Transp Porous Med (2016) 111:479–497 DOI 10.1007/s11242-015-0605-7
Investigating the Effects of Seepage-Pores and Fractures on Coal Permeability by Fractal Analysis Yidong Cai1 · Dameng Liu1 Yao Che1 · Zhihua Liu1
· Zhejun Pan2 ·
Received: 29 April 2015 / Accepted: 12 November 2015 / Published online: 27 November 2015 © Springer Science+Business Media Dordrecht 2015
Abstract Permeability is one of the key petrophysical properties for the coalbed methane (CBM) reservoirs, which directly impact the CBM production rate and the amount of CBM that can be ultimately recovered. Due to the complex and heterogeneous nature of coals, an accurate determination for permeability of coals is required. Coal permeability is often determined by fractures (or cleats), which correlates with the aperture of cleats and cleats frequency. However, the gases flow path in coals covers fractures (or cleats), and pores with pore width >100 nm; thus, the effect of pores on permeability should not be neglected, especially in the process of outgassing for methane release from pores over 100 nm (defined as seepage-pores) in the coal seams. Understanding of this issue is limited. Therefore, the determination of the pore size distribution in coal cores was conducted by using mercury intrusion porosimetry. With a specific interest in larger pores (>100 nm), the larger pores are linked to their contribution to permeability in coal cores with core permeability by the transient pulse method. Based on 33 coal samples with vitrinite reflectance in the range of 0.54–2.99 %, this work examines the seepage-pores contribution on core permeability by using classic geometry and thermodynamics fractal model. Moreover, a pore fractal permeability model was established to acquire the seepage-pores permeability, which can be used to interpret the permeability evolution of coals during coalification. Coal pore surfaces generally have very high heterogeneity with fractal dimension of 2.75–2.96 from thermodynamics model (Dts ), which presents a cubic polynomial relation with coal rank. The fractal dimensions from thermodynamics model show a consistent result, which indicates that the pore size/volume distribution was one of the key parameters affecting seepage-pores permeability. Finally, an ideal coal permeability (including seepage-pores and fractures contributed) evolution model during coalification was proposed and the seepage-pores contributed permeability generally covers ∼10 to ∼30 % of the entire coal permeability.
B
Dameng Liu
[email protected]
1
School of Energy Resources, China University of Geosciences, Beijing 100083, China
2
CSIRO Earth Science and Resource Engineering, Ian Wark Laboratory, Bayview Avenue, Clayton, VIC 3169, Australia
123
480
Keywords
Y. Cai et al.
Seepage-pores · Fractal · Fractures · Permeability · Coal
1 Introduction Coal, a heterogeneous porous material, has a variety of pores and fractures (Close 1993), which develops during the coalification and structural deformation of the coal. The distribution and connectivity of pores and fractures during coalification and structural deformation affect the gas desorption in coal reservoir (Yao and Liu 2012; Liu et al. 2015a, b). There are multiple classifications for pore and fracture system of coal reservoir (Hodot 1966; IUPAC 1982; Cai et al. 2013). The size covers from a few nanometers to over centimeters (Close 1993), which includes the micropores in coal matrix for gas adsorption/diffusion (Pillalamarry et al. 2011; Pan et al. 2015) and the non-uniformly distributed macropores (Cai et al. 2013) and microfractures (Cai et al. 2014a) for Darcy flow. A dual pore system is often used (Clarkson and Bustin 1996; Rodrigues and Lemos de Sousa 2002; Cui et al. 2004; Moore 2012), and there are some coals in which the mesoporosity (102 –103 nm) is limited. However, it can be used as a simple dual porosity in this work. We expanded the micropores scale in larger mesopores. To better understand the effects of pores and fractures on gas permeability, the classification for pore size (Hodot 1966) is used: micropores (<100 nm), mesopores (102 –103 nm), macropores (>103 nm). Based on width (aperture) and length of the fractures, the fractures were divided into four types (Liu et al. 2009). Pore properties are of great importance to gas storage and flow behavior in coal (Pan et al. 2010). Adsorption pores (generally <100 nm) are critical for coalbed methane (CBM) adsorption and diffusion. Seepage-pores (>100 nm) are important permeable pathways for gas and water migration during CBM production (Cai et al. 2013) and gases (such as CO2 and N2 ) used to enhance coalbed methane. Although technologies such as X-ray computerized tomography imaging (Karacan and Okandan 2001), high-resolution transmission electron microscopy (Harris and Yust 1976), small-angle X-ray scattering (Mitropoulos et al. 1998; Cai et al. 2014b), smallangle neutron scattering (Radlinski et al. 2004), nuclear magnetic resonance spectroscopy (Yao et al. 2010) and magnetic resonance imaging (Ramanathan and Bencsik 2001) can be used to investigate the pore characteristics, mercury porosimetry combined with fractal theory (Cai et al. 2011a) is still the foremost method to describe the pore structure quantitatively. Fractal characteristic of mesopores and fissures in coal is quantitatively determined by using fractal method (Xie 1996; Zhao et al. 1998). The classic geometry (Menger sponge model) model (Mandelbrot 1983) and thermodynamics model (Zhang and Li 1995) have distinct characteristics, respectively, in coal pores research. The classic geometry fractal model is based on the geometric characteristics, and the thermodynamics model originated from the energy characteristics when mercury was intruded into the pores. Both quantitative fractal dimensions of coal pores can reflect the pore structure, adsorption/diffusivity and seepage-pores permeability (Yao et al. 2009; Zhang et al. 2014; Othman and Helwani 2010). In this work, a classic fractal model coal pore size/volume distribution (PS/VD), pore structures, and microfractures of coal cores for the different rank coals from the North China and Northeast China were used to assess the isolate effect of the pores on gas flow capability. An integrated method to characterize the above pore and fracture features were applied: optical microscopy was used to acquire the maceral composition and the apertures, length and frequency of micro-fractures; and N2 adsorption/desorption at 77 K was conducted to acquire the Brunauer–Emmett–Teller (BET) specific surface area
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(Brunauer et al. 1938; Liu et al. 2009); mercury porosimetry is used to study the pore structure including PS/VD and connectivity; the permeability of core samples were acquired by using transient pulse technique of helium; finally the seepage-pores contributed permeability were calculated with fractal model, and its impact on core permeability was evaluated.
2 Sampling and Laboratory Works 2.1 Sampling Sites and Coal Analysis The high (1.72–2.99 % in Ro,m ), medium (1.2–1.68 % in Ro,m ) and low (0.54–1.19 % in Ro,m ) rank coals are from the Qinshui, Ordos and Sanjiang coal bearing basins as listed in Table 1, respectively. Standard coal analyses and N2 adsorption/desorption experiments were conducted as previous research (Yao and Liu 2009; Cai et al. 2011a, 2013). The coal types were mostly semi-bright and bright coals. The coal rank ranges from high-volatile bituminous coal to anthracite (0.54–2.99 % in Ro,m ). The area based coal composition reveals that vitrinite ranges from 0.5 to 93.6 %, inertinite varies from 0.6 to 93 %, liptinite changes from 0 to 18.2 % and minerals ranges from 0.1 to 23.2 %. Proximate analysis indicates 0.15–2.47 % moisture, 4.4–43.57 % ash yield, 44.4–85.72 % carbon and 2.35–8.76 % hydrogen as listed in Table 1. Based on the width and length of the fracture, the fracture was divided into three types (Cai et al. 2015): type A + B with W 5 µm and L 10 mm, type C with W 5 µm and L 300 µm, and type D with W 5 µm and L 300 µm. The micro-fractures were acquired by optical microscope through statistic analysis on polished block coal samples with an area of 3 × 3cm2 , reveals that the coals include 0–8 (fracture frequency per 9 cm2 ) for type B, 6–61 (fracture frequency per 9 cm2 ) for type C and 1–312 (fracture frequency per 9 cm2 ) for type D as documented in Table 2. The frequent micro-fractures will influence the permeability.
2.2 Mercury Intrusion Porosimetry, Porosity and Permeability The experiments procedure of mercury intrusion porosimetry (MIP) was detailed documented in previous research (Cai et al. 2011a). Assuming pores are composed with a variety of cylindrical pores, the relationship between the pore radius and pressure can be revealed by the Washburn Equation (Washburn 1921): Pc = 2δ cos θ/rc
(1)
where Pc is the absolute injection pressure (MPa), which increased from 0 to 35 MPa; rc is the pore radius (µm) when mercury enters at the pressure Pc (MPa); θ is the contact angle (assumed to be 140◦ ); and δ is the interfacial tension of mercury (0.48 J/m2 ). The basic parameters including coal petrophysics, mercury porosimetry were documented in Table 2. The porosity of cylindrical coal core that cored into bedding plane with 2.5 cm in diameter (length >2.5 cm) was measured using helium expansion. Permeability of coal core was acquired by using transient pulse technique of helium with pore pressure 1000 psi as previous work (Cai et al. 2011b).
123
123
1.19
1.20
Sanjiang
Sanjiang
L17
L20
1.06
1.37
1.42
Qinshui
M7
1.48
1.5
1.56
1.59
Qinshui
Qinshui
Ordos
Qinshui
Ordos
Ordos
Ordos
M14
M17
M20
M22
M23
M25
M28
1.68
1.63
1.60
1.44
Qinshui
Qinshui
M9
M12
1.25
Qinshui
Ordos
M1
M3
1.17
1.13
Sanjiang
Qinshui
L14
0.94
0.93
L16
Sanjiang
L11
0.89
Ordos
Sanjiang
L9
L10
0.84
0.87
Sanjiang
Ordos
L5
L7
0.54
0.65
Sanjiang
Sanjiang
L1
L2
Ro,m (%)
Sampling sites
Sample no.
2
71
11
8
11
2
3
2
3
3
3
10
47
47
9
91
15
11
2
2
9
15
18
Seam no.
SB
SB
SD
B
SB
SB
B
B
SB
SB
B
SB
SD
SD
SB
SD
D
D
SB
SB
SD
SD
D
Coal type
87.0
82.9
46.7
88.5
80.7
72.5
70.4
25.9
80.2
82.9
66.8
52.4
81.4
81.5
75.0
79.7
34.0
75.9
69.4
48.4
76.8
78.3
70.5
11.7
9.7
13.5
49.1
9.4
15.1
23.9
21.3
72.2
15.9
14.1
29.5
38.3
16.3
16.1
24.3
19.1
62.7
5.6
19.8
39.2
17.5
10.3
17.3
0.4
1.1
1.2
0.9
3.0
3.4
3.1
0.6
1.6
0.0
1.3
7.7
1.6
1.5
0.0
0.7
1.7
18.2
10.0
9.7
4.8
11.1
0.5
2.9
2.5
3.0
1.2
1.2
0.2
5.2
1.3
2.3
3.0
2.4
1.6
0.7
0.9
0.7
0.5
1.6
0.3
0.8
2.7
0.9
0.3
11.29
28.88
*
23.41
13.19
16.98
6.08
10.55
13.40
17.38
9.70
13.63
4.48
15.37
15.27
4.52
21.81
18.00
10.14
5.87
6.22
13.42
9.81
0.53
*
0.16
0.32
0.25
0.26
0.27
0.54
0.33
0.15
0.26
0.40
0.94
0.90
0.21
0.92
0.72
1.02
1.06
1.19
1.43
1.48
2.47
Mad
6.83
*
7.33
4.06
5.77
3.89
4.60
5.36
2.88
4.40
3.94
4.23
5.65
5.56
5.43
6.02
5.74
7.51
7.35
7.06
9.01
9.07
11.63
Vad
60.29
*
63.88
76.88
71.22
85.72
80.52
76.72
75.37
80.85
78.13
84.20
74.87
74.27
82.98
67.50
71.50
76.28
80.87
80.95
71.64
74.88
70.05
FCd
Aad
M
Proximate and ultimate analysis results (%) L
V
I
Coal maceral (%)
Table 1 Sampling sites and petrographic analysis results of the different rank coals
3.07
*
3.21
3.32
3.39
3.75
3.70
3.56
3.64
4.20
3.77
4.45
4.06
4.00
4.68
3.75
4.04
5.05
4.57
4.35
4.50
4.76
4.82
Hdaf
482 Y. Cai et al.
Qinshui
Qinshui
H12
H13
2.99
2.46
2.28
2.26
2.18
1.89
1.88
1.81
1.77
1.75
1.72
Ro,m (%)
5
2
2
2
3
3
3
3
15
15
15
Seam no.
B
B
B
B
SB
SB
SB
SB
B
B
B
Coal type
58.9
43.9
67.6
75.7
0.5
89.9
87.8
93.4
89.5
67.1
90.1
7.6
38.3
53.6
24.9
21.4
76.3
8.0
11.4
5.2
9.0
32.8
0.0
0.0
0.0
5.3
1.2
0.0
0.0
0.0
0.0
0.0
0.0
2.3
2.8
2.5
2.2
1.7
23.2
2.1
0.8
1.4
1.5
0.1
8.12
*
*
*
*
15.32
29.40
19.43
17.71
11.22
18.60
*
*
*
*
0.98
0.54
0.41
0.37
0.60
0.41
0.41
Mad
*
*
*
*
5.20
6.24
3.75
8.71
3.55
4.43
4.27
Vad
*
*
*
*
75.06
60.64
72.70
69.63
80.14
72.71
82.72
FCd
Aad
M
Proximate and ultimate analysis results (%) L
V
I
Coal maceral (%)
*
*
*
*
3.02
2.82
3.46
3.26
3.38
3.28
3.40
Hdaf
*, no acquired data; V, vitrinite; I, inertinite; M, minerals; Ro,m , mean max vitrinite reflectance; D, dull; SD, semi-dull; B, bright; SB, semi-bright; Aad, ash (as received basis); Mad, moisture (as received basis); Vad, volatile (as received basis); FCd, fixed carbon (dry basis); Hdaf, hydrogen (dry ash for free basis)
Qinshui
Qinshui
H10
H11
Qinshui
Qinshui
H8
H9
Ordos
Ordos
H5
Qinshui
H4
H7
Qinshui
Qinshui
H1
H2
Sampling sites
Sample no.
Table 1 continued
Investigating the Effects of Seepage-Pores and Fractures on... 483
123
123
1.34
1.59
1.6
1.63
1.68
M22
M23
M25
M28
1.50
1.56
M17
M20
1.48
M14
1.54
1.42
1.44
1.37
M7
M9
1.25
M3
M12
1.33
1.20
M1
1.33
1.53
1.82
1.44
1.31
1.42
1.31
0.37
1.42
1.29
1.28
1.32
1.17
1.19
L17
1.37
1.32
1.40
1.29
1.32
1.24
1.49
1.80
3.80
1.00
2.60
6.30
2.40
2.30
7.30
1.70
4.70
4.70
5.70
5.10
3.20
1.33
7.80
1.30
1.80
2.90
1.60
3.30
1.49
0.06
0.10
5.52
0.92
1.13
0.03
1.80
0.05
0.35
0.30
0.32
0.09
3.92
2.35
0.32
0.04
0.63
0.18
0.02
2.26
2.21
0.43
6.79
1.85
0.64
0.23
1.99
7.13
2.91
3.98
4.77
8.79
6.52
11.96
0.54
0.67
1.96
2.72
1.85
2.98
4.83
1.62
0.54
1.77
Spore
2.00
0.15
3.60
2.31
2.94
2.86
3.14
3.07
4.04
3.12
2.64
2.12
0.02
0.02
2.52
0.15
0.15
3.15
2.80
0.30
0.08
0.20
SC
Kt
De
Po
MIP results
Petrophysical results
L20
1.06
1.13
0.94
L11
L14
0.89
L9
L16
0.84
0.87
L5
L7
0.54
0.65
L1
L2
Ro,m (%)
Sample no.
Table 2 Petrophysical and mercury intrusion porosimetry results of different rank coals
31.75
21.72
32.27
31.89
31.88
32.21
32.18
30.56
3.71
32.44
31.82
31.72
3.84
27.01
32.29
19.17
23.59
31.94
32.61
32.56
7.67
19.83
MPS
49.99
74.31
41.69
44.53
52.64
67.61
38.94
69.57
28.18
39.37
51.27
46.35
33.29
49.17
39.18
76.75
66.27
51.50
71.71
51.89
53.31
58.61
EMW
0
0
0
3
2
0
1
1
8
2
1
1
0
0
3
0
3
3
2
1
4
0
B
13
18
8
14
21
11
16
10
61
18
8
10
14
14
17
6
24
17
19
29
18
18
C
Microfractures/per 9cm2
12
30
2
53
27
5
19
3
58
29
3
44
25
25
63
67
213
51
42
119
52
44
D
484 Y. Cai et al.
2.99
H13
1.46
1.39
1.37
1.42
1.39
1.42
1.38
1.39
1.31
1.40
1.61
6.00
1.90
1.70
1.30
2.60
5.40
2.20
5.30
4.90
7.40
3.20
0.92
0.01
0.02
0.15
3.44
0.04
0.16
0.19
2.98
0.02
0.15
0.71
11.34
6.98
3.47
15.95
6.85
8.52
22.80
4.72
13.96
8.70
2.99
2.70
3.06
2.41
1.66
2.87
2.09
1.90
2.35
2.42
1.57
MIP results Spore
SC
Kt
De
Po
Petrophysical results
31.75
32.01
10.37
32.23
31.97
32.27
32.05
32.28
32.14
32.19
32.04
MPS
64.45
78.41
58.82
59.05
70.36
74.27
56.51
61.84
47.35
68.91
51.04
EMW
2
2
3
1
1
1
1
0
3
1
2
B
29
8
21
7
6
16
13
8
43
29
32
C
Microfractures/per 9cm2
28
26
34
11
5
19
10
17
105
43
47
D
De, density (g/cm3 ); Po, porosity (%); Kt, tested permeability (mD); spore, specific surface area (m2 /g); MIP, mercury intrusion porosimetry; SC, sorted coefficient; MPS, mid-value pressure of saturation (MPa); EMW, efficiency of mercury withdrawal (%); type of microfractures includes: A+B, with W ≥ 5µm and L ≤ 10mm; C, with W ≤ 5µm and L ≥ 300µm, and D, with W ≤ 5µm and L ≤ 300µm; Petrophysical results and MIP results were acquired at air dry basis; Microfractures results were tested on as received basis
2.28
2.46
H11
2.26
H10
H12
1.89
2.18
H9
1.88
H7
H8
1.77
1.81
H4
H5
1.72
1.75
H1
H2
Ro,m (%)
Sample no.
Table 2 continued
Investigating the Effects of Seepage-Pores and Fractures on... 485
123
486
Y. Cai et al.
3 Model Theories 3.1 Fractal Dimension Calculation of Coal Pore Space 3.1.1 Geometry Model A variety of coal pores have geometric fractal characteristics as confirmed by previous research (Mandelbrot 1983; Jacquin and Adler 1987). Relation between dVr /dr and r was proposed (Pfeifer and Avnir 1983): log(−dVr /dr ) ∝ (2 − D) log(r )
(2)
where r is the pore radius (µm) at the pressure P (MPa) for mercury intrusion; D is the pore fractal dimension. Equations (1) and (2) can be synthesized, then get the Eq. (3) log(dV p /d p) ∝ (Dgs − 4) log( p)
(3)
where V p is the cumulative injection volume at a given pressure p. Therefore, the pore fractal dimension Dgs can be acquired by: Dgs = 4 + A. A is the slope of Eq. (3).
3.1.2 Thermodynamics Model The thermodynamics model was detailed explained and used to evaluate the pore structure in previous research (Cai et al. 2011a). Thus the construction of this model here will be briefly discussed. The increment of mercury squeezed into the pores (Q n ) has a correlation with the increment of the surface energy (Wn ) (Zhang and Li 1995). And then, Eq. (4) will be acquired: ln(Wn ) = C + ln(Q n ); C = ln C (4) Using mercury intrusion data Vi , Pi of certain samples and ri which can be predicted by Eq. (1). After that, the Eq. (4) was revised for simple calculation (Rootare and Prenzlow 1967; Zhang et al. 2006): 1/3 ln Wn /rn2 = C + Dts × ln Vn /rn (5) The surface fractal dimension Dts reflects the roughness of the pore surface.
3.2 Calculated Permeability with Pore Fractal Dimensions The relationships between permeability and porosity, fractal dimensions were acquired based on Kozeny–Carman equation (Kozeny 1927; Carman 1937; Pape et al. 2000): k=
r g2 φ 8 τ
2φ 3τ (1 − φ)
2 D−1
(6)
where rg is the average grain radius; Tortuosity τ can be calculated from φ and Archie’s first law as proposed (Archie 1942):τ/φ = aφ −m , the statistical results of a = 0.7 and m = 2 were used to investigate the seepage-pores in coal. The rg can be replaced by specific surface area Spore , as follows 3 1−φ (7) rg = Spore φ
123
Investigating the Effects of Seepage-Pores and Fractures on...
487
Finally, general permeability–porosity relationship with pore fractal dimension was derived:
1−φ k = 1.607 S por e
2
0.952φ 2 1−φ
2 D−1
(8)
4 Results and Discussions 4.1 Fractal Characteristics for Seepage-Pores 4.1.1 Calculated Fractal Dimensions From the contribution of seepage-pores (>100 nm) on core permeability, the two fractal dimensions Dgs and Dts from classic geometry model and thermodynamics model were applied. Dgs can reflect the volume heterogeneity of coal pores, and Dts can reflect the surface heterogeneity of coal pores (Cai et al. 2011a). Previous research (Friesen and Ogunsola 1995; Mahamud et al. 2003) have confirmed the validity of this classic fractal geometry model and established the correlation of log (dV /d P) and log (P) as shown in Fig. 1. The mercury intrusion porosimetry is performed on the cores from different rank coals. This study confirms 2 ) as the correlation between log (dV /d P) and log (P), with average coefficient of 0.93 (Rgs shown in Table 3. The calculated fractal dimensions from geometry model (Dgs ) range from 2.44 to 3.56. Fractal dimensions of pores from geometry model (Dgs ) are 3.12 for the low-rank coals with standard deviation of 0.38, 2.93 for the medium-rank coals with standard deviation
Fig. 1 The calculation of fractal dimensions from the thermodynamics (left) and geometry (right) models from mercury intrusion data (H 1 high-rank coal, M1 medium-rank coal, L1 low-rank coal)
123
488
Y. Cai et al.
Table 3 Calculated fractal dimensions and permeabilities from two fractal models of the different rank coals Sample no.
Ro,m (%)
Dts
2 Rts
Dgs
2 Rgs
Kct (mD)
PCPPt (%)
L1
0.54
2.956
0.99
3.561
0.98
0.130
30.14
L2
0.65
2.832
0.99
2.985
0.94
0.529
23.93
L5
0.84
2.944
0.99
3.55
0.95
0.504
22.31
L7
0.87
2.886
0.99
2.978
0.95
0.010
62.50
L9
0.89
2.785
0.99
2.769
0.94
0.060
32.68
L11
0.94
2.938
0.99
3.394
0.99
0.110
17.44 67.69
L14
1.06
2.946
0.99
3.407
0.98
0.027
L16
1.13
2.856
0.99
3.383
0.96
1.507
*
L17
1.17
2.861
0.99
2.824
0.95
0.311
13.24
L20
1.19
2.785
0.99
2.443
0.97
2.265
57.78
M1
1.20
2.902
0.99
3.392
0.77
0.019
21.12
M3
1.25
2.781
0.99
2.86
0.86
0.055
17.27
M7
1.37
2.809
0.99
3.126
0.94
0.022
7.19
M9
1.42
2.748
0.99
2.881
0.96
0.059
16.99 29.79
M12
1.44
2.848
0.99
2.952
0.95
0.014
M14
1.48
2.763
0.99
2.642
0.97
0.443
24.62
M17
1.5
2.851
0.99
2.708
0.92
0.008
25.62 9.29
M20
1.56
2.823
0.99
2.9
0.99
0.105
M22
1.59
2.846
0.99
2.908
0.99
67.899
M23
1.60
2.752
0.99
2.577
0.86
0.872
* 15.80
M25
1.63
2.946
0.99
3.39
0.98
0.034
34.24
M28
1.68
2.856
0.99
2.925
0.9
0.028
45.46 32.50
H1
1.72
2.882
0.99
3.127
0.95
0.048
H2
1.75
2.871
0.99
2.881
0.89
0.005
24.18
H4
1.77
2.823
0.99
2.933
0.95
0.211
7.07
H5
1.81
2.852
0.99
2.94
0.9
0.004
2.16
H7
1.88
2.799
0.99
2.87
0.95
0.029
17.74
H8
1.89
2.841
0.99
2.917
0.9
0.008
22.75
H9
2.18
2.89
0.99
3.161
0.86
0.012
0.34
H10
2.26
2.872
0.99
3.194
0.96
0.051
34.26 11.90
H11
2.28
2.87
0.99
3.085
0.95
0.003
H12
2.46
2.882
0.99
2.989
0.94
0.002
28.10
H13
2.99
2.863
0.99
3.022
0.86
0.599
64.79
2 , correlation coefficient for thermodynamDts , fractal dimension calculated from thermodynamics model; Rts 2 , correlation coefficient for geometry ics model; Dgs , fractal dimension calculated from geometry model; Rgs model; Kct , calculated permeability using thermodynamics fractal model; PCPPt , pore-contributed permeability using thermodynamics model; *, abnormal data
of 0.26 and 3.01 for the high-rank coals with standard deviation of 0.12 respectively, which may indicate that the pore structure tends to be uniform at the medium-rank stage due to the compression and geothermal effect. Surface fractal dimensions can reflect the complexity of the coal pore surface; thus, the surface fractal dimensions should vary from 2 to 3. However,
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some of the calculated surface dimensions from geometry model (Dgs ) exceed 3, which are abnormal. There are several possible reasons for the values of surface fractal dimensions beyond 3, which are (1) pore surface between coal particles (Friesen and Ogunsola 1995), (2) pore structure destruction (Ehrburger-Dolle et al. 1994) and (3) pore-equaled fracture surface. The calculated fractal dimensions from thermodynamics model (Dts ) range from 2.75 to 2.96. The values of thermodynamics model (Dts ) are slightly lower than that of geometry model (Dgs ). However, the fractal dimensions from thermodynamics model show a consistent result, which have average surface fractal dimensions of 2.88, 2.82 and 2.85 for the low-, medium- and high-rank coals, respectively.
4.1.2 Fractal Characteristics for the Different Rank Coals The fractal dimension of coal pores means a complexity of the pore structure of coals, which is also related to the coalification and coal composition. There is a cubic polynomial following increasing coal rank. The Dts exhibit a rapid exponential decay with increasing coal rank from 2.96 (0.5 % Ro,m ) to 2.83 (1.5 % Ro,m ), a slow exponential increase with increasing coal rank from 2.83 (1.5 % Ro,m ) to 2.88 (2.9 % Ro,m ) as shown in Fig. 2, which is consistent with the results from the geometry model. Coal has similar crystal structure named basic structure unit (BSU), which is composed of aromatic nucleus composite. The aromatic nucleus composite is mainly aromatic, branched chain of hydrocarbon and the composition of various functional groups. Many oxygen containing functional groups, side chain, bridge bond and hydrogen bond exist in low-rank coal and medium-rank coals, and their structures are loose. Coalification is a process of enriching carbon, dehydrogen and deoxidization process (Stach et al. 1982). Besides the side chains and functional groups have been decomposed to be various hydrocarbons and other small molecules. At the same time, the molecular were rearranged and turned to be denser with increasing coalification and there is a structural alignment and rearrangement. The degree of order increases, and BSU was also increased through the aromatization and polycondensation. During the early stage of coalification (<1.5 % Ro,m ), the aromatic materials coalesce into larger clusters, while the aliphatic fraction is gradually removed or incorporated. Meanwhile, the orientation of the elementary units becomes increasing parallel to the bedding planes as stated by previous research (Orem and Finkelman 2003; Zhang et al. 2014), which caused the inner surface roughness of the pores decrease. The blocking of generated hydrocarbons in micropores could be another possible reason. Therefore, there is a sharp decrease in Dts with increasing rank. And also the moisture and micropores contents may have effects on Dts as showed by previous research (Prinz and Littke 2005; Yao et al. 2008). The stable increase in Dts at the medium to anthracite stage (Fig. 2, with 1.5–3.0 % Ro,m ) may also change with the micropores and maceral compositions in coals. The increasing surface areas produce rougher pore surface and much micropores content (Yao et al. 2008), resulting in more anisotropic pore diameter distribution.
4.2 Pore Structure and Permeability of the Ranked Coals 4.2.1 Measured Core Porosity and Permeability Measured core porosity generally includes pore-contributed and fracture-contributed porosity, which shows a reversed U-shaped relationship with coal rank as shown in Fig. 3. Previous research (Rodrigues and Lemos de Sousa 2002) revealed that the percentage of macropores decreases from 0.7 to >1.4 % Ro,m (e.g., high-volatile to medium volatile bituminous)
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Fig. 2 Fractal dimension distribution of the ranked coals from two fractal models and its correlation (a fractal dimension from thermodynamics model and vitrinite reflectance; b fractal dimension from geometry model and vitrinite reflectance; c linear relation between fractal dimension from thermodynamics model and fractal dimension from geometry model)
and then increases as secondary porosity in higher-rank coal (>3.0 % Ro,m ). Comparing whole coals to whole coals, here the secondary porosity should be the contribution of microfractures. There is also an impact on the cleat frequency due to lithotype. Vitrain tends to be more highly fractured. The average PS/VD of low-rank coals is generally larger than that of high-rank coals (Yao et al. 2011). However, the relationship between pores contributed
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Fig. 3 Helium measured porosity and permeability for the low-, medium- and high-rank coals
porosity and coal rank should present a regular U-shaped correlation as revealed by previous research (Gan et al. 1972; Levine 1993). The high porosity in medium-rank coals should be related to the well-developed micro-fractures as shown in Table 2. However, some samples without developed fractures (such as L20 with low rank, M23 with medium rank, H9 with high rank) have obviously higher permeability, which may be related to high total porosity, high macroporosity and feeder pores. The helium measured core porosity for air-dried coals ranges from 1.0 to 9.3 % with an average of 3.9 %, which exhibits that the coals generally have low porosity compared with the conventional gas reservoirs. Coal porosity, pore volume and frequency are controlled by coal rank and composition (Gan et al. 1972; Mastalerz et al. 2008; Adeboye and Bustin 2013). Vitrinite predominantly contains micropores, and inertinite mostly contains mesopores and macropores based on the pore classification by IUPAC (1982). Permeability as the most important property of the coal reservoir was mainly controlled by pore-fracture system (including seepage-pores, endogenetic and exogenetic cleats) development and direction (Flores 2014). Although the coals may contain significant quantities of gases, the low permeability constrains gas recovery and production. The gas measured core permeability ranges from 0.01 to 20.30 mD with an average of 2.12 mD as listed in Table 2, which demonstrates coal heterogeneity. For coals with permeability greater than 0.2 mD, the permeability correlates with the fracture density and connectivity. Figure 4 shows that the type D and total fracture density have positive relationship with measured core permeability. Normally, the type D fractures (with width 5 µm and length 300 µm) are dominant (with an average of 59 fractures per 9 cm2 ), which are generally well connected. Therefore, the fracture permeability in coal is mainly constrained by the micro-fractures density and connectivity.
4.2.2 Pore Structure and Pore-Contributed (matrix) Permeability Previous research (Liu et al. 2015a) confirmed that the pore structure of coals can be evaluated by measuring and analyzing nuclear magnetic resonance T2 values (the transverse relaxation time) of water in the water saturated cores. The T2 spectrum, which normally ranges from 0.1 to 10,000 ms, provides the PS/VD by Fig. 5. The T2 spectrum at less than 10 ms corresponds to micropores; the T2 spectrum between 10 and 100 ms corresponds to mesopores; while the T2 spectrum at longer than 100 ms corresponds to macropores/microfractures. Relation between increased coal ranks and seepage-pores volume (Liu et al. 2015a) presents a nega-
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Fig. 4 Relationship between varied micro-fractures for the three types (A + B; C; D and total) and coal core permeability (tested)
Fig. 5 Pore distribution with elevated coal ranks (bottom to top) from nuclear magnetic resonance (redrafted from Liu et al. 2015a)
tive correlation through NMR method as shown in Fig. 5, which indicates that seepage-pores have an important contribution to core permeability in the medium and low-rank coals, and thus would be useful for evaluation of seepage-pore permeability. Due to the good correlation between the above two fractal models and the theoretical meaning of Eq. (11), the
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Fig. 6 Calculated total permeability (Kct ) and helium measured permeability (Kt ) with increased coal ranks
seepage-pores permeability was evaluated by using the thermodynamics fractal model. The pore-contributed permeability ranges from 0.002 to 2.265 mD except an abnormal value of 67.899 mD as shown in Table 3, which presents a consistence with previous results of matrix permeability less than 0.1 mD (Flores 2014). And an interesting phenomenon was found that seepage-pore permeability has a decreasing trend with increasing coal rank, which should be closely related to the differential compaction during coalification. Generally, the seepagepores contributed permeability for varied rank coals is less than 2.5 mD, which has strong heterogeneity that varied from coal to coal. Furthermore, the seepage-pores contributed permeability has no obvious correlation with total helium measure core porosity. However, the seepage-pores contributed permeability has a positive relationship with seepage-pores volume, which is consistent with the result from previous research (Cai et al. 2013). Based on the local enlargement of Fig. 6, almost 80 % of the coals have seepage pore-contributed (matrix) permeability of <0.2 mD, which is equivalent to tight gas sand permeability. Therefore, this low permeability has a significant role in the release rate during coalbed methane production, which will cause a long stable and low rate CBM production.
4.2.3 Fracture-Contributed Permeability Based on the data of Table 2, the fracture-contributed permeability ranges from 0.01 to 5.52 mD. The significant difference of micro-fractures density between Pennsylvanian and Permian coals from north China is in relationship to the genesis (Liu et al. 2009), which reported that exogenetic fractures (e.g., micro-fractures formed by tectonic stress) have fracture density of >100 per 9 cm2 with normally developed fracture density of 110–200 per 9 cm2 and ultra developed greater density. Endogenetic fractures (e.g., micro-fractures related to macrolithotype) have fracture density of <100 per 9 cm2 . Both genetically related fractures, except the ultra developed micro-fractures density, have significant relationship with
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Fig. 7 The relation between capillary pressure and mercury saturation (left) and pore size distribution (right) of mercury porosimetry characteristics of the different rank coals with low permeability (L7 low-rank coal, M17 medium-rank coal, H 17 high-rank coal)
permeability with higher fracture density having better permeability (Cai et al. 2011b; Flores 2014). Based on the fracture density data from Table 2, the type D and total fracture density have positive relationship with measured core permeability. The fracture-contributed permeability occupied the predominate position in core permeability, which covers the proportion of core permeability from 32.31 to 99.66 % with an average of 73.52 %. The low value of 32.31 % for sample L11 is due to the few factures existed in the tested coal.
4.3 Permeability Evolution During Coalification Figure 7 shows that the seepage-pores contributed permeability of these three samples have similar pore connectivity and structure. The pore permeability was constrained by the lack of partial large pores (103 –104 nm), which yields the extremely low permeability. For most coals with permeability less than 0.1 mD, the PS/VD and connectivity are relatively poor as shown in Fig. 8. Normally, the pore connectivity and pore size distribution can be determined by mercury intrusion porosimetry. Poor connectivity between pores causes methane cannot easily flow out of the micropores to the macropores or fractures. However, connectivity is a matter of scale, specifically for seepage-pores. Hereby the mesopores are important, which is the interlinkage between multiple micropores that ∼90 % methane absorbed and
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Fig. 8 A sketch map showing the contribution of seepage-pores to the helium permeability ranges from 30 to 10 %
the macropores that the pathway gas flows. Unlike the origin of porosity, which inherently originates within the organic matter and structures, the origins of permeability have proposed dual origins (Flores 2014): (1) inherent to progressive coalification and (2) tectonic stresses during deformation. The coalification has an important effect on seepage-pores contributed permeability, while the tectonic stress may have predominate effect on fracture permeability. Therefore, more focuses should be put on the seepage-pores contributed permeability for the coal reservoirs presented in a stable geologic condition. Figure 8 exhibits a sketch diagram of ideal coal permeability evolution during coalification, which indicates that the seepage-pores contributed permeability decrease with increasing coal ranks. The maximum contribution for core permeability may reach at ∼30 % for the low-rank coal, ∼20 % for the medium-rank coal and ∼10 % for the high-rank coal, respectively. This permeability decreases should be related to the evolution of pore space during coalification process due to mechanical and chemical compaction.
5 Conclusions In this work, a fractal permeability model was established to acquire the seepage-pores permeability based on mercury porosimetry and Kozeny–Carman equation. Fractal characteristics for seepage-pores show that the pore structure of medium-rank coal is more uniform than that of low- and high-rank coals. Measured core porosity shows a reversed U-shaped relationship with coal rank. For coals with permeability greater than 0.2 mD, the permeability generally correlates with the fracture density and connectivity. Seepage-pores contributed permeability has no obvious correlation with total helium measure core porosity, while it correlates with seepage-pores volume. Fracture permeability is constrained by the fracture density and connectivity, which occupied the predominate position in core permeability. Finally, a sketch diagram of ideal coal permeability evolution during coalification is proposed, which indicates that the seepage-pores contributed permeability decrease with increasing coal ranks. The seepage-pores contributed permeability generally covers from ∼10 to ∼30 %; thus, it should not be neglected in some certain coal reservoirs.
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Acknowledgments This research was funded by the United Foundation from the National Natural Science Foundation of China and the Petrochemical Foundation of PetroChina (Grant No. U1262104), the Research Program for Excellent Doctoral Dissertation Supervisor of Beijing (Grant No. YB20101141501), the Fundamental Research Funds for Central Universities (Grant No. 35832015136) and Key Project of Coal-based Science and Technology in Shanxi Province-CBM accumulation model and reservoir evaluation in Shanxi province (Grant No. MQ2014-01).
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