basis,the threshold pressure was introduced to determine the pore radius at which the wetted phase can displace oil.The proposed new SI model was verified by imbibition experimental data.The study shows that for weakly heterogeneous cores with permeability of 0-1 m D,the traditional SI model can characterize the imbibition process relatively accurately,and the new imbibition model can increase the coefficient of determination by 1.05 times.However,traditional model has serious deviations in predicting the imbibition recovery for cores with permeability of 10-50 m D.The new SI model coupling with heterogeneity of pore seepage channels and threshold pressure effectively solves this problem,and the determination coefficient is increased from 0.344 to 0.922,which is increased by2.68 times.For low-permeability reservoirs,the production of the oil in transitional pores(0.01-0.1μm)and mesopores(0.1-1μm)significantly affects the imbibition recovery,as the research shows that when the heterogeneity of pore seepage channels is ignored,the oil recovery in transitional pores and mesopores decreases by 7.54%and 4.26%,respectively.Sensitivity analysis shows that increasing interfacial tension,decreasing contact angle,oil-water viscosity ratio and threshold pressure will increase imbibition recovery.In addition,there are critical values for the influence of these factors on the imbibition recovery,which provides theoretical support for surfactant optimization.
基金Project supported by the National Key Research and Development Program of China(Grant No.2022YFA1404500)the National Natural Science Foundation of China(Grant Nos.T2222024 and 12034005)the STCSM Science and Technology Innovation Plan of Shanghai Science and Technology Commission(Grant Nos.20ZR1404200 and 21JC1400300)。
文摘Natural creatures and ancient cultures are full of potential sources to provide inspiration for applied sciences.Inspired by the fractal geometry in nature and the fretwork frame in ancient culture,here we design the acoustic metasurface to realize sound anomalous modulation,which manifests itself as an incident-dependent propagation behavior:sound wave propagating in the forward direction is allowed to transmit with high efficiency while in the backward direction is obviously suppressed.We quantitatively investigate the dependences of asymmetric transmission on the propagation direction,incident angle and operating frequency by calculating sound transmittance and energy contrast.This compact fractal fretwork metasurface for acoustic anomalous modulation would promote the development of integrated acoustic devices and expand versatile applications in acoustic communication and information encryption.
基金Funded by the Guizhou Province Outstanding Young Scientifc and Technological Talents Training Plan(No.Qian Kehe Platform Talents-YQK[2023]012)National Natural Science Foundation of China(Nos.52104080,52264004)+4 种基金Guizhou Science and Technology Fund(No.[2021]401)Guizhou Science and Technology Fund(Qiankehe Support[2023]136)Guizhou Science and Technology Fund(Qiankehe Support[2022]227)Guizhou Science and Technology Fund(Qiankehe Strategic Search for Minerals[2022]ZD005)Natural Science Special(Special Post)Scientifc Research Fund Project of Guizhou University(No.[2021]51)。
文摘To study the damage and failure of shale with different fracture inclination angles under uniaxial compression loading,in this work,RFPA2D-Thermal,a two-dimensional real failure process analysis software,was used for numerical simulation.Numerical simulation results show that quartz in shale mainly affects the tensile and compressive strength of shale by increasing rock brittleness.The coupling of temperature and pressure will cause lateral and volume destruction of shale,which enables the shale body to be more easily broken.Fracture inclination is the key factor affecting shale damage patterns.The failure mode of shale with low-and high-angle fractures is mainly shear failure,and the compressive strength does not vary with crack inclination.The damage mode of obliquely intersecting fractured shale is slip damage along the fracture face,the compressive strength decreases and then increases with the fracture inclination,and a minimum value exists.The acoustic emission simulation results of the damage process effectively reflect the accumulated internal damage and macroscopic crack appearance until fracture instability when the prefabricated fractured shale is subjected to uniaxial compressive loading.The crack inclinations of 0°and 120℃ corresponds to the most complex"N"shape damage mode.The crack inclinations of 30°and 60°,and the damage mode is an inverted"λ"shape.
基金supported by the Open Research Fund Program of State Key Laboratory of Hydroscience and Engineering(No.sk lhse-2022-D-03)the National Natural Science Foundation of China(Nos.U2006213,42277139)the Taishan Scholars Program(No.tsqn202306297).
文摘The microscopic characterization of isolated bubbles in gassy soil plays an important role in the macroscopic physical properties of sediments and is a key factor in the study of geological hazards in gas-bearing strata.Based on the box-counting method and the pore fractal features in porous media,a fractal model of bubble microstructure parameters in gassy soil under different gas con-tents and vertical load conditions is established by using an industrial X-ray CT scanning system.The results show that the fractal di-mension of bubbles in the sample is correlated with the volume fraction of bubbles,and it is also restricted by the vertical load.The three-dimensional fractal dimension of the sample is about 1 larger than the average two-dimensional fractal dimension of all the slices from the same sample.The uniform porous media fractal model is used to test the equivalent diameter,and the results show that the variation of the measured pore diameter ratio is jointly restricted by the volume fraction and the vertical load.In addition,the measured self-similarity interval of the bubble area distribution is tested by the porous media fractal capillary bundle model,and the fitting curve of measured pore area ratio in a small loading range is obtained in this paper.
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.
文摘Efforts to protect electric power systems from faults have commonly relied on the use of ultra-high frequency(UHF)antennas for detecting partial discharge(PD)as a common precursor to faults.However,the effectiveness of existing UHF antennas suffers from a number of challenges such as limited bandwidth,relatively large physical size,and low detection sensitivity.The present study addresses these issues by proposing a compact microstrip patch antenna with fixed dimensions of 100 mm×100 mm×1.6 mm.The results of computations yield an optimized antenna design consisting of 2nd-order Hilbert fractal units positioned within a four-layer serpentine arrangement with a fractal unit connection distance of 3.0 mm.Specifically,the optimized antenna design achieves a detection bandwidth for which the voltage standing wave ratio is less than 2 that is approximately 97.3%of the UHF frequency range(0.3–3 GHz).Finally,a prototype antenna is fabricated using standard printed circuit board technology,and the results of experiments demonstrate that the proposed antenna is capable of detecting PD signals at a distance of 8 m from the discharge source.
文摘Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short when evaluating actual geographic features. In our study, we took a novel approach by analyzing map projection distortion from a geometric perspective. We computed the fractal dimensions of different stretches of coastline before and after projection using the divide-and-conquer algorithm and image processing. Our findings revealed that map projections, even when preserving basic shapes, inevitably stretch and compress coastlines in diverse directions. This analysis method provides a more realistic and practical way to measure map-induced distortions, with significant implications for cartography, geographic information systems (GIS), and geomorphology. By bridging the gap between theoretical analysis and real-world features, this method greatly enhances accuracy and practicality when evaluating map projections.
文摘The study of the hydrate formation process in porous media is of great significance for hydrate application.In this work,the formation process of methane hydrate in porous media was monitored in situ by a low-field magnetic resonance imaging(MRI)system.The formation characteristics of methane hydrate in porous media and the change of fractal dimension of pore space were studied through the change of residual water saturation and T2 relaxation time distribution.The experimental results show that the hydrate formation process is divided into two stages:fast and slow.During the formation process,the water in the pores is continuously consumed and transformed into hydrate,and the overall T2 distribution gradually shifts to the left.In the formation process of hydrate,the pore space becomes more complex,the change of fractal dimension from top to bottom of the reactor gradually increases,and the hydrate formation rate also gradually increases.
基金supported by National Natural Science Foundation of China(Grants Nos.11071224 and 11371329)Program for New Century Excellent Talents in University+1 种基金Natural Science Foundation of Zhejiang Province(Grants Nos.LY12F02011 and LR13A1010001)Foundation of Zhejiang Educational Committee(Grant No.Y201226044)
文摘This paper studies the self-similar fractals with overlaps from an algorithmic point of view.A decidable problem is a question such that there is an algorithm to answer"yes"or"no"to the question for every possible input.For a classical class of self-similar sets{E b.d}b,d where E b.d=Sn i=1(E b,d/d+b i)with b=(b1,...,b n)∈Qn and d∈N∩[n,∞),we prove that the following problems on the class are decidable:To test if the Hausdorff dimension of a given self-similar set is equal to its similarity dimension,and to test if a given self-similar set satisfies the open set condition(or the strong separation condition).In fact,based on graph algorithm,there are polynomial time algorithms for the above decidable problem.
文摘The main contents in this note are: 1. introduction; 2. locally compact groups and local fields; 3. calculus on fractals based upon local fields; 4. fractional calculus and fractals; 5. fractal function spaces and PDE on fractals.
文摘At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynamics i.e. deterministic chaos and fractal geometry is the best mathematical theory to apply to the problems of high energy particle physics and cosmology. In the present work we give a short survey of some recent achievements of applying nonlinear dynamics to notoriously difficult subjects such as quantum entanglement as well as the origin and true nature of dark energy, negative absolute temperature and the fractal meaning of the constancy of the speed of light.
文摘A new model of multirange fractals is proposed to explain the experimental results observed on the fractal dimensions of the fractured surfaces in materials. A new explanation to the Williford's multifractal curve on the relationship of fractal dimension with fracture properties in materials has been given. It shows the importance of fractorizing out the effect of fractal structure from other physical causes and separating the appropriate range of scale from multirange fractals. Mechanical alloying process under ball milling as a non-equilibrium dynamical system has been also analyzed.