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nitrogen mixtures
Energy 36 (2011) 5521e5524
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Effect of low temperature on the flammability limits of methane/nitrogen mixtures Zhenming Li a, b, Maoqiong Gong a, *, Eryan Sun a, c, Jianfeng Wu a,1, Yuan Zhou a a
Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, P. O. Box 2711, Beijing 100190, China China Electric Power Research Institute, Beijing 100192, China c Graduate university of Chinese Academy of Sciences, Beijing 100049, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 December 2010 Received in revised form 9 July 2011 Accepted 13 July 2011 Available online 10 August 2011
An experimental setup was established to measure the flammability limits of flammable gases at low temperatures. The flammability limits of methane/nitrogen mixtures in air were measured at atmospheric pressure and wide temperature range from 150 to 300 K. The estimated uncertainty of the experimental values was 0.2 vol%. The results reveal that as initial temperature decreases, the upper flammability limits (UFL) decrease while the lower flammability limits (LFL) increase. Therefore, the critical flammability ratio (CFR) decreases as the initial temperature decreases. In addition, the variation in the UFL is more sensitive than that in the LFL as the molar ratio of nitrogen to methane increases. In addition, an extended Le Chatelier’s formula with higher-order and temperature terms was proposed to correlate and predict the flammability limits at each temperature. The calculated values conformed to the experimental results for both the LFL and the UFL. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Flammability limits Low temperature range Methane Nitrogen Dilution effect
1. Introduction Coal-bed methane is considered as a new source of energy with great potential economic value. In addition, the extraction of coalbed methane could reduce the explosion accidents in coal mines and protect the atmospheric environment. It can be transported, stored, and utilized by liquefaction and purification expediently because of its high density during liquid phase. However, the liquefaction and purification may induce explosion by the oxygen in the original coal-bed methane. Hence, the flammability limit and the critical flammability ratio (CFR) of methane/nitrogen mixtures should be determined to ensure safety. Based on previous studies, the flammability limit ranges of methane at low temperatures are relatively narrower than those at normal and elevated temperatures [1e7]. A circular stainless steel tube approximately 50 mm in diameter and just over 1 m in length uniformly cooled by circulating liquid nitrogen was used to measure the lower flammability limits (LFL) of methane from 140 to 298 K and the upper flammability limits (UFL) of methane/
* Corresponding author. Tel./fax: þ86 10 82543728. E-mail addresses: [email protected] (M. Gong), [email protected] (J. Wu). 1 Tel./fax: þ86 10 62627843. 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.07.023
hydrogen mixtures at 213 K [5,7]. However, the experimental deviations were significantly high because of the increased lengthto-diameter ratio of the vessel [8]. There are few reports on the detailed effect of low temperature on the flammability characteristics and the CFR of methane/nitrogen/air mixtures. In the present study, an experimental apparatus was developed to measure the flammability limits of methane/nitrogen mixtures at low temperatures. Numerical correlation was also done to fit the flammability limits of methane in methane/nitrogen/air mixtures based on the results.
2. Experimental setup To date, a uniform experimental apparatus that can measure flammability limits at low temperatures has not yet been developed. In this study, an experimental setup was designed and established, as shown in Fig. 1. The explosion vessel is a vertical stainless steel cylinder with a length of 200 mm and an inner diameter of 100 mm. The total vessel is placed in a cryostat filled with gaseous nitrogen. Compared with Karim’s apparatus [5], the ratio of length to diameter is quite small to reduce the effect of vessel on the experimental measurement. The low temperature is provided by a self-made multi-component mixture Joule-Thomson cryocooler, by which the lowest temperature of 115 K can be obtained. Furthermore, the refrigeration cost for the cryogenic
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Z. Li et al. / Energy 36 (2011) 5521e5524
5
7
6
T
12
11 2
T
8 10
T
3 9
1
13
14 15 16
4
A
B
C
Fig. 1. Experimental apparatus 1 Cryostat; 2 Explosion vessel; 3 Electrode; 4 Igniting circuit; 5 Temperature measurement system; 6 Safe valve; 7 Pressure measurement system; 8 Evaporator; 9 Compressor; 10 Condenser; 11 Throttle; 12 Mixing vessel; 13 Desiccator; 14 Air; 15 Testing sample (Methane & Nitrogen); 16 Vacuum pump; A Measurement area; B Refrigeration area; C Mixture preparation area.
environment is also reduced. Great caution should be observed to ensure that the methane/nitrogen/air mixture is in the equilibrium state with the explosion vessel just before ignition. A pair of tungsten spark electrodes is positioned at 50 mm over the bottom of the vessel, and the distance between the two electrodes is approximately 5 mm. An electric spark is initiated by a 10 kV neon transformer, and the spark duration is 0.5 s. This induction spark between the couple electrodes is used as the ignition source. The provided energy is sufficient to overcome the minimum ignition threshold. The criteria for flammability are determined by whether the temperature increase is more than 100 K or the pressure increase is more than 10 kPa [9]. Some details about the experimental instruments are listed in Table 1. First, the methane/nitrogen blend is prepared in a mixing vessel based on the partial pressure ratio. The methane/nitrogen/air mixture is then prepared in another mixing vessel using the same
DyCH4
L ¼
a1 þ a2 2
pCH4 pCH4 þN2 ¼ pCH4 þ PN2 pCH4 þN2 þ pair
(1)
Table 1 Experimental instruments for measurement. Instrument
Measurement
Range
PT100 thermometer
Nitrogen bath temperature Initial temperature
80e300 K 0.1 K 70e600 K 1 K
Initial pressure Mixture preparation pressure
0e1 MPa 1 kPa 0 0.6 kPa e1.5 MPa
Copper-constantan thermocouple ZQ-BZ pressure transducer PMP4010 pressure transducer
Difference
(2)
If ja3 a4 j < 0:2 vol%,
U ¼
a3 þ a4 2
(3)
The uncertainty comes from the partial pressure measurement. The uncertainty can be expressed using the following equations:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 vyCH4 vyCH4 vyCH4 vyCH4 DPCH4 þ DPN2 þ DPCH4 þN2 þ DPair ¼ vPCH4 vPN2 vPCH4 þN2 vPair
method. The molar composition of methane can be obtained by the following equation:
yCH4
Before charging the premixed methane/nitrogen/air mixture, the explosion vessel is purged at least thrice with pure nitrogen to evacuate the remains of previous tests. After the desired mixture is introduced into the explosion vessel, there is at least a 10-min interval between introduction and ignition. Equations (2) and (3) show the determination of LFL and UFL. If ja1 a2 j < 0:1 vol%,
rffiffiffiffiffiffiffiffiffiffiffi 1 Dy u ¼ 2 i
(4)
(5)
Thus, the molar composition of methane in the mixture is estimated with the maximum uncertainty of 0.2 vol%, which is the uncertainty for the flammability limit. The flammability limit of methane was measured and compared with the referenced values [3]. The reference values were obtained in a 12 L3 spherical glass flask at 308 K and ambient pressure. As shown in Table 2, the absolute deviation was 0.1 vol% for the LFL and 0.1 vol% for the UFL. This experimental setup was proved to measure the explosion limits of flammable gases accurately. The sample gases of methane and nitrogen used in the present study were provided by Beijing Hepubeifen Company and Beijing Qianxijingcheng Company, respectively. The purity of both methane and nitrogen was 99.9 vol%. All sample materials were directly used without further purification.
Z. Li et al. / Energy 36 (2011) 5521e5524 Table 2 Comparison experimental values with referenced values of flammability limits for methane.
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Table 4 Critical flammability ratio (CFR) for methane/nitrogen mixtures at low temperatures.
Flammability Limits
Exp (vol%)
Ref (vol%)
Exp-Ref (vol%)
Temperature (K)
CFR
L0 U0
5.0 15.7
4.9 15.8
0.1 0.1
300 250 200 150
8.2 7.6 6.8 6.1
(0.1) (0.1) (0.1) (0.1)
Numbers in parentheses are measurement uncertainties.
3. Results and discussion The dilution effect of nitrogen on the flammability limits of methane was measured at atmospheric pressure and at 150, 200, 250, and 300 K. Data of flammability limits are summarized in Table 3. The CFR was determined experimentally and is shown in Table 4. CFR is the minimum concentration ratio of diluent to fuel in the ternary system of fuel/diluent/air when the mixture can never be flammable regardless of the air concentration [10]. As shown in Fig. 2, the UFL of methane decreases while the LFL remains nearly constant as the molar ratio of nitrogen to methane increases; both the flammable region area and the CFR decrease as the initial temperature decreases from 300 to 150 K. In general, flammability limits of mixtures may be calculated by Le Chatelier’s rule if the flammability limits of each component are known [11]. Although this rule can reasonably predict the flammability limits well, it is not applicable to mixtures with an inert gas. A detailed analysis was made on the molar heat of combustion of the flammability limit mixture; and an extended Le Chatelier’s formula was proposed to correlate the experimental results [3]. The
Table 3 Comparison calculated values with experimental values of flammability limits. Temperature r (K)
300
250
200
150
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 8.20 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 7.60 0.00 1.00 2.00 3.00 4.00 5.00 6.00 6.80 0.00 1.00 2.00 3.00 4.00 5.00 6.00 6.10
UfT
LfT Exp (vol%)
Calc (vol%)
Exp-Calc (vol%)
Exp (vol%)
Calc (vol%)
Exp-Calc (vol%)
5.00 4.95 4.83 4.83 4.86 4.87 4.84 4.86 5.03 5.07 5.10 5.00 4.94 5.00 4.97 5.04 5.06 5.11 5.23 5.34 5.33 5.28 5.27 5.29 5.24 5.30 5.44 5.45 5.50 5.45 5.47 5.39 5.50 5.64 5.70
5.00 4.99 4.98 4.97 4.96 4.96 4.97 5.01 5.06 5.08 5.15 5.14 5.13 5.11 5.10 5.11 5.12 5.16 5.19 5.30 5.29 5.28 5.26 5.25 5.25 5.27 5.30 5.46 5.45 5.43 5.42 5.41 5.41 5.43 5.43
0.00 0.04 0.15 0.14 0.10 0.09 0.13 0.15 0.03 0.01 0.05 0.14 0.19 0.11 0.13 0.07 0.06 0.05 0.04 0.04 0.04 0.00 0.01 0.04 0.01 0.03 0.14 0.01 0.05 0.02 0.05 0.02 0.09 0.21 0.27
15.70 12.25 10.03 8.78 7.74 6.86 6.24 5.71 5.16 5.07 15.60 12.10 10.02 8.59 7.57 6.82 6.19 5.61 5.23 14.85 11.78 9.75 8.42 7.43 6.68 6.01 5.44 14.35 11.55 9.52 8.34 7.36 6.62 5.76 5.70
15.70 11.40 10.20 9.10 7.98 6.93 6.05 5.46 5.28 5.29 15.28 11.12 9.97 8.92 7.83 6.80 5.94 5.37 5.21 14.86 10.84 9.74 8.73 7.67 6.67 5.82 5.35 14.45 10.57 9.52 8.54 7.52 6.53 5.71 5.64
0.00 0.85 0.17 0.32 0.24 0.07 0.19 0.25 0.12 0.22 0.32 0.98 0.05 0.33 0.26 0.02 0.25 0.24 0.02 0.01 0.94 0.01 0.31 0.24 0.01 0.19 0.09 0.01 0.98 0.00 0.20 0.16 0.09 0.05 0.06
Fig. 2. Flammability limits of methane diluted with nitrogen at atmospheric pressure and low temperatures.
dilution effect of the inert gas on the flammability limits of the fuel gas is more explicit. In this study, high-order and temperature terms were introduced into the extended Le Chatelier’s formula to improve the correlation accuracy and predict the flammability limits at each temperature from 150 to 300 K. The independent variable is the molar ratio of inert gas to fuel gas instead of the molar fraction of inert gas in the fuel-inert gas blend. The calculation is illustrated in Equation (6) to 8. The LFLs correlation (8) is written as follows:
c1 c1 ¼ þ br þ cr 2 LfT L0 ½1 þ aðT T0 Þ
(6)
Similarly, the UFL correlation can be expressed as
c 1 n1 c1 n1 ¼ þ er þ fr 2 þ gr 3 UfT 100 U0 ½1 þ dðT T0 Þ 100 c1
(7)
The value of n1 is determined by the following equation:
n1 ¼
0:21f100 U0 ½1 þ dðT T0 Þg U0 ½1 þ dðT T0 Þ
(8)
Table 5 Parameter values resulting from fitting calculation to flammability limits. Case
Lf Uf
Parameter values a, d
b, e
c, f
g
6.0857 104 5.323 104
2.049 104 7.748 104
3 105 1.7 104
e 1.09 105
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Z. Li et al. / Energy 36 (2011) 5521e5524
Table 6 The calculation difference resulting from fitting calculation to flammability limits. Case
Absolute difference Average (vol%)
Maximum (vol%)
Lf Uf
0.08 0.23
0.27 0.98
The calculated flammability limits are also listed in Table 3. The resulting parameter values and the calculated deviations are presented in Tables 5 and 6, respectively. The average absolute deviation was 0.08 vol% for the LFL and 0.23 vol% for the UFL; the maximum absolute deviation was 0.27 vol% for the LFL and 0.98 vol % for the UFL. The calculated values were in agreement with the experimental results for both the LFL and the UFL. 4. Conclusion An experimental setup was established to measure the flammability limits of methane/nitrogen/air mixtures at low temperatures. In the present study, the flammability limits of methane/nitrogen mixtures were measured at 150, 200, 250, and 300 K. The flammability limits were correlated by the extended Le Chatelier’s formula with higher-order and temperature terms to predict the flammability limits at each temperature from 150 to 300 K. The calculated values conformed to the experimental results for both the LFL and the UFL. Acknowledgements This investigation has been performed with the financial support of the National Natural Science Foundation of China (NSFC, Grant No.50776096). References [1] Takahashi A, Urano Y, Tokuhashi K, Nagai H, Kaise M, Kondo S. Fusing ignition of various metal wires for explosion limits measurement of methane/air mixture. Journal of Loss Prevention in the Process Industries 1998;11:353e60. [2] Vanderstraeten B, Tuerlinckx D, Berghmans J, Vliegen S, Van’t Oost E, Smit B. Experimental study of the pressure and temperature dependence on the upper flammability limit of methane/air mixtures. Journal of Hazardous Materials 1997;56:237e46.
[3] Kondo S, Takizawa K, Takahashi A, Tokuhashi K. Extended Le Chatelier’s formula and nitrogen dilution effect on the flammability limits. Fire Safety Journal 2006;41:406e17. [4] Chen CC, Wang TC, Liaw HJ, Chen HC. Nitrogen dilution effect on the flammability limits for hydrocarbons. Journal of Hazardous Materials 2009;166: 880e90. [5] Karim GA, Wierzba I, Boon S. The lean flammability limits in air of methane, hydrogen and carbon monoxide at low temperatures. Cryogenics 1984;24:305e8. [6] Wierzba I, Harris K, Karim GA. Effect of low temperature on the rich flammability limits of some gaseous fuels and their mixtures. Journal of Hazardous Materials 1990;25:257e65. [7] Wierzba I, Harris K, Karim GA. Effect of low temperature on the rich flammability limits in air of hydrogen and some fuel mixtures containing hydrogen. International Journal of Hydrogen Energy 1992;17:149e52. [8] Takahashi A, Urano Y, Tokuhashi K, Kondo S. Effect of vessel size and shape on experimental flammability limits of gases. Journal of Hazardous Materials 2003;105:27e37. [9] Shebeko YUN, Tsarichenko SG, Korolchenko AYA. Burning velocity and flammability limits of gasous mixtures at elevated temperatures and pressures. Combustion and Flame 1995;102:427e37. [10] Girodroux F, Kusmierz A, Dahn CJ. Determination of the critical flammability ratio (CFR) of refrigerant blends. Journal of Loss Prevention in the Process Industries 2000;13:385e92. [11] Le Chatelier H, Boudouard O. Limits of flammability of gaseous mixtures. Bulletin de la Société Chimique de Paris 1898;19:483e8.
Glossary a1: lowest gas concentration at which the flame can propagate a2: highest gas concentration at which the flame can’t propagate a3: highest gas concentration when the flame is capable of propagating a4: lowest gas concentration when the flame isn’t capable of propagating c1: molar fraction of methane in the methane/nitrogen blend CFR: critical flammability ratio L: Lower flammability limits L0: lower flammability limit of methane itself in air at normal temperature LfT: molar fraction of methane in the lower flammability limit mixture at low temperature T n1: mole number of oxygen consumed as the combustion of 1 mol methane in the upper flammability limit mixture pCH4: partial pressure of methane pN2: partial pressure of nitrogen pair: partial pressure of air pCH4þN2: pressure of the methane/nitrogen blend r: molar ratio of nitrogen to methane u: measurement uncertainty for the flammability limit U: upper flammability limits U0: upper flammability limit of methane itself in air at normal temperature UfT: molar fraction of methane in the upper flammability limit mixture at low temperature T yCH4: molar fraction of methane in the whole gas mixture a, b, c, d, e, f, g: correlated parameters to be determined by experimental values
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Effect of low temperature on the flammability limits of methane/nitrogen mixtures Zhenming Li a, b, Maoqiong Gong a, *, Eryan Sun a, c, Jianfeng Wu a,1, Yuan Zhou a a
Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, P. O. Box 2711, Beijing 100190, China China Electric Power Research Institute, Beijing 100192, China c Graduate university of Chinese Academy of Sciences, Beijing 100049, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 December 2010 Received in revised form 9 July 2011 Accepted 13 July 2011 Available online 10 August 2011
An experimental setup was established to measure the flammability limits of flammable gases at low temperatures. The flammability limits of methane/nitrogen mixtures in air were measured at atmospheric pressure and wide temperature range from 150 to 300 K. The estimated uncertainty of the experimental values was 0.2 vol%. The results reveal that as initial temperature decreases, the upper flammability limits (UFL) decrease while the lower flammability limits (LFL) increase. Therefore, the critical flammability ratio (CFR) decreases as the initial temperature decreases. In addition, the variation in the UFL is more sensitive than that in the LFL as the molar ratio of nitrogen to methane increases. In addition, an extended Le Chatelier’s formula with higher-order and temperature terms was proposed to correlate and predict the flammability limits at each temperature. The calculated values conformed to the experimental results for both the LFL and the UFL. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Flammability limits Low temperature range Methane Nitrogen Dilution effect
1. Introduction Coal-bed methane is considered as a new source of energy with great potential economic value. In addition, the extraction of coalbed methane could reduce the explosion accidents in coal mines and protect the atmospheric environment. It can be transported, stored, and utilized by liquefaction and purification expediently because of its high density during liquid phase. However, the liquefaction and purification may induce explosion by the oxygen in the original coal-bed methane. Hence, the flammability limit and the critical flammability ratio (CFR) of methane/nitrogen mixtures should be determined to ensure safety. Based on previous studies, the flammability limit ranges of methane at low temperatures are relatively narrower than those at normal and elevated temperatures [1e7]. A circular stainless steel tube approximately 50 mm in diameter and just over 1 m in length uniformly cooled by circulating liquid nitrogen was used to measure the lower flammability limits (LFL) of methane from 140 to 298 K and the upper flammability limits (UFL) of methane/
* Corresponding author. Tel./fax: þ86 10 82543728. E-mail addresses: [email protected] (M. Gong), [email protected] (J. Wu). 1 Tel./fax: þ86 10 62627843. 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.07.023
hydrogen mixtures at 213 K [5,7]. However, the experimental deviations were significantly high because of the increased lengthto-diameter ratio of the vessel [8]. There are few reports on the detailed effect of low temperature on the flammability characteristics and the CFR of methane/nitrogen/air mixtures. In the present study, an experimental apparatus was developed to measure the flammability limits of methane/nitrogen mixtures at low temperatures. Numerical correlation was also done to fit the flammability limits of methane in methane/nitrogen/air mixtures based on the results.
2. Experimental setup To date, a uniform experimental apparatus that can measure flammability limits at low temperatures has not yet been developed. In this study, an experimental setup was designed and established, as shown in Fig. 1. The explosion vessel is a vertical stainless steel cylinder with a length of 200 mm and an inner diameter of 100 mm. The total vessel is placed in a cryostat filled with gaseous nitrogen. Compared with Karim’s apparatus [5], the ratio of length to diameter is quite small to reduce the effect of vessel on the experimental measurement. The low temperature is provided by a self-made multi-component mixture Joule-Thomson cryocooler, by which the lowest temperature of 115 K can be obtained. Furthermore, the refrigeration cost for the cryogenic
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Z. Li et al. / Energy 36 (2011) 5521e5524
5
7
6
T
12
11 2
T
8 10
T
3 9
1
13
14 15 16
4
A
B
C
Fig. 1. Experimental apparatus 1 Cryostat; 2 Explosion vessel; 3 Electrode; 4 Igniting circuit; 5 Temperature measurement system; 6 Safe valve; 7 Pressure measurement system; 8 Evaporator; 9 Compressor; 10 Condenser; 11 Throttle; 12 Mixing vessel; 13 Desiccator; 14 Air; 15 Testing sample (Methane & Nitrogen); 16 Vacuum pump; A Measurement area; B Refrigeration area; C Mixture preparation area.
environment is also reduced. Great caution should be observed to ensure that the methane/nitrogen/air mixture is in the equilibrium state with the explosion vessel just before ignition. A pair of tungsten spark electrodes is positioned at 50 mm over the bottom of the vessel, and the distance between the two electrodes is approximately 5 mm. An electric spark is initiated by a 10 kV neon transformer, and the spark duration is 0.5 s. This induction spark between the couple electrodes is used as the ignition source. The provided energy is sufficient to overcome the minimum ignition threshold. The criteria for flammability are determined by whether the temperature increase is more than 100 K or the pressure increase is more than 10 kPa [9]. Some details about the experimental instruments are listed in Table 1. First, the methane/nitrogen blend is prepared in a mixing vessel based on the partial pressure ratio. The methane/nitrogen/air mixture is then prepared in another mixing vessel using the same
DyCH4
L ¼
a1 þ a2 2
pCH4 pCH4 þN2 ¼ pCH4 þ PN2 pCH4 þN2 þ pair
(1)
Table 1 Experimental instruments for measurement. Instrument
Measurement
Range
PT100 thermometer
Nitrogen bath temperature Initial temperature
80e300 K 0.1 K 70e600 K 1 K
Initial pressure Mixture preparation pressure
0e1 MPa 1 kPa 0 0.6 kPa e1.5 MPa
Copper-constantan thermocouple ZQ-BZ pressure transducer PMP4010 pressure transducer
Difference
(2)
If ja3 a4 j < 0:2 vol%,
U ¼
a3 þ a4 2
(3)
The uncertainty comes from the partial pressure measurement. The uncertainty can be expressed using the following equations:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 vyCH4 vyCH4 vyCH4 vyCH4 DPCH4 þ DPN2 þ DPCH4 þN2 þ DPair ¼ vPCH4 vPN2 vPCH4 þN2 vPair
method. The molar composition of methane can be obtained by the following equation:
yCH4
Before charging the premixed methane/nitrogen/air mixture, the explosion vessel is purged at least thrice with pure nitrogen to evacuate the remains of previous tests. After the desired mixture is introduced into the explosion vessel, there is at least a 10-min interval between introduction and ignition. Equations (2) and (3) show the determination of LFL and UFL. If ja1 a2 j < 0:1 vol%,
rffiffiffiffiffiffiffiffiffiffiffi 1 Dy u ¼ 2 i
(4)
(5)
Thus, the molar composition of methane in the mixture is estimated with the maximum uncertainty of 0.2 vol%, which is the uncertainty for the flammability limit. The flammability limit of methane was measured and compared with the referenced values [3]. The reference values were obtained in a 12 L3 spherical glass flask at 308 K and ambient pressure. As shown in Table 2, the absolute deviation was 0.1 vol% for the LFL and 0.1 vol% for the UFL. This experimental setup was proved to measure the explosion limits of flammable gases accurately. The sample gases of methane and nitrogen used in the present study were provided by Beijing Hepubeifen Company and Beijing Qianxijingcheng Company, respectively. The purity of both methane and nitrogen was 99.9 vol%. All sample materials were directly used without further purification.
Z. Li et al. / Energy 36 (2011) 5521e5524 Table 2 Comparison experimental values with referenced values of flammability limits for methane.
5523
Table 4 Critical flammability ratio (CFR) for methane/nitrogen mixtures at low temperatures.
Flammability Limits
Exp (vol%)
Ref (vol%)
Exp-Ref (vol%)
Temperature (K)
CFR
L0 U0
5.0 15.7
4.9 15.8
0.1 0.1
300 250 200 150
8.2 7.6 6.8 6.1
(0.1) (0.1) (0.1) (0.1)
Numbers in parentheses are measurement uncertainties.
3. Results and discussion The dilution effect of nitrogen on the flammability limits of methane was measured at atmospheric pressure and at 150, 200, 250, and 300 K. Data of flammability limits are summarized in Table 3. The CFR was determined experimentally and is shown in Table 4. CFR is the minimum concentration ratio of diluent to fuel in the ternary system of fuel/diluent/air when the mixture can never be flammable regardless of the air concentration [10]. As shown in Fig. 2, the UFL of methane decreases while the LFL remains nearly constant as the molar ratio of nitrogen to methane increases; both the flammable region area and the CFR decrease as the initial temperature decreases from 300 to 150 K. In general, flammability limits of mixtures may be calculated by Le Chatelier’s rule if the flammability limits of each component are known [11]. Although this rule can reasonably predict the flammability limits well, it is not applicable to mixtures with an inert gas. A detailed analysis was made on the molar heat of combustion of the flammability limit mixture; and an extended Le Chatelier’s formula was proposed to correlate the experimental results [3]. The
Table 3 Comparison calculated values with experimental values of flammability limits. Temperature r (K)
300
250
200
150
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 8.20 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 7.60 0.00 1.00 2.00 3.00 4.00 5.00 6.00 6.80 0.00 1.00 2.00 3.00 4.00 5.00 6.00 6.10
UfT
LfT Exp (vol%)
Calc (vol%)
Exp-Calc (vol%)
Exp (vol%)
Calc (vol%)
Exp-Calc (vol%)
5.00 4.95 4.83 4.83 4.86 4.87 4.84 4.86 5.03 5.07 5.10 5.00 4.94 5.00 4.97 5.04 5.06 5.11 5.23 5.34 5.33 5.28 5.27 5.29 5.24 5.30 5.44 5.45 5.50 5.45 5.47 5.39 5.50 5.64 5.70
5.00 4.99 4.98 4.97 4.96 4.96 4.97 5.01 5.06 5.08 5.15 5.14 5.13 5.11 5.10 5.11 5.12 5.16 5.19 5.30 5.29 5.28 5.26 5.25 5.25 5.27 5.30 5.46 5.45 5.43 5.42 5.41 5.41 5.43 5.43
0.00 0.04 0.15 0.14 0.10 0.09 0.13 0.15 0.03 0.01 0.05 0.14 0.19 0.11 0.13 0.07 0.06 0.05 0.04 0.04 0.04 0.00 0.01 0.04 0.01 0.03 0.14 0.01 0.05 0.02 0.05 0.02 0.09 0.21 0.27
15.70 12.25 10.03 8.78 7.74 6.86 6.24 5.71 5.16 5.07 15.60 12.10 10.02 8.59 7.57 6.82 6.19 5.61 5.23 14.85 11.78 9.75 8.42 7.43 6.68 6.01 5.44 14.35 11.55 9.52 8.34 7.36 6.62 5.76 5.70
15.70 11.40 10.20 9.10 7.98 6.93 6.05 5.46 5.28 5.29 15.28 11.12 9.97 8.92 7.83 6.80 5.94 5.37 5.21 14.86 10.84 9.74 8.73 7.67 6.67 5.82 5.35 14.45 10.57 9.52 8.54 7.52 6.53 5.71 5.64
0.00 0.85 0.17 0.32 0.24 0.07 0.19 0.25 0.12 0.22 0.32 0.98 0.05 0.33 0.26 0.02 0.25 0.24 0.02 0.01 0.94 0.01 0.31 0.24 0.01 0.19 0.09 0.01 0.98 0.00 0.20 0.16 0.09 0.05 0.06
Fig. 2. Flammability limits of methane diluted with nitrogen at atmospheric pressure and low temperatures.
dilution effect of the inert gas on the flammability limits of the fuel gas is more explicit. In this study, high-order and temperature terms were introduced into the extended Le Chatelier’s formula to improve the correlation accuracy and predict the flammability limits at each temperature from 150 to 300 K. The independent variable is the molar ratio of inert gas to fuel gas instead of the molar fraction of inert gas in the fuel-inert gas blend. The calculation is illustrated in Equation (6) to 8. The LFLs correlation (8) is written as follows:
c1 c1 ¼ þ br þ cr 2 LfT L0 ½1 þ aðT T0 Þ
(6)
Similarly, the UFL correlation can be expressed as
c 1 n1 c1 n1 ¼ þ er þ fr 2 þ gr 3 UfT 100 U0 ½1 þ dðT T0 Þ 100 c1
(7)
The value of n1 is determined by the following equation:
n1 ¼
0:21f100 U0 ½1 þ dðT T0 Þg U0 ½1 þ dðT T0 Þ
(8)
Table 5 Parameter values resulting from fitting calculation to flammability limits. Case
Lf Uf
Parameter values a, d
b, e
c, f
g
6.0857 104 5.323 104
2.049 104 7.748 104
3 105 1.7 104
e 1.09 105
5524
Z. Li et al. / Energy 36 (2011) 5521e5524
Table 6 The calculation difference resulting from fitting calculation to flammability limits. Case
Absolute difference Average (vol%)
Maximum (vol%)
Lf Uf
0.08 0.23
0.27 0.98
The calculated flammability limits are also listed in Table 3. The resulting parameter values and the calculated deviations are presented in Tables 5 and 6, respectively. The average absolute deviation was 0.08 vol% for the LFL and 0.23 vol% for the UFL; the maximum absolute deviation was 0.27 vol% for the LFL and 0.98 vol % for the UFL. The calculated values were in agreement with the experimental results for both the LFL and the UFL. 4. Conclusion An experimental setup was established to measure the flammability limits of methane/nitrogen/air mixtures at low temperatures. In the present study, the flammability limits of methane/nitrogen mixtures were measured at 150, 200, 250, and 300 K. The flammability limits were correlated by the extended Le Chatelier’s formula with higher-order and temperature terms to predict the flammability limits at each temperature from 150 to 300 K. The calculated values conformed to the experimental results for both the LFL and the UFL. Acknowledgements This investigation has been performed with the financial support of the National Natural Science Foundation of China (NSFC, Grant No.50776096). References [1] Takahashi A, Urano Y, Tokuhashi K, Nagai H, Kaise M, Kondo S. Fusing ignition of various metal wires for explosion limits measurement of methane/air mixture. Journal of Loss Prevention in the Process Industries 1998;11:353e60. [2] Vanderstraeten B, Tuerlinckx D, Berghmans J, Vliegen S, Van’t Oost E, Smit B. Experimental study of the pressure and temperature dependence on the upper flammability limit of methane/air mixtures. Journal of Hazardous Materials 1997;56:237e46.
[3] Kondo S, Takizawa K, Takahashi A, Tokuhashi K. Extended Le Chatelier’s formula and nitrogen dilution effect on the flammability limits. Fire Safety Journal 2006;41:406e17. [4] Chen CC, Wang TC, Liaw HJ, Chen HC. Nitrogen dilution effect on the flammability limits for hydrocarbons. Journal of Hazardous Materials 2009;166: 880e90. [5] Karim GA, Wierzba I, Boon S. The lean flammability limits in air of methane, hydrogen and carbon monoxide at low temperatures. Cryogenics 1984;24:305e8. [6] Wierzba I, Harris K, Karim GA. Effect of low temperature on the rich flammability limits of some gaseous fuels and their mixtures. Journal of Hazardous Materials 1990;25:257e65. [7] Wierzba I, Harris K, Karim GA. Effect of low temperature on the rich flammability limits in air of hydrogen and some fuel mixtures containing hydrogen. International Journal of Hydrogen Energy 1992;17:149e52. [8] Takahashi A, Urano Y, Tokuhashi K, Kondo S. Effect of vessel size and shape on experimental flammability limits of gases. Journal of Hazardous Materials 2003;105:27e37. [9] Shebeko YUN, Tsarichenko SG, Korolchenko AYA. Burning velocity and flammability limits of gasous mixtures at elevated temperatures and pressures. Combustion and Flame 1995;102:427e37. [10] Girodroux F, Kusmierz A, Dahn CJ. Determination of the critical flammability ratio (CFR) of refrigerant blends. Journal of Loss Prevention in the Process Industries 2000;13:385e92. [11] Le Chatelier H, Boudouard O. Limits of flammability of gaseous mixtures. Bulletin de la Société Chimique de Paris 1898;19:483e8.
Glossary a1: lowest gas concentration at which the flame can propagate a2: highest gas concentration at which the flame can’t propagate a3: highest gas concentration when the flame is capable of propagating a4: lowest gas concentration when the flame isn’t capable of propagating c1: molar fraction of methane in the methane/nitrogen blend CFR: critical flammability ratio L: Lower flammability limits L0: lower flammability limit of methane itself in air at normal temperature LfT: molar fraction of methane in the lower flammability limit mixture at low temperature T n1: mole number of oxygen consumed as the combustion of 1 mol methane in the upper flammability limit mixture pCH4: partial pressure of methane pN2: partial pressure of nitrogen pair: partial pressure of air pCH4þN2: pressure of the methane/nitrogen blend r: molar ratio of nitrogen to methane u: measurement uncertainty for the flammability limit U: upper flammability limits U0: upper flammability limit of methane itself in air at normal temperature UfT: molar fraction of methane in the upper flammability limit mixture at low temperature T yCH4: molar fraction of methane in the whole gas mixture a, b, c, d, e, f, g: correlated parameters to be determined by experimental values