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The influence of gas storage parameters on gas emission rate from borehole
Safety Science 50 (2012) 869–872
Contents lists available at SciVerse ScienceDirect
Safety Science journal homepage: www.elsevier.com/locate/ssci
Special Issue Article: The first international symposium on mine safety science and engineering
The influence of gas storage parameters on gas emission rate from borehole q Gao Jian-liang a,b,⇑, Shang Bin c a
School of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo 454003, China State Key Laboratory Cultivation Base for Gas Geology and Gas Control, Jiaozuo 454003, China c Mine 6, Hebi Coal Group Co., Ltd., Hebi 458000, China b
a r t i c l e
i n f o
Article history: Available online 10 September 2011 Keywords: Borehole Gas flow rate Gas storage Original gas pressure Permeability coefficient
a b s t r a c t Gas emission rate from borehole is one of the most important indexes for the coal and gas outburst prediction. The mathematical model of gas flow in the coal seam, gas flow into the measuring chamber, gas pressure change in the measuring chamber, and gas flow out of the chamber through the pipe is established. Gas migration in the coal seam, gas pressure in borehole chamber and gas flow in pipe is simulated using the finite difference method. Gas emission rate is obtained under dynamic boundary conditions. The influence of gas storage parameters on gas emission rate from borehole is analyzed. Results show that: the gas pressure and the permeability coefficient have great impacts on the value of gas flow quantity in borehole. The larger the original gas pressure of coal seam and the permeability coefficient of coal seam are, the greater the maximum value of gas emission rate form borehole and the later the maximum appears. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Initial velocity of gas emission from borehole was first proposed by the former Soviet Union and then widely used in China for mine gas outburst prediction. There are many factors affecting the gas emission speed form borehole, such as the original coal seam gas pressure, gas content, permeability, coal adsorption constant, strength of coal, and resistance of testing equipment. The gas migration law in the coal seam is the basis to study the gas emission from borehole. In the 1970s, Chinese scholars began to study the initial velocity of gas emission from borehole. The mathematical model of coal seam gas migration was established (Zhou, 1990; Zhou and Lin, 1999), and the model was applied to the calculation
of the initial velocity of gas emission from borehole (Wang and Yu, 1989; Wang, 1993; Wang et al., 2001). This model provides theoretical basis to study the initial velocity of gas emission from borehole. Other scholars also put forward a lot of research methods about initial velocity of gas emission from borehole (Wei and Zhang, 2004; Liu et al., 2009). These researches did not consider the dynamic boundary conditions of gas pressure change in the measuring chamber after borehole sealing, and the influence of pipe resistance losses. In this paper, the influence of gas pressure in the coal seam and permeability coefficient on the gas emission rate form borehole is studied, by considering the pipe and flow meter resistance losses, and dynamic boundary conditions of gas pressure change in the measuring chamber. 2. Mathematical model of gas emission from borehole
q
The First International Symposium on Mine Safety Science and Engineering (ISMSSE2011) will be held in Beijing on October 26–29, 2011. The symposium is authorized by the State Administration of Work Safety and is sponsored by China Academy of Safety Science & Technology (CASST), China University of Mining & Technology (Beijing) (CUMTB), Datong Coal Mine Group, McGill University (Canada) and University of Wollongong (Australia) with participation from several other universities from round the world, research institutes, professional associations and large enterprises. The topics will focus on mines safety field: theory on mine safety science and engineering technology, coal mine safety science & engineering technology, metal and nonmetal mines safety science & engineering technology, petroleum and natural gas exploitation safety science & engineering technology, mine safety management and safety standardization science & technology, occupational health and safety in mine, emergent rescue engineering technology in mine, etc. ⇑ Corresponding author at: School of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo 454003, China. Tel.: +86 13903899150. E-mail address: [email protected] (J.-l. Gao). 0925-7535/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssci.2011.08.016
2.1. Control equations of gas flow in the coal seam The gas flow in the coal seam is a very complex seepage process. To simplify the calculation, following assumptions is made: (i) Original gas pressure in the coal seam is uniformly distributed; (ii) coal seam roof and floor is sealed and without gas; (iii) gas flow process is isothermal; (iv) gas can be regarded as ideal gas and obeys the ideal gas state equation; (v) gas flow in coal seam obeys Darcy’s law; (vi) the gas adsorption quantity in the coal seam obeys Langmuir equation; (vii) drilling process has no impact on the gas pressure in the coal seam around the measuring chamber. Based on the above assumptions, the gas flow in the coal seam obeys the following equations: (1) Continuity equation; (2) Darcy’s
870
J.-l. Gao, B. Shang / Safety Science 50 (2012) 869–872
law; (3) ideal gas state equation; (4) gas content equation. The gas flow control equation can be obtained:
@p K @ 2 p2 @ 2 p2 @ 2 p2 f ðpÞ ¼ þ þ 2 @t 2lp0 @x2 @y2 @z
! ð1Þ
In which,
f ðpÞ ¼
n abr þ p0 ð1 þ bpÞ2
ð2Þ
where r is the Bulk density of coal, t/m3; p, the gas pressure in the coal seam, MPa; K, the permeability of coal seam, m2; l, the gas dynamic viscosity, MPa s; p0, the standard atmospheric pressure, MPa; n, the porosity, %; a, the adsorption constant and b is the adsorption constant. 2.2. Calculation of gas quantity and gas pressure in the measuring chamber Because of the coal seam gas pressure gradient, gas flows from the coal seam into the measuring chamber. Gas emission quantity from the coal seam into the borehole mainly depends on gas pressure in the coal seam and the gas pressure differential on the surface of the borehole. Usually we use the gas pressure gradient between the node on surface of the borehole and the adjacent node in the coal seam as the approximate gas pressure gradient around the measuring chamber. The gas pressure gradient on the surface of the borehole can also be calculated according to the gas pressure fitting curve to get more accurate results. We assume that the gas quantity in the measuring chamber is m1 at t1 time. According to Darcy’s law, the gas emission rate from unit area of borehole surface into the measuring chamber can be obtained, then the amount of gas dm1 released into the measuring chamber from the coal seam can be calculated. The gas quantity that flows out from the measuring chamber through the pipe within the time dt is defined as dm2. After dt time, the gas quantity in the measuring chamber is m2 at t2 time. The mass balance equation can be obtained for the measuring chamber as follows:
m2 ¼ m1 þ dm1 dm2
ð3Þ
According to the gas state equation, the gas pressure in the measuring chamber is expressed by the following formula:
pc ¼ m2 RT=MV
ð4Þ
where pc is the gas pressure in the measuring chamber, MPa; M, the molar mass of gas, kg/mol; R, the gas constant of gas, R = 518.2 J/ (kg k); V, the volume of the measuring chamber, m3 and T is the absolute temperature of gas, T = 273 + t. 2.3. The gas flow equation in the pipe As the gas pressure increases in the measuring chamber, the gas will flow out through the pipe. According to the circular tube frictional resistance losses formula, we can obtain the gas flow rate from the pipe:
pc p0 ¼ Rf Q 2 Rf ¼ k d
l q d 2S2
By solving simultaneous Eqs. (1), (3), (4), and (5), we can obtain gas flow rate out of the pipe under dynamic pressure boundary conditions in the measuring chamber. Solution steps are as follows: According to the Eq. (1), use finite difference method for calculating the gas pressure distribution under initial conditions; and calculate the gas quantity released into the measuring chamber from the coal seam. According to the Eq. (3), calculate the gas quantity in the measuring chamber. According to the Eq. (4), calculate the gas pressure in the measuring chamber. According to the Eq. (5), calculate the gas quality that flows through the airway; According to the Eq. (4), recalculate the gas pressure in the measuring chamber. With the new gas pressure value in the measuring chamber, repeat the above steps for the next round of calculation. 3. Gas emission from borehole calculations When used the different pipe to determine the initial velocity of gas emission from borehole, the measured values are different because of the different resistance coefficient of the pipe. In this paper, we use copper pipe with 3 m in length and 1 cm in diameter (kd = 0.1). Fig. 1 is the schematic diagram measuring the gas emission rate. The values of gas storage parameters are shown in Table 1 taken for simulate the gas migration in coal seam and for calculating the gas emission. 3.1. The influence of gas pressure on gas emission rate from the pipe When the original gas pressure of coal seam is 2.0 MPa and 1.0 MPa, the variation of gas flow in borehole through the copper pipe with time is shown in Fig. 2. The figure shows that after the borehole is sealed, the gas emission rate increases rapidly and reached the maximum value quickly. Then the gas emission rate begins to attenuation rapidly, and the attenuation rate gets smaller and smaller. When the original gas pressure of coal seam is 2.0 MPa, the maximum value of gas emission rate is 144.4 L/min and appeared at 148 s. When the original gas pressure of coal seam is 1.0 MPa, the maximum value of gas emission rate is 60.6 L/min and appeared at 77 s. Compared with 2.0 MPa pressure in coal seam, when the original gas pressure of coal seam is 1.0 MPa, the maximum value of gas flow in borehole appeared 71 s earlier, and is 83.8 L/min less reduced by 58%. When the original gas pressure of coal seam is 2.0 MPa and 1.0 MPa, respectively, the value of gas emission rate in borehole is Q1 and Q2 respectively, so their difference is Q2–Q1. The value of (Q2–Q1)/Q1 is shown in Fig. 3. It can bee seen that as time
0.5m
2
1
ð5Þ ð6Þ
where Q is the gas flow rate out of the pipe, m3/s; pc, the gas pressure in the measuring chamber, Pa; po, the gas pressure in the roadway, Pa; Rf, the airway resistance, kg/m7; kd, the frictional loss coefficient; l, the airway length, m; d, the airway diameter, m; S, the airway cross-sectional area, m2 and q is the gas density, kg/m3.
3
5
4
6
3.5m 1-roadway 2-pipe 3-flowmeter 4-borehole 5-hole packer 6-measuring chamber Fig. 1. Shematic diagram measuring the initial velocity of gas emission.
871
J.-l. Gao, B. Shang / Safety Science 50 (2012) 869–872 Table 1 Values of gas storage parameters taken for simulation. ps (MPa)
p0 (MPa) 0.1
Gas emission rate (L/min)
2.0/1.0
k (m2)
l (MPa s) 1.08 10
12
3.6 10
q (kg/m3) 17
17
/1.8 10
0.716
140
Ps =2.0MPa
100
Ps =1.0MP
40 20 0
400
800
1200
1600
2000
Time (s) Fig. 2. Variation of gas emission rate with time at different gas pressure.
75%
Gas emission rate
1.45 10
a (m3/kg) 3
3
28 10
b (MPa1)
A (%)
M (%)
0.47
20
1.8
3.2. The influence of permeability coefficient on gas emission rate from the pipe
80 60
0
0.2
pm (t/m3)
which is 71.7%. After the maximum appeared, the difference falls slowly, and it varies around 71% nearby after the borehole sealing 30 min.
160 120
n (%)
70% 65% 60% 55% 50% 0
400
800
1200
1600
2000
When the permeability coefficient of coal seam is 6 m2/(MPa2 d) and 3 m2/(MPa2 d), respectively, the variation of gas emission rate through the copper pipe is shown in Fig. 4. When the permeability coefficient of coal seam is 6 m2/(MPa2 d), the maximum value of gas emission rate is 144.4 L/min and appeared at 148 s. When the permeability coefficient of coal seam is 3 m2/(MPa2 d), the maximum value of gas emission rate is 105.2 L/min and appeared at 125 s. Compared with 6 m2/(MPa2 d), when the permeability coefficient of coal seam is 3 m2/(MPa2 d), the maximum value of gas emission rate appeared earlier 23 s, reduce 39.2 L/min, by 27%. After the gas emission rate in borehole reaches the maximum, it begins to attenuation. The maximum value of gas emission rate and its appear time, and the attenuation rate at two different permeability coefficients of coal seam are shown in Table 2. The table shows that the smaller the permeability coefficient of coal seam is, the smaller the gas flow in borehole, and the earlier it appears. When the permeability coefficient of coal is smaller, the gas emission rate attenuation is faster. The value of gas emission rate from pipe attenuation reaches up to 60% when the permeability coefficient of coal seam is 3 m2/(MPa2 d).
Time (s)
Gas emission rate (L/min)
Fig. 3. Gas emission rate difference caused by coal seam pressure.
4. Conclusions The mathematical model of gas migration in the coal seam, gas flow into the measuring chamber, gas pressure change in the measuring chamber, and gas flow out of the chamber through the pipe is established. Gas migration in the coal seam, gas pressure in borehole chamber and gas flow in pipe is simulated using the finite difference method. Gas emission rate is obtained under dynamic boundary conditions. The influence of gas storage parameters on gas emission rate from borehole is analyzed.
210 180 150 120 90 60 30 0
0
400
800
1200
1600
2000
Time (s) Fig. 4. Variation of gas emission rate with time at different permeability coefficients of coal seam.
increases, the difference between the values of gas emission rate caused by the difference of original gas pressure in coal seam increased rapidly. At 471 s, the difference achieves the maximum
(1) After the borehole is sealed, the value of gas emission rate increases rapidly and reaches the maximum within 3 min. The larger the original gas pressure of coal seam and the permeability coefficient of coal seam are, the later the maximum gas emission rate appears. (2) Original gas pressure and permeability coefficient have great impacts on the value of gas emission rate. The difference increases rapidly within several minutes after the borehole is sealed, and then keeps stable. When the original gas pressure of coal seam is 2.0 MPa and 1.0 MPa, the difference of gas emission rate basically stays at about 71% after the
Table 2 Gas emission rate attenuation rate with time after reached the maximum. Permeability coefficient m2/(MPa2 d)
3.0 6.0
Maximum (L/min)
105.2 144.4
Appear time (s)
125 148
Attenuation rate 1 min (%)
2 min (%)
3 min (%)
15 min (%)
30 min (%)
2.7 1.7
8.5 5.3
14.9 9.8
50.3 43.4
60.0 53.0
872
J.-l. Gao, B. Shang / Safety Science 50 (2012) 869–872
borehole is sealed for 30 min. When the permeability coefficient of coal seam is 6 m2/(MPa2 d) and 3 m2/(MPa2 d), the difference of gas emission rate basically stays at about 38% after the borehole is sealed for 30 min. (3) The gas emission rate begins to attenuation after it reaches the maximum. The attenuation rate is related to the original gas pressure and the permeability coefficient. The larger the gas pressure and the permeability coefficient are, the slower the attenuation after the gas emission rate reached the maximum. Acknowledgment The research project is sponsored by National Nature Science Foundation of China (Grant No. 51174079) and Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20104116110001). Thanks to NSFC and RFDP for the financial support.
References Liu, Haibo, Cheng, Yuanping, Wang, Haifeng, Shang, ZHengjie, 2009. Chang rule of initial speed of gas emission from borehole in outburst coal seam before and after pressure relief. Journal of Mining & Safety Engineering 26 (2), 225–228 (in Chinese). Wang, Kequan, 1993. Back analysis method of gas flow for determining gas pressure distribution around bore in coal seam. Journal of Xi’an Mining Institute 4, 309– 315 (in Chinese). Wang, Kequan, Yu, Bufan, 1989. Analysis the influence factors of initial velocity of gas emission from borehole. Coal Engineer 2, 32–36 (in Chinese). Wang, Kai, Yu, Qixiang, Jiang, Cheng-lin, 2001. Study of dynamic gas emission during boring process by using numerical simulation. Journal of China Coal Society 26 (3), 279–284 (in Chinese). Wei, Fengqing, Zhang, Pujing, 2004. Discussion on test depth of initial speed from borehole gas emission. Coal Science and Technology 32 (5), 61–64 (in Chinese). Zhou, Shining, 1990. Mechanism of gas flow in coal seams. Journal of China Coal Society 15 (1), 15–24 (in Chinese). Zhou, Shining, Lin, Boquan, 1999. The Theory of Gas Flow and Storage in Coal Seams. China Coal Industry Publishing House, Beijing, p. 69 (in Chinese).
Contents lists available at SciVerse ScienceDirect
Safety Science journal homepage: www.elsevier.com/locate/ssci
Special Issue Article: The first international symposium on mine safety science and engineering
The influence of gas storage parameters on gas emission rate from borehole q Gao Jian-liang a,b,⇑, Shang Bin c a
School of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo 454003, China State Key Laboratory Cultivation Base for Gas Geology and Gas Control, Jiaozuo 454003, China c Mine 6, Hebi Coal Group Co., Ltd., Hebi 458000, China b
a r t i c l e
i n f o
Article history: Available online 10 September 2011 Keywords: Borehole Gas flow rate Gas storage Original gas pressure Permeability coefficient
a b s t r a c t Gas emission rate from borehole is one of the most important indexes for the coal and gas outburst prediction. The mathematical model of gas flow in the coal seam, gas flow into the measuring chamber, gas pressure change in the measuring chamber, and gas flow out of the chamber through the pipe is established. Gas migration in the coal seam, gas pressure in borehole chamber and gas flow in pipe is simulated using the finite difference method. Gas emission rate is obtained under dynamic boundary conditions. The influence of gas storage parameters on gas emission rate from borehole is analyzed. Results show that: the gas pressure and the permeability coefficient have great impacts on the value of gas flow quantity in borehole. The larger the original gas pressure of coal seam and the permeability coefficient of coal seam are, the greater the maximum value of gas emission rate form borehole and the later the maximum appears. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Initial velocity of gas emission from borehole was first proposed by the former Soviet Union and then widely used in China for mine gas outburst prediction. There are many factors affecting the gas emission speed form borehole, such as the original coal seam gas pressure, gas content, permeability, coal adsorption constant, strength of coal, and resistance of testing equipment. The gas migration law in the coal seam is the basis to study the gas emission from borehole. In the 1970s, Chinese scholars began to study the initial velocity of gas emission from borehole. The mathematical model of coal seam gas migration was established (Zhou, 1990; Zhou and Lin, 1999), and the model was applied to the calculation
of the initial velocity of gas emission from borehole (Wang and Yu, 1989; Wang, 1993; Wang et al., 2001). This model provides theoretical basis to study the initial velocity of gas emission from borehole. Other scholars also put forward a lot of research methods about initial velocity of gas emission from borehole (Wei and Zhang, 2004; Liu et al., 2009). These researches did not consider the dynamic boundary conditions of gas pressure change in the measuring chamber after borehole sealing, and the influence of pipe resistance losses. In this paper, the influence of gas pressure in the coal seam and permeability coefficient on the gas emission rate form borehole is studied, by considering the pipe and flow meter resistance losses, and dynamic boundary conditions of gas pressure change in the measuring chamber. 2. Mathematical model of gas emission from borehole
q
The First International Symposium on Mine Safety Science and Engineering (ISMSSE2011) will be held in Beijing on October 26–29, 2011. The symposium is authorized by the State Administration of Work Safety and is sponsored by China Academy of Safety Science & Technology (CASST), China University of Mining & Technology (Beijing) (CUMTB), Datong Coal Mine Group, McGill University (Canada) and University of Wollongong (Australia) with participation from several other universities from round the world, research institutes, professional associations and large enterprises. The topics will focus on mines safety field: theory on mine safety science and engineering technology, coal mine safety science & engineering technology, metal and nonmetal mines safety science & engineering technology, petroleum and natural gas exploitation safety science & engineering technology, mine safety management and safety standardization science & technology, occupational health and safety in mine, emergent rescue engineering technology in mine, etc. ⇑ Corresponding author at: School of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo 454003, China. Tel.: +86 13903899150. E-mail address: [email protected] (J.-l. Gao). 0925-7535/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssci.2011.08.016
2.1. Control equations of gas flow in the coal seam The gas flow in the coal seam is a very complex seepage process. To simplify the calculation, following assumptions is made: (i) Original gas pressure in the coal seam is uniformly distributed; (ii) coal seam roof and floor is sealed and without gas; (iii) gas flow process is isothermal; (iv) gas can be regarded as ideal gas and obeys the ideal gas state equation; (v) gas flow in coal seam obeys Darcy’s law; (vi) the gas adsorption quantity in the coal seam obeys Langmuir equation; (vii) drilling process has no impact on the gas pressure in the coal seam around the measuring chamber. Based on the above assumptions, the gas flow in the coal seam obeys the following equations: (1) Continuity equation; (2) Darcy’s
870
J.-l. Gao, B. Shang / Safety Science 50 (2012) 869–872
law; (3) ideal gas state equation; (4) gas content equation. The gas flow control equation can be obtained:
@p K @ 2 p2 @ 2 p2 @ 2 p2 f ðpÞ ¼ þ þ 2 @t 2lp0 @x2 @y2 @z
! ð1Þ
In which,
f ðpÞ ¼
n abr þ p0 ð1 þ bpÞ2
ð2Þ
where r is the Bulk density of coal, t/m3; p, the gas pressure in the coal seam, MPa; K, the permeability of coal seam, m2; l, the gas dynamic viscosity, MPa s; p0, the standard atmospheric pressure, MPa; n, the porosity, %; a, the adsorption constant and b is the adsorption constant. 2.2. Calculation of gas quantity and gas pressure in the measuring chamber Because of the coal seam gas pressure gradient, gas flows from the coal seam into the measuring chamber. Gas emission quantity from the coal seam into the borehole mainly depends on gas pressure in the coal seam and the gas pressure differential on the surface of the borehole. Usually we use the gas pressure gradient between the node on surface of the borehole and the adjacent node in the coal seam as the approximate gas pressure gradient around the measuring chamber. The gas pressure gradient on the surface of the borehole can also be calculated according to the gas pressure fitting curve to get more accurate results. We assume that the gas quantity in the measuring chamber is m1 at t1 time. According to Darcy’s law, the gas emission rate from unit area of borehole surface into the measuring chamber can be obtained, then the amount of gas dm1 released into the measuring chamber from the coal seam can be calculated. The gas quantity that flows out from the measuring chamber through the pipe within the time dt is defined as dm2. After dt time, the gas quantity in the measuring chamber is m2 at t2 time. The mass balance equation can be obtained for the measuring chamber as follows:
m2 ¼ m1 þ dm1 dm2
ð3Þ
According to the gas state equation, the gas pressure in the measuring chamber is expressed by the following formula:
pc ¼ m2 RT=MV
ð4Þ
where pc is the gas pressure in the measuring chamber, MPa; M, the molar mass of gas, kg/mol; R, the gas constant of gas, R = 518.2 J/ (kg k); V, the volume of the measuring chamber, m3 and T is the absolute temperature of gas, T = 273 + t. 2.3. The gas flow equation in the pipe As the gas pressure increases in the measuring chamber, the gas will flow out through the pipe. According to the circular tube frictional resistance losses formula, we can obtain the gas flow rate from the pipe:
pc p0 ¼ Rf Q 2 Rf ¼ k d
l q d 2S2
By solving simultaneous Eqs. (1), (3), (4), and (5), we can obtain gas flow rate out of the pipe under dynamic pressure boundary conditions in the measuring chamber. Solution steps are as follows: According to the Eq. (1), use finite difference method for calculating the gas pressure distribution under initial conditions; and calculate the gas quantity released into the measuring chamber from the coal seam. According to the Eq. (3), calculate the gas quantity in the measuring chamber. According to the Eq. (4), calculate the gas pressure in the measuring chamber. According to the Eq. (5), calculate the gas quality that flows through the airway; According to the Eq. (4), recalculate the gas pressure in the measuring chamber. With the new gas pressure value in the measuring chamber, repeat the above steps for the next round of calculation. 3. Gas emission from borehole calculations When used the different pipe to determine the initial velocity of gas emission from borehole, the measured values are different because of the different resistance coefficient of the pipe. In this paper, we use copper pipe with 3 m in length and 1 cm in diameter (kd = 0.1). Fig. 1 is the schematic diagram measuring the gas emission rate. The values of gas storage parameters are shown in Table 1 taken for simulate the gas migration in coal seam and for calculating the gas emission. 3.1. The influence of gas pressure on gas emission rate from the pipe When the original gas pressure of coal seam is 2.0 MPa and 1.0 MPa, the variation of gas flow in borehole through the copper pipe with time is shown in Fig. 2. The figure shows that after the borehole is sealed, the gas emission rate increases rapidly and reached the maximum value quickly. Then the gas emission rate begins to attenuation rapidly, and the attenuation rate gets smaller and smaller. When the original gas pressure of coal seam is 2.0 MPa, the maximum value of gas emission rate is 144.4 L/min and appeared at 148 s. When the original gas pressure of coal seam is 1.0 MPa, the maximum value of gas emission rate is 60.6 L/min and appeared at 77 s. Compared with 2.0 MPa pressure in coal seam, when the original gas pressure of coal seam is 1.0 MPa, the maximum value of gas flow in borehole appeared 71 s earlier, and is 83.8 L/min less reduced by 58%. When the original gas pressure of coal seam is 2.0 MPa and 1.0 MPa, respectively, the value of gas emission rate in borehole is Q1 and Q2 respectively, so their difference is Q2–Q1. The value of (Q2–Q1)/Q1 is shown in Fig. 3. It can bee seen that as time
0.5m
2
1
ð5Þ ð6Þ
where Q is the gas flow rate out of the pipe, m3/s; pc, the gas pressure in the measuring chamber, Pa; po, the gas pressure in the roadway, Pa; Rf, the airway resistance, kg/m7; kd, the frictional loss coefficient; l, the airway length, m; d, the airway diameter, m; S, the airway cross-sectional area, m2 and q is the gas density, kg/m3.
3
5
4
6
3.5m 1-roadway 2-pipe 3-flowmeter 4-borehole 5-hole packer 6-measuring chamber Fig. 1. Shematic diagram measuring the initial velocity of gas emission.
871
J.-l. Gao, B. Shang / Safety Science 50 (2012) 869–872 Table 1 Values of gas storage parameters taken for simulation. ps (MPa)
p0 (MPa) 0.1
Gas emission rate (L/min)
2.0/1.0
k (m2)
l (MPa s) 1.08 10
12
3.6 10
q (kg/m3) 17
17
/1.8 10
0.716
140
Ps =2.0MPa
100
Ps =1.0MP
40 20 0
400
800
1200
1600
2000
Time (s) Fig. 2. Variation of gas emission rate with time at different gas pressure.
75%
Gas emission rate
1.45 10
a (m3/kg) 3
3
28 10
b (MPa1)
A (%)
M (%)
0.47
20
1.8
3.2. The influence of permeability coefficient on gas emission rate from the pipe
80 60
0
0.2
pm (t/m3)
which is 71.7%. After the maximum appeared, the difference falls slowly, and it varies around 71% nearby after the borehole sealing 30 min.
160 120
n (%)
70% 65% 60% 55% 50% 0
400
800
1200
1600
2000
When the permeability coefficient of coal seam is 6 m2/(MPa2 d) and 3 m2/(MPa2 d), respectively, the variation of gas emission rate through the copper pipe is shown in Fig. 4. When the permeability coefficient of coal seam is 6 m2/(MPa2 d), the maximum value of gas emission rate is 144.4 L/min and appeared at 148 s. When the permeability coefficient of coal seam is 3 m2/(MPa2 d), the maximum value of gas emission rate is 105.2 L/min and appeared at 125 s. Compared with 6 m2/(MPa2 d), when the permeability coefficient of coal seam is 3 m2/(MPa2 d), the maximum value of gas emission rate appeared earlier 23 s, reduce 39.2 L/min, by 27%. After the gas emission rate in borehole reaches the maximum, it begins to attenuation. The maximum value of gas emission rate and its appear time, and the attenuation rate at two different permeability coefficients of coal seam are shown in Table 2. The table shows that the smaller the permeability coefficient of coal seam is, the smaller the gas flow in borehole, and the earlier it appears. When the permeability coefficient of coal is smaller, the gas emission rate attenuation is faster. The value of gas emission rate from pipe attenuation reaches up to 60% when the permeability coefficient of coal seam is 3 m2/(MPa2 d).
Time (s)
Gas emission rate (L/min)
Fig. 3. Gas emission rate difference caused by coal seam pressure.
4. Conclusions The mathematical model of gas migration in the coal seam, gas flow into the measuring chamber, gas pressure change in the measuring chamber, and gas flow out of the chamber through the pipe is established. Gas migration in the coal seam, gas pressure in borehole chamber and gas flow in pipe is simulated using the finite difference method. Gas emission rate is obtained under dynamic boundary conditions. The influence of gas storage parameters on gas emission rate from borehole is analyzed.
210 180 150 120 90 60 30 0
0
400
800
1200
1600
2000
Time (s) Fig. 4. Variation of gas emission rate with time at different permeability coefficients of coal seam.
increases, the difference between the values of gas emission rate caused by the difference of original gas pressure in coal seam increased rapidly. At 471 s, the difference achieves the maximum
(1) After the borehole is sealed, the value of gas emission rate increases rapidly and reaches the maximum within 3 min. The larger the original gas pressure of coal seam and the permeability coefficient of coal seam are, the later the maximum gas emission rate appears. (2) Original gas pressure and permeability coefficient have great impacts on the value of gas emission rate. The difference increases rapidly within several minutes after the borehole is sealed, and then keeps stable. When the original gas pressure of coal seam is 2.0 MPa and 1.0 MPa, the difference of gas emission rate basically stays at about 71% after the
Table 2 Gas emission rate attenuation rate with time after reached the maximum. Permeability coefficient m2/(MPa2 d)
3.0 6.0
Maximum (L/min)
105.2 144.4
Appear time (s)
125 148
Attenuation rate 1 min (%)
2 min (%)
3 min (%)
15 min (%)
30 min (%)
2.7 1.7
8.5 5.3
14.9 9.8
50.3 43.4
60.0 53.0
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borehole is sealed for 30 min. When the permeability coefficient of coal seam is 6 m2/(MPa2 d) and 3 m2/(MPa2 d), the difference of gas emission rate basically stays at about 38% after the borehole is sealed for 30 min. (3) The gas emission rate begins to attenuation after it reaches the maximum. The attenuation rate is related to the original gas pressure and the permeability coefficient. The larger the gas pressure and the permeability coefficient are, the slower the attenuation after the gas emission rate reached the maximum. Acknowledgment The research project is sponsored by National Nature Science Foundation of China (Grant No. 51174079) and Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20104116110001). Thanks to NSFC and RFDP for the financial support.
References Liu, Haibo, Cheng, Yuanping, Wang, Haifeng, Shang, ZHengjie, 2009. Chang rule of initial speed of gas emission from borehole in outburst coal seam before and after pressure relief. Journal of Mining & Safety Engineering 26 (2), 225–228 (in Chinese). Wang, Kequan, 1993. Back analysis method of gas flow for determining gas pressure distribution around bore in coal seam. Journal of Xi’an Mining Institute 4, 309– 315 (in Chinese). Wang, Kequan, Yu, Bufan, 1989. Analysis the influence factors of initial velocity of gas emission from borehole. Coal Engineer 2, 32–36 (in Chinese). Wang, Kai, Yu, Qixiang, Jiang, Cheng-lin, 2001. Study of dynamic gas emission during boring process by using numerical simulation. Journal of China Coal Society 26 (3), 279–284 (in Chinese). Wei, Fengqing, Zhang, Pujing, 2004. Discussion on test depth of initial speed from borehole gas emission. Coal Science and Technology 32 (5), 61–64 (in Chinese). Zhou, Shining, 1990. Mechanism of gas flow in coal seams. Journal of China Coal Society 15 (1), 15–24 (in Chinese). Zhou, Shining, Lin, Boquan, 1999. The Theory of Gas Flow and Storage in Coal Seams. China Coal Industry Publishing House, Beijing, p. 69 (in Chinese).