International Journal of Mining Science and Technology 25 (2015) 819–825
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Gas desorption characteristics of the high-rank intact coal and fractured coal Lu Shouqing a,b,⇑, Cheng Yuanping a,b,c, Qin Liming a,b, Li Wei a,b, Zhou Hongxing a,b, Guo Haijun a,b a
National Engineering Research Center of Coal Gas Control, China University of Mining & Technology, Xuzhou 221116, China School of Safety Engineering, China University of Mining & Technology, Xuzhou 221116, China c Key Laboratory of Gas and Fire Control for Coal Mine, China University of Mining & Technology, Xuzhou 221116, China b
a r t i c l e
i n f o
Article history: Received 3 January 2015 Received in revised form 27 February 2015 Accepted 17 April 2015 Available online 5 August 2015 Keywords: Intact coal Fractured coal Isosteric adsorption heat Diffusion coefficient
a b s t r a c t The objective of this work is to study the gas desorption characteristics of the high-rank intact coal and fractured coal. The gas adsorption, mercury porosimetry and gas desorption experiments were carried out in this study. Then, the theories of thermodynamics, diffusion mechanism and desorption kinetics were used to estimate the gas desorption characteristics. The results of gas adsorption experiments show that the initial isosteric adsorption heat of the intact coal is greater than that of the fractured coal, indicating that the gas molecules desorb more easily from fractured coal than intact coal. Using the mercury porosimetry, we find that the diffusion channels of fractured coal are more developed than those of intact coal. The difficult diffusion form dominates in the intact coal during the gas diffusing, while the easy diffusion form dominates in the fractured coal. The results of gas desorption experiments show that the initial gas desorption volume and velocity of the fractured coal are both greater than those of the intact coal. Using the Fick diffusion law, the study calculates the gas diffusion coefficients of the intact coal and fractured coal. The diffusion coefficients of the fractured coal are 2 times and 10 times greater than those of the intact coal at the time of 0–120 and 0–10 min, respectively. Ó 2015 Published by Elsevier B.V. on behalf of China University of Mining & Technology.
1. Introduction Under the comprehensive function of geostress, gas pressure and coal structure, coal and gas outburst is caused by mining [1–3]. Certain conditions must be met for the occurrence of coal and gas outburst. It is found that most of the coal and gas outburst accidents occurred in the thick fractured coal zone [4]. Coal is a special type of rock with a low strength and high Poisson’s ratio and is uniquely sensitive to stress and strain. Therefore, fractured coal can well record the effect of tectonic stress in stratum [5,6]. The thickening of the fractured coal zones increases the capacity for gas storage. It may act as tectonic screens, blocking gas migration, which can lead to high-pressure pockets of gas pressure. Therefore, a thick zone of the fractured coal provides favorable conditions for coal and gas outbursts [7]. Intact coal means that the coal is not or less affected by the tectonic stress, so its intact structure remains relatively complete. Fractured coal is the one that experiences plastic, ductile and flowing deformation due to repeated tectonic activities. Gas desorption
⇑ Corresponding author. Tel.: +86 13914895276. E-mail address:
[email protected] (S. Lu).
characteristics of the fractured coal play a key role in the occurrence and development of coal and gas outburst [8]. Li found that the initial gas desorption velocity of the fractured coal was 1.36– 2.84 times greater than that of the intact coal [9]. Wen thought that the gas desorption velocity of the fractured coal was much higher than that of the intact coal when the CH4 desorption volumes were compared in the same place [10]. Zhang suggested that the gas desorption volume and diffusion coefficient of the fractured coal in the first 60 min were both higher than those of the intact coal [11]. Using an MD method for simulation, Jing found that the diffusion coefficient of the fractured coal was greater than that of the intact coal. The results also showed that the activation energy for diffusion in the fractured coal was less than that in the intact coal, so it is easier for gas molecules to diffuse in the fractured coal [12]. Despite many achievements of the gas desorption characteristics have been obtained, most of them focused on the desorption kinetics of the intact coal and fractured coal. Few of the results are made to comprehensively analyze the thermodynamics, diffusion mechanism and desorption kinetics. Considering those factors above, the study investigates the gas desorption characteristics of the high-rank intact coal and fractured coal. It not only can provide a new research method, but also will help us to find the reason for
http://dx.doi.org/10.1016/j.ijmst.2015.07.018 2095-2686/Ó 2015 Published by Elsevier B.V. on behalf of China University of Mining & Technology.
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the greater gas desorption capacity of the fractured coal. Finally, it is greatly important for the reasonable prediction and prevention of the fractured coal and gas outburst. 2. Method and theory
ffiffi
DHad p = T RT
bðTÞ ¼ b0 e
ð2Þ
where b0 is a constant associated with the molecular weight of adsorbed gas; DHad the adsorption enthalpy, J/mol; R the ideal gas constant of 8.414 J/(mol K); and T the equilibrium temperature, K. Eq. (2) can be rewritten as follows:
2.1. Experimental coal samples and method
pffiffiffi DHad lnðb T Þ ¼ lnðb0 Þ RT
The coal samples were selected from the No. 3 coal seam of Daning Coal Mine. With the hazards of coal and gas outbursts, the No. 3 coal seam is a high-rank anthracite. The No. 3 coal seam often contains several intact coal and fractured coal sub-layers, and the middle-lower part of the No. 3 coal seam is a deformed sub-layer with a thickness of 0.2–0.5 m. Fig. 1 shows the scene of the intact coal and fractured coal sub-layers distribution. The intact coal and fractured coal for the gas desorption experiments were selected from different sub-layers at the same location. The coal samples were crushed into the particle with the size 1–3 mm. 99.9% CH4 gas and the gas desorption instrument of geological exploration (FHJ-5) were used in the gas desorption experiments. First, the 50 g coal samples were placed into the sample cell. The sample cell was connected to a vacuum pump at a pressure of 13 kPa for 24 h. Second, CH4 was injected into the sample cell. The sample cell was placed in a water bath at a temperature of 303 K. Finally, the samples were held at a desired high pressure (0.8, 1.3, 2.4, 3.3 or 4.0 MPa) for a few days to reach the sorption equilibrium. Then, the valve of the cell was opened. Until the pressure gauge of the cell was 0 MPa, the sample cell was connected to the gas desorption instrument of geological exploration (FHJ-5) for 120 min. Fig. 2 presents the main equipments for the gas desorption experiments. Table 1 displays the key parameters, including the proximate analysis, macerals, the maximum vitrinite reflectance and firmness coefficient of the intact coal and fractured coal.
pffiffiffi According to Eq. (3), there is a linear relation between lnðb T Þ and 1/T, and the adsorption enthalpy (DHad) and constant (b0) can be calculated by the formula fitting method. The isosteric adsorption heat (Qst) can be defined as the enthalpy change (DHst) when n mol gas is adsorbed by adsorbent with a constant surface area (S) at a constant temperature and pressure. The isosteric adsorption heat can indirectly reflect the intermolecular forces between adsorbent and adsorbate molecules. According to the Clausius–Clapeyron equation, the isosteric adsorption heat can be expressed as follows [16]:
2.2. Thermodynamic model for the isosteric adsorption heat There are numerous theoretical isothermal sorption models, including Langmuir monolayer sorption model, BET multilayer sorption model and Polyanyi sorption model. The adsorption behavior and mechanism of different gases on coal were discussed by various international and domestic academics [13,14]. The Langmuir model is commonly used to research the adsorption characteristics of coal in its concise form. Therefore, Langmuir model and its equation used in this paper are as follows:
V¼
abP 1 þ bP
ð1Þ
where a is the limiting adsorption volume of dry ash free, mL/g daf; b an adsorption constant, MPa1; and V the gas adsorbed volume of coal per unit mass at a constant temperature and pressure, mL/g daf. According to the thermodynamics, the relation between b in the Langmuir adsorption model and the temperature T can be expressed as follows [15]: Intact coal
Q st ¼ DHst ¼
@ DHst @ ln P ¼ RT 2 @T V @n T;P;S
ð3Þ
ð4Þ
Chen believes that there is a linear relation between Langmuir adsorption constant a and temperature T [17]. The Eq. (2) is connected to the Eq. (4), then
Q st ¼ DHst ¼ DHad þ
RT RT 2 @a þ 2 V a @T
ð5Þ
where R is a known quantity. And the relation of a and temperature T, @a=@T, DHad and b0 can be calculated. Therefore, the isosteric adsorption heat Qst is a function of gas adsorbed volume V and temperature T. 2.3. Dynamics model for the diffusion coefficient Gas diffusion in coal is monitored by Fick diffusion law. The diffusion coefficient D is one of the most important kinetic parameters for gas diffusion in coal. It can intuitively reflect the ability of gas diffusion in coal. The method that fitting the data of the gas desorption experiments is the simplest one for getting the diffusion coefficient. In this case, the coal particles are supposed into spherical particles of the same size. Based on the Fick diffusion law, the differential equation can be solved under the given initial conditions and boundary conditions. The analytical solution can be obtained as follows [18]:
1
1 Qt 6 X 1 n2 Bt ¼ e Q 1 p2 n¼1 n2
ð6Þ
where Qt is the gas accumulated desorption volume of the coal particles at time t, mL/g; and Q1 the gas limiting desorption volume of the coal particles, mL/g; B = pD/r2; D the diffusion coefficient, and r the radius of spheres, m2/s. The analytical solution is numerically simulated by the computer, then the equation can be obtained as follows [19]:
Q t =Q 1 ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 eKBt
ð7Þ
Fractured coal
where K, a constant, is equal to 1. Eq. (7) can be rewritten as follows:
lnð1 ðQ t =Q 1 Þ2 Þ ¼ KBt
Fig. 1. Scene of the intact coal and fractured coal sub-layers distribution.
ð8Þ
According to Eq. (8), there is a linear relation between ln(1 (Qt/Q1)2) and time t. KB is the slope of the line. In the laboratory, t and Qt are both known quantities. The gas limiting desorption volume (Q1) can be calculated by Eq. (9) [20]. Then, KB can be gained by linear regression. The diffusion coefficient (D) is got.
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S. Lu et al. / International Journal of Mining Science and Technology 25 (2015) 819–825 Pressure gauges
Pressure gauges
Decompression cell
Four-way valve Water bath Sample cell
Vacuum pump
CH 4
Measuring cylinder
Fig. 2. Main apparatuses for the gas desorption experiments.
Table 1 Key parameters of the intact coal and fractured coal. Sample no.
Proximate analysis (%, by weight)
Macerals (%, by volume)
Mad
Aad
Vdaf
Vitrinite
Inertinite
Mineral
Intact coal Fractured coal
1.46 1.95
18.14 22.15
12.29 11.01
75.79 84.35
21.87 6.63
2.44 6.02
Ro,max (%)
Firmness coefficient
3.16 3.29
2.00 0.33
Table 2 Langmuir adsorption constants of the intact coal and fractured coal. Sample no.
Langmuir constant
Intact coal
Constant Constant Constant Constant
Fractured coal
a b a b
(mL/g daf) (MPa1) (mL/g daf) (MPa1)
303 (K)
313 (K)
323 (K)
333 (K)
51.8892 1.3778 50.7703 1.1005
49.1426 1.2013 48.5056 0.9786
46.1807 1.0902 45.5454 0.9291
44.5580 0.9247 43.0619 0.7862
Q1 ¼
abP 1 abP 0 ð1 wf Af Þ 1 þ bP1 1 þ bP 0
Temperature
ð9Þ
where P1 is the definite equilibrium pressure, MPa; P0 the atmospheric pressure in the laboratory, MPa; wf the moisture of coal, %; and Af the ash of coal, %.
3. Results and discussion 3.1. Thermodynamics characteristics of the coal samples To obtain the isosteric adsorption heats, the isothermal CH4 adsorption experiments of the coal samples are carried out at different temperatures (303, 313, 323 or 333 K). The experimental data are corrected by the moisture and ash. Then, the Langmuir adsorption constants of dry ash-free are obtained as shown in Table 2. pffiffiffi According to Eq. (9), the linear relations between lnðb T Þ and 1/T are shown in Fig. 3(a). The calculated DHad and b0 are shown in Table 3. The linear relations between a and T are shown in Fig. 3(b), and the fitting relationships are listed in Table 3. The parameters in Table 3 are taken into the Eq. (9). Then, the relations for the isosteric adsorption heats of the intact coal and fractured coal are obtained as shown in Fig. 4. There are two reasons for the isosteric adsorption heat changing with the adsorption volume [21]. First, the intermolecular forces between adsorbent and adsorbate molecules will increase with
an increase of adsorption. It will lead to the increase of isosteric adsorption heat with the increase of adsorption. Second, the surface of coal is uneven and anisotropic, which leads to the unequal adsorption energy on the coal surface [22]. The gas molecules are initially adsorbed on the coal surface with higher adsorption energy. It will intensify the non-uniformity phenomenon on the coal surface. Then, the isosteric adsorption heat decreases with the increase of adsorption. At the same temperature, the isosteric adsorption heats of the coal samples increase slowly with the increase of adsorption. Therefore, the intermolecular forces come first, then followed by the uneven and anisotropic of the coal surface. At the same adsorption volume, the isosteric adsorption heats will increase with the increase of temperature. Although this will increase the chances of the gas molecules colliding with the coal surface, the coal surface needs more adsorption potential energy to capture the gas molecules. In this case, part of the coal surface cannot capture the gas molecules, while the gas molecules can be captured at a lower temperature. At the same conditions, the isosteric adsorption heat of the intact coal is greater than that of the fractured coal. The initial isosteric adsorption heats of the intact coal and fractured coal are 14.46 and 12.73 kJ/mol, respectively. The initial isosteric adsorption heat directly reflects the relation between coal surface and gas molecules [23]. The results demonstrate that the intermolecular forces of the intact coal are stronger than those of the fractured coal. Therefore, gas molecules desorb more easily from the fractured coal than the intact coal.
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3.3
Intact coal Fractured coal
Adsorption constant a (mL/g·daf)
3.2
ln(b*T 0.5)
3.1 3.0 2.9 2.8 2.7 0.0031
0.0032
50 45 40 35 300
2.6 0.0030
55
0.0033
305
310
320
315
325
330
335
Temperature T (K)
1/T (K-1)
(b) Adsorption constant b changes with temperature T
(a) Adsorption constant a changes with temperature T
Fig. 3. Adsorption constants a, b change with temperature T.
Table 3 Relation between Langmuir constant and temperature. pffiffiffi Relations between lnðb T Þ and 1/T pffiffiffi lnðb T Þ = 1143.8/T 0.5926 pffiffiffi lnðb T Þ = 907.77/T 0.0374
Sample no. Intact coal Fractured coal
DHad (J/mol)
b0
Relation between a and T
9509.55
0.5529
a = 0.2496T + 127.34
7547.20
0.9633
a = 0.2609T + 129.96
40
adsorption Isosteric heat of (kJ/mol)
adsorption Isosteric heat of (kJ/mol)
40
22.87 kJ/mol
30 16.11 kJ/mol
20
10 0
14.46 kJ/mol
330 5 Ad
10
15 sor pti 20 (mL on co / g nstan ·da f) t
310 25
e( tur era mp e T
22.24 kJ/mol
14.52 kJ/mol
20
12.73 kJ/mol
10 0
330 5
320
17.91 kJ/mol
30
K)
(a) Isosteric adsorption heat of the intact coal
10 16.50 kJ/mol sor 15 pti 20 (mL on co /g·d nstan 25 af ) t
Ad
320 ) (K re atu r e mp Te
310
(b) Isosteric adsorption heat of the fractured coal
Fig. 4. Isosteric adsorption heats of the intact coal and fractured coal.
3.2. Gas diffusion mechanism of the coal samples The mercury porosimetry experiments were carried out to compare the diffusion channels of the two coals. Fig. 5 shows the pore size distribution of the intact coal and fractured coal. According to Fig. 5, the fractured coal pores with a diameter of 10–1000 nm and >1000 nm are 4.8 and 12.3 times greater than those of the intact coal, respectively. However, the pores with a diameter less than 10 nm of the intact coal are greater than those of the fractured coal. The pores of the intact coal are primarily made up of the pores with a diameter less than 10 nm, accounting for 61.34%. The pores of the fractured coal are primarily composed of the pores with a diameter more than 10 nm, accounting for 84.72%. It is possible to conclude that the diffusion channels of the fractured coal are more developed than those of the intact coal. According to the molecular motion theory, gas diffusion in coal is caused by the irregular thermal motion of gas molecules. The gas diffusion model of coal can be classified according to the relations between the pore diameter and the mean free path of gas molecules [24]. When d P 10k, the collisions mainly occur between gas molecules, called as Fick diffusion. When 0.1k < d < 10k, the
collisions of gas molecules are equivalently important to the collisions of gas molecules and pore wall, named as transition diffusion. When d 6 0.1k, the collisions mainly occur between gas molecules and pore wall, termed as Knudsen diffusion. On the conventional condition, the mean free path of gas is 100 nm. The pore diameters for Fick diffusion, transition diffusion and Knudsen diffusion are d P 1000 nm, 10 nm < d < 1000 nm and d 6 10 nm, respectively [25]. Combining the pore size distribution in Fig. 5(b), the gas diffusion model of the intact coal comes Knudsen diffusion first, transition diffusion second and Fick diffusion last. However, the gas diffusion model of the fractured coal comes transition diffusion first, Fick diffusion second and Knudsen diffusion last. Therefore, the difficult diffusion form dominates in the intact coal during the gas diffusing, while the easy diffusion form dominates in the fractured coal. Because the gas in the macropores can easily diffusing outside at the beginning, Fick diffusion is the main form of gas diffusion [26]. According to Fig. 5, the pores with a diameter more than 1000 nm of the fractured coal are much greater than those of the intact coal. At the beginning of the gas desorption, the diffusion capacity of the fractured coal is much higher than that of the intact coal.
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0.0040
0.04 0.0219
0.0165
0.02
0.0104
0.0034
0.0025 0
10 nm
0.0020
1000 nm
10-1000 nm
Pore size (nm) 80
0.0015
Pore volume percent (%)
Pore volume (mL/g)
0.0030
0.0497 0.0418
Pore volume (mL/g)
Intact coal Fractured coal
0.0035
0.0010 0.0005
100
1000
10000
46.02
40 15.28
0
100000
38.7
29.14
20
0 10
61.34
60
9.52
10 nm
1000 nm
10-1000 nm
Pore size (nm)
Pore size distribution (nm) (a) Pore volume changing with pore size distribution
(b) Pore volume and pore volume percent distribution
Fig. 5. Pore size distribution of the intact coal and fractured coal.
20 0.8 MPa 1.3 MPa 2.4 MPa 3.3 MPa 4.0 MPa
60
Desorption volume (mL/g)
Desorption volume (mL/g)
80
40
20
0
20
40
60
80
100
16 12
8 4
0
120
20
40
60
80
100
Time (min)
Time (min)
(a) Gas desorption kinetics curves of the intact coal
(b) Gas desorption kinetics curves of the fractured coal
120
Fig. 6. Relations for gas accumulated desorption volume and time.
0
0
-0.01
-0.1
-0.02
0.10 0.05
-0.03 0
2
4
6
8
0.8 MPa 1.3 MPa 2.4 MPa 3.3 MPa 4.0 MPa
-0.15 -0.20
0
-0.3 0
-0.05 -0.10
-0.2
10 ln(1-(Qt/Q∞)2)
ln(1-(Qt/Q∞)2)
0
0.2
2
4
6
8
10
-0.2 -0.4 -0.6
-0.25
-0.8 0
20
40
60
80
100
0
120
20
40
60
80
100
120
Time (min)
Time (min) (a) Relations between ln(1-(Qt/Q∞)2)
(b) Relations between ln(1-(Qt/Q∞)2)
and time of the intact coal
and time of the fractured coal 2
Fig. 7. Relations between ln(1 (Qt/Q1) ) and time of the intact coal and fractured coal.
3.3. Characteristics of gas desorption kinetics of the coal samples 3.3.1. Characteristics of gas desorption kinetics curves of the coal samples The gas desorption experiments for gas desorption was carried out. Fig. 6 presents the relations for the gas accumulated desorption volume and time at different pressures.
According to Fig. 6, the gas accumulated desorption volume increases with time under a definite pressure. For any gas desorption curve, the initial slope of the curve is the largest, and the latter slope of the curve is less than the former one. Therefore, the initial gas desorption velocity is the largest. Then, the gas desorption velocity gradually decreases. For one coal sample, the gas desorption volume and desorption velocity at the same time are greater.
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Table 4 Gas diffusion coefficients of the coal samples. Sample no.
P (MPa)
0–120 (min) KB
0–10 (min) 2
D (m /s)
R 12
2
KB
D (m2/s)
R2 12
Intact coal
0.8 1.3 2.4 3.3 4.0
0.00152 0.00148 0.00167 0.00217 0.00220
2.5668 10 2.4993 1012 2.8201 1012 3.6645 1012 3.7151 1012
0.9994 0.9981 0.9988 0.9973 0.9960
0.00134 0.00141 0.00170 0.00250 0.00270
2.2628 10 2.3811 1012 2.8708 1012 4.2217 1012 4.5595 1012
0.9949 0.9973 0.9970 0.9989 0.9989
Fractured coal
0.8 1.3 2.4 3.3 4.0
0.00474 0.00388 0.00295 0.00303 0.00285
8.0044 1012 6.5521 1012 4.9816 1012 5.1167 1012 4.8128 1012
0.8227 0.7795 0.7855 0.7784 0.7580
0.02243 0.01818 0.01533 0.01556 0.01650
3.7877 1011 3.0700 1011 2.5888 1011 2.6276 1011 2.7863 1011
0.9593 0.9521 0.9439 0.9608 0.9262
At the same pressure, the initial gas desorption volume and velocity of the fractured coal are greater than those of the intact coal. After a certain period, the gas desorption curve of the fractured coal will be more flat than that of the intact coal, which suggests that the gas desorption velocity of the fractured coal will decrease more quickly than that of the intact coal. 3.3.2. Diffusion coefficient of gas desorption kinetics of the coal samples To compare the comprehensive and the initial diffusion coefficients, the experimental data of 0–120 and 0–10 min are fitted, respectively. Fig. 7 shows the relations between ln(1 (Qt/Q1)2) and time of the coal samples. Table 4 lists the gas diffusion coefficients. According to Fig. 7 and Table 4, we find that the Yang’s theory formula could well describe the gas desorption kinetics behavior of the intact coal at any time, with a high fitting precision (R2 > 0.99). It can also well describe that of the high-rank fractured coal at the time of 0–10 min, with a fitting precision (R2 > 0.90). However, it is fail to describe the gas desorption kinetics behavior of the fractured coal at the time of 0–120 min, with a low fitting precision (R2 < 0.90). At the time of 0–120 min, the gas diffusion coefficients of the intact coal and fractured coal are 2.4993 1012 to 3.7151 1012 m2/s and 4.8128 1012 to 8.0044 1012 m2/s, respectively. At the time of 0–10 min, the gas diffusion coefficients of the intact coal and fractured coal are 2.2628 1012 to 4.5595 1012 m2/s and 2.5888 1011 to 3.7877 1011 m2/s, respectively. The diffusion coefficients of the fractured coal are 2 times and 10 times greater than those of the intact coal at the time of 0–120 min and 0–10 min, respectively. The larger diffusion coefficient of the fractured coal is related to the weaker intermolecular forces and more macropores in it than that in the intact coal. In this paper, the range of the diffusion coefficient is between 1012 and 1011 m2/s, and it has the same order of magnitudes with the results obtained by Chen [27]. 4. Conclusions The theoretical analysis and experiments of the gas desorption characteristics are introduced, and a comprehensive analysis is made on the thermodynamics, diffusion mechanism and desorption kinetics. The conclusions are as follows: (1) From the thermodynamics aspect, the initial isosteric adsorption heat of 14.46 kJ/mol for the intact coal is greater than that of 12.73 kJ/mol for the fractured coal, indicating that the gas molecules desorb more easily from the fractured coal than the intact coal. (2) From the diffusion mechanism aspect, the pores with a diameter less than 10 nm account for 61.34% in the intact coal, and the pores with a diameter more than 10 nm
account for 84.72% in the fractured coal. The diffusion channels of the fractured coal are more developed than those of the intact coal. The difficult diffusion form dominates in the intact coal during the gas diffusing, and the easy diffusion form dominates in the fractured coal. (3) From the desorption kinetics aspect, the results show that the initial gas desorption volume and velocity of the fractured coal are both greater than those of the intact coal. The gas desorption velocity of the fractured coal will decrease more quickly than that of the intact coal. The diffusion coefficients of the fractured coal are 2 times and 10 times greater than those of the intact coal at the time of 0–120 min and 0–10 min, respectively. Therefore, the larger diffusion coefficient of the fractured coal is linked to the weaker intermolecular forces and more macropores in it than that in the intact coal.
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