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Natural Gas Geoscience ›› 2020, Vol. 31 ›› Issue (7): 1028-1040.doi: 10.11764/j.issn.1672-1926.2020.03.013

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Fractal analysis of micropore structures in coal and shale based on low-temperature CO2 adsorption

Yi-hua XIONG1(),Shang-wen ZHOU2,Peng-fei JIAO2,Ming-wei YANG2,Jun-ping ZHOU3,Wei WEI1,Jian-chao CAI1()   

  1. 1.Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China
    2.PetroChina Research Institute of Petroleum Exploration and Development, Beijing 100083, China
    3.The State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China
  • Received:2019-12-28 Revised:2020-03-29 Online:2020-07-10 Published:2020-07-02
  • Contact: Jian-chao CAI E-mail:lingkongdaxia@163.com;caijc@cug.edu.cn
  • Supported by:
    The China National Science and Technology Major Projects(2017ZX05035002-002);The Natural Science Foundation of China(41722403)

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Abstract:

An effective method to accurately characterize and quantify the pore structure of coal and shale is a key issue. At present, the fractal dimension of surface roughness (D2) of coal and shale is mainly analyzed based on the low-temperature nitrogen adsorption experiments and Frenkel-Halsey-Hill (FHH) model, but the micropore fractal dimension (Dm) is still rarely studied. This paper based on the micropore-filling theory and micropore-aperture distribution theory, a Dm model of coal and shale was proposed. The low-temperature CO2 adsorption experiments were done, and the fractal analysis of CO2 adsorption isotherms corresponding to coal and shale samples were carried out by using the Dm method. The results show that the Dm of coal is ranging from 2.6 to 2.8, with an average of 2.75, while that of shale ranges from 2.8 to 2.9, with an average of 2.88. The specific surface area of micropore of shale is ranging from 15 m2/g to 30 m2/g, while the specific surface area of micropore of coal is ranging from 100 m2/g to 300 m2/g. It shows that the pore distribution of shale is scattered and the number of pore is small, indicating that shale has a more complicated and heterogeneous micropore structure. The Dm and D2 are compared. The pore volume and specific surface area of micropore of coal are much larger than that of macropores, and the micropore structure is more complex. Meanwhile, the small number of mesopores and macropores, small specific surface area and smooth pore surface, make Dm of coal larger than D2. Dm and D2 are respectively affected by the complexity of microporous structure and the roughness of mesopore and macropore surface. Complex micropore structure and rough pore surface will increase the fractal dimension.

Key words: Micropore fractal dimension, FHH model, Low-temperature CO2 adsorption, Low-temperature N2 adsorption

CLC Number: 

  • TE151

Table 1

Petrophysical information of the selected shale samples"

样品 编号层位黏土矿物 含量/%脆性矿物 含量/%

TOC

/%

核磁孔隙度

/%

Y-1龙马溪组22.561.40.88.58
Y-2龙马溪组27.949.30.78.00
Y-3龙马溪组17.746.93.23.71
Y-4龙马溪组24.744.61.97.28
Y-5龙马溪组20.343.71.710.27
Y-6龙马溪组14.447.41.76.45
Y-7五峰组3.327.22.05.98
Y-8五峰组16.520.74.62.71
Y-9五峰组38.042.94.88.07

Table 2

Petrophysical information of the selected coal samples"

样品编号层位总有机质含量/%镜质组含量/%RO/%氦测孔隙度/%渗透率/（10-3 μm2）
M-1山西组81.671.91.41.70.002 7
M-2山西组76.782.31.45.60.329 3
M-3太原组83.486.01.51.30.105 0
M-4本溪组84.291.41.51.30.005 3
M-5本溪组76.683.71.72.40.001 1
M-6本溪组77.979.21.71.20.155 1
M-7本溪组80.587.21.81.4-

Fig. 1

CO2 adsorption and desorption isotherms of coal (a) and shale (b) samples"

Fig.2

Pore size distribution (PSD) of coal (a,b) and shale (c,d) samples obtained from CO2 adsorption isotherms"

Fig.3

Comparisons of the micropore volume of the coal and shale samples"

Table 3

The value of ρ and v of the coal and shale samples"

样品编号ρ/（kJ·mol）v样品编号ρ/（kJ·mol）v
M-113.002.05Y-114.632.03
M-213.162.05Y-214.811.98
M-313.332.08Y-315.052.02
M-413.222.09Y-415.132.08
M-512.921.99Y-515.022.00
M-610.362.08Y-614.982.05
M-79.552.10Y-715.042.03
Y-815.872.09
Y-915.031.98

Fig.4

Plots of Ln(x) vs Ln(J(x)) reconstructed from CO2 adsorption isotherms of coal (a) and shale (b) samples"

Table 4

Fitting formula and correlation coefficient of micropore fractal dimension(MFD) model of coal and shale samples"

样品编号拟合公式R2样品编号拟合公式R2
M-1y=-0.781 3x－1.172 40.988 3Y-1y=-0.850 6x－1.060 60.995 6
M-2y=-0.789 3x－1.160 40.988 7Y-2y=-0.882 4x－1.070 70.995 9
M-3y=-0.784 8x－1.141 70.988 8Y-3y=-0.881 6x－1.050 60.996 1
M-4y=-0.775 9x－1.148 60.988 5Y-4y=-0.858 5x－1.026 60.996 1
M-5y=-0.804 9x－1.191 70.988 6Y-5y=-0.888 4x－1.058 60.996 1
M-6y=-0.663 7x－1.466 80.981 3Y-6y=-0.860 5x－1.039 50.995 9
M-7y=-0.629 2x－1.598 50.978 8Y-7y=-0.874 8x－1.046 30.996 1
Y-8y=-0.908 6x－1.010 30.996 9
Y-9y=-0.897 2x－1.065 00.996 1

Table 5

Micropore fractal dimensions of coal and shale samples by the MFD model"

样品编号V0 /（cm3/g ）比表面积/（m2/g）Dm样品编号V0 /（cm3/g ）比表面积/（m2/g）Dm
M-121.95100.232.78Y-14.7821.852.85
M-223.77108.552.79Y-24.1218.802.88
M-337.82172.672.78Y-32.7012.322.88
M-436.93168.642.78Y-43.5015.972.86
M-532.20147.022.80Y-53.3715.392.89
M-660.14274.592.66Y-63.6016.432.86
M-764.48294.442.63Y-73.2614.862.87
Y-81.707.782.91
Y-94.3619.932.90

Fig.5

N2 adsorption and desorption isotherms of coal (a) and shale (b) samples(solid point: adsorption point； empty point: desorption point)"

Fig.6

BJH pore volume of coal and shale samples based on low-temperature N2 adsorption experiments"

Fig.7

Plots of Ln(Ln(p0/p)) vs LnV reconstructed from N2 adsorption isotherms of coal (a) and shale (b) samples"

Table 6

Fitting formula and correlation coefficient of FHH model of coal and shale samples"

样品编号D1D2
拟合公式R2拟合公式R2
M-1y=-0.480 1x－1.341 40.967 7y=-0.449 3x－1.458 60.997 6
M-2y=-0.459 5x－1.793 40.941 5y=-0.321 5x－1.793 20.994 3
M-3y=-0.165 4x－2.500 80.606 3y=-0.504 1x－2.832 50.997 3
M-4y=-0.095 0x－2.446 60.213 9y=-0.511 6x－2.936 60.993 8
M-5y=-0.350 7x－1.493 30.925 5y=-0.505 8x－1.703 40.995 3
M-6y=0.061 7x－2.321 50.146 9y=-0.675 8x－2.988 90.986 0
M-7y=-0.454 7x－1.615 50.947 0y=-0.455 3x－1.785 10.989 4
Y-1y=-0.332 3x+1.942 00.991 1y=-0.265 2x+1.934 60.998 9
Y-2y=-0.346 2x+1.850 30.994 4y=-0.282 5x+1.847 50.998 8
Y-3y=-0.326 0x+2.258 10.993 5y=-0.285 8x+2.255 00.998 5
Y-4y=-0.330 7x+1.993 10.991 8y=-0.251 9x+1.997 90.997 6
Y-5y=-0.334 4x+2.019 00.991 7y=-0.254 5x+2.031 70.996 7
Y-6y=-0.310 4x+1.830 10.982 6y=-0.212 0x+1.867 60.980 7
Y-7y=-0.303 1x+2.485 90.982 7y=-0.194 9x+2.518 80.989 3
Y-8y=-0.328 3x+2.358 30.993 0y=-0.215 1x+2.374 60.999 6
Y-9y=-0.304 7x+1.969 50.983 8y=-0.209 8x+1.999 00.989 8

Table 7

Fractal dimensions of coal and shale derived from the FHH model"

样品编号V0/(m3/g）比表面积/（m2/g）D1D2
M-10.180.792.522.55
M-20.120.512.542.68
M-30.060.262.832.50
M-40.070.282.902.49
M-50.160.702.652.49
M-60.070.323.062.32
M-70.140.612.552.54
Y-14.6820.392.712.74
Y-24.2618.522.692.72
Y-36.4327.992.712.75
Y-44.9321.462.712.76
Y-55.0522.002.702.76
Y-64.2118.322.732.82
Y-78.1235.362.742.83
Y-87.1230.982.722.79
Y-94.8421.082.732.81

Fig.8

Plots of pore volume and specific surface area of coal (a) and shale (b)"

Fig.9

Plots of fractal dimension and specific surface area of coal [(a),(c)] and shale [(b),(d)]"

Fig.10

Plots of fractal dimension and pore volume of coal [(a),(c)] and shale [(b),(d)]"

Fig.11

Comparisons of micropore fractal dimension of coal and shale samples"

Fig.12

Comparisons of FHH fractal dimension (D2) of coal and shale samples"

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