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Effect of the lump size on methane desorption from anthracite
Journal of Natural Gas Science and Engineering 20 (2014) 337e346
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Effect of the lump size on methane desorption from anthracite Junqing Guo, Tianhe Kang*, Jianting Kang, Guofei Zhao, Zhiming Huang Institute of Mining Technology, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 May 2014 Received in revised form 13 July 2014 Accepted 14 July 2014 Available online
Anthracite fracture and pore structure of four different sized coal samples were measured using a light microscope and mercury porosimetry, respectively. The desorption kinetics of methane, at three different pressures, were also studied on six size fractions of coal samples using a volumetric experimental apparatus. The effect of lump size on methane desorption from anthracite combined with its pore structure was further discussed. The results showed that (1) for the lump coals, three pressure regimes in the process of mercury injection are indicated by distinct values of the fractal dimension; in order of increasing pressure, these correspond to cleat penetration, pore penetration, and coal matrix compressibility; (2) When the lump coal size drops below the coal matrix size, the pore volume and average pore size increase with decreasing grain size. When the lump size exceeds the coal matrix size, pore-fracture structural characteristics of anthracite, such as cleat aperture, cleat porosity, the matrix average pore size, and matrix porosity are basically invariant; (3) with increasing lump size, the desorption time constant changes according to positive exponential rules, eventually obtaining a stable value after the lump size fraction of 70e75 mm; the ultimate desorption ratio, initial desorption rate, attenuation index of the desorption rate and gas diffusivity decrease significantly and then change little when the lump size exceeds the coal matrix size. © 2014 Elsevier B.V. All rights reserved.
Keywords: Desorption characteristics Lump anthracite size Mercury porosimetry Fracture volume Coal matrix
1. Introduction During mining operations and CBM exploitations, excavation engineering and hydrofracturing can destroy the integrity of coal, which affects methane desorption characteristics. Fast desorbing coals generally yield most of their gas within a very short time, which may cause gas outbursts in coal mines or collapse of a wellbore in coal-bed methane production (Beamish and Crosdale, 1998). Therefore, studies of the effect of lump size on methane desorption from coal have a guiding significance for understanding gas migration in coal seams, predicting methane-related accidents and enhancing CBM production. In recent years, many studies (Bertand et al., 1970; Yang and Wang, 1988; Banerjee, 1988; Siemons et al., 2003; Busch et al., 2004) have focused on the effect of coal size on the methane desorption rate and shown that the desorption rate will be practically independent of the size distribution when the dimensions of the pieces exceed the fissuring network of coal. When the size distribution of the coal drops below this network size, the desorption rate becomes inversely proportional to the square of the
* Corresponding author. Tel.: þ86 0351 6014760. E-mail address: [email protected] (T. Kang). http://dx.doi.org/10.1016/j.jngse.2014.07.019 1875-5100/© 2014 Elsevier B.V. All rights reserved.
size of the particles. However, there is little research on the mechanisms of this phenomenon and the effect of the lump size on desorption time and methane diffusivity. In this study, anthracite fracture and pore structure of four different sized coal samples have been measured using a light microscope and mercury porosimetry. The desorption kinetics of methane, at three different adsorption equilibrium pressures, were studied on six size fractions to analyze the effect of lump size on methane desorption characteristics. 2. Experimental 2.1. Coal samples and apparatus The experiments were conducted on the anthracite with a helium density of 1.52 cm3 g1. The large coal blocks were directly collected from the No.15 coal seam in the Southeast Qinshui basin from Sihe coal mine (Shanxi Province, China). The coal samples were processed into six different size fractions: 0.8e1 mm, 8e10 mm, 20e25 mm, 45e50 mm, 70e75 mm and 130e140 mm (see Fig. 1). There are variances in samples; however, because the coal used in this work is anthracite, the difference of the samples should be relatively small. Before testing, the coal samples weighing approximately 3 kg each were dried in an oven at 105e110 C until a constant weight was achieved.
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Fig. 1. Coal samples.
r¼
2d cos q P
(1)
where r is the pore radium (mm) when mercury enters at the pressure P (MPa); s is the surface tension of mercury and q is the mercuryesolid contact angle.
Fig. 2. Diagram of volumetric experimental apparatus.
The volumetric apparatus used for the desorption kinetics experiment of coal samples is shown schematically in Fig. 2. It mainly consists of an adsorption canister, reference canister, thermostatic water bath, methane cylinder, vacuum pump, and measuring cylinder. The adsorption canister is 150 mm in diameter and 200 mm tall. 2.2. Experimental method and schemes In this study, based on the measurement of anthracite fracture and pore structure of different sized samples, the desorption kinetics of methane were studied on six size fractions of coal samples using a volumetric experimental apparatus. 1) Polished-surface analysis was performed using an incident-light microscope. Prior to the analysis, coal samples were mounted in epoxy resin and the surfaces were polished. An Optec DV320 microscope (Optec, China) was used to acquire the images of coal surfaces. Objective lens of 4 and eyepiece of 10 were used for magnification. Adobe Photoshop software with the PhotoMerge plug-in was used for merging these digitized images. Fracture aperture, lengths, spacing, mineral-filled and connectivity were obtained from digital image analysis. 2) The pore structures of four sized coal samples were measured by mercury porosimetry. The experiments were performed using an Autopore 9505 Instrument (Micro-meritics, US), which permits the mercury filling at as low as 3.5 103 MPa, up to 207 MPa. The coal samples were processed into 0.8e1.2 mm and 2e4 mm grain sized fractions and two cubes with 6 mm and 10 mm edge lengths. The dry sample was evacuated from the instrument to <50 mmm Hg. The volume of mercury penetration into the sample was measured with increasing applied pressure. A contact angle of 130 and surface tension of 485 dyn/cm were used in the Washburn equation (1) to determine the pore size distribution.
3) Based on the volumetric method, methane desorption kinetics experiments were carried out with six size fractions of coal samples according to the following steps. (1) The sample was sealed in an adsorption canister and degassed at 60 C to obtain a static vacuum of 1 Pa within 3 days. (2) Adjust the temperature of the water bath to 25 C, and then fill the adsorption canister with methane. The methane was taken up by the sample at a constant temperature and constant pressure (25 C, 1 MPa). (3) When the pressure difference in the adsorption canister was less than 0.001 MPa d1, the coal methane emission was carried out under atmospheric pressure and bled into an inverted graduated cylinder filled with water. The methane volume was carefully measured in a series of readings over a period of weeks or months, until little or no more gas was produced. (4) Change the adsorption equilibrium pressure (in order, 25 C, 2 MPa; 25 C, 3 MPa) and repeat the above steps. For most coals with a multimodal pore distribution, bidisperse model may better represent the CH4 desorption rate behavior over the full timescale of desorption (Clarkson and Bustin, 1999a,b; Pan et al., 2010; Smith and Williams, 1984a,b). The simplified bidisperse model encounters a fast macropore diffusion stage and a much slower micropore diffusion stage. For the first (fast) stage, the uptake is given by Ruckenstein et al. (1971): f Ma 6 X 1 ¼1 2 exp M∞ p n¼1 n2
Da n2 p2 t R2a
! (2)
where Ma is the total amount of gas desorbed in the macropores at time t, Ra is the macrosphere radius and Da is the macropore effective diffusivity. For the second (slow) stage, the uptake is given by Ruckenstein et al. (1971): f Mi 6 X 1 ¼1 2 exp M∞ p n¼1 n2
Di n2 p2 t R2i
! (3)
where Mi is the total amount of gas desorbed in the micropores at time t, Ri is the microsphere radius and Di is the micropore effective diffusivity. Hence, the overall uptake is:
Mt Ma þ Mi Ma M ¼ ¼b þ ð1 bÞ i M∞ Ma∞ þ Mi∞ Ma∞ Mi∞
(4)
where b ¼ ðMa∞ =ðMi∞ þ Ma∞ ÞÞ is the ratio of macropore desorption to the total desorption.
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3. Results and discussion 3.1. Fracture characteristics of anthracite The polished surface of a coal sample is shown in Fig. 3. The coal has a mutually orthogonal and nicely developed ideal structure of fractures. According to its geometry, these fractures are called cleats, which are divided into face cleats and butt cleats (Laubach et al., 1998). In general, face cleats (see region 1e3 in Fig. 3) have good continuity and extensibility, and butt cleats with shorter length (see region 4e6 in Fig. 3) often terminate into face cleats. The characteristics of the cleats are summarized in Table 1. Most of the face cleat apertures fall into the 32e341 mm range, and the butt cleat apertures fall into the 25e63 mm range. Moreover, these cleats are mostly filled with minerals, a disadvantageous feature for the gas transport to main fractures (Karacan and Okandan, 2000). According to the average spacing of these cleat systems, the coal matrix has an average dimension of 4.21 mm wide and 5.66 mm long. 3.2. Pore structure of different sized coal samples Fig. 4 shows the pore size distributions of four different sized coal samples. Fig. 4 clearly illustrates that the pore size distribution of the 6 mm sample is basically the same as the 10 mm sample, and there is a peak in the pore volume of 0.293 cm3 g1 around a pore size of 91 mm for both the two samples. Considering that coal is a dual porosity rock containing micropores (matrix) and a network of natural fractures known as cleats (Harpalani and Chen, 1995), it is possible that the value of this peak may be representative of the volume of cleats with an aperture width of 91 mm. When the lump coal size decreased to 3 mm and 1 mm, the pore volume at a pore size of 91.3 mm increased to 0.961 cm3 g1and 1.164 cm3 g1, respectively, and the pore size corresponding to the peak also
Fig. 4. Pore size distribution curve of different sized coal samples.
increase from 91.3 mm to 361 mm. Because the pore volume of grain size coal, which is measured using mercury porosimetry, consists of inter-particle voids and intra-particle voids and in general the aperture width of inter-particle voids is larger than the aperture width of fractures in lump coal, the measured pore volume of grain size coal is larger than the lump coal. Therefore, the measured pore volume of grain size coal needed to be corrected in order to obtain the true total pore volume. When the pore size is between 1 mm and 10 mm, the pore volume for the 3 mm and 1 mm sample is higher than the other two lump coals, and this change gradually move toward smaller pore with decreasing grain size. It may be due to the destruction of coal matrix which widens the pores. When the pore size is less than 100 nm, the pore volume for both 6 mm and 10 mm samples increase significantly. However, the pore volume for the 3 mm sample begins to increase at a pore size of 20 nm and the 1 mm sample at a pore size of 10 nm. To further understand the variation of the pore structure of coal samples with the lump size decreased, fractal analysis for the four different sized coal samples has been conducted in this study. Pfeifer and Avnir (1983) stated that the volume injection curve of a pore structure with a fractal surface must obey the relation:
dVr fð2 Ds ÞlogðrÞ log dr
(5)
where Vr is the cumulative injection volume at a given pore radius r and Ds is the surface fractal dimension. Following the work of Pfeifer and Avnir (1983) combined Eqs. (1) and (5), and obtained a relation between the cumulative injection volume (Vp) derivative with respect to pressure (p) and the surface fractal dimension (Ds)
dVp fð4 Ds ÞlogðpÞ log dp
Fig. 3. Microscopic fractures of a coal sample, 40.
Table 1 Characteristics of the coal fracture. Fracture marshalling
Fracture number
Fracture length/mm
Fracture aperture/mm
Fracture spacing/mm
1
1 2 3
4.26 6.21 6.95
246 341 32
4.21
2
4 5 6
3.69 4.12 4.98
25 49 63
5.66
(6)
where Vp is the cumulative injection volume at a given pressure p. Using these relations, the surface fractal dimension can be calculated without pore surface area calculations. The logarithm of the derivative of diff injection volume (log(dV/dp)) is plotted versus pressure logarithm (log(p)) and shown in Fig. 5. If the pore surface is fractal within certain ranges of the pore radius, a linear trend should be observed from the slope (A) of the logarithm line (Fig. 5), and D is calculated by D ¼ 4 þ A. From these results, it is possible to distinguish three regions of pressuredlow (P < 0.1 MPa), intermediate (0.1 P < 5 MPa) and high (5 MPa)dwhich are characterized by the fractal dimensions D1, D2, and D3 compiled in Table 2. In all cases, the low, intermediate and high pressure data are similar, giving 1 < D1 < 3, 2 < D2 < 3, and 3 < D3 < 4, respectively. For the 1 mm and 3 mm coal particles, the range of D1 is 1 < D1 < 2, which is similar with the result studied by
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1mm 3mm 6mm 10mm
0.9
3
Vpore(cm /g)
1.2
0.6
0.3 0
50
100
150
200
Pressure (MPa) Fig. 6. Mercury porosimetry data in the pressure range 5e200 MPa. Fig. 5. Logelog plot of dV/dP for four different sized coal samples. The data for different samples have been displaced along the vertical axis for clarity.
Table 2 Fractal dimensions and compressibility parameters from four different sized samples. Lump Fractal dimension size/ D1 D2 D3 mm
Intercept Gradient 105 Compressibility 1011 (cm3/g) (cm3/g MPa) (m2/N)
1 3 6 10
1.240 0.771 0.225 0.259
1.46 1.27 2.18 2.22
2.08 2.15 2.58 2.53
3.47 3.56 3.89 3.91
3.10 5.63 7.93 8.26
4.71 8.56 12.05 12.56
Friesen and Mikula (1987). They interpret D1 as the fractal dimension for a bulk porous medium. For the 6 mm and 10 mm lump coal, the range of D1 is 2 < D1 < 3, which is also reported by Laubach [7] who found that cumulative frequency of cleats having apertures follows a power law and determined that values of fractal dimension determined from volumetric sampling of cleat apertures (2.74e2.82) are larger by ~2. Therefore, for the lump coals, an increase in the pore volume is due primarily to mercury intrusion into the fracture system. The fractal dimensions of both the 6 mm and 10 mm samples are basically the same, indicating that they have a similar fracture systemdnicely developed ideal structure of cleats. When the lump size decreased to 3 mm and 1 mm, the increase in pore volume is due primarily to mercury intrusion into the interparticle voids (Friesen and Mikula, 1988). In the region of intermediate pressures, the increase in pore volume is due primarily to mercury intrusion into the pores of the coal matrix. The fractal dimension D2 decreases as the lump size decreases from 6 mm to 1 mm, which indicates that the decreased lump size simplifies the pore structure of the coal matrix. At pressures higher than approximately 5 MPa, the fractal dimensions for the four sized coal samples undergo a drastic change to values of D3 > 3. These values are nonphysical from a geometric point of view and can be attributed to the compressibility of the coal (Zwietering and Krevelen, 1954). The value D3 of the 6 mm sample is basically the same as that of the 10 mm sample, indicating similar compressibility. Fig. 6 shows a typical result of mercury penetration in the region of high pressures. A rectilinear relation between pressure (P) and Pore volume (Vpore) is found and the fitted values of the intercept and slope are shown in Table 2. The intercept at the ordinate in Fig. 6 represents the pore volume that does not include compressibility. The compressibility (c) of coal is by the following Eq. (7) (Toda and Toyoda, 1972) and shown in Table 2.
c¼ rk
(7)
where r is helium density (g/cm3) and k is the gradient of rectilinear relation (cm3/g$MPa). The pressure threshold corresponding to compressibility for the 6 mm and 10 mm samples is approximately 8 MPa, and the compressibility is approximately 12 1011 m2/N, indicating that both samples have the same dimension of coal matrix. However, the pressure threshold for the 3 mm sample is 80 MPa, corresponding to a compressibility of 8.56 1011 m2/N. The pressure threshold for the 1 mm sample is 130 MPa, corresponding to a compressibility of 4.71 1011 m2/N. This result shows that the coal matrix structure is seriously destroyed when the lump size drops below the coal matrix size, which also changes the bearing capacity and compressibility of coal. The results of the pore structure parameters of the four sized coal samples are listed in Table 3. When the lump size exceeds the coal matrix size (5.66 mm 4.21 mm), pore-fracture structural characteristics of anthracite, such as cleat volume, cleat aperture, cleat porosity, matrix pore volume, the matrix average pore size and matrix porosity, are basically invariant. When grain size drops from 4 mm to 2 mm, pore volume and average pore size increase. 3.3. Desorption characteristics of different sized coal samples 3.3.1. Effect of lump size on the desorption time and desorption ratio The methane desorption ratio is used to describe desorption kinetics processes in coal samples and can be calculated according to Eq. (8).
h ¼ V=Qe
(8)
where h is the methane desorption ratio (%), V is the methane desorption capacity (L), and Qe is the methane adsorption capacity (L) when the final adsorption equilibrium appeared to have been reached. The methane desorption ratio of the six size fractions of coal samples at different pressures versus time are shown in Fig. 7, and the corresponding experimental results are shown in Table 4. It is described below: (1) At the same pressure, lump size has no discernable effect on the equilibrium adsorption capacity. Moffat and Weale (1955) had a similar conclusion. It is due to that the adsorption volume of methane mainly depends on the surface area which is mostly affected by the number of micropores. Anthracite has highly developed micropores; the decreased lump size has little effect on micropores with a pore size less than 7.2 nm (Zhang et al., 2005; Clarkson and Bustin, 1999a,b). Fig. 8 shows the Langmuir adsorption
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Table 3 The results of pore structure parameters for different sized coal samples. Lump size/mm
Injection volumea/ (mL g1)
Cleat volume/ (mL g1)
Cleat aperture/ mm
Cleat porosity/%
Matrix pore volumeb/ (mL g1)
The matrix average pore size/nm
Matrix porosity/%
1 3 6 10
1.2357 0.7670 0.2233 0.2574
e e 0.2233 0.2574
e e 78.35 72.00
e e 24.47 27.17
0.0051 0.0039 0.0025 0.0016
1267 875 598 571
5.80 3.12 0.36 0.23
Mercury intrusion when pressure is less than 0.1 MPa. The matrix pore volume does not include compressibility and can be calculated using incident and cleat volume.
70
80 desorption ratio (%)
63 desorption ratio (%)
56 49
0.8-1mm 20-25mm 70-75mm
42
8-10mm 45-50mm 130-140mm
35
70 60 0 8-1mm 20-25mm 70-75mm
50
8-10mm 45-50mm 130-140mm
40 0
200
400
600
800
1000
1200
1400
0
150
300
time (h)
450
600
750
900
time (h)
(a) 1MPa
(b) 2MPa
90 desorption ratio (%)
a b
80 70
0.8-1mm 20-25mm 70-75mm
60 0
100
200
300
8-10mm 45-50mm 130-140mm 400
500
time (h)
(c) 3MPa Fig. 7. The desorption ratio of the six size fractions of coal samples versus time.
isotherms for the six size fractions of coal samples. With increasing pressure, the adsorption volume increase and tend to a constant because methane is physically adsorbed on coal and the adsorption confirms with the Langmuir isotherm (Zhao and Tang, 2002). (2) The time to reach desorption equilibrium for the six size fractions of coal samples is different and basically increases with increasing lump size. When the pressure was 1 MPa, the desorption equilibration for these lump size fractions (0.8e1, 20e25 and 130e140 mm) appeared to have been reached after approximately 31, 635 and 1475 h, respectively. When the pressure was 2 MPa, the desorption equilibration for these lump size fractions (0.8e1, 20e25 and 130e140 mm) appeared to have been reached after approximately 23, 358 and 796 h, respectively. When the pressure was 3 MPa, equilibration was reached after approximately 18, 218 and 479 h, respectively. These findings also indicate that the desorption time decreases with increasing pressure and the change is more evident for a large lump coal. (3) Except for the 1 mm sample, the desorption ratio of the other lump coals tend to the same constant over time and increase with increasing pressure. When the pressure was 1 MPa, the
final desorption ratio was approximately 51%. When the pressure was 2 MPa, the final desorption ratio is approximately 70%. When the pressure was increased to 3 MPa, the final desorption ratio increased to 77%. The reason why the desorption ratio increased with pressure is that the final desorption pressure was constant (atmospheric). The absolute amount of gas remaining at atmospheric pressure was approximately constant, but decreased with increasing initial pressure as a fraction of the total adsorbed. The desorption kinetics experimental data of methane from coal samples were nonlinearly fitted and confirmed to the following Eq. (9) (Airey, 1968).
n t Qt ¼ A 1 exp t0
(9)
where Qt is the methane desorption capacity (L), A is the ultimate desorption capacity (L), t0 is the desorption time constant, and n is a coefficient. Table 5 gives the fitting results of the desorption kinetics data of methane from coal samples. The correlation coefficient is greater than 0.95, showing a great fit. Airey (1968) obtained
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80
Lump size/mm
The final Mass/ Pressure/ Adsorption Desorption The final g MPa capacity/L equilibrium desorption desorption capacity/L ratio, % time/h
0.8e1
3000
1 2 3
82.91 101.67 107.12
31 23 18
58.24 85.20 96.61
70.24 83.81 90.18
8e10
3000
1 2 3
83.13 100.10 106.93
318 231 132
51.57 69.43 83.91
62.04 69.36 78.47
20e25
3000
1 2 3
82.18 100.59 107.31
635 358 218
51.55 70.32 84.71
62.73 69.91 78.94
45e50
3000
1 2 3
82.05 100.53 106.62
827 526 337
50.78 69.39 83.18
61.89 69.03 78.02
70e75
3000
1 2 3
81.27 99.32 105.72
1268 658 419
50.29 67.67 81.38
61.88 68.14 76.98
130e140 3000
1 2 3
80.76 98.80 105.83
1475 796 479
50.06 67.87 82.01
61.95 68.69 77.48
Adsorption capacity (L)
120 100
0.8-1mm 8-10mm 20-25mm 45-50mm 70-75mm 130-140mm
80 102
60 40
100
20 98 1.9
0 0.0
0.5
2.0
1.0
2.1
1.5
2.2
2.0
2.5
3.0
Pressure (MPa) Fig. 8. Langmuir adsorption isotherms for the six size fractions of coal samples.
Desorption time costant (h)
Table 4 The desorption kinetics data of methane on the six size fractions of coal samples (25 C).
1MPa
2MPa
3MPa
60 40 20 0
0
30
60
90
120
150
Lump size (mm) Fig. 9. Desorption time constant of coal samples versus lump size.
the same equation during a study of gas emissions from broken coal, where the coefficient (n) is related to the type of cracking. The relationships between the desorption time constant and lump size of coal samples, at three different pressures, are shown in Fig. 9. It can be observed that: (1) With increasing lump size, the desorption time constant changes according to positive exponential rules and approaches a constant value after the lump size fraction of 70e75 mm. It is due to the increase of lump size which extends the distance from the inner pores of the coal matrix to the external coal surface layer. Crosdale et al. (1998) considered gas movement through coal to be a three-stage process: (i) free flow in large pores out of the coal system, (ii) gas diffusion through the micropore structure toward larger pores and (iii) gas desorption from the internal surfaces. When the lump size drops below the coal matrix size, methane transport through coal matrix is only controlled by diffusion, and the desorption time constant is proportional to the square of the coal size. When the lump size exceeds the coal matrix size, methane transport through coal is controlled by a combined diffusion and flow process. Since the resistance of gas diffusion in small pores is far more than the resistance of gas flow in fractures or larger pores (Zhou,
Table 5 The fitting results of the desorption kinetics of methane on the six size fractions of coal samples. Lump size/mm
Mass/g
Pressure/ MPa
The ultimate desorption capacity/L
The ultimate desorption ratio/%
The coefficient, n
0.8e1
3000
1 2 3
58.24 85.20 95.70
74.09 85.45 91.99
0.59 0.57 0.56
8e10
3000
1 2 3
53.32 69.15 83.03
61.89 69.03 77.63
20e25
3000
1 2 3
51.43 69.08 89.45
45e50
3000
1 2 3
70e75
3000
130e140
3000
The desorption time constant/h
Correlation coefficient
The desorption rate attenuation index
The initial desorption rate/(L min1)
Correlation coefficient
0.49 0.47 0.40
0.9607 0.9538 0.9550
1.2941 1.3319 1.3333
23.87 48.57 51.60
0.9737 0.9807 0.9790
0.37 0.41 0.37
7.36 4.86 2.54
0.9881 0.9854 0.9863
0.9337 0.9389 0.9364
4.63 6.76 8.81
0.9921 0.9923 0.9882
63.19 67.04 78.38
0.40 0.40 0.41
18.24 9.14 4.36
0.9934 0.9911 0.9937
0.9224 0.9299 0.9239
4.56 6.61 8.29
0.9948 0.9897 0.9714
52.59 68.61 78.56
64.68 72.12 76.21
0.37 0.37 0.41
37.68 17.35 7.26
0.9894 0.9873 0.9935
0.9087 0.9024 0.9124
3.55 5.03 6.92
0.9939 0.9939 0.9872
1 2 3
41.28 70.89 90.86
63.13 71.13 78.60
0.38 0.37 0.37
62.10 27.45 10.27
0.9893 0.9838 0.9949
0.8813 0.8913 0.8770
2.16 4.13 5.82
0.9916 0.9978 0.9891
1 2 3
50.99 66.16 76.31
62.36 71.60 75.67
0.37 0.37 0.38
60.58 25.47 10.19
0.9913 0.9951 0.9821
0.8888 0.8973 0.8954
3.06 4.40 5.73
0.9957 0.9938 0.9932
J. Guo et al. / Journal of Natural Gas Science and Engineering 20 (2014) 337e346
1990), methane diffusion is considered to be a greater control. Combined with the restriction of diffusion distance by the coal matrix size, the desorption time constant is eventually constant. However, experimental results show that the lump size (70e75 mm) corresponding to constant value is far larger than the coal matrix size. It may be due to cleat-filling minerals which block the seepage channels. (2) As the adsorption equilibrium pressure increased, the desorption time constant for the same size sample gradually decrease. For the 0.8e1 mm sample, the desorption time constants at 1, 2 and 3 MPa pressures are approximately 0.49, 0.47 and 0.4 h, respectively. For the 130e140 mm sample, the desorption time constants at pressures of 1, 2 and 3 MPa are approximately 60.58, 25.47 and 10.19 h, respectively. It is primarily due to the fact that at lower pressures, diffusion appears to be in a transition region where the number of moleculeeporewall and moleculeemolecule collisions is on the same order. This change from Knudsen to bulk diffusion with increasing pressure is expected because the mean free path of the gas is decreasing, which enhances the ability of gaseous diffusion and accelerates gas flow rate. These results are in good agreement with other studies (Simith and William, 1984; Charriere et al., 2010). The relationships between the ultimate desorption ratio and lump size for coal samples, at three different pressures, are shown in Fig. 10. It can be observed that: (1) When the lump coal size drops below 10 mm, the ultimate desorption ratio of methane decreases significantly with increasing lump size. For the 1 MPa pressure, the ultimate desorption ratio decreases from 74% to 62%. For the 2 MPa pressure, the ultimate desorption ratio decreases from 85% to 70%. For the 3 MPa pressure, the ultimate desorption ratio decreases from 92% to 77%. When the lump size exceeds 10 mm, the ultimate desorption ratio of methane do not vary with lump size. It is due to the higher initial desorption rate for the 1 mm sample which will be discussed further in the following section. The average collision frequency equation (10) of gas molecules is (Wu, 2011)
Z¼
pffiffiffi 2pd2 vn
(10)
T h e u ltim a te d e s o r p tio n r a tio ( % )
where Z is the average collision frequency of gas molecules (s1), d is the effective diameter of molecules (m), v is the average speed of the molecules (m s1), and n is the number of gas molecules per unit volume. The higher rate of methane release can increase the average collision frequency of the gas molecules, which provide energy for methane desorption from the internal coal surface. 1MPa
90
2MPa
3.3.2. Effect of lump size on the rates of desorption The methane desorption rates of the six size fractions of coal samples at three different pressures versus time are shown in Fig. 11. It can be observed that: (1) The methane desorption rate gradually decreases over time and tends toward zero. (2) The desorption rate gradually decreases with increasing lump size. For the 1 MPa pressure, the desorption rates at 0.15 h for these size fraction (0.8e1, 20e25 and 130e140 mm) samples are 1.192, 0.677 and 0.385 L/min, respectively. The desorption rates at 0.8 h for these size fraction (0.8e1, 20e25 and 130e140 mm) samples are 0.196, 0.106 and 0.081 L/min, respectively. The differences in the desorption rate between 0.15 h and 0.8 h are 0.996, 0.571 and 0.304 L/min, respectively. For the 3 MPa pressure, the desorption rates at 0.15 h for these size fraction (0.8e1, 20e25 and 130e140 mm) samples are 5.491, 0.872 and 0.665 L/min, respectively. The desorption rates at 0.8 h for these size fraction (0.8e1, 20e25 and 130e140 mm) samples are 0.278, 0.27 and 0.168 L/min, respectively. The differences in the desorption rate between 0.15 h and 0.8 h are 5.213, 0.602 and 0.497 L/min, respectively. However, the desorption rate and its corresponding difference of the 70e75 mm sample is less than that of the 130e140 mm sample. It may be due to the more developed fractures in the 70e75 mm sample. (3) With increasing the adsorption equilibrium pressure, the desorption rate of the same size coal sample at the same time increase and the change for the 0.8e1 mm sample is more evident than the other samples. At 0.15 h, the desorption rates for the 0.8e1 mm sample, at the 1, 2 and 3 MPa pressures, are 1.192, 2.246 and 5.491 L/min, respectively. The corresponding change between 1 MPa and 3 MPa are 4.299 L/ min. The desorption rates for the 20e25 mm sample, at the 1, 2 and 3 MPa pressures, are 0.677, 0.776 and 0.872 L/min. The corresponding change between 1 MPa and 3 MPa is 0.195 L/ min. The desorption rates for the 130e140 mm sample, at the 1, 2 and 3 MPa pressures, are 0.385, 0.613 and 0.665 L/min. The corresponding change between 1 MPa and 3 MPa is 0.28 L/min. The desorption rate of methane from coal samples versus time are fitted to the following Eq. (11).
kt t ta
(11)
where vt and va are the rates of desorption in mL min1 at times t and ta, respectively, and kt is the constant characterizing the desorption process and reflecting the attenuation degree of desorption rate (Banerjee, 1988). Winter and Janas (1996) obtained the same equation during a study of gas emission rates from coal and named the rate of desorption at 1 min as v1. Eq. (11) can be written as follow.
84 78 72 66 60
(2) As adsorption equilibrium pressure increased, the ultimate desorption ratio of methane for coal samples increase. The reason has been explained in the former part.
vt ¼ va
3MPa
343
0
20
40
60
80
100
120
140
Lump size (mm) Fig. 10. The ultimate desorption ratio of coal samples versus lump size.
v1 ¼ va takt
(12)
Eq. (12) can be logarithmically transformed as follow.
Ln va ¼ kt Ln ta þ Ln v1
(13)
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5
0.8-1mm 8-10mm 20-25mm 45-50mm 70-75mm 130-140mm
4 3 2
desorption rate(L/min)
desorption rate (L/min)
5
1 0 0.0
0.2
0.4
0.6 0.8 time (h)
1.0
1.2
0.8-1mm 8-10mm 20-25mm 45-50mm 70-75mm 130-140mm
4 3 2 1 0 0.0
0.2
0.4 0.6 time (h)
1.0
(b) 2 MPa
(a) 1 MPa 6
0.8-1mm 8-10mm 20-25mm 45-50mm 70-75mm 130-140mm
5 desorption rate (L/min)
0.8
4 3 2 1 0 0.0
0.2
0.4 0.6 time (h)
0.8
(c) 3 MPa
Table 5 gives the fitting results of the constant kt and v1. The correlation coefficient is greater than 0.97, showing a great fit. v1 is the initial desorption rate in the first minute of desorption, and kt is desorption rate attenuation index characterizing the ratio between the volume of methane adsorbed in the macropores and cleats in the first minute after the pressure was released and the total desorption volume (Du, 1985). The desorption rate attenuation index and the initial desorption rate for coal samples versus lump size are shown in Figs. 12 and 13, respectively. The values of kt and v1 decrease significantly when the lump size increases from 1 mm to 10 mm. When the lump size exceeds 10 mm, the decrease in kt and v1 is not evident as the lump size increased. Fig. 14 shows a model of methane transport through coal. As can be seen in Fig. 14, transport of methane is only controlled by diffusion when the lump size drops below the coal
D e s o r p tio n r a te a tte n u a tio n in d e x
1.4
1MPa
2MPa
3MPa
1.3 1.2 1.1 1.0 0.9 0.8
0
30
60
90
120
150
Lump size (mm) Fig. 12. Desorption rate attenuation index of coal samples versus lump size.
The initial desorption rate (mL/g·min)
Fig. 11. The desorption rate of the six size fractions of coal samples versus time.
0.30
1MPa
2MPa
3MPa
0.25 0.20 0.15 0.10 0.05 0.00
0
30
60
90
120
150
Lump size (mm) Fig. 13. The initial desorption rate of coal samples versus lump size.
matrix size. The smaller the lump size, the larger the average pore size, which accelerates methane desorption (see Fig. 14(a)). When the lump size exceeds the coal matrix size, the methane migration from the coal matrix to the seepage channels is restricted by cleat apertures, which control the values of kt and v1 (see Fig. 14(b)). This model can also explain why gas outbursts are always accompanied by small-scale compressively geological structures where mylonitic coals often occur. Because mylonitic coals are highly deformed and create mylonite of particle sizes which release large quantities of gas very rapidly (Xue et al., 2012), it is prone to outburst when combined with their low strength. Williams and Weissmann (1995) believed that the most important parameter of an outburst is gas desorption rate, in conjunction with the gas pressure gradient ahead of the face. In addition, the desorption rate attenuation index is independent of pressure, while the initial desorption rate increases with increasing pressure.
J. Guo et al. / Journal of Natural Gas Science and Engineering 20 (2014) 337e346
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Fig. 14. A model of methane transport through coal: (a) the lump size drops below the coal matrix size; (b) the lump size exceeds the coal matrix size.
3.3.3. Effect of lump size on methane diffusivity The representation using the bidisperse diffusion model is plotted along with the experimental data in Fig. 15 as a demonstration of the quality of the modeling results and the parameters are summarized in Table 6. It can be seen from Table 6 that macropore diffusivity decrease with lump size increase for the same pressure step and then change little when the lump size is larger than 25 mm; micropore diffusivity decrease with lump size increase and then change little when the lump size is larger than 10 mm. Also methane diffusivities tend to increase with pressure increase when the lump size is constant. This observation agrees with the findings by Smith and Williams (1984a,b). Moreover, the b value is relatively small because b represents the ratio of gas adsorption in the macropores as defined in the bidisperse model. In order to illustrate more clearly how lump size affects the diffusivities, the average is taken to eliminate the effect of pressure on diffusivity and the results are shown in Figs. 16 and 17. Figs. 16 and 17 show the effects of lump size on macropore diffusivity and micropore diffusivity, respectively. It can be seen from these figures that lump size has significant impact on both averaged macropore and micropore diffusivities. The averaged macropore diffusivity decreases from 0.29 s1 to 5.74 103 s1 when the lump size increases from 1 mm to 25 mm; the average micropore diffusivity decreases from 1.38 103 s1 to 5.99 106 s1 when the lump size increases from 1 mm to 10 mm. This suggests that the impact of lump size on gas diffusion in pores with different size is different. A possible explanation is that the macropores are disturbed in the first place as lump size decreased.
Table 6 Methane diffusivities for the six size fractions of coal samples. (s1)
(s1)
Lump size/mm
Pressure (MPa)
b
Di R2i
0.8e1
1 2 3
0.0163 0.0175 0.0172
6.88 104 1.63 103 2.12 103
0.19 0.32 0.36
0.9812 0.9842 0.9841
8e10
1 2 3
2.81 103 1.62 103 2.86 103
1.87 106 7.56 106 8.53 106
0.011 0.016 0.025
0.9275 0.9255 0.9482
20e25
1 2 3
1.38 103 1.17 103 1.22 103
2.71 106 5.12 106 7.46 106
2.35 103 6.61 103 8.25 103
0.9237 0.9435 0.9739
45e50
1 2 3
1.01 103 2.02 103 1.54 103
2.28 106 2.86 106 4.96 106
1.56 103 3.73 103 9.01 103
0.9486 0.9524 0.9609
70e75
1 2 3
1.16 103 1.46 103 1.52 103
1.14 106 1.63 106 2.21 106
1.08 103 1.62 103 4.93 103
0.9283 0.9756 0.8706
130e140
1 2 3
2.72 104 2.29 104 9.51 104
1.09 106 2.96 106 3.43 106
1.10 103 2.27 103 6.41 103
0.9510 0.9430 0.9395
Da R2a
Correlation coefficient
In addition, it can be seen from the correlation coefficient that the bidisperse model cannot represent the desorption rate behavior well for these coal samples except for 1 mm grain size. Because for the other lump size coal samples, small transport pathways in the form of cleats or cracks can trigger fast gas distribution around the matrix blocks (Busch and Gensterblum, 2011), gas transport
0.30 0.25
2
-1
Da/Ra (s )
0.20 0.15 0.10 0.05 0.00 0
20
40
60
80
100
120
140
Lump size (mm) Fig. 15. Sample experimental results of desorption rate at 2 MPa.
Fig. 16. Average macro-diffusivity of coal samples versus lump size.
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0.0014 0.0012 0.0008
2
-1
Di/Ri (s )
0.0010 0.0006 0.0004 0.0002 0.0000 -0.0002
0
20
40
60
80
100
120
140
Lump size (mm) Fig. 17. Average micro-diffusivity of coal samples versus lump size.
through the coal fracture system, which is dependent upon relative permeability, is therefore considered to be a greater control upon long-term desorption. 4. Conclusions A combined light microscopic measurement, mercury porosimetry, and methane desorption kinetics analysis have been conducted on different sized anthracite to determine the effects of lump size on methane desorption from coal. The following conclusions can be made: (1) For the lump coals, three pressure regimes in the process of mercury injectiondlow (P < 0.1 MPa), intermediate (0.1 P < 5 MPa), and high (5 MPa), are indicated by distinct values of the fractal dimension; in order of increasing pressure, these correspond to cleat penetration, pore penetration, and coal matrix compressibility. (2) When the coal size drops below the coal matrix size, the pore volume and average pore size increase with decreasing grain size. When the lump size exceeds the coal matrix size, the characteristics of fracture and pore structure of anthracite, such as cleat volume, cleat aperture, cleat porosity, matrix pore volume, the matrix average pore size and matrix porosity, are basically invariant. (3) With increasing lump size, the desorption time constant changes according to positive exponential rules and approaches a constant value after a lump size fraction of 70e75 mm; the final desorption ratio, the desorption rate in the first minute, the attenuation index of desorption rate and gas diffusivity decrease significantly and then change little when the lump size exceeds the coal matrix size. Acknowledgments This research was supported financially by the National Natural Science Foundation of China, grant No. 51174141 and 50974093. References Airey, E.M., 1968. Gas emission from broken coal: an experimental and theoretical investigation. Int. J. Rock Mech. Min. Sci. 5 (6), 475e494.
Beamish, B.B., Crosdale, P.J., 1998. Instantaneous outbursts in underground coal mines: an overview and association with coal type. Int. J. Coal Geol. 35 (1/4), 27e55. Banerjee, B.D., 1988. Spacing of fissuring network and rate of desorption of methane from coals. Fuel 60 (11), 1584e1586. Bertand, C., Bruyet, B., Gunther, J., 1970. Determination of desorbable gas concentration of coal (direct method). Int. J. Rock Mech. Min. Sci. 7 (1), 43e65. Busch, A., Gensterblum, Y., Krooss, B.M., et al., 2004. Methane and carbon dioxide adsorptionediffusion experiments on coal: upscaling and modeling. Int. J. Coal Geol. 60 (2/4), 151e168. Busch, A., Gensterblum, Y., 2011. CBM and CO2-ECBM related sorption processes in coal: a review. Int. J. Coal Geol. 87, 49e71. re, D., Pokryszka, Z., Behra, P., 2010. Effect of pressure and temperature on Charrie diffusion of CO2 and CH4 into coal from Lorraine basin (France). Int. J. Coal Geol. 81 (4), 373e380. Clarkson, C.R., Bustin, R.M., 1999a. The effect of pore structure and gas pressure upon the transport properties of coal: a laboratory and modeling study. 1. Isotherms and pore volume distributions. Fuel 78 (11), 1333e1344. Clarkson, C.R., Bustin, R.M., 1999b. The effect of pore structure and gas pressure upon the transport properties of coal: a laboratory and modeling study. 2. Adsorption rate modeling. Fuel 78, 1345e1362. Crosdale, P.J., Beamish, B.B., Valix, M., 1998. Coalbed methane sorption related to coal composition. Int. J. Coal Geol. 35 (1/4), 147e158. Du, B., 1985. The initial gas desorption rate as an index of burst of coal and gas: about the parameter of Kt. Saf. Coal Mines 5, 56e63. Friesen, W.I., Mikula, R.J., 1987. Fractal dimensions of coal particles. J. Colloid Interf. Sci. 120 (l), 263e271. Friesen, W.I., Mikula, R.J., 1988. Mercury porosimetry of coals: pore volume distribution and compressibility. Fuel 67, 1516e1520. Harpalani, S., Chen, G., 1995. Estimation of changes in fracture porosity of coal with gas emission. Fuel 74 (10), 1491e1498. Karacan, C.O., Okandan, E., 2000. Fracture/cleat analysis of coals from Zonguldak Basin (northwestern Turkey) relative to the potential of coalbed methane production. Int. J. Coal Geol. 44 (2), 109e125. Laubach, S.E., Marrett, R.A., Olsen, J.E., et al., 1998. Characteristics and origins of coal cleat: a review. Int. J. Coal Geol. 35 (1/4), 175e207. Moffat, D.H., Weale, K.E., 1955. Sorption by coal of methane at high pressures. Fuel 54, 449e462. Pan, Z., Connell, L.D., Camilleri, M., et al., 2010. Effect of matrix moisture on gas diffusion and flow in coal. Fuel 89, 3207e3217. Pfeifer, P., Avnir, D., 1983. Chemistry in non integer dimensions between 2 and 3, I: fractal theory of heterogenous surface. J. Chem. Phys. 79 (7), 3558e3565. Ruckenstein, E., Vaidyanathan, A.S., Youngquist, G.R., 1971. Sorption by solids with bidisperse pore structures. Chem. Eng. Sci. 26, 1305e1318. Siemons, N., Delft, T.U., Bruining, H., et al., 2003. Assessing the Kinetics and Capacity of Gas Adsorption in Coals by a Combined Adsorption/diffusion Method. Society of Petroleum Engineers, pp. 1e5. Smith, D.M., Williams, F.L., 1984a. Diffusional effects in the recovery of methane from coalbed. SPE J. 5, 529e535. Smith, D.M., Williams, F.L., 1984b. Diffusion models for gas production from coal: determination of diffusion parameters. Fuel 63, 256e261. Toda, Y., Toyoda, S., 1972. Application of mercury porosimetry to coal. Fuel 51 (3), 199e201. Williams, R.J., Weissmann, J.J., 1995. Gas emission and outburst assessment in mixed CO2 and CH4 environments. In: Proc. ACIRL Underground Mining Sem. Australian Coal Industry Res. Lab., North Ryde, 12 pp. Winter, K., Janas, H., 1996. Gas emission characteristics of coal and methods of determining the desorbale gas content by means of desorbmeters. In: 14th International Conference of Coal Mine Safety Research. Wu, J., 2011. Thermology Statistical Physics. Northwestern Polytechnical University Press, Beijing, p. 49. Xue, G., Liu, H., Li, W., 2012. Deformed coal types and pore characteristics in Hancheng coalmines in Eastern Weibei coalfields. Int. J. Min. Sci. Technol. 22, 681e686. Yang, Q., Wang, Y., 1988. Mathematical simulation of the radial methane flow in spherical coal grains. J. China Univ. Min. Technol. 3, 55e61. Zhang, X., Sang, S., Qin, Y., et al., 2005. Isotherm adsorption of coal samples with different grain size. J. China Univ. Min. Technol. 34 (4), 427e432. Zhao, Z., Tang, X., 2002. Discussion about Langmuir equation concerning methane adsorption by coal. J. Jiaozuo Inst. Technol. 21 (1), 1e4. Zhou, S., 1990. Mechanism of gas flow in coal seams. J. China Coal Soc. 15, 15e24. Zwietering, P., Krevelen, D.W., 1954. Chemical structure and properties of coal IVPore structure. Fuel 33, 331.
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Effect of the lump size on methane desorption from anthracite Junqing Guo, Tianhe Kang*, Jianting Kang, Guofei Zhao, Zhiming Huang Institute of Mining Technology, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 May 2014 Received in revised form 13 July 2014 Accepted 14 July 2014 Available online
Anthracite fracture and pore structure of four different sized coal samples were measured using a light microscope and mercury porosimetry, respectively. The desorption kinetics of methane, at three different pressures, were also studied on six size fractions of coal samples using a volumetric experimental apparatus. The effect of lump size on methane desorption from anthracite combined with its pore structure was further discussed. The results showed that (1) for the lump coals, three pressure regimes in the process of mercury injection are indicated by distinct values of the fractal dimension; in order of increasing pressure, these correspond to cleat penetration, pore penetration, and coal matrix compressibility; (2) When the lump coal size drops below the coal matrix size, the pore volume and average pore size increase with decreasing grain size. When the lump size exceeds the coal matrix size, pore-fracture structural characteristics of anthracite, such as cleat aperture, cleat porosity, the matrix average pore size, and matrix porosity are basically invariant; (3) with increasing lump size, the desorption time constant changes according to positive exponential rules, eventually obtaining a stable value after the lump size fraction of 70e75 mm; the ultimate desorption ratio, initial desorption rate, attenuation index of the desorption rate and gas diffusivity decrease significantly and then change little when the lump size exceeds the coal matrix size. © 2014 Elsevier B.V. All rights reserved.
Keywords: Desorption characteristics Lump anthracite size Mercury porosimetry Fracture volume Coal matrix
1. Introduction During mining operations and CBM exploitations, excavation engineering and hydrofracturing can destroy the integrity of coal, which affects methane desorption characteristics. Fast desorbing coals generally yield most of their gas within a very short time, which may cause gas outbursts in coal mines or collapse of a wellbore in coal-bed methane production (Beamish and Crosdale, 1998). Therefore, studies of the effect of lump size on methane desorption from coal have a guiding significance for understanding gas migration in coal seams, predicting methane-related accidents and enhancing CBM production. In recent years, many studies (Bertand et al., 1970; Yang and Wang, 1988; Banerjee, 1988; Siemons et al., 2003; Busch et al., 2004) have focused on the effect of coal size on the methane desorption rate and shown that the desorption rate will be practically independent of the size distribution when the dimensions of the pieces exceed the fissuring network of coal. When the size distribution of the coal drops below this network size, the desorption rate becomes inversely proportional to the square of the
* Corresponding author. Tel.: þ86 0351 6014760. E-mail address: [email protected] (T. Kang). http://dx.doi.org/10.1016/j.jngse.2014.07.019 1875-5100/© 2014 Elsevier B.V. All rights reserved.
size of the particles. However, there is little research on the mechanisms of this phenomenon and the effect of the lump size on desorption time and methane diffusivity. In this study, anthracite fracture and pore structure of four different sized coal samples have been measured using a light microscope and mercury porosimetry. The desorption kinetics of methane, at three different adsorption equilibrium pressures, were studied on six size fractions to analyze the effect of lump size on methane desorption characteristics. 2. Experimental 2.1. Coal samples and apparatus The experiments were conducted on the anthracite with a helium density of 1.52 cm3 g1. The large coal blocks were directly collected from the No.15 coal seam in the Southeast Qinshui basin from Sihe coal mine (Shanxi Province, China). The coal samples were processed into six different size fractions: 0.8e1 mm, 8e10 mm, 20e25 mm, 45e50 mm, 70e75 mm and 130e140 mm (see Fig. 1). There are variances in samples; however, because the coal used in this work is anthracite, the difference of the samples should be relatively small. Before testing, the coal samples weighing approximately 3 kg each were dried in an oven at 105e110 C until a constant weight was achieved.
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Fig. 1. Coal samples.
r¼
2d cos q P
(1)
where r is the pore radium (mm) when mercury enters at the pressure P (MPa); s is the surface tension of mercury and q is the mercuryesolid contact angle.
Fig. 2. Diagram of volumetric experimental apparatus.
The volumetric apparatus used for the desorption kinetics experiment of coal samples is shown schematically in Fig. 2. It mainly consists of an adsorption canister, reference canister, thermostatic water bath, methane cylinder, vacuum pump, and measuring cylinder. The adsorption canister is 150 mm in diameter and 200 mm tall. 2.2. Experimental method and schemes In this study, based on the measurement of anthracite fracture and pore structure of different sized samples, the desorption kinetics of methane were studied on six size fractions of coal samples using a volumetric experimental apparatus. 1) Polished-surface analysis was performed using an incident-light microscope. Prior to the analysis, coal samples were mounted in epoxy resin and the surfaces were polished. An Optec DV320 microscope (Optec, China) was used to acquire the images of coal surfaces. Objective lens of 4 and eyepiece of 10 were used for magnification. Adobe Photoshop software with the PhotoMerge plug-in was used for merging these digitized images. Fracture aperture, lengths, spacing, mineral-filled and connectivity were obtained from digital image analysis. 2) The pore structures of four sized coal samples were measured by mercury porosimetry. The experiments were performed using an Autopore 9505 Instrument (Micro-meritics, US), which permits the mercury filling at as low as 3.5 103 MPa, up to 207 MPa. The coal samples were processed into 0.8e1.2 mm and 2e4 mm grain sized fractions and two cubes with 6 mm and 10 mm edge lengths. The dry sample was evacuated from the instrument to <50 mmm Hg. The volume of mercury penetration into the sample was measured with increasing applied pressure. A contact angle of 130 and surface tension of 485 dyn/cm were used in the Washburn equation (1) to determine the pore size distribution.
3) Based on the volumetric method, methane desorption kinetics experiments were carried out with six size fractions of coal samples according to the following steps. (1) The sample was sealed in an adsorption canister and degassed at 60 C to obtain a static vacuum of 1 Pa within 3 days. (2) Adjust the temperature of the water bath to 25 C, and then fill the adsorption canister with methane. The methane was taken up by the sample at a constant temperature and constant pressure (25 C, 1 MPa). (3) When the pressure difference in the adsorption canister was less than 0.001 MPa d1, the coal methane emission was carried out under atmospheric pressure and bled into an inverted graduated cylinder filled with water. The methane volume was carefully measured in a series of readings over a period of weeks or months, until little or no more gas was produced. (4) Change the adsorption equilibrium pressure (in order, 25 C, 2 MPa; 25 C, 3 MPa) and repeat the above steps. For most coals with a multimodal pore distribution, bidisperse model may better represent the CH4 desorption rate behavior over the full timescale of desorption (Clarkson and Bustin, 1999a,b; Pan et al., 2010; Smith and Williams, 1984a,b). The simplified bidisperse model encounters a fast macropore diffusion stage and a much slower micropore diffusion stage. For the first (fast) stage, the uptake is given by Ruckenstein et al. (1971): f Ma 6 X 1 ¼1 2 exp M∞ p n¼1 n2
Da n2 p2 t R2a
! (2)
where Ma is the total amount of gas desorbed in the macropores at time t, Ra is the macrosphere radius and Da is the macropore effective diffusivity. For the second (slow) stage, the uptake is given by Ruckenstein et al. (1971): f Mi 6 X 1 ¼1 2 exp M∞ p n¼1 n2
Di n2 p2 t R2i
! (3)
where Mi is the total amount of gas desorbed in the micropores at time t, Ri is the microsphere radius and Di is the micropore effective diffusivity. Hence, the overall uptake is:
Mt Ma þ Mi Ma M ¼ ¼b þ ð1 bÞ i M∞ Ma∞ þ Mi∞ Ma∞ Mi∞
(4)
where b ¼ ðMa∞ =ðMi∞ þ Ma∞ ÞÞ is the ratio of macropore desorption to the total desorption.
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339
3. Results and discussion 3.1. Fracture characteristics of anthracite The polished surface of a coal sample is shown in Fig. 3. The coal has a mutually orthogonal and nicely developed ideal structure of fractures. According to its geometry, these fractures are called cleats, which are divided into face cleats and butt cleats (Laubach et al., 1998). In general, face cleats (see region 1e3 in Fig. 3) have good continuity and extensibility, and butt cleats with shorter length (see region 4e6 in Fig. 3) often terminate into face cleats. The characteristics of the cleats are summarized in Table 1. Most of the face cleat apertures fall into the 32e341 mm range, and the butt cleat apertures fall into the 25e63 mm range. Moreover, these cleats are mostly filled with minerals, a disadvantageous feature for the gas transport to main fractures (Karacan and Okandan, 2000). According to the average spacing of these cleat systems, the coal matrix has an average dimension of 4.21 mm wide and 5.66 mm long. 3.2. Pore structure of different sized coal samples Fig. 4 shows the pore size distributions of four different sized coal samples. Fig. 4 clearly illustrates that the pore size distribution of the 6 mm sample is basically the same as the 10 mm sample, and there is a peak in the pore volume of 0.293 cm3 g1 around a pore size of 91 mm for both the two samples. Considering that coal is a dual porosity rock containing micropores (matrix) and a network of natural fractures known as cleats (Harpalani and Chen, 1995), it is possible that the value of this peak may be representative of the volume of cleats with an aperture width of 91 mm. When the lump coal size decreased to 3 mm and 1 mm, the pore volume at a pore size of 91.3 mm increased to 0.961 cm3 g1and 1.164 cm3 g1, respectively, and the pore size corresponding to the peak also
Fig. 4. Pore size distribution curve of different sized coal samples.
increase from 91.3 mm to 361 mm. Because the pore volume of grain size coal, which is measured using mercury porosimetry, consists of inter-particle voids and intra-particle voids and in general the aperture width of inter-particle voids is larger than the aperture width of fractures in lump coal, the measured pore volume of grain size coal is larger than the lump coal. Therefore, the measured pore volume of grain size coal needed to be corrected in order to obtain the true total pore volume. When the pore size is between 1 mm and 10 mm, the pore volume for the 3 mm and 1 mm sample is higher than the other two lump coals, and this change gradually move toward smaller pore with decreasing grain size. It may be due to the destruction of coal matrix which widens the pores. When the pore size is less than 100 nm, the pore volume for both 6 mm and 10 mm samples increase significantly. However, the pore volume for the 3 mm sample begins to increase at a pore size of 20 nm and the 1 mm sample at a pore size of 10 nm. To further understand the variation of the pore structure of coal samples with the lump size decreased, fractal analysis for the four different sized coal samples has been conducted in this study. Pfeifer and Avnir (1983) stated that the volume injection curve of a pore structure with a fractal surface must obey the relation:
dVr fð2 Ds ÞlogðrÞ log dr
(5)
where Vr is the cumulative injection volume at a given pore radius r and Ds is the surface fractal dimension. Following the work of Pfeifer and Avnir (1983) combined Eqs. (1) and (5), and obtained a relation between the cumulative injection volume (Vp) derivative with respect to pressure (p) and the surface fractal dimension (Ds)
dVp fð4 Ds ÞlogðpÞ log dp
Fig. 3. Microscopic fractures of a coal sample, 40.
Table 1 Characteristics of the coal fracture. Fracture marshalling
Fracture number
Fracture length/mm
Fracture aperture/mm
Fracture spacing/mm
1
1 2 3
4.26 6.21 6.95
246 341 32
4.21
2
4 5 6
3.69 4.12 4.98
25 49 63
5.66
(6)
where Vp is the cumulative injection volume at a given pressure p. Using these relations, the surface fractal dimension can be calculated without pore surface area calculations. The logarithm of the derivative of diff injection volume (log(dV/dp)) is plotted versus pressure logarithm (log(p)) and shown in Fig. 5. If the pore surface is fractal within certain ranges of the pore radius, a linear trend should be observed from the slope (A) of the logarithm line (Fig. 5), and D is calculated by D ¼ 4 þ A. From these results, it is possible to distinguish three regions of pressuredlow (P < 0.1 MPa), intermediate (0.1 P < 5 MPa) and high (5 MPa)dwhich are characterized by the fractal dimensions D1, D2, and D3 compiled in Table 2. In all cases, the low, intermediate and high pressure data are similar, giving 1 < D1 < 3, 2 < D2 < 3, and 3 < D3 < 4, respectively. For the 1 mm and 3 mm coal particles, the range of D1 is 1 < D1 < 2, which is similar with the result studied by
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1mm 3mm 6mm 10mm
0.9
3
Vpore(cm /g)
1.2
0.6
0.3 0
50
100
150
200
Pressure (MPa) Fig. 6. Mercury porosimetry data in the pressure range 5e200 MPa. Fig. 5. Logelog plot of dV/dP for four different sized coal samples. The data for different samples have been displaced along the vertical axis for clarity.
Table 2 Fractal dimensions and compressibility parameters from four different sized samples. Lump Fractal dimension size/ D1 D2 D3 mm
Intercept Gradient 105 Compressibility 1011 (cm3/g) (cm3/g MPa) (m2/N)
1 3 6 10
1.240 0.771 0.225 0.259
1.46 1.27 2.18 2.22
2.08 2.15 2.58 2.53
3.47 3.56 3.89 3.91
3.10 5.63 7.93 8.26
4.71 8.56 12.05 12.56
Friesen and Mikula (1987). They interpret D1 as the fractal dimension for a bulk porous medium. For the 6 mm and 10 mm lump coal, the range of D1 is 2 < D1 < 3, which is also reported by Laubach [7] who found that cumulative frequency of cleats having apertures follows a power law and determined that values of fractal dimension determined from volumetric sampling of cleat apertures (2.74e2.82) are larger by ~2. Therefore, for the lump coals, an increase in the pore volume is due primarily to mercury intrusion into the fracture system. The fractal dimensions of both the 6 mm and 10 mm samples are basically the same, indicating that they have a similar fracture systemdnicely developed ideal structure of cleats. When the lump size decreased to 3 mm and 1 mm, the increase in pore volume is due primarily to mercury intrusion into the interparticle voids (Friesen and Mikula, 1988). In the region of intermediate pressures, the increase in pore volume is due primarily to mercury intrusion into the pores of the coal matrix. The fractal dimension D2 decreases as the lump size decreases from 6 mm to 1 mm, which indicates that the decreased lump size simplifies the pore structure of the coal matrix. At pressures higher than approximately 5 MPa, the fractal dimensions for the four sized coal samples undergo a drastic change to values of D3 > 3. These values are nonphysical from a geometric point of view and can be attributed to the compressibility of the coal (Zwietering and Krevelen, 1954). The value D3 of the 6 mm sample is basically the same as that of the 10 mm sample, indicating similar compressibility. Fig. 6 shows a typical result of mercury penetration in the region of high pressures. A rectilinear relation between pressure (P) and Pore volume (Vpore) is found and the fitted values of the intercept and slope are shown in Table 2. The intercept at the ordinate in Fig. 6 represents the pore volume that does not include compressibility. The compressibility (c) of coal is by the following Eq. (7) (Toda and Toyoda, 1972) and shown in Table 2.
c¼ rk
(7)
where r is helium density (g/cm3) and k is the gradient of rectilinear relation (cm3/g$MPa). The pressure threshold corresponding to compressibility for the 6 mm and 10 mm samples is approximately 8 MPa, and the compressibility is approximately 12 1011 m2/N, indicating that both samples have the same dimension of coal matrix. However, the pressure threshold for the 3 mm sample is 80 MPa, corresponding to a compressibility of 8.56 1011 m2/N. The pressure threshold for the 1 mm sample is 130 MPa, corresponding to a compressibility of 4.71 1011 m2/N. This result shows that the coal matrix structure is seriously destroyed when the lump size drops below the coal matrix size, which also changes the bearing capacity and compressibility of coal. The results of the pore structure parameters of the four sized coal samples are listed in Table 3. When the lump size exceeds the coal matrix size (5.66 mm 4.21 mm), pore-fracture structural characteristics of anthracite, such as cleat volume, cleat aperture, cleat porosity, matrix pore volume, the matrix average pore size and matrix porosity, are basically invariant. When grain size drops from 4 mm to 2 mm, pore volume and average pore size increase. 3.3. Desorption characteristics of different sized coal samples 3.3.1. Effect of lump size on the desorption time and desorption ratio The methane desorption ratio is used to describe desorption kinetics processes in coal samples and can be calculated according to Eq. (8).
h ¼ V=Qe
(8)
where h is the methane desorption ratio (%), V is the methane desorption capacity (L), and Qe is the methane adsorption capacity (L) when the final adsorption equilibrium appeared to have been reached. The methane desorption ratio of the six size fractions of coal samples at different pressures versus time are shown in Fig. 7, and the corresponding experimental results are shown in Table 4. It is described below: (1) At the same pressure, lump size has no discernable effect on the equilibrium adsorption capacity. Moffat and Weale (1955) had a similar conclusion. It is due to that the adsorption volume of methane mainly depends on the surface area which is mostly affected by the number of micropores. Anthracite has highly developed micropores; the decreased lump size has little effect on micropores with a pore size less than 7.2 nm (Zhang et al., 2005; Clarkson and Bustin, 1999a,b). Fig. 8 shows the Langmuir adsorption
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Table 3 The results of pore structure parameters for different sized coal samples. Lump size/mm
Injection volumea/ (mL g1)
Cleat volume/ (mL g1)
Cleat aperture/ mm
Cleat porosity/%
Matrix pore volumeb/ (mL g1)
The matrix average pore size/nm
Matrix porosity/%
1 3 6 10
1.2357 0.7670 0.2233 0.2574
e e 0.2233 0.2574
e e 78.35 72.00
e e 24.47 27.17
0.0051 0.0039 0.0025 0.0016
1267 875 598 571
5.80 3.12 0.36 0.23
Mercury intrusion when pressure is less than 0.1 MPa. The matrix pore volume does not include compressibility and can be calculated using incident and cleat volume.
70
80 desorption ratio (%)
63 desorption ratio (%)
56 49
0.8-1mm 20-25mm 70-75mm
42
8-10mm 45-50mm 130-140mm
35
70 60 0 8-1mm 20-25mm 70-75mm
50
8-10mm 45-50mm 130-140mm
40 0
200
400
600
800
1000
1200
1400
0
150
300
time (h)
450
600
750
900
time (h)
(a) 1MPa
(b) 2MPa
90 desorption ratio (%)
a b
80 70
0.8-1mm 20-25mm 70-75mm
60 0
100
200
300
8-10mm 45-50mm 130-140mm 400
500
time (h)
(c) 3MPa Fig. 7. The desorption ratio of the six size fractions of coal samples versus time.
isotherms for the six size fractions of coal samples. With increasing pressure, the adsorption volume increase and tend to a constant because methane is physically adsorbed on coal and the adsorption confirms with the Langmuir isotherm (Zhao and Tang, 2002). (2) The time to reach desorption equilibrium for the six size fractions of coal samples is different and basically increases with increasing lump size. When the pressure was 1 MPa, the desorption equilibration for these lump size fractions (0.8e1, 20e25 and 130e140 mm) appeared to have been reached after approximately 31, 635 and 1475 h, respectively. When the pressure was 2 MPa, the desorption equilibration for these lump size fractions (0.8e1, 20e25 and 130e140 mm) appeared to have been reached after approximately 23, 358 and 796 h, respectively. When the pressure was 3 MPa, equilibration was reached after approximately 18, 218 and 479 h, respectively. These findings also indicate that the desorption time decreases with increasing pressure and the change is more evident for a large lump coal. (3) Except for the 1 mm sample, the desorption ratio of the other lump coals tend to the same constant over time and increase with increasing pressure. When the pressure was 1 MPa, the
final desorption ratio was approximately 51%. When the pressure was 2 MPa, the final desorption ratio is approximately 70%. When the pressure was increased to 3 MPa, the final desorption ratio increased to 77%. The reason why the desorption ratio increased with pressure is that the final desorption pressure was constant (atmospheric). The absolute amount of gas remaining at atmospheric pressure was approximately constant, but decreased with increasing initial pressure as a fraction of the total adsorbed. The desorption kinetics experimental data of methane from coal samples were nonlinearly fitted and confirmed to the following Eq. (9) (Airey, 1968).
n t Qt ¼ A 1 exp t0
(9)
where Qt is the methane desorption capacity (L), A is the ultimate desorption capacity (L), t0 is the desorption time constant, and n is a coefficient. Table 5 gives the fitting results of the desorption kinetics data of methane from coal samples. The correlation coefficient is greater than 0.95, showing a great fit. Airey (1968) obtained
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80
Lump size/mm
The final Mass/ Pressure/ Adsorption Desorption The final g MPa capacity/L equilibrium desorption desorption capacity/L ratio, % time/h
0.8e1
3000
1 2 3
82.91 101.67 107.12
31 23 18
58.24 85.20 96.61
70.24 83.81 90.18
8e10
3000
1 2 3
83.13 100.10 106.93
318 231 132
51.57 69.43 83.91
62.04 69.36 78.47
20e25
3000
1 2 3
82.18 100.59 107.31
635 358 218
51.55 70.32 84.71
62.73 69.91 78.94
45e50
3000
1 2 3
82.05 100.53 106.62
827 526 337
50.78 69.39 83.18
61.89 69.03 78.02
70e75
3000
1 2 3
81.27 99.32 105.72
1268 658 419
50.29 67.67 81.38
61.88 68.14 76.98
130e140 3000
1 2 3
80.76 98.80 105.83
1475 796 479
50.06 67.87 82.01
61.95 68.69 77.48
Adsorption capacity (L)
120 100
0.8-1mm 8-10mm 20-25mm 45-50mm 70-75mm 130-140mm
80 102
60 40
100
20 98 1.9
0 0.0
0.5
2.0
1.0
2.1
1.5
2.2
2.0
2.5
3.0
Pressure (MPa) Fig. 8. Langmuir adsorption isotherms for the six size fractions of coal samples.
Desorption time costant (h)
Table 4 The desorption kinetics data of methane on the six size fractions of coal samples (25 C).
1MPa
2MPa
3MPa
60 40 20 0
0
30
60
90
120
150
Lump size (mm) Fig. 9. Desorption time constant of coal samples versus lump size.
the same equation during a study of gas emissions from broken coal, where the coefficient (n) is related to the type of cracking. The relationships between the desorption time constant and lump size of coal samples, at three different pressures, are shown in Fig. 9. It can be observed that: (1) With increasing lump size, the desorption time constant changes according to positive exponential rules and approaches a constant value after the lump size fraction of 70e75 mm. It is due to the increase of lump size which extends the distance from the inner pores of the coal matrix to the external coal surface layer. Crosdale et al. (1998) considered gas movement through coal to be a three-stage process: (i) free flow in large pores out of the coal system, (ii) gas diffusion through the micropore structure toward larger pores and (iii) gas desorption from the internal surfaces. When the lump size drops below the coal matrix size, methane transport through coal matrix is only controlled by diffusion, and the desorption time constant is proportional to the square of the coal size. When the lump size exceeds the coal matrix size, methane transport through coal is controlled by a combined diffusion and flow process. Since the resistance of gas diffusion in small pores is far more than the resistance of gas flow in fractures or larger pores (Zhou,
Table 5 The fitting results of the desorption kinetics of methane on the six size fractions of coal samples. Lump size/mm
Mass/g
Pressure/ MPa
The ultimate desorption capacity/L
The ultimate desorption ratio/%
The coefficient, n
0.8e1
3000
1 2 3
58.24 85.20 95.70
74.09 85.45 91.99
0.59 0.57 0.56
8e10
3000
1 2 3
53.32 69.15 83.03
61.89 69.03 77.63
20e25
3000
1 2 3
51.43 69.08 89.45
45e50
3000
1 2 3
70e75
3000
130e140
3000
The desorption time constant/h
Correlation coefficient
The desorption rate attenuation index
The initial desorption rate/(L min1)
Correlation coefficient
0.49 0.47 0.40
0.9607 0.9538 0.9550
1.2941 1.3319 1.3333
23.87 48.57 51.60
0.9737 0.9807 0.9790
0.37 0.41 0.37
7.36 4.86 2.54
0.9881 0.9854 0.9863
0.9337 0.9389 0.9364
4.63 6.76 8.81
0.9921 0.9923 0.9882
63.19 67.04 78.38
0.40 0.40 0.41
18.24 9.14 4.36
0.9934 0.9911 0.9937
0.9224 0.9299 0.9239
4.56 6.61 8.29
0.9948 0.9897 0.9714
52.59 68.61 78.56
64.68 72.12 76.21
0.37 0.37 0.41
37.68 17.35 7.26
0.9894 0.9873 0.9935
0.9087 0.9024 0.9124
3.55 5.03 6.92
0.9939 0.9939 0.9872
1 2 3
41.28 70.89 90.86
63.13 71.13 78.60
0.38 0.37 0.37
62.10 27.45 10.27
0.9893 0.9838 0.9949
0.8813 0.8913 0.8770
2.16 4.13 5.82
0.9916 0.9978 0.9891
1 2 3
50.99 66.16 76.31
62.36 71.60 75.67
0.37 0.37 0.38
60.58 25.47 10.19
0.9913 0.9951 0.9821
0.8888 0.8973 0.8954
3.06 4.40 5.73
0.9957 0.9938 0.9932
J. Guo et al. / Journal of Natural Gas Science and Engineering 20 (2014) 337e346
1990), methane diffusion is considered to be a greater control. Combined with the restriction of diffusion distance by the coal matrix size, the desorption time constant is eventually constant. However, experimental results show that the lump size (70e75 mm) corresponding to constant value is far larger than the coal matrix size. It may be due to cleat-filling minerals which block the seepage channels. (2) As the adsorption equilibrium pressure increased, the desorption time constant for the same size sample gradually decrease. For the 0.8e1 mm sample, the desorption time constants at 1, 2 and 3 MPa pressures are approximately 0.49, 0.47 and 0.4 h, respectively. For the 130e140 mm sample, the desorption time constants at pressures of 1, 2 and 3 MPa are approximately 60.58, 25.47 and 10.19 h, respectively. It is primarily due to the fact that at lower pressures, diffusion appears to be in a transition region where the number of moleculeeporewall and moleculeemolecule collisions is on the same order. This change from Knudsen to bulk diffusion with increasing pressure is expected because the mean free path of the gas is decreasing, which enhances the ability of gaseous diffusion and accelerates gas flow rate. These results are in good agreement with other studies (Simith and William, 1984; Charriere et al., 2010). The relationships between the ultimate desorption ratio and lump size for coal samples, at three different pressures, are shown in Fig. 10. It can be observed that: (1) When the lump coal size drops below 10 mm, the ultimate desorption ratio of methane decreases significantly with increasing lump size. For the 1 MPa pressure, the ultimate desorption ratio decreases from 74% to 62%. For the 2 MPa pressure, the ultimate desorption ratio decreases from 85% to 70%. For the 3 MPa pressure, the ultimate desorption ratio decreases from 92% to 77%. When the lump size exceeds 10 mm, the ultimate desorption ratio of methane do not vary with lump size. It is due to the higher initial desorption rate for the 1 mm sample which will be discussed further in the following section. The average collision frequency equation (10) of gas molecules is (Wu, 2011)
Z¼
pffiffiffi 2pd2 vn
(10)
T h e u ltim a te d e s o r p tio n r a tio ( % )
where Z is the average collision frequency of gas molecules (s1), d is the effective diameter of molecules (m), v is the average speed of the molecules (m s1), and n is the number of gas molecules per unit volume. The higher rate of methane release can increase the average collision frequency of the gas molecules, which provide energy for methane desorption from the internal coal surface. 1MPa
90
2MPa
3.3.2. Effect of lump size on the rates of desorption The methane desorption rates of the six size fractions of coal samples at three different pressures versus time are shown in Fig. 11. It can be observed that: (1) The methane desorption rate gradually decreases over time and tends toward zero. (2) The desorption rate gradually decreases with increasing lump size. For the 1 MPa pressure, the desorption rates at 0.15 h for these size fraction (0.8e1, 20e25 and 130e140 mm) samples are 1.192, 0.677 and 0.385 L/min, respectively. The desorption rates at 0.8 h for these size fraction (0.8e1, 20e25 and 130e140 mm) samples are 0.196, 0.106 and 0.081 L/min, respectively. The differences in the desorption rate between 0.15 h and 0.8 h are 0.996, 0.571 and 0.304 L/min, respectively. For the 3 MPa pressure, the desorption rates at 0.15 h for these size fraction (0.8e1, 20e25 and 130e140 mm) samples are 5.491, 0.872 and 0.665 L/min, respectively. The desorption rates at 0.8 h for these size fraction (0.8e1, 20e25 and 130e140 mm) samples are 0.278, 0.27 and 0.168 L/min, respectively. The differences in the desorption rate between 0.15 h and 0.8 h are 5.213, 0.602 and 0.497 L/min, respectively. However, the desorption rate and its corresponding difference of the 70e75 mm sample is less than that of the 130e140 mm sample. It may be due to the more developed fractures in the 70e75 mm sample. (3) With increasing the adsorption equilibrium pressure, the desorption rate of the same size coal sample at the same time increase and the change for the 0.8e1 mm sample is more evident than the other samples. At 0.15 h, the desorption rates for the 0.8e1 mm sample, at the 1, 2 and 3 MPa pressures, are 1.192, 2.246 and 5.491 L/min, respectively. The corresponding change between 1 MPa and 3 MPa are 4.299 L/ min. The desorption rates for the 20e25 mm sample, at the 1, 2 and 3 MPa pressures, are 0.677, 0.776 and 0.872 L/min. The corresponding change between 1 MPa and 3 MPa is 0.195 L/ min. The desorption rates for the 130e140 mm sample, at the 1, 2 and 3 MPa pressures, are 0.385, 0.613 and 0.665 L/min. The corresponding change between 1 MPa and 3 MPa is 0.28 L/min. The desorption rate of methane from coal samples versus time are fitted to the following Eq. (11).
kt t ta
(11)
where vt and va are the rates of desorption in mL min1 at times t and ta, respectively, and kt is the constant characterizing the desorption process and reflecting the attenuation degree of desorption rate (Banerjee, 1988). Winter and Janas (1996) obtained the same equation during a study of gas emission rates from coal and named the rate of desorption at 1 min as v1. Eq. (11) can be written as follow.
84 78 72 66 60
(2) As adsorption equilibrium pressure increased, the ultimate desorption ratio of methane for coal samples increase. The reason has been explained in the former part.
vt ¼ va
3MPa
343
0
20
40
60
80
100
120
140
Lump size (mm) Fig. 10. The ultimate desorption ratio of coal samples versus lump size.
v1 ¼ va takt
(12)
Eq. (12) can be logarithmically transformed as follow.
Ln va ¼ kt Ln ta þ Ln v1
(13)
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5
0.8-1mm 8-10mm 20-25mm 45-50mm 70-75mm 130-140mm
4 3 2
desorption rate(L/min)
desorption rate (L/min)
5
1 0 0.0
0.2
0.4
0.6 0.8 time (h)
1.0
1.2
0.8-1mm 8-10mm 20-25mm 45-50mm 70-75mm 130-140mm
4 3 2 1 0 0.0
0.2
0.4 0.6 time (h)
1.0
(b) 2 MPa
(a) 1 MPa 6
0.8-1mm 8-10mm 20-25mm 45-50mm 70-75mm 130-140mm
5 desorption rate (L/min)
0.8
4 3 2 1 0 0.0
0.2
0.4 0.6 time (h)
0.8
(c) 3 MPa
Table 5 gives the fitting results of the constant kt and v1. The correlation coefficient is greater than 0.97, showing a great fit. v1 is the initial desorption rate in the first minute of desorption, and kt is desorption rate attenuation index characterizing the ratio between the volume of methane adsorbed in the macropores and cleats in the first minute after the pressure was released and the total desorption volume (Du, 1985). The desorption rate attenuation index and the initial desorption rate for coal samples versus lump size are shown in Figs. 12 and 13, respectively. The values of kt and v1 decrease significantly when the lump size increases from 1 mm to 10 mm. When the lump size exceeds 10 mm, the decrease in kt and v1 is not evident as the lump size increased. Fig. 14 shows a model of methane transport through coal. As can be seen in Fig. 14, transport of methane is only controlled by diffusion when the lump size drops below the coal
D e s o r p tio n r a te a tte n u a tio n in d e x
1.4
1MPa
2MPa
3MPa
1.3 1.2 1.1 1.0 0.9 0.8
0
30
60
90
120
150
Lump size (mm) Fig. 12. Desorption rate attenuation index of coal samples versus lump size.
The initial desorption rate (mL/g·min)
Fig. 11. The desorption rate of the six size fractions of coal samples versus time.
0.30
1MPa
2MPa
3MPa
0.25 0.20 0.15 0.10 0.05 0.00
0
30
60
90
120
150
Lump size (mm) Fig. 13. The initial desorption rate of coal samples versus lump size.
matrix size. The smaller the lump size, the larger the average pore size, which accelerates methane desorption (see Fig. 14(a)). When the lump size exceeds the coal matrix size, the methane migration from the coal matrix to the seepage channels is restricted by cleat apertures, which control the values of kt and v1 (see Fig. 14(b)). This model can also explain why gas outbursts are always accompanied by small-scale compressively geological structures where mylonitic coals often occur. Because mylonitic coals are highly deformed and create mylonite of particle sizes which release large quantities of gas very rapidly (Xue et al., 2012), it is prone to outburst when combined with their low strength. Williams and Weissmann (1995) believed that the most important parameter of an outburst is gas desorption rate, in conjunction with the gas pressure gradient ahead of the face. In addition, the desorption rate attenuation index is independent of pressure, while the initial desorption rate increases with increasing pressure.
J. Guo et al. / Journal of Natural Gas Science and Engineering 20 (2014) 337e346
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Fig. 14. A model of methane transport through coal: (a) the lump size drops below the coal matrix size; (b) the lump size exceeds the coal matrix size.
3.3.3. Effect of lump size on methane diffusivity The representation using the bidisperse diffusion model is plotted along with the experimental data in Fig. 15 as a demonstration of the quality of the modeling results and the parameters are summarized in Table 6. It can be seen from Table 6 that macropore diffusivity decrease with lump size increase for the same pressure step and then change little when the lump size is larger than 25 mm; micropore diffusivity decrease with lump size increase and then change little when the lump size is larger than 10 mm. Also methane diffusivities tend to increase with pressure increase when the lump size is constant. This observation agrees with the findings by Smith and Williams (1984a,b). Moreover, the b value is relatively small because b represents the ratio of gas adsorption in the macropores as defined in the bidisperse model. In order to illustrate more clearly how lump size affects the diffusivities, the average is taken to eliminate the effect of pressure on diffusivity and the results are shown in Figs. 16 and 17. Figs. 16 and 17 show the effects of lump size on macropore diffusivity and micropore diffusivity, respectively. It can be seen from these figures that lump size has significant impact on both averaged macropore and micropore diffusivities. The averaged macropore diffusivity decreases from 0.29 s1 to 5.74 103 s1 when the lump size increases from 1 mm to 25 mm; the average micropore diffusivity decreases from 1.38 103 s1 to 5.99 106 s1 when the lump size increases from 1 mm to 10 mm. This suggests that the impact of lump size on gas diffusion in pores with different size is different. A possible explanation is that the macropores are disturbed in the first place as lump size decreased.
Table 6 Methane diffusivities for the six size fractions of coal samples. (s1)
(s1)
Lump size/mm
Pressure (MPa)
b
Di R2i
0.8e1
1 2 3
0.0163 0.0175 0.0172
6.88 104 1.63 103 2.12 103
0.19 0.32 0.36
0.9812 0.9842 0.9841
8e10
1 2 3
2.81 103 1.62 103 2.86 103
1.87 106 7.56 106 8.53 106
0.011 0.016 0.025
0.9275 0.9255 0.9482
20e25
1 2 3
1.38 103 1.17 103 1.22 103
2.71 106 5.12 106 7.46 106
2.35 103 6.61 103 8.25 103
0.9237 0.9435 0.9739
45e50
1 2 3
1.01 103 2.02 103 1.54 103
2.28 106 2.86 106 4.96 106
1.56 103 3.73 103 9.01 103
0.9486 0.9524 0.9609
70e75
1 2 3
1.16 103 1.46 103 1.52 103
1.14 106 1.63 106 2.21 106
1.08 103 1.62 103 4.93 103
0.9283 0.9756 0.8706
130e140
1 2 3
2.72 104 2.29 104 9.51 104
1.09 106 2.96 106 3.43 106
1.10 103 2.27 103 6.41 103
0.9510 0.9430 0.9395
Da R2a
Correlation coefficient
In addition, it can be seen from the correlation coefficient that the bidisperse model cannot represent the desorption rate behavior well for these coal samples except for 1 mm grain size. Because for the other lump size coal samples, small transport pathways in the form of cleats or cracks can trigger fast gas distribution around the matrix blocks (Busch and Gensterblum, 2011), gas transport
0.30 0.25
2
-1
Da/Ra (s )
0.20 0.15 0.10 0.05 0.00 0
20
40
60
80
100
120
140
Lump size (mm) Fig. 15. Sample experimental results of desorption rate at 2 MPa.
Fig. 16. Average macro-diffusivity of coal samples versus lump size.
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0.0014 0.0012 0.0008
2
-1
Di/Ri (s )
0.0010 0.0006 0.0004 0.0002 0.0000 -0.0002
0
20
40
60
80
100
120
140
Lump size (mm) Fig. 17. Average micro-diffusivity of coal samples versus lump size.
through the coal fracture system, which is dependent upon relative permeability, is therefore considered to be a greater control upon long-term desorption. 4. Conclusions A combined light microscopic measurement, mercury porosimetry, and methane desorption kinetics analysis have been conducted on different sized anthracite to determine the effects of lump size on methane desorption from coal. The following conclusions can be made: (1) For the lump coals, three pressure regimes in the process of mercury injectiondlow (P < 0.1 MPa), intermediate (0.1 P < 5 MPa), and high (5 MPa), are indicated by distinct values of the fractal dimension; in order of increasing pressure, these correspond to cleat penetration, pore penetration, and coal matrix compressibility. (2) When the coal size drops below the coal matrix size, the pore volume and average pore size increase with decreasing grain size. When the lump size exceeds the coal matrix size, the characteristics of fracture and pore structure of anthracite, such as cleat volume, cleat aperture, cleat porosity, matrix pore volume, the matrix average pore size and matrix porosity, are basically invariant. (3) With increasing lump size, the desorption time constant changes according to positive exponential rules and approaches a constant value after a lump size fraction of 70e75 mm; the final desorption ratio, the desorption rate in the first minute, the attenuation index of desorption rate and gas diffusivity decrease significantly and then change little when the lump size exceeds the coal matrix size. Acknowledgments This research was supported financially by the National Natural Science Foundation of China, grant No. 51174141 and 50974093. References Airey, E.M., 1968. Gas emission from broken coal: an experimental and theoretical investigation. Int. J. Rock Mech. Min. Sci. 5 (6), 475e494.
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