scholarly journals A Novel Porous Media Permeability Model Based on Fractal Theory and Ideal Particle Pore-Space Geometry Assumption

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 510 ◽  
Author(s):  
Yongquan Hu ◽  
Qiang Wang ◽  
Jinzhou Zhao ◽  
Shouchang Xie ◽  
Hong Jiang
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Great Influence ◽  
Particle Radius ◽  
Particle Model ◽  
Permeability Model ◽  
Minimum Value ◽  
Pore Area ◽  
The Impact

In this paper, a novel porous media permeability model is established by using particle model, capillary bundle model and fractal theory. The three-dimensional irregular spatial characteristics composed of two ideal particles are considered in the model. Compared with previous models, the results of our model are closer to the experimental data. The results show that the tortuosity fractal dimension is negatively correlated with porosity, while the pore area fractal dimension is positively correlated with porosity; The permeability is negatively correlated with the tortuosity fractal dimension and positively correlated with the integral fractal dimension of pore surface and particle radius. When the tortuosity fractal dimension is close to 1 and the pore area fractal dimension is close to 2, the faster the permeability changes, the greater the impact. Different particle arrangement has great influence on porous media permeability. When the porosity is close to 0 and close to 1, the greater the difference coefficient is, the more the permeability of different arrangement is affected. In addition, the larger the particle radius is, the greater the permeability difference coefficient will be, and the greater the permeability difference will be for different particle arrangements. With the increase of fractal dimension, the permeability difference coefficient first decreases and then increases. When the pore area fractal dimension approaches 2, the permeability difference coefficient changes faster and reaches the minimum value, and when the tortuosity fractal dimension approaches 1, the permeability difference coefficient changes faster and reaches the minimum value. Our research is helpful to further understand the connotation of medium transmission in porous media.

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 Mathematical Model for Effective Gas Diffusion Coefficient in Multi-scale Fractal Porous Media

2021 ◽  
Vol 248 ◽  
pp. 01026
Author(s):  
Du Zhehua
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Diffusion Coefficient ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Effective Diffusion ◽  
Gas Diffusion ◽  
Pore Connectivity ◽  
Multi Scale ◽  
Pore Area

Based on the capillary hypothesis and fractal theory, a mathematical model for calculating the effective gas diffusion coefficient in porous media is established. By using fractal geometry theory, pore area fractal dimension, tortuosity fractal dimension and pore connectivity are introduced to quantitatively characterize the real internal structure in the porous media. An effective gas diffusion coefficient model for the fractal porous media is derived, and the influence of multi-scale porous media microstructure parameters on the effective gas diffusion coefficient is discussed. The results show that effective gas diffusion coefficient approximates to linearly increase with the increase of porosity, the pore area fractal dimension and the effective gas diffusion coefficient is positive correlation, but the tortuosity fractal dimension is negatively related to it. In the case of different porosities, the gas effective diffusion coefficient varies with the change of the pore diameter ratio, the effective gas diffusion coefficient increases with the increase of pore connectivity.

scholarly journals Green Preparation, Spheroidal, and Superior Property of Nano-1,3,5,7-Tetranittro-1,3,5,7-Tetrazocane

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Xinlei Jia ◽  
Jingyu Wang ◽  
Conghua Hou ◽  
Yingxin Tan
Keyword(s):  
Activation Energy ◽  
Particle Size ◽  
Fractal Dimension ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Fractal Theory ◽  
Crystal Form ◽  
Decomposition Temperature ◽  
Scanning Calorimetry ◽  
The Impact

Herein, a green process for preparing nano-HMX, mechanical demulsification shearing (MDS) technology, was developed. Nano-HMX was successfully fabricated via MDS technology without using any chemical reagents, and the fabrication mechanism was proposed. Based on the “fractal theory,” the optimal shearing time for mechanical emulsification was deduced by calculating the fractal dimension of the particle size distribution. The as-prepared nano-HMX was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and differential scanning calorimetry (DSC). And the impact sensitivities of HMX particles were contrastively investigated. The raw HMX had a lower fractal dimension of 1.9273. The ideal shearing time was 7 h. The resultant nano-HMX possessed a particle size distribution ranging from 203.3 nm to 509.1 nm as compared to raw HMX. Nano-HMX particles were dense spherical, maintaining β-HMX crystal form. In addition, they had much lower impact sensitivity. However, the apparent activation energy as well as thermal decomposition temperature of nano-HMX particles was decreased, attributing to the reduced probability for hotspot generation. Especially when the shearing time was 7 h, the activation energy was markedly decreased.

A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory

2018 ◽  
Vol 29 (02) ◽  
pp. 1850019 ◽  
Author(s):  
X.-H. Tan ◽  
C.-Y. Liu ◽  
X.-P. Li ◽  
H.-Q. Wang ◽  
H. Deng
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Stress Sensitivity ◽  
Maximum Diameter ◽  
Proposed Model ◽  
Fractal Parameters ◽  
Stress Changes ◽  
Capillary Bundle ◽  
Definition Of

A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster [Formula: see text] become bigger with an increase of stress. However, the pore fractal dimension of solid cluster [Formula: see text] and capillary bundle [Formula: see text] remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

A FRACTAL PERMEABILITY MODEL FOR REAL GAS IN SHALE RESERVOIRS COUPLED WITH KNUDSEN DIFFUSION AND SURFACE DIFFUSION EFFECTS

Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050017 ◽  
Author(s):  
TAO WU ◽  
SHIFANG WANG
Keyword(s):  
Fractal Dimension ◽  
Surface Diffusion ◽  
Shale Gas ◽  
Gas Transport ◽  
Fractal Theory ◽  
Knudsen Diffusion ◽  
Apparent Permeability ◽  
Permeability Model ◽  
Real Gas ◽  
Shale Reservoirs

A better comprehension of the behavior of shale gas transport in shale gas reservoirs will aid in predicting shale gas production rates. In this paper, an analytical apparent permeability expression for real gas is derived on the basis of the fractal theory and Fick’s law, with adequate consideration of the effects of Knudsen diffusion, surface diffusion and flexible pore shape. The gas apparent permeability model is found to be a function of microstructural parameters of shale reservoirs, gas property, Langmuir pressure, shale reservoir temperature and pressure. The results show that the apparent permeability increases with the increase of pore area fractal dimension and the maximum effective pore radius and decreases with an increase of the tortuosity fractal dimension; the effects of Knudsen diffusion and surface diffusion on the total apparent permeability cannot be ignored under high-temperature and low-pressure circumstances. These findings can contribute to a better understanding of the mechanism of gas transport in shale reservoirs.

INVESTIGATION OF DYNAMIC TEXTURE AND FLOW CHARACTERISTICS OF FOAM TRANSPORT IN POROUS MEDIA BASED ON FRACTAL THEORY

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940013 ◽  
Author(s):  
FEI WANG ◽  
HAIFENG LI ◽  
DONGXING DU ◽  
XU DONG
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Quantitative Description ◽  
Flow Characteristics ◽  
Transport In Porous Media ◽  
Steady Stage ◽  
Profile Control ◽  
Fractal Characteristics

Foam fluid has found wide applications in oilfield development, such as profile control, water plugging, gas channeling control, fracturing, and so on. As a non-Newtonian fluid, the successful application of foam is significantly influenced by its structure. The foam texture, however, is complex and irregular, and becomes even more complicated in porous media by the boundary effects. Therefore, the description of dynamic foam structure is crucial and a quantitative description method for foam fluid is worth exploring. In this paper, the fractal characteristics of foam in porous media are verified and combined with foam microdisplacement experiment, and the fractal rule of foam is found. The relationship between fractal dimension and pressure is also discussed. The results show that foam has dynamic fractal characteristics during transport in porous media and the box-counting fractal dimension ranges from 1 to 2. Furthermore, the dynamic change of foam fractal dimension during transport in porous media could be divided into three stages. In the first stage when no foam forms, the fractal dimension is about 2; in the second unsteady foam stage, the fractal dimension is reduced from 1.9 to 1.6; the last one is the steady stage and the fractal dimension is almost constant (about 1.6). Besides, the fractal dimension of foam fluid is closely related to displacement pressure. Low pressure corresponds to higher fractal dimension, and high pressure corresponds to lower fractal dimension. Pressure is negatively linearly correlated with fractal dimension. These results are expected to enrich the understanding of the foam dynamic characteristics in their advanced applications.

A model for allometric permeation in fractal branching channel net driven by capillary pressure

2015 ◽  
Vol 25 (8) ◽  
pp. 1886-1895 ◽  
Author(s):  
Jie Fan ◽  
Na Zhu ◽  
Zhi Liu ◽  
Qian Cheng ◽  
Yong Liu
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Capillary Pressure ◽  
Design Methodology ◽  
Fractal Theory ◽  
Geometrical Parameters ◽  
Content Type ◽  
Artificial Materials ◽  
Net Affect

Purpose – The purpose of this paper is to investigate the allometric permeation performance in fractal branching channel net driven by capillary pressure and analyze how the geometrical parameters of the branching channel net affect the permeability of the fluid transportation. Design/methodology/approach – An allometric permeation model is proposed based on the fractal theory by considering capillary pressure as the main driven force of fluid permeation. Findings – It is found that the permeability efficiency is a function of fractal dimension, bifurcation number, and number of branching level. Different fluid permeation efficiencies of the channel net can be obtained by changing the three parameters. Originality/value – The allometric permeation model established provides a better understanding of the permeation mechanism in fractal porous media which could further help with the design of bio-mimetic artificial materials.

A FRACTAL MODEL FOR KOZENY–CARMAN CONSTANT AND DIMENSIONLESS PERMEABILITY OF FIBROUS POROUS MEDIA WITH ROUGHENED SURFACES

Fractals ◽  
2019 ◽  
Vol 27 (07) ◽  
pp. 1950116 ◽  
Author(s):  
BOQI XIAO ◽  
YIDAN ZHANG ◽  
YAN WANG ◽  
GUOPING JIANG ◽  
MINGCHAO LIANG ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fluid Transport ◽  
Fractal Theory ◽  
Fractal Model ◽  
Physical Mechanisms ◽  
Relative Roughness ◽  
Fibrous Porous Media ◽  
Effect Of Surface ◽  
Good Agreement

In this paper, fluid transport through fibrous porous media is studied by the fractal theory with a focus on the effect of surface roughness of capillaries. A fractal model for Kozeny–Carman (KC) constant and dimensionless permeability of fibrous porous media with roughened surfaces is derived. The determined KC constant and dimensionless permeability of fibrous porous media with roughened surfaces are in good agreement with available experimental data and existing models reported in the literature. It is found that the KC constant of fibrous porous media with roughened surfaces increases with the increase of relative roughness, porosity, area fractal dimension of pore and tortuosity fractal dimension, respectively. Besides, it is seen that the dimensionless permeability of fibrous porous media with roughened surfaces decreases with increasing relative roughness and tortuosity fractal dimension. However, it is observed that the dimensionless permeability of fibrous porous media with roughened surfaces increases with porosity. With the proposed fractal model, the physical mechanisms of fluids transport through fibrous porous media are better elucidated.

scholarly journals A Leakage Model of Contact Mechanical Seals Based on the Fractal Theory of Porous Medium

Coatings ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 20
Author(s):  
Xingya Ni ◽  
Chenbo Ma ◽  
Jianjun Sun ◽  
Yuyan Zhang ◽  
Qiuping Yu
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Pore Diameter ◽  
Fractal Theory ◽  
Leakage Rate ◽  
Contact Interface ◽  
Mechanical Seals ◽  
The Real ◽  
Leakage Model ◽  
Contact Mechanical

A theoretical model for calculating the leakage rate of contact mechanical seals based on the fractal theory of the porous media, which can consider the real seal contact interface and objectively reflect the flow of the interfacial fluid from a microscopic perspective, is established. In order to obtain the microstructural parameters of the porous media included in the leakage model, such as the fractal dimension and the maximum pore diameter, the real seal contact interface obtained from experiments is reconstructed, a contact model between the dynamic and static rings is proposed, and then the calculation methods for the interface characteristic parameters are provided. Numerical simulation results show that as the contact pressure increases from 0.05 to 0.5 MPa, the interface porosity and the maximum pore diameter decreases gradually. Furthermore, the fractal dimension of the pore area increases and the leakage rate of the interface decreases from 0.48 to 0.33 mL/h. The proposed method provides a novel way of calculating the leakage rate of contact mechanical seals.

scholarly journals Dynamic Compression Damage Energy Consumption and Fractal Characteristics of Shale

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Guoliang Yang ◽  
Jingjiu Bi ◽  
Linian Ma
Keyword(s):  
Fractal Dimension ◽  
Energy Consumption ◽  
Energy Dissipation ◽  
Strain Rate ◽  
Split Hopkinson Pressure Bar ◽  
Dynamic Compression ◽  
Fractal Theory ◽  
Dissipated Energy ◽  
Impact Tests ◽  
The Impact

Studying the relationship between energy consumption and crushed size of shale under different loading conditions is the key to efficient shale cracking. The split Hopkinson pressure bar system was used to study the dynamic mechanical properties of shale under parallel- and vertical-bedding loading, and energy dissipation in the impact tests was calculated. Relationships between the average crushed size of shale fracture products and energy dissipation and between the fractal dimension and dissipated energy were studied using fractal theory. The experimental results showed that the dynamic compressive strength of shale under parallel- and vertical-bedding conditions had an obvious positive correlation with the strain rate. Dissipative energy of the shale samples under loading in both directions increased with the increase of strain rate. The increase of the strain rate enhanced crushing of the sample. The vertical-bedding shale samples had stronger ability to absorb energy and more internal crack propagation. Dissipative energies of the shale samples in the parallel- and vertical-bedding impact tests were positively related to the fractal dimension. The fractal dimension increased with the increase of dissipative energy during sample failure; with further increase in the dissipative energy, its effect on the change of fractal dimension gradually weakened.

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