Tight oil is the most viable target for unconventional oil and gas exploration, but the complexity of micro-/nanopore throat systems significantly affects the oil content of reservoirs. To investigate the causes of he...Tight oil is the most viable target for unconventional oil and gas exploration, but the complexity of micro-/nanopore throat systems significantly affects the oil content of reservoirs. To investigate the causes of heterogeneity in oil-bearing reservoirs, a high-pressure mercury injection experiment combined with fractal theory was conducted to analyze the micro pore throat structure characteristics of the tight sandstone of Chang 7 Member reservoirs in the Ordos Basin. The factors controlling the variations in oil content among tight sandstone samples were identified based on mineral composition characteristics. The results indicate that the pore throat radius distribution is mainly unimodal an bimodal. In oil-bearing samples, the pore throat distributions align well with the corresponding permeability contribution curves, while in oil-free samples, there is a clear deviation from these curves. Mesopore throats exert the greatest influence on seepage capacity. Differences in fractal characteristics are primarily reflected in D1 values, with oil-free samples exhibiting D1 values close to 3, indicating an extremely nonuniform pore throat structure at this scale. The content of quartz, plagioclase, and chlorite is significantly higher in oil-bearing samples than in oil-free samples, whereas calcite content is lower in oil-bearing samples. There is a positive correlation between the contents of quartz, plagioclase, and chlorite with D1;their increased presence contributes to a more favorable pore throat structure.Conversely, the calcite contents show an inverse relationship with D1. Cementation increases the complexity of pore throat structures, while multiple diagenetic processes simultaneously control these characteristics, leading to variations in oil content.展开更多
The pore structure of rocks significantly influences the porosity and permeability of reservoirs and the migration ability of oil and gas,and being the key task on the development of volcanic gas reservoirs.Nine volca...The pore structure of rocks significantly influences the porosity and permeability of reservoirs and the migration ability of oil and gas,and being the key task on the development of volcanic gas reservoirs.Nine volcanic rock samples from the Yingcheng Formation and Huoshiling Formation in the Longfengshan area of the Changling Fault Depression in the Songliao Basin were selected for this study.The pore structures of the volcanic rocks in the study area were investigated using high-pressure mercury injection,X-ray diffraction combined with fractal theory.The relationships between the fractal dimension and physical properties characteristics,pore structure parameters,and mineral content were analyzed to provide guidance for the development of volcanic rock gas reservoirs.The results show that the reservoir can be divided into 3 types(I,II,and III)based on the shape of the capillary pressure curve,and the physical properties deteriorate successively.Different types of reservoirs exhibit different fractal characteristics.For typesⅠ,ⅡandⅢ,the average total fractal dimensions were 2.3418,2.6850,and 2.9203,respectively.The larger the fractal dimension,the stronger the heterogeneity of reservoir.A small number of macro-pores primarily contributed to permeability.The fractal dimension was negatively correlated with porosity and permeability.The fractal dimension of the rock was strongly correlated with quartz and feldspar contents,and the mineral composition and content are closely related to the pore evolution of the reservoir,which are the internal factors affecting the fractal dimension of volcanic rock.展开更多
Shales from the Lower Cambrian Niutitang Formation of Yangtze Platform have been widely investigated due to its shale gas potential.To better illustrate the pore structure and fractal characteristics of shale,a series...Shales from the Lower Cambrian Niutitang Formation of Yangtze Platform have been widely investigated due to its shale gas potential.To better illustrate the pore structure and fractal characteristics of shale,a series of experiments were conducted on outcrop samples from the Lower Cambrian Niutitang Formation on Yangtze Platform,including X-ray diffraction(XRD),field-emission scanning electron microscopy(FE-SEM) and low-temperature nitrogen adsorption.Frenkel-Halsey-Hill(FHH) model was adopted to calculate the fractal dimensions.Furthermore,the relationships between fractal dimensions and pore structure parameters and mineral composition are discussed.FE-SEM observation results show that interparticle pores are most developed in shale,followed by intraparticle pores.This study identified the fractal dimensions D1(ranging from 2.558 0 to 2.710 2) and D2(ranging from 2.541 5 to 2.765 2).The pore structure of the Niutitang Formation shale is primarily controlled by quartz and clay content.Fractal dimensions are able to characterize the pore structure complexity of Niutitang Formation shale because D1 and D2 correlate well with average pore diameter and quartz content.展开更多
Based on 10 shale samples collected from 4 wells in Qinshui Basin,we investigate the full-sized pore structure and fractal characteristics of Marine-Continental transitional shale by performing organic geochemistry,mi...Based on 10 shale samples collected from 4 wells in Qinshui Basin,we investigate the full-sized pore structure and fractal characteristics of Marine-Continental transitional shale by performing organic geochemistry,mineralogical composition,Nitrogen gas adsorption(N2 adsorption)and Nuclear Magnetic Resonance(NMR)measurements and fractal analysis.Results show that the TOC content of the shale samples is relatively high,with an average value of 2.44wt%,and the thermal evolution is during the mature-over mature stage.The NMR T2 spectrum can be used to characterize the fullsized pore structure characteristics of shale.By combining N2 adsorption pore structure parameters and NMR T2 spectrums,the surface relaxivity of samples are calculated to be between 1.7877 um/s and 5.2272 um/s.On this basis,the T2 spectrums are converted to full-sized pore volume and surface area distribution curves.The statistics show that the pore volume is mainly provided by mesopore,followed by micropore,and the average percentages are 65.04%and 30.83%respectively;the surface area is mainly provided by micropore,followed by mesopore,and the average percentages are 60.8004%and 39.137%respectively;macropore contributes little to pore volume and surface area.The pore structure characteristics of shale have no relationship with TOC,but strong relationships with clay minerals content.NMR fractal dimensions Dmicro and Dmeso have strong positive relationships with the N2 adsorption fractal dimensions D1 and D2 respectively,indicating that Dmicro can be used to characterize the fractal characteristics of pore surface,and Dmeso can be used to characterize the fractal characteristics of pore structure.The shale surface relaxivity is controlled by multiple factors.The increasing of clay mineral content,pore surface area,pore surface fractal dimension and the decreasing of average pore size,will all lead to the decreasing of shale surface relaxivity.展开更多
Quantitative analyses of the spatial distribution of fault structures can provide a theoretical basis for forecasting prospective ore deposits. Characteristics and complexity of fault structure distribution in the Qit...Quantitative analyses of the spatial distribution of fault structures can provide a theoretical basis for forecasting prospective ore deposits. Characteristics and complexity of fault structure distribution in the Qitianling area, Southern Hunan Province, China, were quantitatively calculated and appraised by fractal and multifractal methods to evaluate the relation between fault structures and ore-prospecting potential. The results show that the lengths of faults can be modeled as multifractals. Multifractal spectra evidently reflect the characteristics of the scaling of fault structures. The box- counting dimension value （D） of fault structures is equal to 1.656, as indicates complexity of the spatial distribution of faults and favorable structural conditions for the formation of ore deposits. Moreover, the D values of sub-regions were calculated and isopleths of their fractal dimension values were plotted accordingly. Overlay analyses of isopleths of fractal dimension values and distributions of known ore deposits show that areas with the larger fractal dimension values of fault structures have more ore deposits. This spatial coupling relationship between D values and ore deposits can be used to forecast and explore other ore deposits. On the basis of complexity theory for ore-forming systems, three exploration targets with high D values were delineated as prospective ore deposits.展开更多
A fractal pore structure model of combustible cartridge cases was established by virtue of the fractal geometry. Pore structure information, such as backbone fractal dimension and pore fractal dimension, of four kinds...A fractal pore structure model of combustible cartridge cases was established by virtue of the fractal geometry. Pore structure information, such as backbone fractal dimension and pore fractal dimension, of four kinds of combustible cartridge case were obtained by mercury intrusion porosimetry (MIP) . The formation mechanism of fractal pore structure of combustible cartridge was studied. The results show that the backbone fractal dimension consists of the component and influenced by the component number and size of components; the pore percolation fractal dimension reflects the pore structures of components; and the fractal dimension of pore structure is positively relative to the tensile strength of combustible cartridge case.展开更多
Exploration practice indicates that free gas is the key to the large-scale development of shale gas,while adsorbed gas is also of great significance to the sustainable development of shale gas,and thus systematic rese...Exploration practice indicates that free gas is the key to the large-scale development of shale gas,while adsorbed gas is also of great significance to the sustainable development of shale gas,and thus systematic researches on absorbed pores are needed.To date,researches on pore structure and multi-scale fractal characteristics of absorbed pores in marine shale are obviously insufficient,limited the understanding of gas production behavior from shale reservoir.In this study,total organic carbon(TOC),X-ray diffraction(XRD),CH_(4) adsorption,field emission electron microscopy(FE-SEM),and low temperature gas(i.e.,CO_(2)and N_(2))adsorption/desorption analyses were conducted on 10 continuously core samples from the Lower Silurian Longmaxi shale in the Fuling region of Sichuan Basin,China.The results indicate that the TOC content of marine shale samples changes from 0.95%to 4.55%with an average of 2.62%,showing an increasing trend with the increase of burial depth;moreover,quartz and clay are the dominated mineral compositions in marine shale,and they show a certain negative correlation.FE-SEM analysis indicates that almost all pore types in marine shale are related to organic matter(OM).Hysteresis loops of marine shale samples mainly belong to Type H2,further indicating that the pores in marine shale are mainly ink-bottle pores(i.e.,OM pores);moreover,adsorption isotherms obtained from CO_(2)adsorption data all belong to typeⅠ,indicating microporous properties for all shale samples.Comprehensive analysis indicates that pore volume and pore surface area of adsorbed pores(<300 nm)is mainly provided by the pores within the pore range of 0.6–0.7,0.80–0.85,and 1.7–5.0 nm.Based on the micropore filling model and the Frenkel-Halsey-Hill(FHH)model,multiscale fractal dimensions(D1,D2,and D3)are calculated from gas adsorption data(i.e.,CO_(2)and N_(2)),corresponding to part of micropore(0.6–1.1 nm),small-mesopore(1.7–5.0 nm),big-mespore and part of macropore(5.0–300 nm),respectively.Relationships between shale compositions,pore structure,and fractal dimensions(D1,D2,and D3)indicate that pore structure and multi-scale fractal characteristics of absorbed pores in marine shale are obviously influenced by the contents of TOC and quartz,while clay minerals have little effect on them.Comprehensive analysis indicates that the complexity of marine shale pores within the range of 0.6–1.1 and 1.7–5.0 nm has significant effects on CH_(4) adsorbability,while the larger pores(5.0–300 nm)almost have no effect.展开更多
One of the most remarkable characteristics of debris flow is the competence for supporting boulders on the surface of flow, which strongly suggests that there should be some structure in the fluid body. This paper ana...One of the most remarkable characteristics of debris flow is the competence for supporting boulders on the surface of flow, which strongly suggests that there should be some structure in the fluid body. This paper analyzed the grain compositions from various samples of debris flows and then revealed the fractal structure. Specifically, the fractality holds in three domains that can be respectively identified as the slurry, matrix, and the coarse content. Furthermore, the matrix fractal, which distinguishes debris flow from other kinds of flows, involves a hierarchical structure in the sense that it might contain ever increasing grains while the total range of grain size increases. It provides a possible mechanism for the boulder suspension.展开更多
In this study,X-ray diffraction,N_(2)adsorption(N_(2)A),and mercury intrusion(MI)experiments were used to investigate the influence of acid treatment on pore structure and fractal characterization of tight sandstones....In this study,X-ray diffraction,N_(2)adsorption(N_(2)A),and mercury intrusion(MI)experiments were used to investigate the influence of acid treatment on pore structure and fractal characterization of tight sandstones.The results showed that acid treatment generated a certain number of ink-bottle pores in fine sandstone,aggravated the ink-bottle effect in the sandy mudstone,and transformed some smaller pores into larger ones.After the acid treatment,both the pore volume in the range of 2–11 nm and 0.271–8μm for the fine sandstone and the entire pore size range for the sandy mudstone significantly increased.The dissolution of sandstone cement causes the fine sandstone particles to fall off and fill the pores;the porosity increased at first but then decreased with acid treatment time.The fractal dimension obtained using the Frenkel-Halsey-Hill model was positively correlated with acid treatment time.However,the total fractal dimensions obtained by MI tests showed different changes with acid treatment time in fine sandstone and sandy mudstone.These results provide good guiding significance for reservoir acidification stimulation.展开更多
Nonwovens are fiber materials which are based on nonwoven technologies. For the complexity and randomness of nonwovens morphologic structures, it is difficult to express them effectively using classical method. Fracta...Nonwovens are fiber materials which are based on nonwoven technologies. For the complexity and randomness of nonwovens morphologic structures, it is difficult to express them effectively using classical method. Fractal geometry gives us a new idea and a powerful tool to study on irregularity of geometric objects. Therefore, we studied on the pore size, pore shape, pore size distribution and fiber orientation distribution of real nonwovens using fractal geometry combined with computer image analysis to evaluate nonwovens’ morphologic structures.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
Accurately reconstructing rock structures using numerical methods is vital in rock mechanics research community,especially when obtaining rock samples is difficult and expensive.The reconstructed models must reflect t...Accurately reconstructing rock structures using numerical methods is vital in rock mechanics research community,especially when obtaining rock samples is difficult and expensive.The reconstructed models must reflect the comprehensive characteristics of natural rock,including mineral content and spatial distributions.This study employs the bubbling method to reconstruct granite containing multiple minerals in both two-(2D)and three-dimensions(3D),proposing a general procedure for granite structure reconstruction.The bubbling method utilizes numerous bubbles(hemispheres or spheres)of varying sizes and gradually changing properties,which are randomly overlapped to create a heterogeneous plane(2D)or space(3D).The properties of these overlapped areas are adjusted based on the sum of neighboring bubbles'properties,allowing specific regions with extreme properties to be selected and intercepted to form the desired mineral shapes.The results demonstrate that the reproduced granite samples can accurately exhibit the mineral distributions and sizes of real granite,quantified by fractal dimension(D)and the hourglass parameter(V_(Sum)=V_(Total)).The proposed method is also suitable for reconstructing anisotropic granite models,with anisotropy described by a fitted elliptic curve derived from ratios between directional mineral sizes and cross-sectional dimensions.Based on these findings,a series of numerical granite models with similar structures were reconstructed and tested.Results indicate that different mineral distributions significantly impact the macroscopic mechanical behaviors,but variability in numerical simulation results decreases with increasing specimen size.The compressive and tensile strength values of the reconstructed numerical models show less variation than those of natural granite specimens.This suggests that,beyond mineral distribution,other factors such as internal defects within natural granite contribute to the observed discrepancies.Additionally,the bubbling method shows great potential for modeling porous structures and offers high computational efficiency.展开更多
The fractal structures formed in rapidly quenched Al_(86)Mn_(14)alloy have been observed on SEM.Their fractal dimensions are from 1.46 to 1.97.The principal phase examined by TEM and X-ray diffractometer is icosahedra...The fractal structures formed in rapidly quenched Al_(86)Mn_(14)alloy have been observed on SEM.Their fractal dimensions are from 1.46 to 1.97.The principal phase examined by TEM and X-ray diffractometer is icosahedral quasicrystalline one with a small amount of Al phase. It is believed that these fractal structures are formed by many aggregated particles during the rapid-quenching process.展开更多
In this paper, the generalized Kuramoto-Sivashinsky equations (GKS) with periodic boundary value problem are considered and the construction of inertial sets in space H-2 is given. Furthermore, this paper gives and pr...In this paper, the generalized Kuramoto-Sivashinsky equations (GKS) with periodic boundary value problem are considered and the construction of inertial sets in space H-2 is given. Furthermore, this paper gives and proves the fractal structure of attractors for GKS equations, and find out an exponentially approximating sequence of compact fractal localizing sets of the attractors, these results sharpen and improve the conclusions of the inertial sets and attractor for GKS equation in [1,3,5,7], which describe a kind of geometrical structure of the attractors.展开更多
When a molybdenum sheet was heated properly at 900℃ in an oxidizing atmosphere, Mo_5O_(14) single crystals will grow.The size of the most coarse single crystal is up to 15×1.1 mm and 310 nm thick as measured by ...When a molybdenum sheet was heated properly at 900℃ in an oxidizing atmosphere, Mo_5O_(14) single crystals will grow.The size of the most coarse single crystal is up to 15×1.1 mm and 310 nm thick as measured by Rutherford backscattering spectrometry.Some fractal structure consisting of many molybdena whiskers were observed after heating at 750℃.An approach to explain the crystal growth and fractal structure has been discussed.展开更多
Ths paper，based on the principles of geometric self-similarity of fractal theory and some research results of rotein chemistry，improved the method of comput－ing protein fractal dimensions，and computed fractal dime...Ths paper，based on the principles of geometric self-similarity of fractal theory and some research results of rotein chemistry，improved the method of comput－ing protein fractal dimensions，and computed fractal dimensions of some protein back bone，secondary and assumed folding structures．The relationship between protein back-bone strucrural fractal dimensions and its spatial structures was investigated．The results indicated that protein backbone fractal dimensions not only have a close relation with protein secondary structure，but also with its folding．In addition，the folding of protein Polypeptide chains in 3-D space may be similar to the other macromolecular chain be haviour described by the self-avoiding walks（SAW）model．展开更多
The geological structure of coal seams in China is remarkably varied and complex,with coalbed methane reservoirs marked by significant heterogeneity and low permeability,creating substantial technical challenges for e...The geological structure of coal seams in China is remarkably varied and complex,with coalbed methane reservoirs marked by significant heterogeneity and low permeability,creating substantial technical challenges for efficient extraction.This study systematically investigates the impact of liquid nitrogen immersion(LNI)on the coal’s pore structure and its mechanism of enhancing permeability with a combination of quantitative nuclear magnetic resonance(NMR)analysis,nitrogen adsorption experiments,and fractal dimension calculations.The results demonstrate that LNI can damage the coal’s pore structure and promote fracture expansion through thermal stress induction and moisture phase transformation,thereby enhancing the permeability of coal seams.The T_(2)peak area in the NMR experiments on coal samples subjected to LNI treatment shows a significant increase,the Brunauer-Emmett-Teller(BET)specific surface area decreases to 6.02 m^(2)/g,and the Barrett-Joyner-Halenda(BJH)total pore volume increases to 14.99 mm^(3)/g.Furthermore,changes in fractal dimensions(D_(1)rising from 2.804 to 2.837,and D_(2)falling from 2.757 to 2.594)indicate a notable enhancement in the complexity of the pore structure.With increasing LNI cycles,the adsorption capacity of the coal samples diminishes,suggesting a significant optimization of the pore structure.This optimization is particularly evident in the reconstruction of the micropore structure,which in turn greatly enhances the complexity and connectivity of the sample’s pore network.In summary,the study concludes that LNI technology can effectively improve the permeability of coal seams and the extraction efficiency of coalbed methane by optimizing the micropore structure and enhancing pore connectivity,which offers a potential method for enhancing the permeability of gas-bearing coal seams and facilitating the development and utilization of coalbed methane.展开更多
Based on the fractal theory, the spatial structure of China＇s vegetation has been analyzed quantitatively in this paper. Some conclusions are drawn as the following. 1） The relationships between size and frequency o...Based on the fractal theory, the spatial structure of China＇s vegetation has been analyzed quantitatively in this paper. Some conclusions are drawn as the following. 1） The relationships between size and frequency of patch area and patch shape index exist objectively for China＇s vegetation. 2） The relationships between perimeter and area exist objectively for China＇s vegetation. 3） The fractal dimension of evergreen needleleaf forests on mountains in subtropical and tropical zones is the largest, while the smallest for deciduous broadleafand evergreen needleleaf mixed forests in temperate zone, reflecting the most complex spatial structure for evergreen needleleaf forests on mountains in subtropical and tropical zones and the simplest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone. 4） The fractal dimensions of China＇s vegetation types tend to decrease from thc subtropics to both sides. 5） The stability of spatial structure of deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone is the largest, while the smallest for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards, reflecting the steadiest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone and the most unstable for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards in spatial structure. 6） The stability of spatial structure of China＇s vegetation tends to decrease from the temperate zone to both sides, it is significantly pertinent to understand the formation, evolution, dynamics and complexity rule of ecosystem of vegetation.展开更多
The ionization rate of Rydberg lithium atoms in a static electric field is examined within semiclassical theory which involves scattering effects off the core. By semiclassical analysis, this ionization process can be...The ionization rate of Rydberg lithium atoms in a static electric field is examined within semiclassical theory which involves scattering effects off the core. By semiclassical analysis, this ionization process can be considered as the promoted valence electrons escaping through the Stark saddle point into the ionization channels. The resulting escape spectrum of the ejected electrons demonstrates a remarkable irregular electron pulse train in time-dependence and a complicated nesting structure with respect to the initial launching angles. Based on the Poincaré} map and homoclinic tangle approach, the chaotic behaviour along with its corresponding fractal self-similar structure of the ionization spectra are analysed in detail. Our work is significant for understanding the quantum-classical correspondence.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 42002139)the Basic Prospective Project of SINOPEC (Grant No. P23240-3)。
文摘Tight oil is the most viable target for unconventional oil and gas exploration, but the complexity of micro-/nanopore throat systems significantly affects the oil content of reservoirs. To investigate the causes of heterogeneity in oil-bearing reservoirs, a high-pressure mercury injection experiment combined with fractal theory was conducted to analyze the micro pore throat structure characteristics of the tight sandstone of Chang 7 Member reservoirs in the Ordos Basin. The factors controlling the variations in oil content among tight sandstone samples were identified based on mineral composition characteristics. The results indicate that the pore throat radius distribution is mainly unimodal an bimodal. In oil-bearing samples, the pore throat distributions align well with the corresponding permeability contribution curves, while in oil-free samples, there is a clear deviation from these curves. Mesopore throats exert the greatest influence on seepage capacity. Differences in fractal characteristics are primarily reflected in D1 values, with oil-free samples exhibiting D1 values close to 3, indicating an extremely nonuniform pore throat structure at this scale. The content of quartz, plagioclase, and chlorite is significantly higher in oil-bearing samples than in oil-free samples, whereas calcite content is lower in oil-bearing samples. There is a positive correlation between the contents of quartz, plagioclase, and chlorite with D1;their increased presence contributes to a more favorable pore throat structure.Conversely, the calcite contents show an inverse relationship with D1. Cementation increases the complexity of pore throat structures, while multiple diagenetic processes simultaneously control these characteristics, leading to variations in oil content.
基金Supported by Key Scientific and Technological Projects of Sinopec(No.P21104-2).
文摘The pore structure of rocks significantly influences the porosity and permeability of reservoirs and the migration ability of oil and gas,and being the key task on the development of volcanic gas reservoirs.Nine volcanic rock samples from the Yingcheng Formation and Huoshiling Formation in the Longfengshan area of the Changling Fault Depression in the Songliao Basin were selected for this study.The pore structures of the volcanic rocks in the study area were investigated using high-pressure mercury injection,X-ray diffraction combined with fractal theory.The relationships between the fractal dimension and physical properties characteristics,pore structure parameters,and mineral content were analyzed to provide guidance for the development of volcanic rock gas reservoirs.The results show that the reservoir can be divided into 3 types(I,II,and III)based on the shape of the capillary pressure curve,and the physical properties deteriorate successively.Different types of reservoirs exhibit different fractal characteristics.For typesⅠ,ⅡandⅢ,the average total fractal dimensions were 2.3418,2.6850,and 2.9203,respectively.The larger the fractal dimension,the stronger the heterogeneity of reservoir.A small number of macro-pores primarily contributed to permeability.The fractal dimension was negatively correlated with porosity and permeability.The fractal dimension of the rock was strongly correlated with quartz and feldspar contents,and the mineral composition and content are closely related to the pore evolution of the reservoir,which are the internal factors affecting the fractal dimension of volcanic rock.
基金supported by the National Natural Science Foundation of China(Nos41690131,41572327,41273001)the Program of Introducing Talents of Discipline to Universities(No.B14031)
文摘Shales from the Lower Cambrian Niutitang Formation of Yangtze Platform have been widely investigated due to its shale gas potential.To better illustrate the pore structure and fractal characteristics of shale,a series of experiments were conducted on outcrop samples from the Lower Cambrian Niutitang Formation on Yangtze Platform,including X-ray diffraction(XRD),field-emission scanning electron microscopy(FE-SEM) and low-temperature nitrogen adsorption.Frenkel-Halsey-Hill(FHH) model was adopted to calculate the fractal dimensions.Furthermore,the relationships between fractal dimensions and pore structure parameters and mineral composition are discussed.FE-SEM observation results show that interparticle pores are most developed in shale,followed by intraparticle pores.This study identified the fractal dimensions D1(ranging from 2.558 0 to 2.710 2) and D2(ranging from 2.541 5 to 2.765 2).The pore structure of the Niutitang Formation shale is primarily controlled by quartz and clay content.Fractal dimensions are able to characterize the pore structure complexity of Niutitang Formation shale because D1 and D2 correlate well with average pore diameter and quartz content.
基金support from the National Science and Technology Major Project of China (Grant No. 2016ZX05034)
文摘Based on 10 shale samples collected from 4 wells in Qinshui Basin,we investigate the full-sized pore structure and fractal characteristics of Marine-Continental transitional shale by performing organic geochemistry,mineralogical composition,Nitrogen gas adsorption(N2 adsorption)and Nuclear Magnetic Resonance(NMR)measurements and fractal analysis.Results show that the TOC content of the shale samples is relatively high,with an average value of 2.44wt%,and the thermal evolution is during the mature-over mature stage.The NMR T2 spectrum can be used to characterize the fullsized pore structure characteristics of shale.By combining N2 adsorption pore structure parameters and NMR T2 spectrums,the surface relaxivity of samples are calculated to be between 1.7877 um/s and 5.2272 um/s.On this basis,the T2 spectrums are converted to full-sized pore volume and surface area distribution curves.The statistics show that the pore volume is mainly provided by mesopore,followed by micropore,and the average percentages are 65.04%and 30.83%respectively;the surface area is mainly provided by micropore,followed by mesopore,and the average percentages are 60.8004%and 39.137%respectively;macropore contributes little to pore volume and surface area.The pore structure characteristics of shale have no relationship with TOC,but strong relationships with clay minerals content.NMR fractal dimensions Dmicro and Dmeso have strong positive relationships with the N2 adsorption fractal dimensions D1 and D2 respectively,indicating that Dmicro can be used to characterize the fractal characteristics of pore surface,and Dmeso can be used to characterize the fractal characteristics of pore structure.The shale surface relaxivity is controlled by multiple factors.The increasing of clay mineral content,pore surface area,pore surface fractal dimension and the decreasing of average pore size,will all lead to the decreasing of shale surface relaxivity.
基金financially supported by the China Geological Survey Project(Grant No.1212011121101)
文摘Quantitative analyses of the spatial distribution of fault structures can provide a theoretical basis for forecasting prospective ore deposits. Characteristics and complexity of fault structure distribution in the Qitianling area, Southern Hunan Province, China, were quantitatively calculated and appraised by fractal and multifractal methods to evaluate the relation between fault structures and ore-prospecting potential. The results show that the lengths of faults can be modeled as multifractals. Multifractal spectra evidently reflect the characteristics of the scaling of fault structures. The box- counting dimension value （D） of fault structures is equal to 1.656, as indicates complexity of the spatial distribution of faults and favorable structural conditions for the formation of ore deposits. Moreover, the D values of sub-regions were calculated and isopleths of their fractal dimension values were plotted accordingly. Overlay analyses of isopleths of fractal dimension values and distributions of known ore deposits show that areas with the larger fractal dimension values of fault structures have more ore deposits. This spatial coupling relationship between D values and ore deposits can be used to forecast and explore other ore deposits. On the basis of complexity theory for ore-forming systems, three exploration targets with high D values were delineated as prospective ore deposits.
基金Sponsored by Young Fund Programs of Explosives&Propellants ( HYZ08010202-4)
文摘A fractal pore structure model of combustible cartridge cases was established by virtue of the fractal geometry. Pore structure information, such as backbone fractal dimension and pore fractal dimension, of four kinds of combustible cartridge case were obtained by mercury intrusion porosimetry (MIP) . The formation mechanism of fractal pore structure of combustible cartridge was studied. The results show that the backbone fractal dimension consists of the component and influenced by the component number and size of components; the pore percolation fractal dimension reflects the pore structures of components; and the fractal dimension of pore structure is positively relative to the tensile strength of combustible cartridge case.
基金financially supported by the PetroChina Innovation Foundation(No.2019D-5007-0107)the National Natural Science Foundation of China(No.42172192)+3 种基金the National Natural Science Foundation for Young Scholars of China(No.41902173)the Fundamental Research Funds for the Central Universities(No.CUG170678)the Natural Science Foundation of Hubei Province(No.2019CFA028)the Program of Introducing Talents of Discipline to Universities(No.B14031)。
文摘Exploration practice indicates that free gas is the key to the large-scale development of shale gas,while adsorbed gas is also of great significance to the sustainable development of shale gas,and thus systematic researches on absorbed pores are needed.To date,researches on pore structure and multi-scale fractal characteristics of absorbed pores in marine shale are obviously insufficient,limited the understanding of gas production behavior from shale reservoir.In this study,total organic carbon(TOC),X-ray diffraction(XRD),CH_(4) adsorption,field emission electron microscopy(FE-SEM),and low temperature gas(i.e.,CO_(2)and N_(2))adsorption/desorption analyses were conducted on 10 continuously core samples from the Lower Silurian Longmaxi shale in the Fuling region of Sichuan Basin,China.The results indicate that the TOC content of marine shale samples changes from 0.95%to 4.55%with an average of 2.62%,showing an increasing trend with the increase of burial depth;moreover,quartz and clay are the dominated mineral compositions in marine shale,and they show a certain negative correlation.FE-SEM analysis indicates that almost all pore types in marine shale are related to organic matter(OM).Hysteresis loops of marine shale samples mainly belong to Type H2,further indicating that the pores in marine shale are mainly ink-bottle pores(i.e.,OM pores);moreover,adsorption isotherms obtained from CO_(2)adsorption data all belong to typeⅠ,indicating microporous properties for all shale samples.Comprehensive analysis indicates that pore volume and pore surface area of adsorbed pores(<300 nm)is mainly provided by the pores within the pore range of 0.6–0.7,0.80–0.85,and 1.7–5.0 nm.Based on the micropore filling model and the Frenkel-Halsey-Hill(FHH)model,multiscale fractal dimensions(D1,D2,and D3)are calculated from gas adsorption data(i.e.,CO_(2)and N_(2)),corresponding to part of micropore(0.6–1.1 nm),small-mesopore(1.7–5.0 nm),big-mespore and part of macropore(5.0–300 nm),respectively.Relationships between shale compositions,pore structure,and fractal dimensions(D1,D2,and D3)indicate that pore structure and multi-scale fractal characteristics of absorbed pores in marine shale are obviously influenced by the contents of TOC and quartz,while clay minerals have little effect on them.Comprehensive analysis indicates that the complexity of marine shale pores within the range of 0.6–1.1 and 1.7–5.0 nm has significant effects on CH_(4) adsorbability,while the larger pores(5.0–300 nm)almost have no effect.
基金the National Natural Science Foundation of China (40671025)the Knowledge Innovation Program of Chinese Academy of Sciences (IMHE1100001061)
文摘One of the most remarkable characteristics of debris flow is the competence for supporting boulders on the surface of flow, which strongly suggests that there should be some structure in the fluid body. This paper analyzed the grain compositions from various samples of debris flows and then revealed the fractal structure. Specifically, the fractality holds in three domains that can be respectively identified as the slurry, matrix, and the coarse content. Furthermore, the matrix fractal, which distinguishes debris flow from other kinds of flows, involves a hierarchical structure in the sense that it might contain ever increasing grains while the total range of grain size increases. It provides a possible mechanism for the boulder suspension.
基金supported by the National Natural Science Foundation of China(51674049,52074044,and 51874053)the Scientific Research Foundation of Hunan Provincial Education Department,China(22B0854)。
文摘In this study,X-ray diffraction,N_(2)adsorption(N_(2)A),and mercury intrusion(MI)experiments were used to investigate the influence of acid treatment on pore structure and fractal characterization of tight sandstones.The results showed that acid treatment generated a certain number of ink-bottle pores in fine sandstone,aggravated the ink-bottle effect in the sandy mudstone,and transformed some smaller pores into larger ones.After the acid treatment,both the pore volume in the range of 2–11 nm and 0.271–8μm for the fine sandstone and the entire pore size range for the sandy mudstone significantly increased.The dissolution of sandstone cement causes the fine sandstone particles to fall off and fill the pores;the porosity increased at first but then decreased with acid treatment time.The fractal dimension obtained using the Frenkel-Halsey-Hill model was positively correlated with acid treatment time.However,the total fractal dimensions obtained by MI tests showed different changes with acid treatment time in fine sandstone and sandy mudstone.These results provide good guiding significance for reservoir acidification stimulation.
文摘Nonwovens are fiber materials which are based on nonwoven technologies. For the complexity and randomness of nonwovens morphologic structures, it is difficult to express them effectively using classical method. Fractal geometry gives us a new idea and a powerful tool to study on irregularity of geometric objects. Therefore, we studied on the pore size, pore shape, pore size distribution and fiber orientation distribution of real nonwovens using fractal geometry combined with computer image analysis to evaluate nonwovens’ morphologic structures.
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funded by the National Key Research and Development Program of China(Grant No.2022YFC2903904)National Natural Science Foundation of China(Grant Nos.U1906208 and U21A20106).
文摘Accurately reconstructing rock structures using numerical methods is vital in rock mechanics research community,especially when obtaining rock samples is difficult and expensive.The reconstructed models must reflect the comprehensive characteristics of natural rock,including mineral content and spatial distributions.This study employs the bubbling method to reconstruct granite containing multiple minerals in both two-(2D)and three-dimensions(3D),proposing a general procedure for granite structure reconstruction.The bubbling method utilizes numerous bubbles(hemispheres or spheres)of varying sizes and gradually changing properties,which are randomly overlapped to create a heterogeneous plane(2D)or space(3D).The properties of these overlapped areas are adjusted based on the sum of neighboring bubbles'properties,allowing specific regions with extreme properties to be selected and intercepted to form the desired mineral shapes.The results demonstrate that the reproduced granite samples can accurately exhibit the mineral distributions and sizes of real granite,quantified by fractal dimension(D)and the hourglass parameter(V_(Sum)=V_(Total)).The proposed method is also suitable for reconstructing anisotropic granite models,with anisotropy described by a fitted elliptic curve derived from ratios between directional mineral sizes and cross-sectional dimensions.Based on these findings,a series of numerical granite models with similar structures were reconstructed and tested.Results indicate that different mineral distributions significantly impact the macroscopic mechanical behaviors,but variability in numerical simulation results decreases with increasing specimen size.The compressive and tensile strength values of the reconstructed numerical models show less variation than those of natural granite specimens.This suggests that,beyond mineral distribution,other factors such as internal defects within natural granite contribute to the observed discrepancies.Additionally,the bubbling method shows great potential for modeling porous structures and offers high computational efficiency.
文摘The fractal structures formed in rapidly quenched Al_(86)Mn_(14)alloy have been observed on SEM.Their fractal dimensions are from 1.46 to 1.97.The principal phase examined by TEM and X-ray diffractometer is icosahedral quasicrystalline one with a small amount of Al phase. It is believed that these fractal structures are formed by many aggregated particles during the rapid-quenching process.
文摘In this paper, the generalized Kuramoto-Sivashinsky equations (GKS) with periodic boundary value problem are considered and the construction of inertial sets in space H-2 is given. Furthermore, this paper gives and proves the fractal structure of attractors for GKS equations, and find out an exponentially approximating sequence of compact fractal localizing sets of the attractors, these results sharpen and improve the conclusions of the inertial sets and attractor for GKS equation in [1,3,5,7], which describe a kind of geometrical structure of the attractors.
文摘When a molybdenum sheet was heated properly at 900℃ in an oxidizing atmosphere, Mo_5O_(14) single crystals will grow.The size of the most coarse single crystal is up to 15×1.1 mm and 310 nm thick as measured by Rutherford backscattering spectrometry.Some fractal structure consisting of many molybdena whiskers were observed after heating at 750℃.An approach to explain the crystal growth and fractal structure has been discussed.
文摘Ths paper，based on the principles of geometric self-similarity of fractal theory and some research results of rotein chemistry，improved the method of comput－ing protein fractal dimensions，and computed fractal dimensions of some protein back bone，secondary and assumed folding structures．The relationship between protein back-bone strucrural fractal dimensions and its spatial structures was investigated．The results indicated that protein backbone fractal dimensions not only have a close relation with protein secondary structure，but also with its folding．In addition，the folding of protein Polypeptide chains in 3-D space may be similar to the other macromolecular chain be haviour described by the self-avoiding walks（SAW）model．
基金Projects(52204226,52104204,52474276)supported by the National Natural Science Foundation of ChinaProject(tsqnz20221140)supported by the Taishan Scholars Project of China+1 种基金Projects(ZR2022QE243,ZR2024ME097)supported by the Natural Science Foundation of Shandong Province of ChinaProject(252300421010)supported by the Excellent Youth Foundation of Henan Scientific Committee,China。
文摘The geological structure of coal seams in China is remarkably varied and complex,with coalbed methane reservoirs marked by significant heterogeneity and low permeability,creating substantial technical challenges for efficient extraction.This study systematically investigates the impact of liquid nitrogen immersion(LNI)on the coal’s pore structure and its mechanism of enhancing permeability with a combination of quantitative nuclear magnetic resonance(NMR)analysis,nitrogen adsorption experiments,and fractal dimension calculations.The results demonstrate that LNI can damage the coal’s pore structure and promote fracture expansion through thermal stress induction and moisture phase transformation,thereby enhancing the permeability of coal seams.The T_(2)peak area in the NMR experiments on coal samples subjected to LNI treatment shows a significant increase,the Brunauer-Emmett-Teller(BET)specific surface area decreases to 6.02 m^(2)/g,and the Barrett-Joyner-Halenda(BJH)total pore volume increases to 14.99 mm^(3)/g.Furthermore,changes in fractal dimensions(D_(1)rising from 2.804 to 2.837,and D_(2)falling from 2.757 to 2.594)indicate a notable enhancement in the complexity of the pore structure.With increasing LNI cycles,the adsorption capacity of the coal samples diminishes,suggesting a significant optimization of the pore structure.This optimization is particularly evident in the reconstruction of the micropore structure,which in turn greatly enhances the complexity and connectivity of the sample’s pore network.In summary,the study concludes that LNI technology can effectively improve the permeability of coal seams and the extraction efficiency of coalbed methane by optimizing the micropore structure and enhancing pore connectivity,which offers a potential method for enhancing the permeability of gas-bearing coal seams and facilitating the development and utilization of coalbed methane.
基金Under the auspices of the National Natural Science Foundation of China (No.40301002, No. 40335046)
文摘Based on the fractal theory, the spatial structure of China＇s vegetation has been analyzed quantitatively in this paper. Some conclusions are drawn as the following. 1） The relationships between size and frequency of patch area and patch shape index exist objectively for China＇s vegetation. 2） The relationships between perimeter and area exist objectively for China＇s vegetation. 3） The fractal dimension of evergreen needleleaf forests on mountains in subtropical and tropical zones is the largest, while the smallest for deciduous broadleafand evergreen needleleaf mixed forests in temperate zone, reflecting the most complex spatial structure for evergreen needleleaf forests on mountains in subtropical and tropical zones and the simplest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone. 4） The fractal dimensions of China＇s vegetation types tend to decrease from thc subtropics to both sides. 5） The stability of spatial structure of deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone is the largest, while the smallest for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards, reflecting the steadiest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone and the most unstable for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards in spatial structure. 6） The stability of spatial structure of China＇s vegetation tends to decrease from the temperate zone to both sides, it is significantly pertinent to understand the formation, evolution, dynamics and complexity rule of ecosystem of vegetation.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10774093 and 10374061)
文摘The ionization rate of Rydberg lithium atoms in a static electric field is examined within semiclassical theory which involves scattering effects off the core. By semiclassical analysis, this ionization process can be considered as the promoted valence electrons escaping through the Stark saddle point into the ionization channels. The resulting escape spectrum of the ejected electrons demonstrates a remarkable irregular electron pulse train in time-dependence and a complicated nesting structure with respect to the initial launching angles. Based on the Poincaré} map and homoclinic tangle approach, the chaotic behaviour along with its corresponding fractal self-similar structure of the ionization spectra are analysed in detail. Our work is significant for understanding the quantum-classical correspondence.
