Surface Fractal Dimension Research Articles

Anisotropy of fracture and permeability in high-rank coal analyzed using digital rock physics

Rock microstructure analysis and physical property simulation by means of digital rock physics (DRP) can overcome the deficiencies such as poor quantification and visibility in traditional petrophysical experiments. The establishment of a complete set of DRP is the basis of analyzing the microstructure of unconventional oil and gas reservoirs. In this study, high-rank coal, a material with anisotropic fracture and permeability properties, was tested using x-ray computer tomography scanning to reconstruct the digital core, and the fracture direction and structural characteristics were quantified with respect to the main inertia axis and the Feret diameter, respectively. A method for calculating the fractal dimension and tortuosity based on DRP is presented, and the optimal interaction between the lattice Boltzmann method seepage simulation and DRP is identified. The results show that the average length, width, aperture, and volume of fractures in the direction of face cleat (DFC) are 1.13, 1.10, 1.11, and 1.09 times that in the direction of butt cleat (DBC), respectively, and their surface area, count, fracture porosity, fractal dimension, and tortuosity are 1.17, 1.16, 1.26, 1.04, and 1.10 times that of DBC, respectively. The permeability of DFC was found to be 3.46 times that of DBC. This study presents an effective method for determining the dominant direction of fracture structure and fluid migration that is not limited to pores and fractures in rock but can also be used to characterize the physical properties of skeletons or solid particles in other materials.

Real-time pore structure evolution difference between deep and shallow coal during gas adsorption: A study based on synchrotron radiation small-angle X-ray scattering

Coal seam CO2 sequestration is an important option to address global warming. A better knowledge on coal pore structure evolution during gas adsorption can provide guidance for coal seams CO2 sequestration. However, few investigations on the pore structure evolution differences between the deep and shallow coal were conducted during gas adsorption. In this study, based on the real-time synchrotron radiation small-angle X-ray scattering (SAXS) observation, the average pore diameter and pore surface fractal dimension evolution differences between deep and shallow coal were investigated from the aspects of coal compositions and stress history. Two types of coal deformation (inner-swelling and outer-swelling) coexist during gas adsorption. Coal compositions have significant impact on the dominance of deformation type. The dominance of inner-swelling in deep coal is induced by the higher ash contents, and there is the decrease of average pore diameter during gas adsorption. The impact of stress-history (burial depth) on adsorption-induced deformation is more prominent than that of gas adsorption capacity. In deep coal, the surface fractal dimension evolution presents a negative correlation with the evolution of pore diameters. In shallow coal, the surface fractal dimension evolution presents a Langmuir-type correlation with the adsorption time.

Characterization, factors, and fractal dimension of pore structure of fly ash-based geopolymers

Fly ash-based geopolymer is a new cementitious material with environmentally friendly characteristics. Generally, the mechanical properties of cementitious materials are influenced by their pore structure. The variation in the pore structural characteristics of the geopolymers with various influencing factors was investigated in this study. A smaller activator modulus and liquid-solid ratio lead to a finer pore structure, while higher activator concentrations also result in a finer pore structure. However, the densification of pore structure does not follow a monotonic relationship with the conserving temperature. Increasing the conserving temperature within a certain range decreases the most probable pore diameter and porosity. Nevertheless, excessive temperature increase has the opposite effect. Furthermore, the fractal dimension was introduced to characterize the pore structure comprehensively. The results show that a lower pore volume, a larger pore-specific surface area, and a smaller most probable pore diameter contribute to increasing pore surface fractal dimension. Further, compared to porosity, the microporous pore surface fractal dimension shows a better linear correlation with compressive strength.

Multi-Objective Optimization of Micro-Milling Parameters—The Trade-Offs between Machining Quality, Efficiency, and Sustainability in the Fabrication of Thin-Walled Microstructures

Micro-milling has found extensive applications in machining components with thin-walled microstructures, such as terahertz slow-wave structures, microfluidic chips, and micro-molds. Due to the influence of size effects, micro-milling exhibits higher specific energy consumption compared with traditional milling, implying that more energy is consumed to remove a unit volume of material, particularly in challenging-to-machine materials like Ti-6Al-4V. Historically, research on parameter optimization for micro-milling has predominantly focused on enhancing machining quality and efficiency, with limited attention given to energy efficiency. However, in the context of the “double carbon” strategy, energy conservation and emissions reduction have garnered significant attention in the manufacturing industry. Therefore, this paper proposes a micro-milling parameter-based power consumption model. Based on this, a specific energy consumption model can be obtained. Moreover, evolutionary algorithms are utilized for the optimization of micro-milling parameters, which aims to achieve comprehensive enhancements in both machinability and sustainability. The optimization objectives encompass improving surface quality, dimensional accuracy, material removal rate, and specific energy consumption during the micro-milling process for thin-walled micro-structures. Among them, NSGA-III achieves the best optimization results. Under conditions in which cutting energy consumption and processing efficiency are very close, the optimization outcomes based on NSGA-III lead to the best machining quality, including the minimum surface roughness and dimensional errors, and the largest surface fractal dimension. The optimal combination of micro-milling parameters is n = 28,800 rpm, fz = 2.6 μm/t, and ap = 62 μm.

Study on the Particle Surface Fractal Characteristics of Sulfide Ores

The fractal dimension is widely used in many fields as a parameter to characterize the geometric complexity and geometric distribution relationship of research objects. To study the surface characteristics of sulfide ore particles, the fractal theory was applied to quantitatively characterize the surface fractal dimension Ds of sulfide ore microparticles in three particle size ranges, 60–100 mesh, 100–140 mesh and >200 mesh, based on the area–perimeter method. Using an optical microscope, grain projection images of the particles were obtained. The grain shape and characteristics of sulfide ore particles were studied by means of an image processing system. The results demonstrate that the grain shape of sulfide ore particles can be expressed by fractal dimension, and the particle surface fractal dimension ranges from 2.4392 to 2.5492. It was found that the fractal properties begin to decrease due to the increasing of the particle size. The larger the fractal dimension, the finer the particles are. The fractal dimension of sulfide ore particles can be used as an important indicator of their particle shape distribution characteristics, which can provide important information for further study of the relevant physical and chemical properties of sulfide ore particles and provide a new theoretical method and basis for the adhesion and removal of sulfide ore dust. With the quantitative description of the fractal distribution of sulfide ore particles, a new way to study the adhesive force between particles is offered for further research.

Investigation on the rheology, self-shrinkage, pore structure, and fractal dimension of coral powder-cement slurry

There is a significant amount of coral powder in coral aggregates, which has a negative impact on the operational performance, mechanical characteristics, and durability of coral reef sand concrete. The present study investigates the effect of coral powder with varying fineness and content on rheological and self-shrinkage properties using an Anton Paar MCR102 rotational rheometer and YC-BWS bellows self-shrinkage apparatus, respectively. The dynamic yield stress, rheological index, and plastic viscosity are obtained according to the Bingham model, Modified Bingham model, and Herschel-Bulkley model. The pore structures of coral powder-cement slurry are studied using a combination of MIP and SEM tests. Fractal theory is used to characterize the pore size distribution. The results demonstrate that the coral powder-cement slurry exhibits a shear thinning phenomenon. The Herschel-Bulkley model is successful in simulating the rheological behavior of cement slurry. The dynamic yield stress and plastic viscosity increase gradually as the fine coral powder content increases. With the increase in the coarse coral powder content, the dynamic yield stress decreases gradually while the plastic viscosity increases. The self-shrinking value of the coral powder-cement slurry increases rapidly within 1d but gradually stabilize with age. The self-shrinkage value increases with the increase in the coral powder admixture. The self-shrinkage value of the fine coral powder-cement slurry is less than that of the coarse coral powder-cement slurry. It is found that increase in the coral powder reduces the compressive strength of the cement paste, however, cement replacement with 10% coral powder is acceptable. Pore surface fractal dimension and capillary pore volume is able to effectively characterize pore size distribution and pore volume, respectively. Furthermore, the strength has a positive and negative linear relationship with the pore surface fractal dimension and capillary pore volume, respectively. The ratio of pore surface fractal dimension to capillary pore volume can be used as a parameter of the strength model. A linear relationship between the strength and the ratio of pore surface fractal dimension to capillary pore volume is proposed, and the model exhibits high accuracy.

An Experimental Study on the Influence of the Fractal Characteristics of X80 Steel Surface Morphology on Water Ring Stability

The surface morphology of X80 steel with hydrophilic underwater oleophobic characteristic is described greater comprehensively and quantitatively in this work by combining fractal dimension and multifractal. X80 steel with hydrophilic underwater oleophobic surface characteristics was constructed using a chemical etching method. Then, with the aid of three wettability parameters—contact angle, rolling angle, and adhesion work—this study investigated the relationship between the surface fractal dimension of X80 and the stability of the water ring in the core annular flow. The results showed that: (1) the fractal dimension of X80 steel specimens increased first and then decreased with the increase of reaction time. Besides that, the value of it was greater than 2, indicating that the surface had obvious fractal characteristics. The spectral difference, Δf(α), and the spectral width, Δα, supplemented the description of the X80 steel surface morphology, which was consistent with the scanning electron microscope results. (2) When the maximum fractal dimension was 2.0808, the minimum contact angle of distilled water on its surface was 50.2°, and the maximum contact angle of underwater oil droplets was 166.4°. The larger the fractal dimension of X80 steel with hydrophilic underwater oleophobic properties, the more hydrophilic and underwater oleophobic it is. This illustrated that there was a strong binding force between the water and the X80 steel pipe wall, and hence the quality and efficiency of the core annular flow was improved, which was more conducive to the promotion of this technology in the field of heavy oil transportation.

Solvent extraction of superfine pulverized coal. Part 3. Small angle X-ray scattering characterization

Because of the unique physicochemical textures induced by reduced particle size, superfine pulverized coal presents attractive characteristics in different utilization processes, including solvent extraction. In this work, the synchrotron radiation-based small angle X-ray scattering (SAXS) with high precision was used to quantitatively characterize all the products during the coal extraction process, including raw coal, extract, and residue. In addition, the evolutions of pore structures (solid state) and aggregate configurations (liquid state) were focused on. The results show that the fractal dimensions of pore surfaces are mainly related to the pore sizes and corresponding quantity distributions. When the particle size is less than 14 μm, the comminution induced mechanical effect on the pore surface gradually changes from impact to polish during the superfine grinding. Additionally, the fractal dimension decreases with the decline of particle size and ash content, whilst increases for the lower ranked coals. As for the extraction process, the extraction effect of tetrahydrofuran on anthracite coal is relatively better, while pyridine is more effective for bituminous coal. The diverse driving force caused by particle size effect leads to different radii of the gyration of the extracted aggregates, indicating the selected bituminous coal has active sites that are susceptible to reacting with aromatic compounds, while anthracite has a large number of active sites that accept electrons. Finally, the surface fractal dimension of the extraction residue declines about 2% and 4% for HN and NMG coal respectively, and the decreasing trend declines for larger coal particles. Interestingly, this decreasing trend of bituminous coal is more evident, which indicates the pore surface of bituminous coal is easier to react with solvent. The research sheds light on thoroughly depicting the pore structure of coal and residue at a molecular level, which promotes a better understanding of the solvent extraction mechanisms. The results also provide a new perspective for constructing more comprehensive coal molecular models in the future.

Efficient Evaluation of Concrete Fracture Surface Roughness Using Fringe Projection Technology.

The evaluation of concrete surface roughness is crucial in the field of civil engineering. The purpose of this study is to propose a no-contact and efficient method for the measurement of the roughness of concrete fracture surfaces based on fringe-projection technology. A simple phase-correction method using one additional strip image is presented for the phase unwrapping to improve the measurement efficiency and accuracy. The experimental results indicate that the measuring error for plane height is less than 0.1mm, and the relative accuracy for measuring a cylindrical object is about 0.1%, meeting the requirements for concrete fracture-surface measurement. On this basis, three-dimensional reconstructions were carried out on various concrete fracture surfaces to evaluate the roughness. The results reveal that the surface roughness (R) and fractal dimension (D) decrease as the concrete strength increases or the water-to-cement ratio decreases, consistent with previous studies. In addition, compared with the surface roughness, the fractal dimension is more sensitive to the change in concrete surface shape. The proposed method is effective for detecting concrete fracture-surface features.

Study of the Microstructure of Coal at Different Temperatures and Quantitative Fractal Characterization.

In order to understand the influence of underground coal fires on coal fractures and pores, mercury intrusion porosimetry (MIP) and scanning electron microscopy (SEM) are combined to study the development of coal pore and fracture under high-temperature treatment and calculate the fractal dimension to analyze the relationship between the development of coal pore and fracture and the fractal dimension. The results show that the volume of pores and fractures of the coal sample (C200) treated at 200 °C (0.1715 mL/g) is greater than that of the coal sample (C400) treated at 400 °C (0.1209 mL/g), and both are greater than the original coal sample (RC) (0.1135 mL/g). The volume increase is mainly due to mesopores and macropores, and the proportions of mesopores and macropores in C200 were 70.15 and 59.97% in C400. The MIP fractal dimension shows a decreasing trend with the increase of temperature, and the connectivity of coal samples improved with the increase of temperature. The changes in volume and three-dimensional fractal dimension of C200 and C400 showed the opposite trend and are related to the different stress of coal matrix at different temperatures. The experimental SEM images confirm that the connectivity of coal fractures and pores improves with the increase of temperature. Based on the SEM experiment, the larger the fractal dimension, the more complex the surface is. The SEM surface fractal dimensions indicate that the surface fractal dimension of C200 is the smallest and that of C400 is the largest, which is consistent with the observations made by SEM. The combination of the two fractal dimensions is used to characterize the self-similarity of coal using the fractal dimension difference. When the temperature increased to 200 °C, the unordered expansion of the coal sample resulted in the largest fractal dimension difference and the lowest self-similarity. When heated to 400 °C, the fractal dimension difference of the coal sample is the smallest, and the microstructure of coal shows a regular groove-like development.

The correlation of fractal dimension to fracture surface slope for fatigue crack initiation analysis under bending-torsion loading in high-strength steels

In this study, the fractal dimension of fatigue fracture surfaces is investigated in order to find an alternative failure loading indicator. Some of many metrological factors are generalized by reducing the fracture surface structure to one factor and develop an entire fracture surface procedure by analyzing the impact of surface slope and calculation resolution. Three notched geometries are studied under cyclic bending-torsion: 34CrNiMo6 high-strength steel bars with transverse blind holes; (ii) 34CrNiMo6 high-strength steel bars with lateral U-shaped notches; and (iii) 18Ni300 maraging steel hollow bars with transverse holes produced by selective laser melting. The surface topographies of fatigue fractures were measured with an optical profilometer. The bending-torsion ratio, maximum local von Mises equivalent stress and the number of cycles to crack initiation are examined using the fractal dimension. Moreover, a comparison was also made for conventional surface topography parameters such as root mean square height and void volume. A fatigue crack initiation model based on surface topography and loading conditions is proposed. The model relies on the product of the maximum local von Mises equivalent stress and the fractal dimension divided by the root mean square height to void volume ratio. The results show that the fracture plane geometry, expressed by the fractal dimension Df, can facilitate the estimation of post-failure loading history. In particular, the analysis based on the enclosing boxes method (EBM) is more accurate when it is used as an extra-fine resolution without any plane leveling.

Microreactor for the characterization of zeolite hydrothermal synthesis by small angle X-ray scattering (SAXS)

During zeolite synthesis, exploring the growth of nanoparticles is crucial for studying the crystallization mechanism. Synchrotron radiation small angle X-ray scattering (SAXS) is a powerful technique for the in-situ characterization of zeolite crystallization. Herein, a microreactor was developed for use at the Beijing Synchrotron Radiation Facility (BSRF) to achieve the in-situ SAXS characterization of the nucleation and growth of zeolite crystallization. The results show that the fractal structure convert from surface fractal during induction nucleation to mass fractal during crystal growth. The surface fractal dimension first fluctuated slightly and increased rapidly, while the mass fractal dimension gradually increased, reflecting the particle growth. This work provides important information for further exploring zeolite crystallization.

Influences of double-sided molding method and initial particle size on fragmentation characteristics of reconstituted coal briquette

Using the reconstituted coal briquette to replace tectonic coal is a forced choice for many experimental studies on the mechanism of coal and gas outbursts. The molding method and initial particle size are two important factors affecting the properties of the soil-like coal briquette. In this study, tectonic coal particles with five different initial sizes were compressed into coal briquettes using three different molding methods. Each coal briquette was evenly divided into five parts along the vertical direction and each subunit was fragmented by a drop hammer to test the firmness. The results show that the briquette density first increases and then decreases with the rise of initial particle size. Briquettes obtained by the traditional one-sided molding method possess the lowest density. The fragment size distributions of the briquettes and the original tectonic coal have segmented and non-segmented fractal characteristics, respectively, which are mainly related to the initial particle size distribution of the coal powder used for making briquettes. Combining the vertical distribution laws of the surface work, Protodyakonov coefficients, and fractal dimension of the briquettes, it is determined that the coal briquettes obtained by the double-sided molding method are soft in the middle and possess a relatively symmetric structure. The surface work and Protodyakonov coefficients of the briquettes (9.03 ± 2.27 J/m2 and 0.10 ± 0.02, respectively) are comparable to those of the in-situ tectonic coal with the highest outburst risk.

Pore structure and gasification activity of coal and coke studied by small-angle X-ray scattering

ABSTRACTCarbonisation is one of the important methods to improve the utilisation of coal. The structural composition of coal plays an important role in coal carbonisation. This work used small-angle X-ray scattering (SAXS) to investigate the pore structure of three kinds of raw coals with different carbon content derived from Xingtai City, Hebei Province, China. The structures of the corresponding cokes obtained through carbonisation at 1200°C were investigated by elemental analysis and SAXS. In addition, the gasification reaction of the three cokes (C1, C2, C3) with CO2 were studied by thermogravimetric analysis. The SAXS results indicate that the surface fractal dimension increases while the pore size decreases, and the pore distribution became wider after carbonisation. In addition, all coals and cokes present a positive deviation from Porod’s law, indicating that there is a micro-fluctuation of electron density in the samples. Besides, it exhibites a negative correlation has been found between the degree of deviation from Porod’s law and the carbon content. The gasification reactivity of cokes C1 and C3 in CO2 are higher than that of C2, indicating that the pore structures affect the gas reactivity of the three different metamorphic degree cokes in CO2.

Assessment of pore structure characteristics and tortuosity of 3D printed concrete using mercury intrusion porosimetry and X-ray tomography

Extrusion-based concrete 3D printing is being increasingly used in the construction industry. This paper gives insights into the porosity and pore structure of 3D printed concrete elements using mercury intrusion porosimetry, and X-ray micro-computed tomography. The experiments were conducted with two different cement systems; among which a Portland cement-blast furnace slag blend and a calcium sulfoaluminate cement-limestone blended system. The study reveals that the interlayer region contains larger and interconnected pores with low tortuosity, which could lead to enhanced transport of ions. Using the MIP data, surface fractal dimension and tortuosity parameters were computed. It was observed that the calcium sulfo aluminate-limestone blended system has higher pore complexity and tortuosity than the Portland cement-blast furnace slag system. Compared to mercury intrusion porosimetry, the X-ray micro-computed tomography technique was able to characterize both open and closed pores present in the printed sample at the resolution of the scanning. A significantly higher open porosity and the presence of more elongated pores with a high aspect ratio were observed in the interlayer compared to the bulk region. The current study can be useful in understanding the transport of ions through different regions in printed elements to assess its durability performance.

Fractal characteristics of porous carbon materials obtained from walnut shells

The structural features of carbon nanoporous materials (CM) were investigated by the low-temperature porometry method. Thuse, the CM has been obtained by thermal carbonization of plant biomass (walnut shells). The parameters of the CM samples were determined. In particular, the Neimark–Kiselev method was used to calculate the fractal dimension and estimate the surface inhomogeneity of the obtained CM samples by analyzing nitrogen adsorption isotherms. It was determined that, with an increase in the carbonization temperature of the raw material, the surface fractal dimension in the range from 1.68 to 2.56. The mineral composition was determined for СM samples using chemical elemental analysis.

Fractal Analysis of Fuel Nozzle Surface Morphology Based on the 3D-Sandbox Method.

The dual oil circuit centrifugal fuel nozzle is made of martensitic stainless steel, which has complex morphological characteristics. The surface roughness characteristics of the fuel nozzle directly affect the degree of fuel atomization and the spray cone angle. The surface characterization of the fuel nozzle is investigated by the fractal analysis method. A sequence of images of an unheated treatment fuel nozzle and a heated treatment fuel nozzle are captured by the super-depth digital camera. The 3-D point cloud of the fuel nozzle is acquired by the shape from focus technique, and its three-dimensional (3-D) fractal dimensions are calculated and analyzed by the 3-D sandbox counting method. The proposed method can characterize the surface morphology well, including the standard metal processing surface and the fuel nozzle surface, and the experiments show that the 3-D surface fractal dimension is positively correlated with the surface roughness parameter. The 3-D surface fractal dimensions of the unheated treatment fuel nozzle were 2.6281, 2.8697, and 2.7620, compared with the heated treatment fuel nozzles dimensions of 2.3021, 2.5322, and 2.3327. Thus, the 3-D surface fractal dimension value of the unheated treatment is larger than that of the heated treatment and is sensitive to surface defects. This study indicates that the 3-D sandbox counting fractal dimension method is an effective method to evaluate the fuel nozzle surface and other metal processing surfaces.

Multi-objective optimization of three-stage running-in process for main bearing of marine diesel engine

Abstract Running-in quality can be improved by optimizing the running-in parameters (load, speed and running-in time). The relationship between running-in quality and the fractal dimensions of friction signal and wear surface is analyzed. It shows that the larger the fractal dimension, the better the running-in quality. A multi-objective optimization design of the running-in parameters of the main bearing is carried out, using a non-dominated sorting genetic algorithm with elite strategy. The optimization targets are the large fractal dimension of friction coefficient, the large fractal dimension of wear surface, and small running-in time. It shows that the selection principles of running-in parameters are different for different stages and priorities. The optimal running-in parameters listed in this paper provides a specific reference to the optimal design of the three-stage running in of main bearing.

Evolution of pore structures and fractal characteristics of coal-based activated carbon in steam activation based on nitrogen adsorption method

To investigate the structures and fractal characteristics of micro- and mesopores during steam activation, a series activated carbons were prepared from Datong bituminous coal by physical activation at 750 and 850 °C. Low-temperature nitrogen adsorption and Frenkel-Halsey-Hill model were employed to determine the fractal dimensions of pore structures. The results demonstrate that micro- and mesopore structures were fully developed during steam activation, and activation at 750 °C was conducive to the development of pore structures, especially mesopores. The samples had similar pore size distributions that the micropore diameters mainly centered at 0.4–0.8 nm and 1.2–1.8 nm, and the mesopores mainly distributed in the range of 2–9 nm. The variation of surface and structure fractal dimensions for activated carbons with different burn-offs indicated that the surface roughness and structure complexity changed during activation process. The fractal dimensions of micropore surface (D1) and micropore structure (D2) had positively linear correlation with Smic/SBET and Vmic/Vtot, respectively. While the mesopore surface fractal dimensions (D1’) have a negative association with Sext/SBET, and the structure fractal dimensions (D2’) have a negative but weak association with Vmes/Vtot.

Effect of water immersion on pore structure of bituminous coal with different metamorphic degrees

It is important to understand the disaster-causing mechanism of dried water-immersed coal by investigating the influence of water immersion on the coal pore structure. In this study, low-temperature nitrogen adsorption experiments of eight bituminous coals with different metamorphic degrees and their dried water-immersed coals were carried out to analyze the adsorption/desorption mechanism and investigate the effects of water immersion on the pore shape, pore-structure parameters, and fractal dimension of coal. The results showed that adsorption of nitrogen on coal mainly includes micropore filling, monolayer adsorption, multilayer adsorption, and capillary condensation. The pores of coal were a continuous system from nanometer pores to relatively unlimited size pores. Water immersion did not significantly affect the pore shape of the coal, decreased the specific surface area and adsorption capacity, and increased the total pore volume and average pore diameter. It had the greatest effect on the average pore size of moderately metamorphosed coals, which may accelerate the oxidation process of coal and aggravate gas emission. The fractal results showed that water immersion reduced the surface fractal dimension of higher and lower metamorphic coal, while it increased that of moderately metamorphic coal, and it had the opposite effect on the structural fractal dimension.