scholarly journals Research On the Fractal Dimensions of the Organic-Rich Shale Pores Via Different Models

2022 ◽  
Vol 2152 (1) ◽  
pp. 012020
Author(s):  
Fangyao Dai
Keyword(s):  
Fractal Dimension ◽  
Gas Adsorption ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Fractal Model ◽  
Relative Pressure ◽  
Longmaxi Formation ◽  
High Relative Pressure ◽  
Adsorption Data ◽  
Different Dimensions

Abstract Fractal dimension can be used to the pore surface characterize. For pore structures in different sizes, the calculation models of fractal theory should be distinguished due to the different principles of the gas adsorption experiments. To further study the adaptability of the fractal model for gas adsorption experimental data, the author collected shale samples of Longmaxi formation from Well JY1, then CO2 and N2 adsorption provided the PSD curves. In addition, the fractal dimensions of micropore and mesopore were calculated by the Jaroniec fractal model and Frenkel–Halsey–Hill (FHH) fractal model respectively. The research shows that the Jaroniec model may be suitable to calculate CO2 adsorption data and could characterize the fractal dimension of micropore, while the FHH model may be suitable to calculate N2 adsorption data in the high relative pressure region. It suggests that the micropore and mesopore could have different dimensions and the evaluation of the structure in shale pores should consider both of them.

FRACTAL ANALYSIS OF GAS DIFFUSION IN POROUS NANOFIBERS

Fractals ◽  
2015 ◽  
Vol 23 (01) ◽  
pp. 1540011 ◽  
Author(s):  
BOQI XIAO ◽  
JINTU FAN ◽  
ZONGCHI WANG ◽  
XIN CAI ◽  
XIGE ZHAO
Keyword(s):  
Experimental Data ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Fractal Model ◽  
Gas Diffusion ◽  
Physical Mechanisms ◽  
Gas Diffusivity ◽  
Model Predictions ◽  
Good Agreement

In this study, with the consideration of pore size distribution and tortuosity of capillaries, the analytical model for gas diffusivity of porous nanofibers is derived based on fractal theory. The proposed fractal model for the normalized gas diffusivity (De/D0) is found to be a function of the porosity, the area fractal dimensions of pore and the fractal dimension of tortuous capillaries. It is found that the normalized gas diffusivity decreases with increasing of the tortuosity fractal dimension. However, the normalized gas diffusivity is positively correlated with the porosity. The prediction of the proposed fractal model for porous nanofibers with porosity less than 0.75 is highly consistent with the experimental and analytical results found in the literature. The model predictions are compared with the previously reported experimental data, and are in good agreement between the model predictions and experimental data is found. The validity of the present model is thus verified. Every parameter of the proposed formula of calculating the normalized gas diffusivity has clear physical meaning. The proposed fractal model can reveal the physical mechanisms of gas diffusion in porous nanofibers.

scholarly journals Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bing Sun ◽  
Shun Liu ◽  
Sheng Zeng ◽  
Shanyong Wang ◽  
Shaoping Wang
Keyword(s):  
Fractal Dimension ◽  
Crack Propagation ◽  
Crack Growth ◽  
Impact Test ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Fractal Dimensions ◽  
Peak Stress ◽  
Dynamic Mechanical Properties ◽  
Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

Research of Coal Pores and Integrity Evaluation Method Based on Fractal Theory

2014 ◽  
Vol 670-671 ◽  
pp. 258-262 ◽  
Author(s):  
Ji Li ◽  
Xin Wu
Keyword(s):  
Fractal Dimension ◽  
Coal Sample ◽  
Evaluation Method ◽  
Structural Integrity ◽  
Gas Adsorption ◽  
Fractal Theory ◽  
Physical And Mechanical Properties ◽  
Box Dimension ◽  
Sem Images ◽  
Sem Image

Coal is a natural porous media, its porosity and structural integrity influenced the gas adsorption and desorption characteristics greatly, as well as physical and mechanical properties of coal. Scanning electron microscopy (SEM) is applied to acquire SEM image of four kinds of coal samples at different zoom levels, and the box dimension can be worked out based on the pore preprocessing of SEM images. Then, the numerical value of box dimension is used to describe the development degree of the four kinds of coal sample and four development degrees’ sequence. At last, the intrinsic relevance between fractal dimension and other parameters is analyzed through mathematic method. The results show as follows: coal sample has self-similarity characteristic; the fractal dimension is related to both the total number of pores and porosity degree; the data of the coal pore, analyzed through fractal dimension, are consistent with that through traditional method; what’s more, fractal dimension has more advantages in describing accuracy and simplicity.

scholarly journals Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

2018 ◽  
Vol 159 ◽  
pp. 01006
Author(s):  
Bagus Hario Setiadji ◽  
Supriyono ◽  
Djoko Purwanto
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Calculation Model ◽  
Careful Consideration ◽  
Upper And Lower Bounds ◽  
Aggregate Gradation ◽  
Fractal Characteristic ◽  
Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

Application of Fractal Theory in Aggregate Gradation Research

2012 ◽  
Vol 204-208 ◽  
pp. 1923-1928
Author(s):  
Bo Tan ◽  
Rui Hua Yang ◽  
Yan Ting Lai
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Aggregate Gradation ◽  
Structure Characteristics ◽  
Aggregate Distribution ◽  
Dimension Formula ◽  
Mass Fractal ◽  
Fractal Characteristics

The paper presents the fractal dimension formula of distribution of asphalt mixture aggregate diameter by the deducing mass fractal characteristics function. Taking AC-20 and SMA-20 as examples, selected 6 groups of representative grading curves within the grading envelope proposed by the present specification, and calculated their fractal dimensions. The asphalt mixture gradation has fractal dimension D (D∈(1,3)), and the fractal of continuous gradation is single while the fractal of gap-gradation shows multi-fractal with 4.75 as the dividing point. Fractal dimension of aggregate gradation of asphalt mixture reflect the structure characteristics of aggregate distribution, that is, finer is aggregate, bigger is the fractal dimension.

Complexity-Based Analysis of the Relation between Human Muscle Reaction and Walking Path

2020 ◽  
Vol 19 (03) ◽  
pp. 2050025 ◽  
Author(s):  
Shahul Mujib Kamal ◽  
Sue Sim ◽  
Rui Tee ◽  
Visvamba Nathan ◽  
Hamidreza Namazi
Keyword(s):  
Fractal Dimension ◽  
Statistical Analysis ◽  
Fractal Theory ◽  
Contact Point ◽  
Fractal Dimensions ◽  
Human Muscle ◽  
Physiological Signals ◽  
Eeg Signal ◽  
Leg Muscles ◽  
Emg Signal

Legs are the contact point of humans during walking. In fact, leg muscles react when we walk in different conditions (such as different speeds and paths). In this research, we analyze how walking path affects leg muscles’ reaction. In fact, we investigate how the complexity of muscle reaction is related to the complexity of path of movement. For this purpose, we employ fractal theory. In the experiment, subjects walk on different paths that have different fractal dimensions and then we calculate the fractal dimension of Electromyography (EMG) signals obtained from both legs. The result of our analysis showed that the complexity of EMG signal increases with the increment of complexity of path of movement. The conducted statistical analysis also supported the result of analysis. The method of analysis used in this research can be further applied to find the relation between complexity of path of movement and other physiological signals of humans such as respiration and Electroencephalography (EEG) signal.

COMPRESSIVE STRENGTH OF FRACTAL-TEXTURED FOAMED CONCRETE

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940003 ◽  
Author(s):  
Y. CHEN ◽  
Y. F. XU
Keyword(s):  
Compressive Strength ◽  
Fractal Dimension ◽  
Porous Structure ◽  
Fractal Theory ◽  
Scaling Law ◽  
Weight Ratio ◽  
High Strength ◽  
Labor Cost ◽  
Fractal Model ◽  
Foamed Concrete

Foamed concrete possesses characteristics such as high strength-to-weight ratio and low density, and widely used to reduce dead loads on the structure and foundation, contributes to energy conservation, and lowers the labor cost during construction. In this paper, the objective is to propose prediction relation for the compressive strength of foamed concrete by fractal theory. A theoretical relation was derived for the compressive strength relating to porosity based on the fractal model for foamed concrete. The proposed relation stands out compared to empirical model since it employs easily measurable parameter, the fractal dimension of porous structure in foamed concrete. The fractal dimension of porous structure can be calculated from the scaling law of the compressive strength of foamed concrete. The fractal model for porous structure serves as a simple and effective tool for predicting the compressive strength of foamed concrete because of its ease in application. The prediction relation of the compressive strength developed in this paper is found to match well with the measured strength.

Study about Characteristics of Cement Paste on Fractal Theory

2013 ◽  
Vol 423-426 ◽  
pp. 1051-1054
Author(s):  
Tian Yang Zhai
Keyword(s):  
Compressive Strength ◽  
Fractal Dimension ◽  
Cement Paste ◽  
Permeability Coefficient ◽  
Fractal Theory ◽  
Fractal Model ◽  
Concrete Compressive Strength ◽  
Internal Pore Structure ◽  
The Relationship ◽  
Internal Pore

A fractal model to simulate cement paste internal pore structure, and on this basis deduce that fractal dimension is D and the corresponding pore is r, the relationship between porosity is P. MIP was measured test. Then calculated the different ages of the fractal dimension of cement and concrete compressive strength, tensile strength and permeability coefficient. The results showed that: compressive strength, permeability and fractal dimension has a good correlation. Whey in cement in the process of hydration of cement products continue to fill the pores, making the compressive strength increased 70%, permeability is declining.

A DIFFUSIVITY MODEL FOR GAS DIFFUSION IN DRY POROUS MEDIA COMPOSED OF CONVERGING–DIVERGING CAPILLARIES

Fractals ◽  
2016 ◽  
Vol 24 (03) ◽  
pp. 1650034 ◽  
Author(s):  
SHIFANG WANG ◽  
TAO WU ◽  
YONGJU DENG ◽  
QIUSHA ZHENG ◽  
QIAN ZHENG
Keyword(s):  
Experimental Data ◽  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Knudsen Diffusion ◽  
Fractal Model ◽  
Gas Diffusion ◽  
Pore Area ◽  
Relative Diffusivity ◽  
Fluctuation Amplitude

Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging–diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging–diverging effect included is in good agreement with reported experimental data.

scholarly journals Quantitative Characterization of Heterogeneity in Different Reservoir Spaces of Low-Permeability Sandstone Reservoirs and Its Influence on Physical Properties

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Fengjuan Dong ◽  
Na Liu ◽  
Zhen Sun ◽  
Xiaolong Wei ◽  
Haonan Wang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Low Permeability ◽  
Quantitative Characterization ◽  
Average Value ◽  
Porosity And Permeability ◽  
Sandstone Reservoirs

The complex pore structure of low-permeability sandstone reservoir makes it difficult to characterize the heterogeneity of pore throat. Taking the reservoir of Sanjianfang formation in QL oilfield as an example, the fractal dimension of different storage spaces is calculated by using fractal theory based on casting thin section, scanning electron microscope, and high-pressure mercury injection, and the correlation between porosity, permeability, and contribution of different storage space permeabilities is analyzed. The results show that the reservoir of Sanjianfang formation in QL oilfield mainly develops small pores, fine pores, and micropores, and the fractal dimension of micropore structure is between 2.6044 and 2.9982, with an average value of 2.8316. The more complex the pore structure is, the stronger the microheterogeneity is. The higher the fractal dimension, the more complex the pore structure and the smaller the porosity and permeability. The fractal dimensions of small pores, fine pores, and micropores increase successively with the decrease in pore radius, and the microstructure heterogeneity of large pores is weaker than that of small pores. It provides a theoretical basis for the exploration and development of low-permeability sandstone reservoirs.

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