Research On The Fractal and Percolation Characteristics of Coal-Based Porous Media For Filtration and Impregnation

2021 ◽  
Author(s):  
Qili Wang ◽  
Jiarui Sun ◽  
Yuehu Chen ◽  
Yuyan Qian ◽  
Shengcheng Fei ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Structure ◽  
Mercury Intrusion Porosimetry ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Infinite Cluster ◽  
Porous Graphite ◽  
Local Aggregation ◽  
Gradual Expansion ◽  
The Difference

Abstract In order to distinguish the difference in the heterogeneous fractal structure of porous graphite used for filtration and impregnation, the fractal dimensions obtained through the mercury intrusion porosimetry (MIP) along with the fractal theory were used to calculate the volumetric FD of the graphite samples. The FD expression of the tortuosity along with all parameters from MIP test was optimized to simplify the calculation. In addition, the percolation evolution process of mercury in the porous media was analyzed in combination with the experimental data. As indicated in the analysis, the FDs in the backbone formation regions of sample vary from 2.695 to 2.984, with 2.923 to 2.991 in the percolation regions and 1.224 to 1.544 in the tortuosity. According to the MIP test, the mercury distribution in porous graphite manifested a transitional process from local aggregation, gradual expansion, and infinite cluster connection to global connection.

scholarly journals FRACTAL DIMENSIONS FOR UNSATURATED POROUS MEDIA

Fractals ◽  
2004 ◽  
Vol 12 (01) ◽  
pp. 17-22 ◽  
Author(s):  
BOMING YU ◽  
JIANHUA LI
Keyword(s):  
Porous Media ◽  
Transport Properties ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Thermal Dispersion ◽  
Unsaturated Porous Media ◽  
Empirical Constant ◽  
Pore Sizes ◽  
Analytical Expressions

The analytical expressions of the fractal dimensions for wetting and non-wetting phases for unsaturated porous media are derived and are found to be a function of porosity, maximum and minimum pore sizes as well as saturation. There is no empirical constant in the proposed fractal dimensions. It is also found that the fractal dimensions increase with porosity of a medium and are meaningful only in a certain range of saturation Sw, i.e. Sw>S min for wetting phase and Sw<S max for non-wetting phase at a given porosity, based on real porous media for requirements from both fractal theory and experimental observations. The present analysis of the fractal dimensions is verified to be consistent with the existing experimental observations and it makes possible to analyze the transport properties such as permeability, thermal dispersion in unsaturated porous media by fractal theory and technique.

Fractal structure of biofilms: new tools for investigation of morphology

1995 ◽  
Vol 32 (8) ◽  
pp. 99-105 ◽  
Author(s):  
S. W. Hermanowicz ◽  
U. Schindler ◽  
P. Wilderer
Keyword(s):  
Laser Scanning ◽  
Cross Correlation ◽  
Fractal Structure ◽  
Fractal Dimensions ◽  
Confocal Laser Scanning Microscope ◽  
Confocal Laser ◽  
Small Scale ◽  
Scanning Microscope ◽  
Topological Dimension ◽  
The Difference

Fractal dimension was used to describe morphology of a biofilm. Images of biofilm sections were obtained with a confocal laser scanning microscope and were further enhanced using image analysis software. Fractal dimensions were estimated from the slopes of cross-correlation functions. Two geometric scales with different fractal dimensions were identified in the biofilm. Small scale biomass clusters (&lt; 5 μm) had fractal dimensions close to the topological dimension while the fractal dimensions of larger aggregates were considerably smaller. Anisotropic morphology was also detected by the difference of fractal dimensions and was possibly related to the direction of water flow.

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.

Fractal Characters of Micro-Pores in the Sinter

2011 ◽  
Vol 197-198 ◽  
pp. 662-666
Author(s):  
Qing Jun Zhang ◽  
Wen Ling Mo ◽  
Yuan Liang Li ◽  
Yu Zhu Zhang
Keyword(s):  
Fractal Structure ◽  
Mercury Intrusion Porosimetry ◽  
Fractal Theory ◽  
Mercury Intrusion ◽  
Relationship Of ◽  
The Relationship ◽  
Important Character

The pore in the sinter is an important character. Because of multiphase and asymmetry in the sinter, the structure of the pore is very complex. To study the character of the pore effectively, the method of mercury intrusion porosimetry is applied to measure the pore in the sinter, and the results are dealt with by the fractal theory. The results prove that the pores in the sinter are actually fractal structure when the size of the pores is more than 204.5 nm because their curves in the log-log plot are linear, and some curves qualified with the linearity obviously possess of the segment linearity character. According to the calculation of the fractal D, the relationship of the strength and fractal D will be established.

May the Piezoresistivity of GNP-Modified Cement Mortar Be Related to Its Fractal Structure?

2021 ◽  
Vol 5 (4) ◽  
pp. 148
Author(s):  
Nanxi Dang ◽  
Jin Tao ◽  
Qiang Zeng ◽  
Weijian Zhao
Keyword(s):  
Fractal Structure ◽  
Mercury Intrusion Porosimetry ◽  
Cement Mortar ◽  
Fractal Dimensions ◽  
Gauge Factor ◽  
Mercury Intrusion ◽  
Multi Scale ◽  
Fractal Models ◽  
Cement Mortars ◽  
Electron Scanning Microscopy

High piezoresistivity of cement-based composites tuned by conductible fillers provides a feasible way to develop self-sensing smart structures and buildings. However, the microstructural mechanisms remain to be properly understood. In the present work, the piezoresistivity of cement mortar with different dosages of graphene nanoplatelets (GNPs) was investigated, and the microstructure was assessed by electron scanning microscopy (SEM) and mercury intrusion porosimetry (MIP). Two surface fractal models were introduced to interpret the MIP data to explore the multi-scale fractal structure of the GNP-modified cement mortars. Results show that the incorporation of GNPs into cement mortar can roughen the fracture surfaces due to the GNPs’ agglomeration. Gauge factor (GF) rises and falls as GNP content increases from 0% to 1% with the optimal piezoresistivity observed at GNP = 0.1% and 0.05%. The GF values of the optimum mortar are over 50 times higher than those of the reference mortar. Fractal dimensions in macro and micro fractal regions change with GNP content. Analysis shows that the fractal dimensions in micro region decrease first and then increase with the increase of GF values. GNPs not only impact the fractal structure of cement mortar, but also alter the tunneling and contact effects that govern the piezoresistivity of composite materials.

A NEW METHOD FOR CALCULATING FRACTAL DIMENSIONS OF POROUS MEDIA BASED ON PORE SIZE DISTRIBUTION

Fractals ◽  
2018 ◽  
Vol 26 (01) ◽  
pp. 1850006 ◽  
Author(s):  
YUXUAN XIA ◽  
JIANCHAO CAI ◽  
WEI WEI ◽  
XIANGYUN HU ◽  
XIN WANG ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Pore Space ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
New Method ◽  
Distribution Data

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

Rapid determination of fractal structure of bacterial assemblages in wastewater treatment: implications to process optimisation

1998 ◽  
Vol 38 (2) ◽  
pp. 9-15 ◽  
Author(s):  
J. Guan ◽  
T. D. Waite ◽  
R. Amal ◽  
H. Bustamante ◽  
R. Wukasch
Keyword(s):  
Wastewater Treatment ◽  
Fractal Structure ◽  
Structural Information ◽  
Rapid Determination ◽  
Fractal Dimensions ◽  
Structure Information ◽  
Treatment Processes ◽  
On Line ◽  
Bacterial Aggregates

A rapid method of determining the structure of aggregated particles using small angle laser light scattering is applied here to assemblages of bacteria from wastewater treatment systems. The structure information so obtained is suggestive of fractal behaviour as found by other methods. Strong dependencies are shown to exist between the fractal structure of the bacterial aggregates and the behaviour of the biosolids in zone settling and dewatering by both pressure filtration and centrifugation methods. More rapid settling and significantly higher solids contents are achievable for “looser” flocs characterised by lower fractal dimensions. The rapidity of determination of structural information and the strong dependencies of the effectiveness of a number of wastewater treatment processes on aggregate structure suggests that this method may be particularly useful as an on-line control tool.

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.

MATHEMATICAL MODELS OF GEOFILTRRATION AND GEOMIGRATION IN POROUS MEDIA WITH FRACTAL STRUCTURE

2020 ◽  
Vol 6 (3) ◽  
pp. 21-27
Author(s):  
R.A. Yusupov ◽  
◽  
Sh.S. Axrolov ◽  
N.M. Mirzanova ◽  
A.N. Nasiriddinov ◽  
...  
Keyword(s):  
Porous Media ◽  
Mathematical Models ◽  
Linear Models ◽  
Fractal Structure ◽  
Fractal Structures

In this study 2-D linear models are coming from generalised, Boussinesq eqution describing geofiltration in soils with fractal structures are presented. In this study are presented too mathematical models geomigration of contaminations with groundwater in classical way and in soils with fractal structures.

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.

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