FRACTAL ANALYSIS OF THE PENETRATION FLOW THROUGH MICRO-NANO POROUS GASKETS WITH EFFECTS OF SLIPPAGE AND STRESS-SENSITIVITY

Fractals ◽  
2019 ◽  
Vol 27 (03) ◽  
pp. 1950031
Author(s):  
XIAOMING HUANG ◽  
JIAWEI SUN ◽  
CHUNYU SHI ◽  
YANG DU ◽  
GUOLIANG XU
Keyword(s):  
Porous Media ◽  
Pore Size ◽  
Transport Theory ◽  
Stress Sensitivity ◽  
Sealing Material ◽  
Proposed Model ◽  
Slippage Effect ◽  
Flow Through ◽  
Gas Penetration ◽  
Flexible Graphite

The airtightness of non-metallic sealing structures undergoing harsh conditions is very crucial to the reliability of equipment in many industrial fields. In this study, the gas penetration through a non-metallic sealing material (NSM) with micro-nano porous structure under stress was investigated in detail based on the transport theory of fractal porous media. A complete theoretical model for predicting the stress sensitivity of the gasket permeability was developed, in which the slippage effect was of concern due to very fine pore size. The permeability of a flexible graphite gasket under different stresses was numerically predicted via scanning electron microscopy (SEM) and image processing. The influencing factors on the permeability of the NSM were analyzed quantitatively and good agreements with existing experimental results demonstrate the validity of the proposed model. Since the effects of the pore-size distribution and flow pattern regime were taken into account, the parameters of the model had a clear physical meaning and the model was suitable for determining the mechanism of penetration leakage through the NSM. In addition, the model could also be used for the analysis of other tight porous media with complex microstructure under stress deformation.

A FRACTAL MODEL FOR WATER FLOW THROUGH UNSATURATED POROUS ROCKS

Fractals ◽  
2018 ◽  
Vol 26 (02) ◽  
pp. 1840015 ◽  
Author(s):  
BOQI XIAO ◽  
XIAN ZHANG ◽  
WEI WANG ◽  
GONGBO LONG ◽  
HANXIN CHEN ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Size ◽  
Capillary Pressure ◽  
Water Flow ◽  
Relative Permeability ◽  
Fractal Model ◽  
Water Phase ◽  
Porous Rocks ◽  
Proposed Model ◽  
Flow Through

In this work, considering the effect of porosity, pore size, saturation of water and tortuosity fractal dimension, an analytical model for the capillary pressure and water relative permeability is derived in unsaturated porous rocks. Besides, the formulas of calculating the capillary pressure and water relative permeability are given by taking into account the fractal distribution of pore size and tortuosity of capillaries. It can be seen that the capillary pressure for water phase decreases with the increase of saturation in unsaturated porous rocks. It is found that the capillary pressure for water phase decreases as the tortuosity fractal dimension decreases. It is further seen that the capillary pressure for water phase increases with the decrease of porosity, and at low porosity, the capillary pressure increases sharply with the decrease of porosity. Besides, it can be observed that the water relative permeability increases with the increase of saturation in unsaturated porous rocks. This predicted the capillary pressure and water relative permeability of unsaturated porous rocks based on the proposed models which are in good agreement with the experimental data and model predictions reported in the literature. The proposed model improved the understanding of the physical mechanisms of water flow through unsaturated porous rocks.

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.

scholarly journals Lattice Boltzmann Model for Gas Flow through Tight Porous Media with Multiple Mechanisms

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 133 ◽  
Author(s):  
Junjie Ren ◽  
Qiao Zheng ◽  
Ping Guo ◽  
Chunlan Zhao
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Lattice Boltzmann ◽  
Gas Flow ◽  
Stress Sensitivity ◽  
Lattice Boltzmann Model ◽  
Flow Through Porous Media ◽  
Gas Slippage ◽  
Flow Through ◽  
Boltzmann Model

In the development of tight gas reservoirs, gas flow through porous media usually takes place deep underground with multiple mechanisms, including gas slippage and stress sensitivity of permeability and porosity. However, little work has been done to simultaneously incorporate these mechanisms in the lattice Boltzmann model for simulating gas flow through porous media. This paper presents a lattice Boltzmann model for gas flow through porous media with a consideration of these effects. The apparent permeability and porosity are calculated based on the intrinsic permeability, intrinsic porosity, permeability modulus, porosity sensitivity exponent, and pressure. Gas flow in a two-dimensional channel filled with a homogeneous porous medium is simulated to validate the present model. Simulation results reveal that gas slippage can enhance the flow rate in tight porous media, while stress sensitivity of permeability and porosity reduces the flow rate. The simulation results of gas flow in a porous medium with different mineral components show that the gas slippage and stress sensitivity of permeability and porosity not only affect the global velocity magnitude, but also have an effect on the flow field. In addition, gas flow in a porous medium with fractures is also investigated. It is found that the fractures along the pressure-gradient direction significantly enhance the total flow rate, while the fractures perpendicular to the pressure-gradient direction have little effect on the global permeability of the porous medium. For the porous medium without fractures, the gas-slippage effect is a major influence factor on the global permeability, especially under low pressure; for the porous medium with fractures, the stress-sensitivity effect plays a more important role in gas flow.

scholarly journals Review Of Applied Mathematical Models For Describing The Behaviour Of Aqueous Humor In Eye Structures

2015 ◽  
Vol 20 (4) ◽  
pp. 757-772
Author(s):  
M. Dzierka ◽  
P. Jurczak
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Aqueous Humor ◽  
Trabecular Meshwork ◽  
Newtonian Fluids ◽  
Flow Through Porous Media ◽  
Rheological Models ◽  
Proposed Model ◽  
Flow Through ◽  
Mathematical Equations

Abstract In the paper, currently used methods for modeling the flow of the aqueous humor through eye structures are presented. Then a computational model based on rheological models of Newtonian and non-Newtonian fluids is proposed. The proposed model may be used for modeling the flow of the aqueous humor through the trabecular meshwork. The trabecular meshwork is modeled as an array of rectilinear parallel capillary tubes. The flow of Newtonian and non-Newtonian fluids is considered. As a results of discussion mathematical equations of permeability of porous media and velocity of fluid flow through porous media have been received.

scholarly journals A Numerical Study on Gas Flow through Anisotropic Sierpinski Carpet with Slippage Effect

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Shuxia Qiu ◽  
Lipei Zhang ◽  
Zhenhua Tian ◽  
Zhouting Jiang ◽  
Mo Yang ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Gas Flow ◽  
Gas Permeability ◽  
Fractal Model ◽  
Numerical Results ◽  
Pore Scale ◽  
Gas Slippage ◽  
Slippage Effect ◽  
Flow Through

A pore-scale model has been developed to study the gas flow through multiscale porous media based on a two-dimensional self-similar Sierpinski carpet. The permeability tensor with slippage effect is proposed, and the effects of complex configurations on gas permeability have been discussed. The present fractal model has been validated by comparison with theoretical models and available experimental data. The numerical results show that the flow field and permeability of the anisotropic Sierpinski model are different from that of the isotropic model, and the anisotropy of porous media can enhance gas permeability. The gas permeability of porous media increases with the increment of porosity, while it decreases with increased pore fractal dimension under fixed porosity. Furthermore, the gas slippage effect strengthens as the pore fractal dimension decreases. However, the relationship between the gas slippage effect and porosity is a nonmonotonic decreasing function because reduced pore size and enhanced flow resistance may be simultaneously involved with decreasing porosity. The proposed pore-scale fractal model can present insights on characterizing complex and multiscale structures of porous media and understanding gas flow mechanisms. The numerical results may provide useful guidelines for the applications of porous materials in oil and gas engineering, hydraulic engineering, chemical engineering, thermal power engineering, food engineering, etc.

Fractal analysis of permeability near the wall in porous media

2014 ◽  
Vol 25 (07) ◽  
pp. 1450021 ◽  
Author(s):  
Mingchao Liang ◽  
Boming Yu ◽  
Li Li ◽  
Shanshan Yang ◽  
Mingqing Zou
Keyword(s):  
Porous Media ◽  
Pore Size ◽  
Pore Space ◽  
Fractal Theory ◽  
Particle Diameter ◽  
Fractal Dimensions ◽  
Fractal Model ◽  
Proposed Model ◽  
Medium Porosity ◽  
The Relationship

In this paper, a fractal model for permeability of porous media is proposed based on Tamayol and Bahrami's method and the fractal theory for porous media. The proposed model is expressed as a function of the mean particle diameter, the length along the macroscopic pressure drop in the medium, porosity, fractal dimensions for pore space and tortuous capillaries, and the ratio of the minimum pore size to the maximum pore size. The relationship between the permeability near the wall and the dimensionless distance from the wall under different conditions is discussed in detail. The predictions by the present fractal model are in good agreement with available experimental data. The present results indicate that the present model may have the potential in comprehensively understanding the mechanisms of flow near the wall in porous media.

scholarly journals STRESS SENSITIVITY ANALYSIS OF FRACTAL POROUS MEDIA BASED ON THE ELASTO-PLASTIC THICK-WALLED CYLINDER MODEL

Fractals ◽  
2021 ◽  
Vol 29 (03) ◽  
pp. 2150162
Author(s):  
ZHAOQIN HUANG ◽  
XIN SU ◽  
YANCHAO LI ◽  
KAI ZHANG ◽  
JUN YAO
Keyword(s):  
Porous Media ◽  
Fractal Theory ◽  
Fractal Model ◽  
Stress Sensitivity ◽  
Proposed Model ◽  
Cylinder Model ◽  
Stress Cycles ◽  
Dependent Flow ◽  
Stress Dependent ◽  
Walled Cylinder

The stress-dependent flow and transport behaviors of porous media are ubiquitous in various scientific and engineering applications. It has been shown that the change of effective stress has important effects on the permeability and porosity of porous media. In this paper, a new stress sensitivity model for porous media is developed based on the fractal theory and the elasto-plastic thick-walled cylinder model. The proposed model is able to predict the elasto-plastic deformation of the fractal porous media under loading–unloading stress cycles, which plays a crucial role on the permanent variations of the permeability and porosity. It is found that the permeability of stress-sensitivity porous media is related to the capillary fractal dimension, capillary fractal tortuosity dimension, minimum and maximum capillary diameters, Young’s modulus and Poisson’s ratio of capillary. Each parameter has a clear physical meaning. The validity of the developed fractal model is verified by comparing the model predictions with the available experimental data.

scholarly journals Instabilities during dispersion flow through porous media: pore-size effect

2020 ◽  
pp. 515-519
Author(s):  
M. Niespodzinska ◽  
J.-P. Gaudet ◽  
P. Royer ◽  
J.-L. Auriault
Keyword(s):  
Porous Media ◽  
Size Effect ◽  
Pore Size ◽  
Flow Through Porous Media ◽  
Flow Through

FRACTAL ANALYSIS OF STRESS SENSITIVITY OF PERMEABILITY IN POROUS MEDIA

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550001 ◽  
Author(s):  
XIAO-HUA TAN ◽  
XIAO-PING LI ◽  
JIAN-YI LIU ◽  
LIE-HUI ZHANG ◽  
JIANCHAO CAI
Keyword(s):  
Porous Media ◽  
Stress Sensitivity ◽  
Maximum Diameter ◽  
Permeability Model ◽  
Minimum Diameter ◽  
Mechanics Of Materials ◽  
Proposed Model ◽  
Fractal Characteristics ◽  
Experimental Expression ◽  
Good Agreement

A permeability model for porous media considering the stress sensitivity is derived based on mechanics of materials and the fractal characteristics of solid cluster size distribution. The permeability of porous media considering the stress sensitivity is related to solid cluster fractal dimension, solid cluster fractal tortuosity dimension, solid cluster minimum diameter and solid cluster maximum diameter, Young's modulus, Poisson's ratio, as well as power index. Every parameter has clear physical meaning without the use of empirical constants. The model predictions of permeability show good agreement with those obtained by the available experimental expression. The proposed model may be conducible to a better understanding of the mechanism for flow in elastic porous media.

Testing the efficiency of ferrofluid impregnation in porous media – recommendations for future magnetic pore fabric studies

2020 ◽  
Author(s):  
Michele Pugnetti ◽  
Yi Zhou ◽  
Andrea Biedermann
Keyword(s):  
Grain Size ◽  
Porous Media ◽  
Magnetic Susceptibility ◽  
Pore Size ◽  
Magnetic Measurements ◽  
Vacuum Impregnation ◽  
Physical Parameters ◽  
High Porosity ◽  
Nanoparticle Distribution ◽  
Flow Through

<p><strong>Testing the efficiency of ferrofluid impregnation in porous media – recommendations for future magnetic pore fabric studies</strong></p><p> </p><p>Michele Pugnetti*, Yi Zhou*, Andrea R. Biedermann*</p><p>* Institute of Geological Sciences, University of Bern, Baltzerstrasse 1+3, CH-3012 Bern, Switzerland ([email protected])</p><p> </p><p>In AMS (anisotropy of magnetic susceptibility)-based pore fabric studies, the role of ferrofluid impregnation is crucial to ensure significant magnetic measurements. However, no standard methods to test the ferrofluid impregnation of porous media have been proposed so far. The details of fluid behaviour in porous media are important in many fields of natural sciences, but nanoparticle distribution in the fluid is particularly important for magnetic measurements. In this study methods to test the impregnation efficiency of ferrofluid in porous media, and nanoparticle distribution are proposed, using different materials: wood, agarose and TEOS (tetraethylorthosilicate) gel, and synthetic samples of given composition and grain size, as well as natural rocks. Magnetic pore fabric measurements are normally performed on natural porous samples to correlate the direction of maximum magnetic susceptibility with the direction of preferred pore elongation, and preferred flow direction. The advantage of using artificial samples is the possibility to control and adjust some physical parameters, including porosity and pore size, to keep them more uniform or fix them to a given value. This allows investigating the nanoparticle distribution in ideal samples without the influence of additional heterogeneities inherent to natural samples and to determine the lowest porosity value and smallest pore size that is possible to impregnate with ferrofluid. In particular, the agarose and TEOS gel have a uniform porous structure controlled by the gel concentration or chemical agents used in sample preparation. The wood has a wider range of porosity compared to rocks and a known intrinsically anisotropic structure. The synthetic samples have a uniform grain size, mineralogy and structure. First the porosity of the samples was measured, then to impregnate the samples different methods were developed and tested, (1) percolation, (2) standard vacuum impregnation, (3) flow-through impregnation, (4) diffusion process in gel structure. Impregnation efficiency was evaluated both optically and magnetically. Different impregnation methods provide different impregnation efficiency depending also on the investigated material; in particular porosity plays an important role in limiting the impregnation efficiency. Initial experiments indicate that in general, flow-through impregnation is more efficient than vacuum impregnation because it combines the effect of vacuum with the pressure applied to the fluid that is pushed through the sample. The best results on natural samples were obtained using calcarenites with relatively high porosity. These results and the methods proposed here will help advance magnetic pore fabrics studies and impregnation processes in general.   </p><p> </p>

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