# Micropore Structure and Fractal Characteristics of Low-Permeability Coal Seams

Authors: Guang-zhe Deng; Rui Zheng
Journal: Advances in Materials Science and Engineering
 (2018)

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## Abstract

With the raw coal from a typical low-permeability coal seam in the coalfield of South Junger Basin in Xinjiang as the research object, this paper examined six kinds of coal samples with different permeabilities using a scanning electron microscope and a low-temperature nitrogen adsorption test that employed a JSM-6460LV high-resolution scanning electron microscope and an ASAP2020 automatic specific surface area micropore analyzer to measure all characteristic micropore structural parameters. According to fractal geometry theory, four fractal dimension calculation models of coal and rock were established, after which the pore structure characteristic parameters were used to calculate the fractal dimensions of the different coal seams. The results show that (1) the low-permeability coal seam in the coalfield of South Junger Basin in Xinjiang belongs to mesoporous medium, with a certain number of large pores and no micropores. The varying adsorption capacities of the different coal seams were positively correlated with pore volume, surface area, and the mesoporous surface area proportions, from which it was concluded that mesopores were the main contributors to pore adsorption in low-permeability coal seams. (2) The raw coal pore fractal dimension had a negative linear relationship to average pore size, a positive linear relationship with total pore volume, total surface area, and adsorption capacity, and a positive correlation with the mesoporous surface area proportion; that is, the higher the fractal dimension, the larger the pore volume and surface area of the raw coal. (3) The permeability of the low-permeability coal seam had a phase correlation with the micropore development degree; that is, the permeability had a phase negative correlation with the pore distribution fractal dimension, and there was a positive correlation between permeability and porosity. These results are of theoretical significance for the clean exploitation of low-permeability coal seam resources.


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## Body

## 1. Introduction

Coal is a complex porous medium, with its macroscopic physical properties (porosity, permeability, and adsorbability) and its physical and mechanical properties being closely related to its microscopic pore structure characteristics. It is important to study the pore structure characteristics of the coal seam for understanding and interpreting coal reservoir [1].Close research attention has been paid to the relationships between micropore structures and the macroscopic physical properties of coal and rock mass. While it is known that the pore structures of coal and rock mass are complex and have obvious heterogeneity, it has been difficult to describe and characterize these pore structures using traditional methods. However, fractal theory has been found to be an effective method for characterizing complex porous media; for example, it can be used for pore structure identification, diffusion coefficient, permeability coefficient measurement, and so on [2–5]. The fractal dimension is a quantitative descriptive parameter for specific fractal characteristics. Therefore, based on fractal theory, the pore structures of sandstone were analyzed, from which a new method for simultaneously measuring porosity and pore surface fractal dimensions was proposed, which allowed for the relationships between the fractal dimensions and residual water saturation to be identified [6–8]. A study of four bituminous coals and oxidized bituminous coal samples at 270°C was able to determine the fractal dimensions and fractal distribution sensitivities to oxidation treatments [9]. Based on the creep fracture damage model of a jointed rock mass, the results show that the greater the number of rock joints, the larger the fractal dimensions, the more the fracture energy absorbs material [10–13]. Coal pore structure has been analyzed using mercury injection experiments, which allowed for the fractal dimensions of the pore coal body surface to be calculated and the pore structure characteristics to be quantitatively characterized [14, 15]. The relationships between the adsorption characteristics of coal samples and the fractal dimension of low-temperature pore surfaces have been established using nitrogen adsorption tests [16–21], and using digital core technology, the relationships between the fractal dimension of pore diameter and permeability have been established [22, 23]. Fractal theory has also been employed to determine the relationships between pore fractal dimensions and permeability [24–26], from which it was found that the compressibility, hardness, and porosity of coal bodies were related to the fractal dimensions [27–29]. A study on the influence of confined pressure and pore water pressure on the coal sample structure and percolation characteristics established a quantitative relationship between pore structure fractals and coal sample permeability [30, 31]. According to the pore structure characteristics of low-permeability coal seams, a 3D pore model for low-permeability coal was constructed, and the influence of porosity on mechanical properties of coal was discussed [32].Although there has been significant research on the physical properties of coal seams, there has been little research focused on the microscopic pore structures of low-permeability coal seams and the effect of these on the macroscopic exploitation and utilization of the coal seams. Therefore, to further explore the relationships between the microstructure characteristics and the macroscopic physical properties of low-permeability coal seams, this paper used the low-permeability coal seam in the coalfield of South Junger Basin in Xinjiang to systematically analyze the coal’s physical characteristics and pore structure using an MTS-815 servo test system, a scanning electron microscope, and a surface microporous fractal instrument, which allowed for all kinds of fractal models used to study and explain the micropore structure of the coal seam. The fractal characteristics of pore structure in low-permeability coal seams and the relationships between the pore structure and the macroscopic physical parameters are also discussed. These results can greatly assist in the interpretation and prediction of the macroscopic properties in coal seams.


## 2. Fractal Description of Coal and Rock Pore Structures

In fractal geometry, the fractal dimension is the objective tool used to measure the degree of “irregularity” and “complexity” in two fractal sets. The fractal dimension definition has the following relations [33]:(1)ϕ=λminλmaxDe−Df,where ϕ is porosity, De is the Euclidean space dimension, and Df is the fractal dimension. In two-dimensional space, De=2,1Df2. In three dimensions, De=3,2Df3;λmin/λmax are the minimum and maximum pore diameters.


### 2.1. Fractal Dimension Pore Distribution Model

To assess the fractal dimension pore distribution, which reflects the inhomogeneity of the pores, the fractal box dimension method has been a widely used fractal measurement method, the rationale for which is as follows.When the fractal figure covers the fractal curve image with a square lattice of a certain scale, some of the mesh may contain part of the curve, while other parts of the mesh remain empty, with the number of nonempty mesh increasing as the mesh side length gradually reduces. If the side length of a square mesh isr, and the number of nonempty mesh is Nr, then the fractal box dimension is [34](2)D=−limr⟶0lnNrlnr.The correspondingNr value is calculated for different grid side lengths r, the logarithmic coordinate curves of r and N≥r are given, and the relation is obtained through fitting [35]:(3)lnN≥r=c−Dlnr.The slopek of Equation (3) is used to fit the straight line, with the box dimension D=−k and having a value between 1 and 2. In this paper, DD is the fractal dimension of pore distribution.


### 2.2. Fractal Dimension Pore Volume Model

From the fractal definition, the density function of the pore radius distribution in porous media has the following relationships [36]:(4)fr=cr−D−1,where r is the pore radius, D is the pore fractal dimension, and c is a constant.If the pore gap is a sphere, the cumulative pore volume is the integral of the radius distribution density function to the radius; therefore, the cumulative pore volumeV≤r with a pore radius less than r can be obtained as follows:(5)V≤r=∫rminrfrar3dr=ac3−Dr3−D−rmin3−D.The cumulative total pore volume isV:(6)V=ac3−Drmax3−D−rmin3−D.Putting Equations (5) and (6) into the following formula, the expression for the cumulative pore volume fraction NV with a pore radius of no more than r can be obtained:(7)NV=V≤rV=r3−D−rmin3−Drmax3−D−rmin3−D.Due to the strong heterogeneity in coal and rock media, the maximum/minimum pore size varies greatly; that is,rmax≫rmin; therefore, Equation (7) can be simplified to(8)NV=rrmax3−D.Equation (9) is then obtained from the logarithm of Equation (8):(9)lnNV=3−Dlnr+C1,where C1=D−3lnrmax is a constant. The fractal dimension of the cumulative pore volume is D=3−k, with the value being between 2 and 3. In this paper, DV is the fractal dimension of pore volume.


### 2.3. Fractal Dimension Pore Area Model

If the pore is a sphere, a cumulative pore areaS≥r with a pore diameter of not less than r can be obtained:(10)S≥r=∫rrmaxfrar2dr=ac2−Drmax2−D−r2−D.The cumulative total pore area isS:(11)S=ac2−Drmax2−D−rmin2−D.Putting Equations (10) and (11) into the following formula, the expression for the cumulative pore area fraction NS with a pore radius of not less than r can be obtained:(12)NS=S≥rS=rmax2−D−r2−Drmax2−D−rmin2−D.Asrmax≫rmin, Equation (12) can be simplified to(13)NS=1−rrmax2−D.Equation (14) is then obtained from the logarithm of Equation (13):(14)ln1−NS=2−Dlnr+C2,where C2=D−2lnrmax is a constant. The fractal dimension of the cumulative pore area is D=2−k, with its value being between 1 and 2. In this paper, DA is the fractal dimension of pore area.


### 2.4. Fractal Dimension Pore Surface Model

Fractal theory states that the surface fractal dimension does not theoretically depend on the size of the pores or the surface; rather, it is an intrinsic characteristic of the surface itself as it is a measure of surface roughness. The Frenkel–Halsey–Hill (FHH) model is an important method for obtaining the specific surface fractal dimension of complex fractal porous media [37], the equation for which is [38](15)lnV=−fDlnlnP0P+C,where V represents the adsorption volume at the equilibrium pressure P, P0 is the vapor saturation pressure, C is the constant, P0/P is the relative pressure, and fD is the fractal dimension D expression.The fractal dimensionD was introduced into the adsorption isotherm equation for microporous solid surfaces [39–41]; fD=3−D; therefore, the fractal FHH equation can be written as [42, 43](16)lnV=D−3lnlnP0P+C.When the low-temperature nitrogen adsorption data,lnV and lnlnP0/P, were plotted, the fitting line slope was k, and the fractal pore surface dimension was calculated as D=k+3, with its value being between 2 and 3. In this paper, DS is the fractal dimension of pore surface.


## 2.1. Fractal Dimension Pore Distribution Model

To assess the fractal dimension pore distribution, which reflects the inhomogeneity of the pores, the fractal box dimension method has been a widely used fractal measurement method, the rationale for which is as follows.When the fractal figure covers the fractal curve image with a square lattice of a certain scale, some of the mesh may contain part of the curve, while other parts of the mesh remain empty, with the number of nonempty mesh increasing as the mesh side length gradually reduces. If the side length of a square mesh isr, and the number of nonempty mesh is Nr, then the fractal box dimension is [34](2)D=−limr⟶0lnNrlnr.The correspondingNr value is calculated for different grid side lengths r, the logarithmic coordinate curves of r and N≥r are given, and the relation is obtained through fitting [35]:(3)lnN≥r=c−Dlnr.The slopek of Equation (3) is used to fit the straight line, with the box dimension D=−k and having a value between 1 and 2. In this paper, DD is the fractal dimension of pore distribution.


## 2.2. Fractal Dimension Pore Volume Model

From the fractal definition, the density function of the pore radius distribution in porous media has the following relationships [36]:(4)fr=cr−D−1,where r is the pore radius, D is the pore fractal dimension, and c is a constant.If the pore gap is a sphere, the cumulative pore volume is the integral of the radius distribution density function to the radius; therefore, the cumulative pore volumeV≤r with a pore radius less than r can be obtained as follows:(5)V≤r=∫rminrfrar3dr=ac3−Dr3−D−rmin3−D.The cumulative total pore volume isV:(6)V=ac3−Drmax3−D−rmin3−D.Putting Equations (5) and (6) into the following formula, the expression for the cumulative pore volume fraction NV with a pore radius of no more than r can be obtained:(7)NV=V≤rV=r3−D−rmin3−Drmax3−D−rmin3−D.Due to the strong heterogeneity in coal and rock media, the maximum/minimum pore size varies greatly; that is,rmax≫rmin; therefore, Equation (7) can be simplified to(8)NV=rrmax3−D.Equation (9) is then obtained from the logarithm of Equation (8):(9)lnNV=3−Dlnr+C1,where C1=D−3lnrmax is a constant. The fractal dimension of the cumulative pore volume is D=3−k, with the value being between 2 and 3. In this paper, DV is the fractal dimension of pore volume.


## 2.3. Fractal Dimension Pore Area Model

If the pore is a sphere, a cumulative pore areaS≥r with a pore diameter of not less than r can be obtained:(10)S≥r=∫rrmaxfrar2dr=ac2−Drmax2−D−r2−D.The cumulative total pore area isS:(11)S=ac2−Drmax2−D−rmin2−D.Putting Equations (10) and (11) into the following formula, the expression for the cumulative pore area fraction NS with a pore radius of not less than r can be obtained:(12)NS=S≥rS=rmax2−D−r2−Drmax2−D−rmin2−D.Asrmax≫rmin, Equation (12) can be simplified to(13)NS=1−rrmax2−D.Equation (14) is then obtained from the logarithm of Equation (13):(14)ln1−NS=2−Dlnr+C2,where C2=D−2lnrmax is a constant. The fractal dimension of the cumulative pore area is D=2−k, with its value being between 1 and 2. In this paper, DA is the fractal dimension of pore area.


## 2.4. Fractal Dimension Pore Surface Model

Fractal theory states that the surface fractal dimension does not theoretically depend on the size of the pores or the surface; rather, it is an intrinsic characteristic of the surface itself as it is a measure of surface roughness. The Frenkel–Halsey–Hill (FHH) model is an important method for obtaining the specific surface fractal dimension of complex fractal porous media [37], the equation for which is [38](15)lnV=−fDlnlnP0P+C,where V represents the adsorption volume at the equilibrium pressure P, P0 is the vapor saturation pressure, C is the constant, P0/P is the relative pressure, and fD is the fractal dimension D expression.The fractal dimensionD was introduced into the adsorption isotherm equation for microporous solid surfaces [39–41]; fD=3−D; therefore, the fractal FHH equation can be written as [42, 43](16)lnV=D−3lnlnP0P+C.When the low-temperature nitrogen adsorption data,lnV and lnlnP0/P, were plotted, the fitting line slope was k, and the fractal pore surface dimension was calculated as D=k+3, with its value being between 2 and 3. In this paper, DS is the fractal dimension of pore surface.


## 3. Fractal Characteristics of the Outer Pores in Low-Permeability Coal Seams

### 3.1. Coal Sampling

In this paper, the typical low-permeability coal seam coal samples B1 + 2 and B3 + 6 were taken as the research objects. The coal sample permeability was measured using an MTS-815 servo test system, which showed that the coal test samples belonged to the low-permeability coal seam, with the permeability coal seam relationships being B-3 < B-4 < B-1 < B-5 < B-2 < B-6 (Table1).Table 1
Permeability of different coal samples.
Coal sample
Porosity (%)
Permeability (md)
Appraise
Classify
B-1
8.2
3.75
Permeability range
Ultralow-permeability reservoir
B-2
7.7
9.77
B-3
7.0
0.29
B-4
5.0
0.43
B-5
6.3
5.32
B-6
6.8
13.2
Poor permeability
Low-permeability reservoir


### 3.2. Electron Microscope Scanning Experiment

A coal sample is usually broken apart to obtain a natural section, after which the sample is scanned to ensure that the scanned image is closer to the true shape of the pore. The pore and fissure structural characteristics observed from coal sample 16 were found to be accurate and stable [44]. In this paper, the coal sample was first cut into 16 sections using small grinding wheels, after which the coal sample sections were broken to form a natural section. To ensure image clarity so as to be able to count the scanning data, the natural sections needed to be smooth.A high-resolution scanning electron microscope test system (Figure1) was used to scan the natural coal sample sections from 6 different coal seams and obtain the SEM images (Figure 2).Figure 1
SEM test system and raw coal sample.
(a)
(b)Figure 2
Raw coal sample SEM images (×1000). (a) B-1 coal sample. (b) B-2 coal sample. (c) B-3 coal sample. (d) B-4 coal. (e) B-5 coal sample. (f) B-6 coal sample.
(a)
(b)
(c)
(d)
(e)
(f)The pore structure was analyzed at 1000 times magnification to be able to analyze the low-permeability coal seam surface pore structure characteristics. The B-1 coal samples were found to have mainly intergranular pores, more mineral crystal particles, and developing cracks and microcracks. The B-2 coal sample was denser, with a smaller quantity of intergranular minerals, a large crack cutting surface or even holes, more regular flat cracks, a stacked fracture, and strong toughness. The B-3 coal sample had a large amount of distributed residual tissue plant pores; from the precipitation of the granular minerals, it is possible to see the xylem retained by the structural silk body and the phloem cell cavity; therefore, the pore level was stronger and more developed, and there were more micropores. The B-4 coal samples were relatively dense, mainly intergranular pores that had a larger pore size and a different pore shape. There were also a small quantity of intergranular pores that had been caused by mineral crystallization, layered cracks, and a small distribution of a number of mineral particles. The B-5 coal sample was compact, with minerals in the intergranular inclusions, a large crack cutting surface, more regular cracks, laminated fractures, and a stronger toughness and stronger crack than the B-2 coal sample. The B-6 coal sample and the B-3 coal sample were similar, as they both had a large distribution of plant residual tissue pores, a precipitation of granular minerals, a structural silk body with retained xylem, and various cellular lumen tissue phloem. Larger more-developed micropores could also be seen at certain magnification rates.


### 3.3. Fractal Dimension Calculation and Analysis

Using an Ostu threshold binarization processing method and MATLAB programming, the SEM images for each coal sample at different magnification rates were processed, and the corresponding binary images were obtained (Figure3), in which the black area are the macropores and the white area is the coal skeleton (including the filling mineral composition).Figure 3
(a) SEM diagram and (b) binary diagram for the B-1 coal sample magnified 500-fold.
(a)
(b)The fractal dimension of pore distribution for the binary sample images was calculated using the “box-counting” algorithm in Fractal Fox 2.0 software, from which it was found that the fractal dimension of pore distribution was between 1 and 2. The software calculation interface and results are shown in Figure4 and Table 2.Figure 4
Calculation of the interface and pore distribution fractal dimension fitting curve using Fractal Fox 2.0 Software.
(a)
(b)Table 2
Fractal dimensions of pore distribution of raw coal samples.
Coal sample
Magnification
Fractal dimension
R
2
Mean fractal dimensionDD
B-1
500
1.9031
0.94326
1.7468
1000
1.7569
0.97957
1000+
1.6339
0.93567
2000
1.7815
0.96458
2000+
1.6586
0.94362
B-2
500
1.7058
0.95124
1.45716
1000
1.3135
0.96959
1000+
1.5879
0.97451
2000
1.1818
0.93462
2000+
1.4968
0.96786
B-3
500
1.9612
0.97896
1.79388
1000
1.4917
0.96323
1000+
1.8141
0.93417
2000
1.8078
0.97489
2000+
1.8946
0.96587
B-4
500
1.8544
0.99452
1.7989
1000
1.6664
0.9764
1000+
1.9731
0.96312
2000
1.6586
0.94754
2000+
1.842
0.96851
B-5
500
1.9859
0.98394
1.8371
1000
1.7858
0.97153
1000+
1.8875
0.96728
2000
1.7415
0.97555
2000+
1.7848
0.96173
B-6
500
1.8909
0.94283
1.69184
1000
1.6697
0.96428
1000+
1.8521
0.95784
2000
1.4124
0.92375
2000+
1.6341
0.97618Table2 shows that the average fractal dimension of pore distribution in the coal samples was B-5 > B-4 > B-3 > B-1 > B-6 > B-2. The maximum fractal dimension of pore distribution was observed in the B-5 coal sample, and the minimum mean fractal dimension was observed in the B-2 coal sample. The average fractal dimensions of the B-1, B-3, B-4, and B-6 coal samples were in the middle, with no significant differences. Fractal theory states that the larger the fractal dimension of coal pore distribution, the more developed the pores and the more uneven the distribution. Therefore, the B-5 coal seam was found to have the most developed pores and the most uneven distribution, with the most undeveloped pores being found in the B-2 coal seam, which was basically consistent with the analysis in Figure 2.


## 3.1. Coal Sampling

In this paper, the typical low-permeability coal seam coal samples B1 + 2 and B3 + 6 were taken as the research objects. The coal sample permeability was measured using an MTS-815 servo test system, which showed that the coal test samples belonged to the low-permeability coal seam, with the permeability coal seam relationships being B-3 < B-4 < B-1 < B-5 < B-2 < B-6 (Table1).Table 1
Permeability of different coal samples.
Coal sample
Porosity (%)
Permeability (md)
Appraise
Classify
B-1
8.2
3.75
Permeability range
Ultralow-permeability reservoir
B-2
7.7
9.77
B-3
7.0
0.29
B-4
5.0
0.43
B-5
6.3
5.32
B-6
6.8
13.2
Poor permeability
Low-permeability reservoir


## 3.2. Electron Microscope Scanning Experiment

A coal sample is usually broken apart to obtain a natural section, after which the sample is scanned to ensure that the scanned image is closer to the true shape of the pore. The pore and fissure structural characteristics observed from coal sample 16 were found to be accurate and stable [44]. In this paper, the coal sample was first cut into 16 sections using small grinding wheels, after which the coal sample sections were broken to form a natural section. To ensure image clarity so as to be able to count the scanning data, the natural sections needed to be smooth.A high-resolution scanning electron microscope test system (Figure1) was used to scan the natural coal sample sections from 6 different coal seams and obtain the SEM images (Figure 2).Figure 1
SEM test system and raw coal sample.
(a)
(b)Figure 2
Raw coal sample SEM images (×1000). (a) B-1 coal sample. (b) B-2 coal sample. (c) B-3 coal sample. (d) B-4 coal. (e) B-5 coal sample. (f) B-6 coal sample.
(a)
(b)
(c)
(d)
(e)
(f)The pore structure was analyzed at 1000 times magnification to be able to analyze the low-permeability coal seam surface pore structure characteristics. The B-1 coal samples were found to have mainly intergranular pores, more mineral crystal particles, and developing cracks and microcracks. The B-2 coal sample was denser, with a smaller quantity of intergranular minerals, a large crack cutting surface or even holes, more regular flat cracks, a stacked fracture, and strong toughness. The B-3 coal sample had a large amount of distributed residual tissue plant pores; from the precipitation of the granular minerals, it is possible to see the xylem retained by the structural silk body and the phloem cell cavity; therefore, the pore level was stronger and more developed, and there were more micropores. The B-4 coal samples were relatively dense, mainly intergranular pores that had a larger pore size and a different pore shape. There were also a small quantity of intergranular pores that had been caused by mineral crystallization, layered cracks, and a small distribution of a number of mineral particles. The B-5 coal sample was compact, with minerals in the intergranular inclusions, a large crack cutting surface, more regular cracks, laminated fractures, and a stronger toughness and stronger crack than the B-2 coal sample. The B-6 coal sample and the B-3 coal sample were similar, as they both had a large distribution of plant residual tissue pores, a precipitation of granular minerals, a structural silk body with retained xylem, and various cellular lumen tissue phloem. Larger more-developed micropores could also be seen at certain magnification rates.


## 3.3. Fractal Dimension Calculation and Analysis

Using an Ostu threshold binarization processing method and MATLAB programming, the SEM images for each coal sample at different magnification rates were processed, and the corresponding binary images were obtained (Figure3), in which the black area are the macropores and the white area is the coal skeleton (including the filling mineral composition).Figure 3
(a) SEM diagram and (b) binary diagram for the B-1 coal sample magnified 500-fold.
(a)
(b)The fractal dimension of pore distribution for the binary sample images was calculated using the “box-counting” algorithm in Fractal Fox 2.0 software, from which it was found that the fractal dimension of pore distribution was between 1 and 2. The software calculation interface and results are shown in Figure4 and Table 2.Figure 4
Calculation of the interface and pore distribution fractal dimension fitting curve using Fractal Fox 2.0 Software.
(a)
(b)Table 2
Fractal dimensions of pore distribution of raw coal samples.
Coal sample
Magnification
Fractal dimension
R
2
Mean fractal dimensionDD
B-1
500
1.9031
0.94326
1.7468
1000
1.7569
0.97957
1000+
1.6339
0.93567
2000
1.7815
0.96458
2000+
1.6586
0.94362
B-2
500
1.7058
0.95124
1.45716
1000
1.3135
0.96959
1000+
1.5879
0.97451
2000
1.1818
0.93462
2000+
1.4968
0.96786
B-3
500
1.9612
0.97896
1.79388
1000
1.4917
0.96323
1000+
1.8141
0.93417
2000
1.8078
0.97489
2000+
1.8946
0.96587
B-4
500
1.8544
0.99452
1.7989
1000
1.6664
0.9764
1000+
1.9731
0.96312
2000
1.6586
0.94754
2000+
1.842
0.96851
B-5
500
1.9859
0.98394
1.8371
1000
1.7858
0.97153
1000+
1.8875
0.96728
2000
1.7415
0.97555
2000+
1.7848
0.96173
B-6
500
1.8909
0.94283
1.69184
1000
1.6697
0.96428
1000+
1.8521
0.95784
2000
1.4124
0.92375
2000+
1.6341
0.97618Table2 shows that the average fractal dimension of pore distribution in the coal samples was B-5 > B-4 > B-3 > B-1 > B-6 > B-2. The maximum fractal dimension of pore distribution was observed in the B-5 coal sample, and the minimum mean fractal dimension was observed in the B-2 coal sample. The average fractal dimensions of the B-1, B-3, B-4, and B-6 coal samples were in the middle, with no significant differences. Fractal theory states that the larger the fractal dimension of coal pore distribution, the more developed the pores and the more uneven the distribution. Therefore, the B-5 coal seam was found to have the most developed pores and the most uneven distribution, with the most undeveloped pores being found in the B-2 coal seam, which was basically consistent with the analysis in Figure 2.


## 4. Fractal Characteristics of the Internal Pores in Low-Permeability Coal Seams

### 4.1. Low-Temperature Liquid Nitrogen Adsorption Experiment

To further study the internal pore structure characteristics of the low-permeability coal seam, a correlation analysis experiment of the specific surface area, the pore diameter, and the pore volume of a raw coal sample was conducted using an ASAP2020 specific surface micropore analyzer. The experimental system and experimental results are shown in Figures5 and 6 and Table 3.Figure 5
ASAP2020 specific surface microanalyzer.Figure 6
Adsorption isotherms of nitrogen for the raw coal samples.Table 3
Specific surface area, pore volume, and pore size of raw coal samples.
Coal sample
Average pore diameter (nm)
Cumulative pore volume (cm3·g−1)
Cumulative specific surface area (m2·g−1)
Pore volume/specific surface area ratio of different pore size segments (%)
Macropore (>50)
Mesopore (2∼50)
B-1
29.2002
0.000589
0.0807
38.71/38.22
61.29/61.78
B-2
31.7096
0.000938
0.1183
34.12/50.14
65.88/49.86
B-3
10.3268
0.008605
3.3331
24.22/5.92
75.78/94.08
B-4
26.7596
0.001153
0.1724
40/34.51
60/65.49
B-5
32.7034
0.00083
0.1015
48.55/47.03
51.45/52.97
B-6
21.6436
0.003718
0.6871
17.59/20.12
82.41/79.88The analysis in Figure6 shows that the adsorption capacity of the different coal seams differed when the relative pressure was the same. The adsorption capacity of the B-3 coal seam was the largest, followed by the B-6 coal seam, with the adsorption capacities of the remaining coal seams being small; that is, B-4 > B-2 > B-5 > B-1.The average pore diameter of the B-1 to B-6 coal seams was 10.33–32.7 nm, the mesoporous volume proportion was more than 51%, and the large pore volume ratio was between 17.59 and 48.55%. The specific mesoporous surface area was more than 50%, and the macroporous specific surface area was 5.92 to 50.14% (Table3). Therefore, it was concluded that the low-permeability coal seam in the South Junger Basin coalfield in Xinjiang belongs to mesoporous material, its pore distribution was more complex, the mesoporous was dominant, there were a certain number of large pores, and there were no micropores. The pore volume and specific surface area of the B-3 coal seam was the largest, followed by the B-6 coal seam, with the relationship between the pore volumes and specific surface areas of the other coal seams being B-4 > B-2 > B-5 > B-1. The results showed that there was a positive correlation between the adsorption capacities, the pore volumes, and the specific surface areas of the different coal seams.


### 4.2. Fractal Dimension Calculation and Analysis

From the liquid nitrogen at low-temperature isothermal adsorption experimental data for the B-1 to B-6 coal seam samples, the pore radiusr, the corresponding volume NV≤r, and the area NS≥r of each coal sample were obtained. From Formulas (9) and (14), a linear relationship between lnNV, ln1−NS and lnr was observed. The fractal dimensions DV for the volume and the fractal dimensions DA for the surface area of the different coal samples were calculated using linear fitting in the double logarithmic coordinate system using origin software (The results are shown in Figures 7–9 and Table 4).Figure 7
Calculation of pore volume fractal dimensions for the B-1 to B-6 coal samples.
(a)
(b)
(c)
(d)
(e)
(f)Figure 8
Calculation of pore surface area fractal dimensions for the B-1 to B-6 coal samples.
(a)
(b)
(c)
(d)
(e)
(f)Figure 9
Fractal dimension of pore structure in different coal seams.Table 4
Maximum and minimum pore radius and volume/area fractal dimension for the B-1 to B-6 coal samples.
Coal sample
Maximum/minimum pore diameter (nm)
Maximum/minimum pore ratio
Volume fractal dimensionDV
R
2
Area fractal dimensionDA
R
2
B-1
193.31/3.7
52.24595
2.25
0.99872
1.46
0.72425
B-2
179.56/8.86
20.26637
2.21
0.99987
1.22
0.75084
B-3
97.71/3.25
30.06461
2.91
0.99895
1.79
0.59082
B-4
133.19/3.01
44.24917
2.28
0.99909
1.55
0.77354
B-5
152.66/2.64
57.82576
2.08
0.9994
1.297
0.75619
B-6
111.49/3.56
31.31742
2.57
0.99976
1.41
0.72505The fitting correlation coefficients are all above 0.72; the results show that the fitting correlation is good.The volume fractal dimension relationship for the coal seams was B-3 > B-6 > B-4 > B-1 > B-2 > B-5, and the surface area fractal dimension relationship for the coal seams was B-3 > B-4 > B-1 > B-6 > B-5 > B-2. The volume fractal dimension and the surface area fractal dimension for B-1, B-4, and B-6 were similar, and the general variation trends were the same, which indicated that these two methods were able to identify the pore radius distribution characteristics of the coal samples (Figure9). The analysis showed that the fractal dimension of the B-3 coal sample was the largest; that is, it had irregular and small pore sizes, with the average pore size measured by the low-temperature adsorption experiment being 10.33 nm, the number of mesoporous being the largest, and the pore structure being the most complex. The fractal dimensions of the B-1, B-4, and B-6 coal samples were almost the same, which corresponded to the number of macropores. The fractal dimensions of the B-2 and B-5 coal samples were the smallest, which was consistent with the largest number of macropores, and the simplest pore structure. According to the analysis of Table 4 and Figure 9, the maximum/minimum pore size ratio has an effect on the correlation coefficient of the fractal dimension of coal sample surface area, but it has no effect on the trend of quantitative characterization of pore structure.The fractal dimension of coal pore surface is a measure of irregular roughness of the pore surface, which reflects the comprehensive index of pore distribution, pore diameter, and pore volume of coal. Based on the low-temperature nitrogen adsorption isotherm experimental data on the coal samples, the pore surface fractal dimensions were calculated using Formula (16) (the results are shown in Figure 10).Figure 10
Calculation of pore surface fractal dimension for the B-1 to B-6 coal samples.
(a)
(b)
(c)
(d)
(e)
(f)The results show that the fitting correlation coefficient was above 0.93, and the correlation was good.The pore surface fractal dimension order was B-3 > B-6 > B-4 > B-2 > B-1 > B-5 (Figure10). The pore surface fractal dimension of the B-3 coal sample was the largest, which was consistent with its complex pore structure. The pore surface fractal dimension of the B-5 coal sample was the smallest, as the pore boundary was smoother compared with the other coal samples. The pore surface fractal dimensions of B-1, B-2, and B-4 coal samples were in the middle, with similar sizes, which indicated that the pore surfaces were generally rough. The pore surface fractal dimension of B-6 was greater than that of B-4, indicating that the pore roughness of the B-6 coal sample was greater than the pore roughness of B-4.


## 4.1. Low-Temperature Liquid Nitrogen Adsorption Experiment

To further study the internal pore structure characteristics of the low-permeability coal seam, a correlation analysis experiment of the specific surface area, the pore diameter, and the pore volume of a raw coal sample was conducted using an ASAP2020 specific surface micropore analyzer. The experimental system and experimental results are shown in Figures5 and 6 and Table 3.Figure 5
ASAP2020 specific surface microanalyzer.Figure 6
Adsorption isotherms of nitrogen for the raw coal samples.Table 3
Specific surface area, pore volume, and pore size of raw coal samples.
Coal sample
Average pore diameter (nm)
Cumulative pore volume (cm3·g−1)
Cumulative specific surface area (m2·g−1)
Pore volume/specific surface area ratio of different pore size segments (%)
Macropore (>50)
Mesopore (2∼50)
B-1
29.2002
0.000589
0.0807
38.71/38.22
61.29/61.78
B-2
31.7096
0.000938
0.1183
34.12/50.14
65.88/49.86
B-3
10.3268
0.008605
3.3331
24.22/5.92
75.78/94.08
B-4
26.7596
0.001153
0.1724
40/34.51
60/65.49
B-5
32.7034
0.00083
0.1015
48.55/47.03
51.45/52.97
B-6
21.6436
0.003718
0.6871
17.59/20.12
82.41/79.88The analysis in Figure6 shows that the adsorption capacity of the different coal seams differed when the relative pressure was the same. The adsorption capacity of the B-3 coal seam was the largest, followed by the B-6 coal seam, with the adsorption capacities of the remaining coal seams being small; that is, B-4 > B-2 > B-5 > B-1.The average pore diameter of the B-1 to B-6 coal seams was 10.33–32.7 nm, the mesoporous volume proportion was more than 51%, and the large pore volume ratio was between 17.59 and 48.55%. The specific mesoporous surface area was more than 50%, and the macroporous specific surface area was 5.92 to 50.14% (Table3). Therefore, it was concluded that the low-permeability coal seam in the South Junger Basin coalfield in Xinjiang belongs to mesoporous material, its pore distribution was more complex, the mesoporous was dominant, there were a certain number of large pores, and there were no micropores. The pore volume and specific surface area of the B-3 coal seam was the largest, followed by the B-6 coal seam, with the relationship between the pore volumes and specific surface areas of the other coal seams being B-4 > B-2 > B-5 > B-1. The results showed that there was a positive correlation between the adsorption capacities, the pore volumes, and the specific surface areas of the different coal seams.


## 4.2. Fractal Dimension Calculation and Analysis

From the liquid nitrogen at low-temperature isothermal adsorption experimental data for the B-1 to B-6 coal seam samples, the pore radiusr, the corresponding volume NV≤r, and the area NS≥r of each coal sample were obtained. From Formulas (9) and (14), a linear relationship between lnNV, ln1−NS and lnr was observed. The fractal dimensions DV for the volume and the fractal dimensions DA for the surface area of the different coal samples were calculated using linear fitting in the double logarithmic coordinate system using origin software (The results are shown in Figures 7–9 and Table 4).Figure 7
Calculation of pore volume fractal dimensions for the B-1 to B-6 coal samples.
(a)
(b)
(c)
(d)
(e)
(f)Figure 8
Calculation of pore surface area fractal dimensions for the B-1 to B-6 coal samples.
(a)
(b)
(c)
(d)
(e)
(f)Figure 9
Fractal dimension of pore structure in different coal seams.Table 4
Maximum and minimum pore radius and volume/area fractal dimension for the B-1 to B-6 coal samples.
Coal sample
Maximum/minimum pore diameter (nm)
Maximum/minimum pore ratio
Volume fractal dimensionDV
R
2
Area fractal dimensionDA
R
2
B-1
193.31/3.7
52.24595
2.25
0.99872
1.46
0.72425
B-2
179.56/8.86
20.26637
2.21
0.99987
1.22
0.75084
B-3
97.71/3.25
30.06461
2.91
0.99895
1.79
0.59082
B-4
133.19/3.01
44.24917
2.28
0.99909
1.55
0.77354
B-5
152.66/2.64
57.82576
2.08
0.9994
1.297
0.75619
B-6
111.49/3.56
31.31742
2.57
0.99976
1.41
0.72505The fitting correlation coefficients are all above 0.72; the results show that the fitting correlation is good.The volume fractal dimension relationship for the coal seams was B-3 > B-6 > B-4 > B-1 > B-2 > B-5, and the surface area fractal dimension relationship for the coal seams was B-3 > B-4 > B-1 > B-6 > B-5 > B-2. The volume fractal dimension and the surface area fractal dimension for B-1, B-4, and B-6 were similar, and the general variation trends were the same, which indicated that these two methods were able to identify the pore radius distribution characteristics of the coal samples (Figure9). The analysis showed that the fractal dimension of the B-3 coal sample was the largest; that is, it had irregular and small pore sizes, with the average pore size measured by the low-temperature adsorption experiment being 10.33 nm, the number of mesoporous being the largest, and the pore structure being the most complex. The fractal dimensions of the B-1, B-4, and B-6 coal samples were almost the same, which corresponded to the number of macropores. The fractal dimensions of the B-2 and B-5 coal samples were the smallest, which was consistent with the largest number of macropores, and the simplest pore structure. According to the analysis of Table 4 and Figure 9, the maximum/minimum pore size ratio has an effect on the correlation coefficient of the fractal dimension of coal sample surface area, but it has no effect on the trend of quantitative characterization of pore structure.The fractal dimension of coal pore surface is a measure of irregular roughness of the pore surface, which reflects the comprehensive index of pore distribution, pore diameter, and pore volume of coal. Based on the low-temperature nitrogen adsorption isotherm experimental data on the coal samples, the pore surface fractal dimensions were calculated using Formula (16) (the results are shown in Figure 10).Figure 10
Calculation of pore surface fractal dimension for the B-1 to B-6 coal samples.
(a)
(b)
(c)
(d)
(e)
(f)The results show that the fitting correlation coefficient was above 0.93, and the correlation was good.The pore surface fractal dimension order was B-3 > B-6 > B-4 > B-2 > B-1 > B-5 (Figure10). The pore surface fractal dimension of the B-3 coal sample was the largest, which was consistent with its complex pore structure. The pore surface fractal dimension of the B-5 coal sample was the smallest, as the pore boundary was smoother compared with the other coal samples. The pore surface fractal dimensions of B-1, B-2, and B-4 coal samples were in the middle, with similar sizes, which indicated that the pore surfaces were generally rough. The pore surface fractal dimension of B-6 was greater than that of B-4, indicating that the pore roughness of the B-6 coal sample was greater than the pore roughness of B-4.


## 5. Relationship between Pore Fractal Dimension and Macrophysical Properties in Low-Permeability Coal Seams

The relationships between the pore structures and the fractal dimensions were determined using origin software, the experimental data, and the fractal dimension calculation results (Figure11).Figure 11
Relationship between the pore fractal dimension and the pore structure parameters for the B-1 to B-6 coal samples.
(a)
(b)
(c)
(d)
(e)
(f)The fractal dimension of pores in different coal seams shows a negative linear relationship with the average pore size and a positive linear relationship with total surface area and total pore volume. The results showed that the larger the average pore radius fractal dimension, the larger the pore volume and surface area. The linear relationships between the volume fractal dimension, the surface area fractal dimension, and the mesoporous surface area ratio were positively correlated. The surface fractal dimension has a positive exponential relationship with the mesoporous surface area ratio. In general, the higher the fractal dimensions of the pores in the different coal seams, the larger the mesoporous proportion.The results showed that coal seam permeability is related to the porosity development degree outside the coal seam. The permeability of B-3 and B-4 was basically consistent, and the corresponding fractal dimensions were basically the same; however, as the permeability of B-2 and B-6 was larger, the corresponding fractal dimensions were the smallest. There was a stage negative correlation found between permeability and the pore distribution fractal dimension and a positive correlation found between permeability and porosity (Figure12). Therefore, these results were consistent with the conclusion that porous media permeability decreases with an increase in the fractal dimension and pore structure complexity [45]. The fractal dimension of pore distribution in different coal seams was B-5 > B-4 > B-3 > B-1 > B-6 > B-2, which indicated that the distribution of the B-5 pores was the most uneven in the plane images, as shown in Figure 2.Figure 12
Fractal dimension, porosity, and permeability for the B-1 to B-6 coal samples.The results showed that the adsorption capacity of the different coal seams was consistent with the change trend of mesoporous surface area, and mesopore is the main part of pore adsorption in low-permeability coal seams (Figure13). With the increase of mesoporous surface area, the surface roughness increases and the adsorption ability of the coal mesoporous surface increases.Figure 13
Adsorption capacity and mesoporous surface area for the B-1 to B-6 coal samples.The surface fractal dimension measures the pore surface characteristics and reflects the adsorption ability of the coal seam. The adsorption capacity of raw coal in low-permeability coal seams has a positive linear relationship with the surface fractal dimension (Figure14), with the relationship being: y=7.76942x−16.17684; 2≤x≤3; R2=0.93.Figure 14
Relationship between adsorption quantity and pore surface fractal dimension.


## 6. Conclusions

This article took the raw coal from a typical low-permeability coal seam in the coalfield of South Junger Basin in Xinjiang as the research object to examine the microscopic pore structures and fractal characteristics of low-permeability coal seams using a high-resolution scanning electron microscope (SEM), fractal software (Fractal fox2.0), and a specific surface microporous analyzer (ASAP2020). The main conclusions were as follows:(1)
From the principles of fractal geometry, a fractal dimension calculation model for the volume, surface area, surface, and pore distribution for the coal micropore structures was established. The validity of the fractal model was verified by a scanning electron microscope and a nitrogen adsorption test at low temperature.(2)
The low-temperature nitrogen adsorption test found that the typical low-permeability coal seam in the coalfield of South Junger Basin in Xinjiang belongs to the mesoporous medium, which is mainly mesoporous, with a certain amount of large pores, no micropores, and a more complex pore distribution. Under the same pressure conditions, a positive correlation was found between the adsorption capacity, the pore volume, and the specific surface area of the coal seam.(3)
The pore fractal dimensions and the pore structural parameters were fitted using origin software, from which it was found that the pore fractal dimension in low-permeability coal seams has a negative linear relationship with average pore size, a positive linear relationship with total surface area and total pore volume, and a positive correlation with the mesoporous surface area ratio; that is, the higher the fractal dimension, the larger the pore volume, surface area, and mesoporous surface area.(4)
The permeability of low-permeability coal seams has a phase correlation with the micropore development degree. Permeability was found to have a phase negative correlation with the pore distribution fractal dimension and a positive correlation with permeability and porosity, which indicated that the micropore has an important influence on the permeability of low-permeability coal seams.(5)
The study on the relationships between pore adsorption capacity, mesoporous surface area, and surface fractal dimensions in low-permeability coal seams showed that coal seam adsorption capacity was positively related to mesoporous surface area because of the mesopores and had a positive linear relationship with the surface fractal dimension, which can quantitatively characterize the adsorption capacity of the coal seam. These results could be of significant value when assessing the adsorption characteristics for coal bed methane exploration.



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*Source: 4186280-2018-10-16.xml*