Transp Porous Med DOI 10.1007/s11242-016-0803-y
Experimental Investigation on the Permeability Evolution of Compacted Broken Coal Tingxiang Chu1,2 · Minggao Yu1 · Deyi Jiang1
Received: 10 July 2016 / Accepted: 25 November 2016 © Springer Science+Business Media Dordrecht 2016
Abstract Given the importance of airflow seepage properties to coal self-oxidation in gob, this paper develops a method and self-designed apparatus to assess seepage properties of compacted broken coal. This study mainly focuses on the strain, porosity and permeability evolution under the different conditions of particle size, vertical stress and temperature. The studied results show: (1) The strain, porosity and permeability were enlarged when the particle size increased under the same loading stress. The porosity and permeability reduced when the vertical stress increased. (2) The non-Darcy coefficient was negative in all tests, but the absolute value of the non-Darcy coefficient generally increased when the vertical stress increased. (3) The experiment results indicated that the larger the particle was, the easier to be compacted. The larger the grain diameter was, the lower the porosity and permeability were, which shown that the void volume in broken coal with larger grain diameters could be easily compacted. (4) The permeability was reduced when the temperature increased, which indicated the permeability of the compacted broken coal decreased during low-temperature oxidation in gob. (5) By the effects of stress and the particle size diameter on the porosity and permeability, the vertical stress recovery and generally increase are advantageous to reduce the porosity and permeability in gob. It is favorable to reduce the porosity and permeability and prevent coal self-heating by reducing the degree of fragmentation and percentage of small particles or consolidate the small particles. Keywords Broken coal · Gob · Particle size · Non-Darcy flow · Compaction · Seepage
B
Tingxiang Chu
[email protected]
1
State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, People’s Republic of China
2
School of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo 454003, People’s Republic of China
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1 Introduction Spontaneous combustion of coal occurs the most frequently in gob (Kuenzer and Stracher 2012). This combustion is a self-heating reaction between broken coal and air (Yuan and Smith 2008). Once the coal temperature increases to a critical temperature, the broken coal would begin to smolder or burn (Taraba and Michalec 2011; Zhu et al. 2013). A large number of factors influence the spontaneous combustion of coal in gob, including internal and external factors (Song et al. 2014). Among these factors, the air leakage is the major factor during mining activities that triggers coal fires. One of the necessary conditions for the spontaneous combustion of coal is the suitable oxygen concentration, which depends on air leakage. The permeability determines the air seepage characteristics in gob. According to the spontaneous combustion of coal, the oxygen volume fraction and distribution have a close relationship with the seepage field in gob (Xia et al. 2015). Therefore, the occurrence and development of coal fires are concerned with the process of air seepage in gob; however, the state of air seepage is affected by the permeability distribution in gob. Due to overburden rock stress recovery, permeability dynamically changes in gob because of the overlying rock sinking and the stress redistribution during the working face advancing. A number of studies have investigated the mechanics of strata deformation which was induced by underground mining (Singh and Kendorski 1981; Kesseru 1984; Singh et al. 1986; Galvin 1987a, b). Forster and Enever (1992) produced a practical hydrogeological model for supercritical long-wall panels. This model is reproduced as shown in Fig. 1, and the authors reported the permeability increased with up to three orders of magnitude in the fractured zone. Karacan (2010) presented a novel method for calculating porosity and permeability based on the size distribution of broken rocks in the long-wall gob. Schatzel et al. (2012) described a study performed at a mine site and provided direct measurements of long-wall mining-induced the fluid flow properties changed in the overlying strata. Adhikary and Guo (2015) conducted a study of in the roof strata near the long-wall gob and indicated more than 1000-fold increase in permeability due to long-wall mining. Equilibrium can be developed in the disturbed overburden with the consolidation of the caved zone after mining operations (Pappas and Mark 1993). In such cases, the geological
Fig. 1 Hydrogeological model proposed for the central coast by Forster and Enever (1992)
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Experimental Investigation on the Permeability Evolution...
conditions and extraction percentage of underground mines (Blodgett and Kuipers 2002; Meng et al. 2011; Miao et al. 2011; Meng and Hou 2012; Bai et al. 2013) are considered. Because the seepage properties of broken rocks play an important role in mining engineering, it is also important to consider the seepage flow characteristics of the broken rocks in caved zones under constant overburden strata loading (Ding et al. 2014). The gob is formed after the advance of working face, and it is filled with the broken rocks and residual coal. There are a certain amount of broken coal reserved in gob because of the limited recovery ratio and the thickness of coal seam. Especially, there is much more residual coal in the thick coal seam of fully-mechanized working face. In addition, the residual coal has a certain height in gob because of the bulking effects, and the residual coal can provide the material basis for the spontaneous combustion in gob. According to the spontaneous combustion of coal, the seepage properties of broken coal are important to coal self-oxidation during compaction process, so it is important to study the permeability evaluation of compacted broken coal. Recently, researchers have focused on the permeability of compacted broken rocks. The seepage model of fractured rock mass was established, and the basic relation of the rock mass effective stress and seepage flow was obtained (McKee et al. 1988; Zhang et al. 2007). Stress-dependent permeability has been extensively studied in fractured rocks (Zimmerman and Bodvarsson 1996; Zimmerman 2000; Min et al. 2004; Liu and Rutqvist 2010). A previous study (Li et al. 2005; Ma et al. 2014, 2016) investigated the permeability measurement of the water flow in crushed rocks. The flow properties of a non-Darcy flow in crushed rocks were obtained, and it showed that the water seepage in crushed rocks no longer obeys the Darcy law but obeys the Forchheimer equation. As shown above, the permeability will be changed because of the stress redistribution after caving, and the vertical stress plays an important role in the permeability evolution. Many studies mainly focused on the water seepage, but few have discussed the relationship between compacted broken coal and spontaneous combustion of coal. Driven by the importance of the non-Darcy seepage properties of airflow in broken coal to coal self-oxidation, this paper is based on the spontaneous combustion of coal in gob, and developed a method that included the non-Darcy condition for measuring, calculating and quantifying the influences of multiple factors on the seepage properties of broken coal. First, the theoretical relation between permeability and coal self-oxidation was presented. Section 2 introduced a self-designed permeability and oxidation test apparatus for compacted broken coal. Section 3 introduced the detailed testing method and procedure. An experimental study on broken coal under the influence of multiple factors and a discussion of the test data were given in Sect. 4. Finally, Sect. 5 concluded the implications of these findings.
2 Forchheimer Equation and Coal Self-Oxidation Generally, the Forchheimer equation is used to describe the relationship between the seepage speed and pressure gradient in broken rocks. This equation can be used to describe the spontaneous combustion of coal in gob (Xia et al. 2014), and the equation is shown as Eq. (1). − ∇P =
cfρ μ V + √ V |V | κ κ
(1)
where P is the mixed gas pressure in gob (MPa); μ is the mixed gas kinematic viscosity (m/s); κ is the permeability, (m2 ); V is seepage speed (m/s); ρ is the density of gas in gob (kg/m3 ); and c f is the gas drag coefficient, dimensionless.
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Given the experimental data processing is convenient, the √fκ in Eq. (1) can be replaced by a factor β, which is equivalent, and then Eq. (1) can also be written as follow. − ∇P =
μ V + ρβV 2 k
(2)
where β is defined as the non-Darcy’s coefficient. According to the process of the coal self-heating in gob, the oxygen volume fraction, the thermal conductivity and the heat release have a close relationship with the seepage field in gob (Xia et al. 2015).The spontaneous combustion of the coal has something to do with the air seepage in gob, and the permeability is one of the key factors during the coal fire process in gob.
3 Test Principles and Method The permeability distribution of broken coal is effected by multiple factors in gob. Studying the permeability evolution of the compacted broken coal is necessary to the coal selfoxidation. So, it is important to base on the environment of the broken coal in gob and develop a reasonable experiment scheme, which is significant for determining the evolution of the permeability.
3.1 Equivalent Mechanical Environment According to the mine pressure theory, the vertical stress will gradually increase while the working face mining, and cause the void volume, the porosity and permeability gradually decrease due to the vertical stress recovery. The residual coal is generally compacted under the overlying strata, and the equivalent mechanical environment of the residual coal can be seen as lateral fixed displacement and only compacted by vertical stress in gob.
3.2 Experimental Facility and Scheme 3.2.1 Experiment Facility Basing on the stress environment of the residual coal in gob, a self-design experimental facility was shown in Fig. 2. Under different particle sizes, different moisture contents, different temperatures and different stresses, various comprehensive tests on the permeability evolution and spontaneous combustion of coal can be carried out by this device. The diameter of the coal sample room is 10 cm, with the maximum height of the sample room as 20 cm, and the cavity cross-sectional area as 0.00785 m2 . The maximum vertical loading strength is 30 MPa, with the accuracy as 0.1 MPa. The displacement sensor precision is 0.01 mm, the gas pressure measurement precision is 0.1 KPa and flow measurement accuracy is 0.001 L/min. The temperature controller can be set with the constant or programmed temperature, the highest heating temperature is 300 ◦ C and the elevation of the temperature gradient is adjustable. Three temperature sensors with the precision as 0.1 ◦ C is used to collect the temperature of the furnace body and coal sample. And the gas chromatography device with the precision as 10−9 is use to detect the outlet gas volume fractions, including N2 , O2 , CO, CO2 and Cm Hn .
123
Experimental Investigation on the Permeability Evolution... Fig. 2 Experiment facility for studying compacted broken coal. 1 Pore pressure test, 2 displacement test, 3 emperature control and monitoring, 4 flow meter, 5 sample room, 6 pressure regulating valve, 7 piezometer, 8 piston, 9 pressure pump
3.2.2 Broken Coal Samples Broken coal samples were gathered from the caved zone of the Gengcun Coal Mine in Henan Province of P.R. China. Due to the principle of the grading scale of rock and soil mechanics, and combining with the diameter of the device, the particle size of coal samples was no more than 20 mm. First, the naturally dry coal samples were selected with diameters <20 mm, and then, the samples were separately screened into groups with diameters of 1–3, 3–6, 6–10, and 10–15 mm. Finally, three mixed coal samples were established under the weight ratio. The 1–3 and 3–6 mm coal samples were mixed with a mass ratio of 1:1 as the 1–6 mm composite sample was, and the 1–3, 3–6 and 6–10 mm coal sample were mixed at a mass ratio of 1:1:1 as the 1–10 mm composite sample was. The 1–3, 3–6, 6–10 and 10–15 mm coal samples were mixed at a mass ratio of 1:1:1:1 as the 1–15 mm composite sample was. The particle groups of the broken coal were mixed according to the grain size distribution shown in Table 1. The broken coal samples were shown in Fig. 3 after separation. The coal actual density was 1.55 × 103 Kg/m3 .
3.2.3 Test Scheme 1. The permeability evolution of the compacted broken coal only considers the diameter, temperature and loading stress during this testing process. The moisture content and other multi-factors will be studied later. 2. Use nitrogen as the seepage material, nitrogen with density ρ N2 = 1.25 kg/m3 and kinetic viscosity μ = 1.76 × 10−5 (Pa/s−1 ) at room temperature (approximately 23 ∼ 27 ◦ C). The kinetic viscosity of N2 at different temperatures is shown in Table 2.
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T. Chu et al. Table 1 Broken coal particle diameters and mass ratio of the samples Sample
Total mass (g)
Mass to each particle size (g) 1–3 mm
3–6 mm
6–10 mm
a
1200
b
1200
c
1200
d
1200
e
1200
600
600
f
1200
400
400
400
g
1200
300
300
300
10–15 mm
1200 1200 1200 1200
300
Fig. 3 Broken coal samples separated by a screening. Particle sizes: a (1–3 mm); b (3–6 mm); c (6–10 mm) and d (10–15 mm)
3. Load vertical stress at 0, 3, 6, 9, 12, 15, 18 MPa for the seven samples and the pressure head at 0.2, 0.25, 0.3, 0.35 MPa, respectively, and the seepage parameters were tested four times at every stress loading level at room temperature. 4. Analyze coal sample “e” permeability at constant temperature of 40, 50, 60, 70, 80 ◦ C, respectively. The vertical stress was gradually loaded at 0, 2, 4, 6, 8, 10, 12, 15 MPa under every temperature. Under each vertical stress condition, the seepage parameters were tested three times which the pressure heads were set at 0.2, 0.25, 0.3 MPa. Replacement
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Experimental Investigation on the Permeability Evolution... Table 2 Kinetic viscosity (μ) of N2 at different temperatures Temperature (◦ C)
μ (Pa/s−1 (10−5 )) Temperature (◦ C)
μ (Pa/s−1 (10−5 )) Temperature (◦ C)
μ (Pa/s−1 (10−5 ))
0
1.664
30
1.804
70
1.983
5
1.686
35
1.827
75
2.004
10
1.711
40
1.845
80
2.026
15
1.735
50
1.895
85
2.047
25
1.76
60
1.939
90
2.069
of the coal samples when a condition completed, and repeat the above operation until complete the five main conditions. 5. Record the height of the initial sample after filling the sample pre-experiment. Record the vertical displacement and the outlet flow when the seepage was stable during each experiment.
3.2.4 Data Processing Methods Combined with seepage equation Eq. (2), the initial quality of the coal sample is assumed to be m0 , the actual density of the samples is ρs , the initial filled height of the coal sample is h 0 and the initial porosity is φ0 . The density of the broke coal after compression is ρ. The strain is εv , the porosity is φ and the height is h σ = (1 − εv ) h 0 . The initial porosity can be calculated by Eq. (3). φ0 =
sh 0 −
m0 ρs
(3)
m0 ρs
where s is the cross-sectional area, 0.00785 m2 . h 0 is the initial height of the sample in the specimen chamber, m. ρs is the actual density of the samples, 1.55 × 103 kg/m3 . Then, the vertical strain can be written as Eq. (4). εv =
∇h h0
(4)
According the porosity definition, the porosity of the broken coal under compacted can be written as Eq. (5). φ=
Vp = V
1 1 2 2 4 φ0 πd h 0 − 4 πd h 0 εv 1 2 4 πd (1 − εv ) h 0
=
φ0 − εv 1 − εv
(5)
The Forchheimer equation, Eq. (2), can be used to model the investigation because it has been proven to fit the flow in crushed rocks well (Miao et al. 2011; Liu et al. 2012; Ma et al. 2014). For a one-dimensional non-Darcy flow, the relationship between pressure and the flow velocity can be expressed as −
dp μ = V + ρ N2 βV 2 dh κ
(6)
where h is the dynamic height of the compacted broken coal samples.
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T. Chu et al.
The permeability and non-Darcy’s coefficient are both material properties. Both κ and β depend on the morphology of the porous medium. The non-Darcy term is measured (or predicted) using a correlation of other properties of the porous medium. In terms of mathematical transformation relationship, by substituting V with qA and ddhp p1 with p2 − h , and by taking two known flow rate values of the adjacent conditions of vertical stress and gas injection pressures, Eq. (6) can be converted into Eqs. (7) and (8), respectively, as shown below. At adjacent operating condition, β can been calculate by Eqs. (7) or (8). A2 p2 − p1 μq1 β= 2 − (7) h Aκ q1 ρ N 2 p2 − p1 A2 μq2 β= 2 − (8) h Aκ q2 ρ N 2
Eqs. (7) and (8) are used to derive Eq. (9), which is used to calculate the permeability values. κ=
μh q1 q2 (q1 − q2 ) A q12 p2 − p1 − q22 ( p2 − p1 )
(9)
Based on Eq. (9), the permeability can be calculated, then bring in Eqs. (7) or (8), β can been calculated. But, this process is complex. Convert Eq. (6) as the following form. −
dP = AV + BV 2 dh
(10)
According to the test data, carrying on the binomial fitting, we can obtain the coefficient A and B. The permeability and non-Darcy’s coefficient can be calculated by Eq. (11). κ = μA (11) β = ρBN 2
Additionally, the gas will expand with the temperature increasing, and the density will change. We should consider this effect during the test of different temperatures. The effect of the temperature on gas density can be written as Eq. (12). ρ=
MP Z RT
(12)
where Z is the function of temperature and pressure of the gas, which reflects the difficulty of the gas compression. R is the universal gas constant(8.314 J/(mol K)). M is the molar mass. P is the pressure of the gas. During the tests, the max temperature was 80 ◦ C, and the max seepage pressure was 0.35 MPa, but the outlet directly connected with the atmosphere. So, the effect of pressure was neglected, and the effect of temperature was only considered. The gas was regarded as the ideal state, and the Z is approximate equal to 1. Basing the mass conservation, the seepage velocity can be modified as Eq. (13). V =
VT (273.15 + t0 ) (273.15 + t)
(13)
where V is the modified seepage victory, m/s. VT is the seepage victory of the outlet. t0 is the temperature under the standard condition, 20 ◦ C. t is the temperature of the outlet, ◦ C.
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Experimental Investigation on the Permeability Evolution...
4 Test Results The non-Darcy seepage properties of the broken coal samples were tested under variable axial stress. According to Eqs (3), (4), (10) and (11), the porosity and permeability as well as the non-Darcy coefficient of each stress level can be calculated.
4.1 Seepage Parameters Tested at Room Temperature 4.1.1 Sample’s Stress–Strain Using the stress–strain of the samples, the porosity and permeability under room temperature (23–27 ◦ C) as well as the stress–strain characteristics were obtained, as shown in Fig. 4, and the porosity values were shown in Table 3. Based on the trend of the curve as shown in Fig. 4a, the main features of the curves between stress and strain were changed in phases and the vertical stress increased. During the A stage, the slopes of the strain curves were larger and the broken coal samples were quickly compacted before loading at 6 MPa. During the B stage, the slopes of the strain curves decreased slowly and the broken coal samples were compacted gently when the vertical stress was between 6 and 12 MPa. The compacted deformations had no apparent
Strain
a
0.425 0.400 0.375 0.350 0.325 0.300 0.275 0.250 0.225 0.200 0.175 0.150 0.125 0.100 0.075 0.050 0.025 0.000 -0.025 -0.050
C stage a:1-3mm b:3-6mm c:6-10mm d:10-15mm e:1-6mm f:1-10mm g:1-15mm
B stage
A stage
0
2
4
6
8
10
12
14
16
18
20
Loading vertical stress(MPa)
b
c 0.40 0.35 0.30
0.30
0.25 0.20 0.15
0.25 0.20 0.15
0.10
0.10
0.05
0.05
0.00
0.00
-0.05
-0.05
0
2
4
e:1-6mm f:1-10mm g:1-15mm
0.35
Strain
Strain
0.40
a:1-3mm b:3-6mm c:6-10mm d:10-15mm
6
8
10
12
14
16
Loading vertical stress(MPa)
18
20
0
2
4
6
8
10
12
14
16
18
20
Loading vertical stress(MPa)
Fig. 4 Tested curves between the stress and strain of the broken samples. a All samples, b single particle size, c mixed samples
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T. Chu et al. Table 3 Porosity of the broken coal samples under vertical loading stress Stress (MPa)
a 1–3 mm
b 3–6 mm
c 6–10 mm
d 10–15 mm
e 1–6 mm
f 1–10 mm
g 1–15 mm
0
0.5517119
0.541287
0.530365
0.506883
0.530365
0.506883
0.48093
3
0.51966493
0.502895
0.463479
0.41231
0.483189
0.426608
0.345608
6
0.456502242
0.42179
0.389434
0.302851
0.4051
0.343946
0.272903
9
0.421199898
0.383874
0.351287
0.257239
0.369292
0.306921
0.227089
12
0.395252996
0.357544
0.326477
0.227524
0.344226
0.281224
0.201882
15
0.377466319
0.340686
0.308839
0.207011
0.326329
0.263836
0.182566
a:1-3mm b:3-6mm c:6-10mm d:10-15mm e:1-6mm f:1-10mm g:1-15mm
0.55 0.50
Porosity
0.45 0.40 0.35 0.30 0.25 0.20 0.15 0
2
4
6
8
10
12
14
16
18
20
Loading vertical stress(MPa) Fig. 5 Tested curves between the stress and porosity of the broken samples
change when processed into the C stage when the vertical stresses exceed 12 MPa. The strain difference of the samples was no longer obvious after loading at 12 MPa, and the samples were fully compacted at 12 MPa. From Fig. 4b, it could be found that the larger the particle diameter was, the larger the strain was. For example, the strain in sample d was larger than that in sample a during the loading stress process, especially at stresses lower than 12 MPa. The strain was larger with the increase in particle size under the same level loading stress. Therefore, coal samples with larger particle sizes were easier to compact. Figure 4c reflected the variations between the stress and strain of the mixed samples. It is shown that the larger the particle size grading scale was, the more obvious the strain was, which indicated that the larger the grading range was, and the easier compaction was. According to Table 3, the relationship between the porosity and vertical stress was shown in Fig. 5. The stress and porosity curves changed with increasing vertical stress, but the diameter significant changed with porosity. The porosity decreasing tendency was obvious with the particle size increasing.
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Experimental Investigation on the Permeability Evolution...
4.1.2 Permeability and Stress Characteristics Based on the data of the fluid speed and gas pressure gradient and according to Eqs. (10) and (11), the permeability κ and non-Darcy coefficient β of each stress level can be determined. The fluid speed and gas pressure gradient of the sample “a” and “g” were examined, as shown in Tables 4 and 5. Then, the curve between the seepage pressure gradient and seepage speed was fitted, the relationship of the seepage flow velocity and pressure gradient was obtained, as shown in Figs. 6 and 7. These two types of sample performed similarly during the experiment, including relationship between the seepage flow velocity and pressure gradient, which was nonlinear. Taking Fig. 6 as an example, the following information could be obtained: (1) the seepage flow velocity increased as the pressure gradient increased at the same vertical stress, but it was shown to be nonlinear; (2) the seepage flow velocity reduced as the vertical stress increased under the pressure gradient isoline; (3) the pressure gradient increased as the vertical stress increased under the velocity isoline. This means that the vertical stress plays an important role in the seepage process of broken coal. Fitting the curve between the seepage flow velocity and pressure gradient, the permeability and non-Darcy coefficient were obtained for the samples as well as the other samples, as shown in Table 6. Fitting the data in Table 6, the permeability and non-Darcy coefficient were obtained under the loading vertical stress, as shown in Figs. 8 and 9. The seepage characteristics of the broken coal samples under different stress levels were shown in Figs. 8 and 9. The macro-trend was that the permeability generally reduced when the vertical stress increased and the absolute value of the non-Darcy coefficient generally increased when the vertical stress increased. However, the non-Darcy coefficient was negative in all tests. The non-Darcy coefficient was negative because the grains were seriously broken with the loading stress. During the process of testing, the device did not set the confining pressure, the coal samples were only under axial compression and would further crush under the loading vertical stress, this phenomenon was agree with the results by the Li et al. (2008). For the single particle sized samples in Fig. 8, the initial permeability and ultimate permeability decreased at different degrees under loading stresses from 0 to 15 MPa during the experiments, as shown in Table 6. The permeability hardly changed when the vertical stress was between 12 and 15 MPa for the samples, illustrating that the coal sample was nearly compacted after 12 MPa. Furthermore, the particle sizes significantly influenced the permeability. The permeability was lower when the particle size increased gradually, as shown in Fig. 9, which indicated that the larger the particle size was, the lower the permeability under the same load stress was. For the mixed samples in Fig. 9, the order of the permeability values was g > f > e, and the most significant difference of the mixed samples was the grading. Therefore, by combining the composition of each of the coal samples, the grading range was much larger and more uniform while the permeability value was lower. However, the non-Darcy coefficient (|β|) increased while the vertical stress increased among the seven specimens. |β| nearly doubled from the start of the experiment to the end.
123
123 1.699E−03
1.324E+06
1.655E+06
1.986E+06
2.317E+06
1.023E−03
1.329E−03
1.665E−03
2.008E−03
1.996E−03
1.652E−03
1.325E−03
1.015E−03
2.047E−03 Vertical stress 12 MPa
1.538E+06
1.795E+06
1.800E−03
2.132E−03
1.045E−03 1.363E−03
Vertical stress 9 MPa
1.026E+06
1.282E+06
1.096E−03
Fluid velocity (m/s)
Gas pressure gradient (Pa/m)
Fluid velocity (m/s)
1.435E−03
Vertical stress 3 MPa
Vertical stress 0 MPa
Table 4 Seepage flow velocity and pressure gradient data (sample a)
2.421E+06
2.075E+06
1.730E+06
1.384E+06
1.923E+06
1.648E+06
1.374E+06
1.099E+06
Gas pressure gradient (Pa/m)
1.979E−03
1.635E−03
1.316E−03
1.006E−03
Vertical stress 15 MPa
2.025E−03
1.669E−03
1.333E−03
1.028E−03
Fluid velocity (m/s)
Vertical stress 6 MPa
2.552E+06
2.188E+06
1.823E+06
1.458E+06
2.176E+06
1.865E+06
1.554E+06
1.243E+06
Gas pressure gradient (Pa/m)
T. Chu et al.
1.567E+06
1.959E+06
2.351E+06
7.219E−04
9.554E−04
1.202E−03
1.185E−03
9.427E−04
7.134E−04
1.274E−03 Vertical stress 12 MPa
1.579E+06
1.452E−03
7.813E−04 1.019E−03
Vertical stress 9 MPa
1.053E+06
1.316E+06
9.214E−04
Fluid velocity (m/s)
Gas pressure gradient (Pa/m)
Fluid velocity (m/s)
1.180E−03
Vertical stress 3 MPa
Vertical stress 0 MPa
Table 5 Data of the seepage flow velocity and pressure gradient (mixed sample g)
2.428E+06
2.023E+06
1.619E+06
1.991E+06
1.659E+06
1.327E+06
Gas pressure gradient (Pa/m)
1.176E−03
9.342E−04
7.091E−04
Vertical stress 15 MPa
1.227E−03
9.809E−04
7.473E−04
Fluid velocity (m/s)
Vertical stress 6 MPa
2.487E+06
2.072E+06
1.658E+06
2.212E+06
1.843E+06
1.474E+06
Gas pressure gradient (Pa/m)
Experimental Investigation on the Permeability Evolution...
123
seepage pressure gradient(Pa/m)
T. Chu et al.
2.6x10
6
2.4x10
6
2.2x10
6
2.0x10
6
1.8x10
6
1.6x10
6
1.4x10
6
1.2x10
6
1.0x10
6
sample a 0 MPa 3 MPa 6 MPa 9 MPa 12 MPa 15 MPa Vertical stress
Velocity isoline
Pressure gradient isoline
-3
1.0x10
-3
1.2x10
-3
-3
1.4x10
-3
1.6x10
1.8x10
-3
-3
2.0x10
2.2x10
Seepage speed(m/s)
Pressure gradient (Pa/m)
Fig. 6 Seepage flow velocity and pressure gradient of sample a 2.6x10
6
2.4x10
6
2.2x10
6
2.0x10
6
1.8x10
6
1.6x10
6
1.4x10
6
1.2x10
6
1.0x10
6
0Mpa 3Mpa 6Mpa 9Mpa 12Mpa 15Mpa 18Mpa Vertical stress
7.0x10
-4
8.0x10
-4
9.0x10
-4
1.0x10
-3
1.1x10
-3
1.2x10
-3
1.3x10
-3
1.4x10
-3
1.5x10
-3
Seepage speed(m/s) Fig. 7 Seepage flow velocity and pressure gradient of sample g
4.2 Permeability at Different Temperatures To identify the effects of temperature on the seepage parameters, the sample room temperatures were set at 40, 50, 60, 70 and 80 ◦ C and the sample “e” permeability was tested. The results were shown in Table 7.
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Experimental Investigation on the Permeability Evolution... Table 6 Permeability and non-Darcy coefficients of the samples Sample
0 MPa
3 MPa
6 MPa
κ/m2
−β/m−1
κ/m2
−β/m−1
κ/m2
−β/m−1
a
1.73E−14
8.48E+10
1.52E−14
1.07E+11
1.31E−14
1.34E+11
b
1.55E−14
1.21E+11
1.43E−14
1.26E+11
1.20E−14
1.59E+11
c
1.49E−14
1.33E+11
1.30E−14
1.50E+11
1.12E−14
1.80E+11
d
1.44E−14
1.52E+11
1.21E−14
1.65E+11
9.96E−15
2.14E+11
e
1.32E−14
1.68E+11
1.11E−14
2.23E+11
9.22E−15
2.90E+11
f
1.20E−14
1.82E+11
1.03E−14
2.73E+11
8.73E−15
3.19E+11
g
1.16E−14
2.16E+11
8.78E−15
3.13E+11
7.55E−15
4.10E+11
Sample
9 MPa
12 MPa
15 MPa
κ/m2
−β/m−1
κ/m2
−β/m−1
κ/m2
−β/m−1
a
1.23E−14
1.39E+11
1.17E−14
1.47E+11
1.10E−14
1.56E+11
b
1.13E−14
1.68E+11
1.07E−14
1.81E+11
1.03E−14
1.90E+11
c
1.05E−14
1.88E+11
1.00E−14
2.02E+11
9.69E−15
2.09E+11
d
9.37E−15
2.20E+11
8.90E−15
2.37E+11
8.60E−15
2.50E+11
e
8.58E−15
3.13E+11
8.11E−15
3.42E+11
7.78E−15
3.65E+11
f
8.16E−15
3.38E+11
7.76E−15
3.64E+11
7.46E−15
3.88E+11
g
7.03E−15
4.39E+11
6.77E−15
4.58E+11
6.58E−15
4.68E+11
-14
1.8x10
κ (a) κ (b) κ (c) κ (d)
-14
1.7x10
-14
1.6x10
β (a) β (b) β (c) β (d)
11
2.6x10
11
2.4x10
11
2.2x10 -14
1.5x10
11
2.0x10
κ ( m2)
1.4x10
11
1.8x10
-14
1.3x10
11
1.6x10
-14
1.4x10
-14
1.2x10
-14
1.0x10
-15
8.0x10
− β(m-1)
-14
11
1.2x10
11
1.1x10
11
1.0x10
10
9.0x10
10
6.0x10
-15
8.0x10
0
2
4
6
8
10
12
14
16
Loading vertical stress(MPa) Fig. 8 Permeability of the single particle size samples (a, b, c, d)
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11
1.4x10
5.0x10
κ (e) κ (f) κ (g) β (e) β (f) β (g)
-14
1.3x10
-14
1.2x10
11
4.5x10
11
4.0x10
-14
1.1x10
2
κ (m )
1.0x10
11
3.0x10
− β(m-1)
11
3.5x10 -14
-15
9.0x10
11
-15
2.5x10
-15
2.0x10
8.0x10
11
7.0x10
-15
6.0x10
11
0
2
4
6
8
10
12
14
16
1.5x10
Loading vertical stress(MPa) Fig. 9 Permeability of the mixed samples (e, f , g)
Table 7 Permeability data for samples tested at different temperatures T
Stress 0 MPa κ/m2
2 MPa
4 MPa
6 MPa
8 MPa
10 MPa
12 MPa
15 MPa
40◦ C
1.29E−14
1.17E−14
9.20E−15
8.34E−15
8.00E−15
7.51E−15
7.28E−15
6.79E−15
50◦ C
1.26E−14
1.15E−14
9.14E−15
8.27E−15
7.88E−15
7.42E−15
7.19E−15
6.64E−15
60◦ C
1.22E−14
1.12E−14
9.00E−15
8.14E−15
7.72E−15
7.28E−15
6.98E−15
6.55E−15
70◦ C
1.19E−14
1.11E−14
8.80E−15
8.06E−15
7.68E−15
7.23E−15
6.78E−15
6.42E−15
80◦ C
1.17E−14
1.08E−14
8.79E−15
7.98E−15
7.56E−15
7.18E−15
6.59E−15
6.38E−15
e
According to Table 7, fitting the curve between temperature and permeability, the change trend between the permeability and temperature was established, as shown in Fig. 10. The permeability was reduced as the temperature increased during loading. For example, the value of permeability was 1.29 × 10−14 m2 at 40 ◦ C and the loading stress was 0 MPa, and the permeability reduced to 1.26 × 10−14 m2 , 1.22 × 10−14 m2 , 1.19 × 10−14 m2 , and 1.17 × 10−14 m2 when the temperature was elevated to 50, 60, 70, and 80 ◦ C, respectively. Under other stress loading conditions, the change trend between the permeability and temperature was similar when the permeability was reduced as the temperature increased under the same loading stress. The effects of temperature on the relative permeability were much weaker in terms of the physical values. The permeability reduced by 1.2× 10−15 m2 when the temperature increased from 40 to 80 ◦ C under the loading stress of 0 MPa. The permeability reduced by 0.9 × 10−15 m2 when the temperature increased from 40 to 80 ◦ C under the loading stress of 2 MPa. The permeability reduced by 0.41 × 10−15 m2 when the temperature
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Experimental Investigation on the Permeability Evolution...
κ m2
-14
1.3x10 -14 1.2x10 -14 1.2x10 -14 1.1x10 -14 1.1x10 -14 1.0x10 -14 1.0x10 -15 9.5x10 -15 9.0x10 -15 8.5x10 -15 8.0x10 -15 7.5x10 -15 7.0x10 -15 6.5x10 -15 6.0x10 -15 5.5x10 -15 5.0x10
0MPa 2MPa 4MPa 6MPa 8MPa 10MPa 12MPa 15MPa
40
50
60
70
80
Temperature°C Fig. 10 Relationship between the permeability and temperature (sample “e”)
increased from 40 to 80 ◦ C under the loading stress of 4 MPa. The permeability reduced by 0.36 × 10−15 m2 when the temperature increased from 40 to 80 ◦ C under the loading stress of 6 MPa. The permeability reduced by 0.44 × 10−15 m2 when the temperature increased from 40 to 80 ◦ C under the loading stress of 8 MPa. The permeability reduced by 0.33 × 10−15 m2 when the temperature increased from 40 to 80 ◦ C under the loading stress of 10 MPa. The permeability reduced by 0.69 × 10−15 m2 when the temperature increased from 40 to 80 ◦ C under the loading stress of 12 MPa. The permeability reduced by 0.41 × 10−15 m2 when the temperature increased from 40 to 80 ◦ C under the loading stress of 15 MPa.
4.3 Analyses and Discussion 4.3.1 Effects of Stress on the Seepage Parameters To establish the relationship between porosity, permeability and the loading stress, the method of comparative analysis was adopted. By contrasting the value of porosity and permeability under each vertical stress with 0 MPa, the attenuation degree of porosity and permeability was determined. According to the porosity data, the attenuation degree was calculated under different loading vertical stress, and the results were shown in Fig. 11. The attenuation degree of the porosity was f (φ, σ ) in Fig. 11. First, the broken coal samples “a,” “b,” “c” and “d” were used as one comparative analysis group, and the coal samples “e,” “ f ” and “g” were used as another comparative analysis group. The tested curves of the attenuation degree of porosity were impacted by the particle size and stress. The attenuation degree of porosity progressively increased as the loading vertical stress increased, and the attenuation degree of porosity was much larger before 12 MPa. The tested curves of the attenuation degree of porosity were nearly parallel after 12 MPa for the broken samples. To the mixed broken coal of “e,” “ f ” and “g,” the attenuation degree of the porosity of sample “e” was lower than the degree of samples “ f ” and “g” at the same level of vertical stress. The largest difference between the two samples was the gradation composition, so the
123
f(φ,σ)
T. Chu et al. 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05
a:1-3mm b:3-6mm c:6-10mm d:10-15mm e:1-6mm f:1-10mm g:1-15mm
0
2
4
6
8
10
12
14
16
18
20
Loading vertical stress(MPa) Fig. 11 Attenuation degree of the porosity under different vertical stresses
gradation composition was surmised to be important and the attenuation degree of porosity was more significant. Second, in view of the particle size and grading, the larger the particle diameter was, the larger the attenuation degree of porosity was. To analyze the effects of the grain composition, the attenuation degree of the porosity of samples “a,” “b” and “e” was analyzed. Sample “e” was compared with samples “a” and “b” under a mass ratio of 1:1, but the attenuation degree of the porosity of sample “e” was larger than that of samples “a” and “b” under the same vertical stress. This is mainly because in the process of mixing rock particles, smaller diameter particles fill in the pores of larger particles. Therefore, the attenuation degree of porosity of the mixed samples is higher than the degree of the particles which were constituted during grading. Basing on Table 5, the dimensionless permeability (κr ) was obtained under different vertical stresses, which was on behalf of the attenuation degree of permeability, as shown in Fig. 12. When the stress increased from 0 to 6.0 MPa, the permeability of the b, c, d, e, and g coal samples dropped by 22.52, 24.83, 30.67, 29.94, and 35.03%, respectively, and when the loading vertical stress was increased to 6MPa, the maximum relative permeability attenuation was 35.03%. The maximum relative permeability attenuation was 9.41% when the vertical stress increased from 6 to 12 MPa, and the maximum relative permeability attenuation was 2.53% when the vertical stress increased from 12 to 15 MPa. The permeability dropped by 33.33, 35.11, 40.17, 40.88 and 43.88% when the stress increased to 15 MPa compared with 0 MPa. Overall, the permeability attenuation increased gradually during the loading process, and the permeability attenuation was more evident before 6 MPa.
4.3.2 Effects of Particle Size on Seepage Parameters To analyze the relationship between the permeability and diameter, the average grain diameter was used as the analysis indicator. The average grain diameters of the tested samples (a, b, c, d) were 2, 4.5, 8 and 12.5 mm, respectively. The curves trends were fitted between porosity, permeability and the average grain diameter and combined with Tables 1, 3 and 6, respectively,
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κ r%
Experimental Investigation on the Permeability Evolution... b(3-6mm) c(6-10mm) d(10-15mm) e(1-6mm) g(1-15mm)
45 42 39 36 33 30 27 24 21 18 15 12 9 6 3 0
Max Δκ=2.53% Max Δκ=9.41%
Max Δκ=35.03% 0
2
4
6
8
10
12
14
16
Loading vertical stress(MPa) Fig. 12 Dimensionless permeability (κr ) sensitive curve of broken coal samples 0.55 0.50
Poroisty
0.45 0.40 0.35
0MPa 3MPa 6MPa 9MPa 12MPa 15MPa Vertical stress
0.30 0.25 0.20 0
2
4
6
8
10
12
14
Average grain diameter(mm) Fig. 13 Relationship between the particle size and porosity
as shown in Figs. 13 and 14. It was found that the porosity and permeability decreased when the average grain diameter increased under the same loading stress. From Figs. 13 and 14, the larger the grain diameter, the lower the porosity and permeability. The pores in broken coal with larger grain diameters can be easily compacted. For example, as shown in Fig. 13, the porosity of sample ‘d’ with a grain diameter of 10–15 mm (with an average diameter of approximately 12.5 mm) was lower than that of the other broken coal samples (a, b, c) under the same vertical stress. As shown in Fig. 14, the permeability of sample ‘d’ was also lower than that of the other broken coal samples (a, b, c) under the same vertical stress. Therefore, the particle size diameters impacted the compaction effects. By the effects of stress and particle size diameter on the porosity and the permeability, we know that the stress
123
1.8x10
-14
1.7x10
-14
1.6x10
-14
1.5x10
-14
1.4x10
-14
1.4x10
-14
1.3x10
-14
1.2x10
-14
1.1x10
-14
1.0x10
-14
9.6x10
-15
8.8x10
-15
0MPa 3MPa 6MPa 9MPa 12MPa 15MPa
2
Permeability(m )
T. Chu et al.
2
4
6
8
10
12
14
Average grain diameter(mm) Fig. 14 Relationship between the particle size and permeability
recovery in gob is advantageous to reduce the porosity and permeability. Reducing the degree of broken coal and the percentage of small particles is favorable to reduce the porosity and permeability and to prevent coal self-heating.
4.3.3 Effects of Temperature on Permeability Comparing permeability data for sample “e” in Tables 6 and 7, the permeability was 1.32 × 10−14 m2 at room temperature (27 ◦ C) with the loading stress 0 MPa. The permeability was 8.73 × 10−15 m2 , 8.11 × 10−15 m2 and 7.78 × 10−15 m2 at room temperature when the loading stress was 6, 12 and 15 MPa, respectively. From Table 7, it is clear that the maximum permeability was 8.34 × 10−15 m2 , 7.28 × 10−15 m2 and 6.79 × 10−15 m2 when the temperature increased from 40 to 80 ◦ C and the loading stress varied at 6, 12, and 15 MPa, respectively. Therefore, the permeability was reduced during temperature increased from room temperature to 80 ◦ C under loading. According to the effects of a temperature increase during coal self-heating, the permeability of the compacted broken coal will reduce during low-temperature oxidation. As above, the effects of the particle size, stress and temperature on permeability were discussed. The results show the porosity and permeability decreases with the increase in loading stress. So, the porosity and permeability gradually decreases during the stress recovery in gob, and the porosity and permeability dynamic changes due to the mine pressure cyclical changes. The porosity and permeability decrease are useful to reduce the air leak and shorten the oxidation zone. Meanwhile, the particle size plays an important role in the permeability evolution, the bigger the particle size is, the smaller the porosity and permeability are. So, increasing the particle size would contribute to decrease the porosity and permeability, and we can reduce the degree of fragmentation, or consolidate the small particles by the ways of grouting yellow mud and silicate gel. Grouting yellow mud and silicate gel are commonly used to preventing the coal self-heating in practice which can consolidate the small particles in some degree and change the porosity and permeability to reduce the air leakage and restrain
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Experimental Investigation on the Permeability Evolution...
the process of coal self-heating. Temperature rises gradually along with the coal oxidation heat releasing in gob. So, we draw a conclusion that the permeability of the compacted broken coal will reduce during low-temperature oxidation in gob by the experiment results.
5 Conclusions In this paper, the effects of the loading vertical stress, grain diameter size and temperature on the permeability of broken coal were studied. The main conclusions are as follows: 1. The strain, porosity and permeability were enlarged when the particle size increases under the same loading stress. The porosity and permeability reduced when the vertical stress increased. 2. The non-Darcy coefficient was negative in all tests, but the absolute value of the nonDarcy coefficient generally increased when the vertical stress increased. 3. The experiment results indicated that the larger particle size is, the easier the particle compaction is. The larger the grain diameter is, the lower the porosity and permeability are, which show that the void volume in broken coal with larger grain diameters can be easily compacted. 4. The permeability reduced when the temperature increased, which indicated the permeability of the compacted broken coal decreased during low-temperature oxidation in gob. 5. By examining the effects of stress and the particle size diameter on the porosity and permeability, the vertical stress recovery and generally increase are advantageous to reduce the porosity and permeability in gob. Reduce the degree of fragmentation and percentage of small particles or consolidate the small particles, which is favorable to reduce the porosity and permeability and prevent coal self-heating. Acknowledgements This work was supported by The National Natural Science Foundation of China (U1361205, 51404090, 51574111), The Scientific Research Foundation of State Key Lab. of Coal Mine Disaster Dynamics and Control (Nos. 2011DA105287-ZD201401).
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