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Experimental measurement and numerical analysis of binary hydrocarbon mixture flammability limits
process safety and environmental protection 8 7 ( 2 0 0 9 ) 94–104
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Process Safety and Environmental Protection journal homepage: www.elsevier.com/locate/psep
Experimental measurement and numerical analysis of binary hydrocarbon mixture flammability limits Fuman Zhao, William J. Rogers, M. Sam Mannan ∗ Mary Kay O’Connor Process Safety Center, Artie McFerrin Department of Chemical Engineering, Texas A&M University System, 3122 TAMU, College Station, TX 77843-3122, USA
a b s t r a c t The flammability limits of binary hydrocarbon mixtures in air were measured in a combustion apparatus using an innovative method developed for this apparatus. The experimental results were obtained at standard conditions (room temperature and ambient atmospheric pressure) with upward flame propagation. The experimentally determined flammability limits for pure hydrocarbons (methane and ethylene) were compared with existing data reported in the literature. Le Chatelier’s Law was fit to all experimental data to obtain LFLs and UFLs for various two-component combinations of saturated and unsaturated hydrocarbons (methane, ethylene, acetylene, propane, propylene, and n-butane). A modification of this law was used if experimental observations showed large deviations from Le Chatelier’s predictions. Also, experimentally measured flammability limit data of the binary hydrocarbon mixtures were analytically related to the stoichiometric concentrations. © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Flammability limits; Experimental measurement; Numerical analysis; Binary hydrocarbon mixtures; Le Chatelier’s Law
1.
Introduction
Flammability limits, sometimes referred to as explosion limits (De Smedt et al., 1999), are defined as the volume percentage concentration range in air in which a flammable substance can produce a fire or explosion when an ignition source (such as a spark or open flame) is present. Additionally, flammability limits are divided into two types: (i) the upper flammable limit (UFL) above which the fuel concentration is too rich (deficient in oxygen) to burn; (ii) the lower flammability limit (LFL) below which the fuel concentration becomes too lean (sufficient in oxygen) to be ignited. Usually, the limits are experimentally obtained by determining the limiting mixture compositions between flammable and non-flammable mixtures (Zabetakis and Richmond, 1953), that is, LFLT,P =
1 (Cg,n + Cl,f ) 2
(1)
UFLT,P =
1 (C + Cl,n ) 2 g,f
(2)
∗
where LFLT,P , UFLT,P are lower flammability limit and upper flammability limit at a specific temperature and pressure; Cg,n , Cl,n are the greatest concentration and the least concentration of a fuel in an oxidant that are nonflammable; Cl,f , Cg,f are the greatest concentration and the least concentration of a fuel in an oxidant that are flammable. Previously, flammability limits were determined by visual identification. This criterion for flammability limit estimation is flame propagation from the point of ignition to a certain distance. The best known experimental method using visual identification for measuring flammability limits of premixed gases is that developed by the Bureau of Mines (BM) (Coward and Jones, 1952). For a mixture to be declared flammable, propagation has to occur at least half way of a glass tube with 1.5 m length and 50 mm i.d. By using this method, BM generated a large body of flammability limits data for pure gases as well as some gas mixtures. Much of the work was done and summarized by Coward and Jones (1952), Zabetakis (1965), and Kuchta (1985) through BM Bulletin publications. In recent years, apparatus with closed, steel, spherical reaction vessels and center ignition also have been used for
Corresponding author. Tel.: +1 979 862 3985. E-mail address: [email protected] (M. Sam Mannan). Received 16 May 2008; Received in revised form 14 June 2008; Accepted 16 June 2008 0957-5820/$ – see front matter © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.psep.2008.06.003
process safety and environmental protection 8 7 ( 2 0 0 9 ) 94–104
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Fig. 1 – Flammability experimental apparatus. flammability limit measurement. Unlike a visual detection apparatus, the detection criterion is the relative pressure increase in a reaction vessel resulting from combustion. Burgess et al. published data from a 25,500 L sphere vessel that incorporated a 7% pressure rise criterion (Burgess et al., 1982), and Cashdollar et al. (2000) published data from 20 to 120 L chambers with 3% and 7% pressure rise criteria, respectively. Flammability limits also have been tested indirectly using counterflow burners, where twin gas jets of premixed fuel and oxidizer are released from opposing nozzles against each other, and ignited to produce twin, planar flames. The average gas exit velocity, often called stretch rate, is measured at different fuel concentrations. The fuel concentration is plotted as a function of stretch rate. The fuel concentration is extrap-
Fig. 3 – Temperature (top) and pressure (bottom) profiles for non-propagation combustion (1.5% methane in air at 25 ◦ C and 14.7 psi).
Fig. 2 – Reaction vessel.
olated linearly to a stretch rate of zero, and the intercept is taken as the flammability limit (Ju et al., 1999). Flammability data for pure fuels are usually available, while industrially, single phase or multiphase flammable mixtures are probably even more important than pure fuels. Unfortunately, our flammability knowledge of mixing fuels is approximately limited to Le Chatelier’s Law. Le Chatelier arrived at his mixture rule for lower flammability limits of gas mixtures (American Society of Heating, 1999). The proposed empirical mixing rule is expressed as Eq. (3). In addition, Kondo et al. (2006) showed that Le Chatelier’s Law
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Fig. 4 – Temperature (top) and pressure (bottom) profiles for flash combustion (4.35% methane in air at 25 ◦ C and 14.7 psi).
Fig. 5 – Temperature (top) and pressure (bottom) profiles for discontinuous flame propagation (5.10% methane in air at 25 ◦ C and 14.7 psi). satisfactory estimation.
can be extended to estimate upper flammability limit for some blended fuels with acceptable accuracy as in Eq. (4). Algebraically, Le Chatelier’s method states that the mixture flammability limit has a value between the maximum and minimum of the pure component flammability limits. Because Le Chatelier’s Law is an empirically summarized formula which is originated from the evaluation of mixing flammability at lower fuel concentrations (LFLs), its extended application at higher fuel concentrations (UFLs) is limited to certain fuel mixtures (Kondo et al., 2006). Mashuga and Crowl (2000) developed a theoretical derivation for this law with several pre-required assumptions. At lower fuel concentrations with greater inter-molecular separation, these assumptions are more consistent with real situations. Therefore, Le Chatelier’s Law can provide more reasonable estimation of lower flammability limits of fuel mixtures. At concentrations of upper flammability limits, the assumptions of this model deviate significantly from real conditions, and result in less
LFLmix =
N
UFLmix =
N
1
(3)
y /LFLi i=1 i 1
(4)
y /UFLi i=1 i
where yi is the mole fraction of the ith component considering only the combustible species; LFLi , UFLi are the lower and upper flammability limit of the ith component in volume percent; LFLmix , UFLmix are the lower and upper flammability limit of the fuel mixtures. In this paper, an innovative detection method was conducted to measure the lower and upper flammability limits of binary saturated/unsaturated hydrocarbon mixtures. The validity of Le Chatelier’s Law was evaluated for those fuel mixtures, and a modification of this law was developed from the experimental data.
Table 1 – Probabilities of continuous flame propagation at different concentrations of methane in air Methane conc. (molar %)a 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 a
Measurement times 10 10 10 10 10 10 10 10
Room temperature (25 ◦ C) and 1 atmospheric pressure.
Continuous flame propagation times 0 2 4 4 7 7 8 10
Probability of continuous propagation (%) 0 20 40 40 70 70 80 100
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Table 2 – Probabilities of continuous flame propagation at different concentrations of ethylene in air Ethylene conc. (molar %)a
Measurement times
2.78 2.79 2.80 2.81 2.82 2.83 2.84 a
Continuous flame propagation times
10 10 10 10 10 10 10
Probability of continuous propagation (%)
0 2 4 6 7 7 10
0 20 40 60 70 70 100
Room temperature (25 ◦ C) and 1 atmospheric pressure.
Table 3 – Low flammability limits of pure methane and pure ethylene in air (25 ◦ C and 1 atm) Methane LFL in air (%)
Ethylene LFL in air (%)
5.3 4.85 4.3 4.95 4.66 5.25 ± 0.05
Apparatus types
3.05 2.62 2.4 2.6 NA 2.81 ± 0.05
Vertical glass cylinder 20 L sphere, 7% pressure rise EN 1839 (T) EN 1839 (B) Counterflow burner This research
Table 4 – Flammability limit data from experimental measurements and Le Chatelier’s Law (methane and n-butane mixtures) xa (CH4 %)
LFLsb This research
0 12.5 25 37.5 50 62.5 75 87.5 100 a b
1.72 1.86 2.05 2.29 2.56 2.95 3.49 4.19 5.25
Le Chatelier’s 1.72 1.88 2.07 2.30 2.59 2.97 3.47 4.18 5.25
UFLsb Dev
Dev (%)
This research
Le Chatelier’s
Dev
Dev (%)
0.00 −0.02 −0.02 −0.01 −0.03 −0.02 0.02 0.01 0.00
0.00 0.96 0.86 0.43 1.22 0.57 0.58 0.28 0.00
8.46 8.91 9.48 10.11 10.83 11.82 12.71 14.12 15.80
8.46 8.98 9.57 10.24 11.02 11.92 12.98 14.25 15.80
0.00 −0.07 −0.09 −0.13 −0.19 −0.10 −0.27 −0.13 0.00
0.00 0.80 0.97 1.33 1.75 0.86 2.15 0.95 0.00
Percentage fractions of methane in methane and n-butane mixtures. Data obtained at room temperature and atmospheric pressure.
Table 5 – Flammability limit data from experimental measurements and Le Chatelier’s Law (methane and propane mixtures) xa (CH4 %)
LFLsb This research
0 12.5 25 37.5 50 62.5 75 87.5 100 a b
2.09 2.24 2.45 2.73 2.97 3.36 3.84 4.40 5.25
UFLsb
Le Chatelier’s
Dev
2.09 2.26 2.46 2.70 2.99 3.35 3.81 4.42 5.25
0.00 −0.02 −0.01 0.03 −0.02 0.03 0.03 −0.02 0.00
Dev (%) 0.00 0.89 0.41 1.11 0.67 0.89 0.78 0.45 0.00
Percentage fractions of methane in methane and propane mixtures. Data obtained at room temperature and atmospheric pressure.
This research
Le Chatelier’s
Dev
Dev (%)
10.09 10.44 10.85 11.47 12.03 12.77 13.46 14.59 15.80
10.09 10.57 11.09 11.67 12.32 13.03 13.84 14.76 15.80
0.00 −0.13 −0.24 −0.20 −0.29 −0.26 −0.38 −0.17 0.00
0.00 1.24 2.21 1.74 2.41 2.04 2.82 1.17 0.00
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Table 6 – Flammability limit data from experimental measurements and Le Chatelier’s Law (methane and ethylene mixtures) xa (CH4 %)
LFLsb This research
0 12.5 25 37.5 50 62.5 75 87.5 100 a b
Le Chatelier’s
2.81 3.01 3.20 3.37 3.68 4.01 4.30 4.71 5.25
2.81 2.98 3.18 3.40 3.66 3.96 4.31 4.74 5.25
UFLsb Dev
Dev (%)
This research
Le Chatelier’s
Dev
Dev (%)
0.00 0.03 0.02 −0.03 0.02 0.05 −0.01 −0.03 0.00
0.00 0.89 0.64 0.98 0.53 1.24 0.32 0.55 0.00
30.61 29.62 26.66 23.54 20.59 18.34 17.11 16.55 15.80
30.61 27.40 24.80 22.65 20.84 19.30 17.97 16.82 15.80
0.00 2.22 1.86 0.89 −0.25 −0.96 −0.86 −0.27 0.00
0.00 7.50 6.98 3.79 1.22 5.25 5.05 1.61 0.00
Percentage fractions of methane in methane and ethylene mixtures. Data obtained at room temperature and atmospheric pressure.
Table 7 – Flammability limit data from experimental measurements and Le Chatelier’s Law (methane and acetylene mixtures) LFLsb
xa (CH4 %) This research 0 12.5 25 37.5 50 62.5 75 87.5 100 a b
Le Chatelier’s
2.42 2.61 2.83 3.00 3.26 3.68 4.08 4.55 5.25
2.42 2.59 2.80 3.03 3.31 3.65 4.06 4.58 5.25
UFLsb Dev
Dev (%)
This research
Le Chatelier’s
Dev
Dev (%)
0.00 0.02 0.03 −0.03 −0.05 0.03 0.02 −0.03 0.00
0.00 0.58 1.17 1.10 1.62 0.83 0.43 0.67 0.00
77.31 72.12 60.53 51.24 46.07 31.45 22.38 19.46 15.80
77.31 52.00 39.18 31.43 26.24 22.52 19.72 17.54 15.80
0.00 20.12 21.35 19.81 19.83 8.93 2.66 1.92 0.00
0.00 27.89 35.27 38.66 43.05 28.40 11.87 9.84 0.00
Percentage fractions of methane in methane and acetylene mixtures. Data obtained at room temperature and atmospheric pressure.
2.
Experimental method
2.1.
Flammability apparatus
The reaction vessel (Fig. 2) is a closed cylinder with dimensions of 11.43 cm o.d., 10.22 cm i.d. and 100 cm length. At the central line of the reaction vessel, there are five evenly separated temperature sensors consisting of NTC thermistors (Thermometrics, FP07DB104N with fast response time 0.1 sec in still air and 100 K resistance at 25 ◦ C), which can detect a flame front in real time and locate a self-sustained frame propagation distance when fuel/air mixtures ignite and combust upwardly. The greatest distance from the ignition source to thermistor 5 is 75 cm. This design is consistent with the
The flammability apparatus used in this research was developed by Wong (2006) at Texas A&M University and is showed in Fig. 1. The apparatus consists of: (i) reaction vessel; (ii) gas feeding system; (iii) gas mixer; (iv) gas mixture ignition system; and (v) data acquisition system.
Table 8 – Flammability limit data from experimental measurements and Le Chatelier’s Law (ethylene and propylene mixtures) xa (C2 H4 %)
LFLsb This research
0 12.5 25 37.5 50 62.5 75 87.5 100 a b
2.28 2.32 2.43 2.41 2.52 2.55 2.64 2.75 2.81
Le Chatelier’s 2.28 2.34 2.39 2.45 2.52 2.58 2.66 2.73 2.81
UFLsb Dev
Dev (%)
This research
Le Chatelier’s
Dev
Dev (%)
0.00 −0.02 0.04 −0.04 0.00 −0.03 −0.02 0.02 0.00
0.00 0.65 1.53 1.81 0.10 1.36 0.59 0.70 0.00
10.25 10.38 11.66 12.81 14.04 17.31 22.64 27.23 30.61
10.25 11.18 12.29 13.66 15.36 17.54 20.45 24.52 30.61
0.00 −0.80 −0.63 −0.85 −1.32 −0.23 2.19 2.71 0.00
0.00 7.70 5.44 6.61 9.38 1.34 9.66 9.95 0.00
Percentage fractions of ethylene in ethylene and propylene mixtures. Data obtained at room temperature and atmospheric pressure.
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Table 9 – Flammability limit data from experimental measurements and Le Chatelier’s Law (ethylene and acetylene mixtures) xa (C2 H4 %)
LFLsb This research
0 12.5 25 37.5 50 62.5 75 87.5 100 a b
2.42 2.44 2.50 2.58 2.61 2.68 2.68 2.72 2.81
Le Chatelier’s 2.42 2.46 2.51 2.55 2.60 2.65 2.70 2.75 2.81
UFLsb Dev
Dev (%)
This research
Le Chatelier’s
Dev
Dev (%)
0.00 −0.02 −0.01 0.03 0.01 0.03 −0.02 −0.03 0.00
0.00 0.93 0.28 1.05 0.37 1.12 0.79 1.27 0.00
77.31 67.42 58.21 52.36 45.54 42.12 38.66 35.25 30.61
77.31 64.93 55.96 49.18 43.86 39.57 36.05 33.11 30.61
0.00 2.49 2.25 3.18 1.68 2.55 2.61 2.14 0.00
0.00 3.70 3.86 6.08 3.70 6.04 6.74 6.07 0.00
Percentage fractions of ethylene in ethylene and acetylene mixtures. Data obtained at room temperature and atmospheric pressure.
flammability apparatus of BM when visual observation is used as a flammability limit detection criterion (Coward and Jones, 1952). Thermistor 1 is located at a distance of 15 cm from the ignition source (at the bottom of reaction vessel). At the top of reaction vessel is a dynamic pressure transducer (Omega DPX 101, with a range of 0–250 psig pressure rise, 0–5 V nominal output signal, 1 s rise time, 1% amplitude linearity and temperature effect of 0.03%/F) mounted on the top plate and used to record the pressure variation when fuel/air mixtures ignite or explode. The gas feeding system includes a manifold that connects to chemical cylinders, a vacuum pump, the mixing vessel, and the reaction vessel. The gas mixtures used with the experimental apparatus are synthesized by loading the individual components from pressurized cylinders. Mixture composition is controlled through partial pressure gauging recommended by BM (Burgess et al., 1982). Theoretically, at the conditions of
Fig. 7 – Temperature (top) and pressure (bottom) profiles for violent and continuous flame propagation (6.53% ethylene in air at 25 ◦ C and 14.7 psi).
Fig. 6 – Temperature (top) and pressure (bottom) profiles for temperately continuous flame propagation (5.25% methane in air at 25 ◦ C and 14.7 psi).
room temperature and ambient pressure, the calculated compressibility factor is very close to 1, so that fuel/air mixtures at standard conditions can be treated as ideal gas mixtures. The feeding gas mixtures are prepared to be homogeneous using a gas mixer which consists of a cylinder containing a cylindrical Teflon block that slides along the length of the vessel. Gas mixing is obtained by rotating the mixer. The ignition source is a 10 mm piece of AWG 40 tinned copper wire, which is vaporized by a 500 VA isolation transformer (Hammond 171 E) at 115 V AC switched on with a zero-crossing solid-state relay (Omega, model #SSRL240DC 100). The gas mixture igniter system used in this research is similar to that outlined in ASTM E 918-83 (ASTM, 1999), which was demonstrated by Mashuga (1999) to be capable of inputting 10 J of energy with a repeatable power delivery.
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Fig. 8 – Determination of LFL of methane in air at standard conditions. Data acquisition is performed with a desktop computer equipped with a Keithley data acquisition card (Keithley KPCI3102, 8 differential inputs with total of 225 signals per second @ 0.05% accuracy), which measures differential voltages of the thermistors and the pressure transducer. The measurement process is controlled by a LabView® program.
2.2.
Calibration for flammability limit estimation
Combustion behavior in the reaction vessel was classified into five categories over a range of concentrations for fuel/air mixtures: (i) non-propagation: lacking flame propagation after ignition and with negligible temperature and pressure fluctuations in the flammability apparatus (Fig. 3); (ii) flash combustion: short distance of vertical flame propagation with little or no horizontal propagation, where flame terminates before reaching the position of thermistor 1 (Fig. 4); (iii) discontinuous flame propagation: flame propagates vertically and horizontally but terminates before reaching the top thermistor (Fig. 5); (iv) temperately continuous flame propagation: flame propagates vertically and horizontally and does not terminate until it reaches the top thermistor; fuel combusts smoothly and pressure varies temperately in the reaction vessel (Fig. 6); and (v) violent and continuous flame propaga-
Fig. 9 – Determination of LFL of ethylene in air at standard conditions.
Fig. 10 – Lower flammability limits (top) and upper flammability limits (bottom) of methane and n-butane mixtures in air at standard conditions. tion: flame propagates upward farther and dynamic pressure varies much more rapidly than the temperately continuous flame propagation (Fig. 7). Data of temperature and pressure profiles were acquired and interpreted to identify these combustion categories. An innovative criterion was developed for the flammability apparatus by matching combustion behavior with the signal vs. time curves of sensors. Wierzba et al. (1988) showed that the probability of flame propagation can vary from 0% to 100% when the fuel is within a certain concentration range near the flammability limits. ASTM (2001) recommended that the lower flammability limit can be estimated by averaging the lowest fuel concentration with flame propagation and the highest concentration in which flame will not propagate, and vice versa for the upper flammability limit. In this research a series of experiments were conducted to measure the probability of continuous flame propagation for a concentration (near the flammability limits) for a fuel/air mixture, and repeated measurements were made at different concentrations. The propagation probabilities were plotted against different fuel concentrations, and by regression a linear function was obtained, where a concentration with a 0.5 or 50% of probability of continuous flame propagation was identified as the lower flammability limit or upper flammability limit of the measured fuel/air mixture. For calibration purposes, the original experiments for flammability limit determination were performed using pure
process safety and environmental protection 8 7 ( 2 0 0 9 ) 94–104
Fig. 11 – Lower flammability limits (top) and upper flammability limits (bottom) of methane and propane mixtures in air at standard conditions. hydrocarbons: methane and ethylene. Table 1 shows the probability of continuous flame propagation at different percentage concentrations of methane in air, where for every concentration the measurement was repeated 10 times, and the result of continuous flame propagation was recorded. Fig. 8 provides a graphical representation of the data presented in Table 1, and the lower flammability limit of methane in air at standard conditions was obtained by finding the concentration point with 0.5 or 50% probability of continuous flame propagation. The same procedure was used to determine the lower flammability limit of ethylene in air at standard conditions (Table 2 and Fig. 9). Using this novel criterion, the experimentally determined lower flammability limits of pure methane and pure ethylene were compared with some literature data from previous research with different experimental apparatus and detection criteria, and the data are shown in Table 3. Although the experimental data from this research differ slightly from previous measurements, differences are expected because flammability behavior changes with different experimental configurations and detection criteria.
3.
Experimental results
The hydrocarbons that were measured in this research consist of combinations of some typical hydrocarbons: saturated alkanes (methane, propane, and n-butane), double-bonded
101
Fig. 12 – Lower flammability limits (top) and upper flammability limits (bottom) of methane and ethylene mixtures in air at standard conditions. unsaturated alkenes (ethylene and propylene), and one triplebonded unsaturated alkyne (acetylene). The uncertainties for flammability estimation were calculated using error propagation from uncertainties of random gas feeding errors and gauging errors, and the magnitudes of uncertainties were indicated by error bars. The experimentally measured lower flammability limits and upper flammability limits (in air at standard conditions) of methane and n-butane, methane and propane, methane and ethylene, methane and acetylene, ethylene and propylene, and ethylene and acetylene are presented in Figs. 10–15, respectively, in which the theoretically calculated lower flammability limits were plotted also by applying Le Chatelier’s Law. As shown in these figures, the experimental data of lower flammability limits were fit very well by Le Chatelier’s Law. At the conditions of upper flammability limits, Le Chatelier’s Law can roughly fit the experimental data for the combinations of methane and n-butane, methane and propane. For the fuel mixtures of methane and ethylene, ethylene and propylene, ethylene and acetylene, the measured upper flammability limits show moderate deviations from Le Chatelier’s predictions, while large deviations are exhibited for the methane and acetylene mixtures. The probable reason for the deviation from Le Chatelier’s Law for the mixtures containing unsaturated hydrocarbon(s) is the even higher tendency of incomplete combustion (e.g. soot formation, cool flame or decomposition) compared with saturated
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Fig. 13 – Lower flammability limits (top) and upper flammability limits (bottom) of methane and acetylene mixtures in air at standard conditions.
Fig. 14 – Lower flammability limits (top) and upper flammability limits (bottom) of ethylene and propylene mixtures in air at standard conditions.
4. mixtures that can be approximated to complete combustion for lower-carbon hydrocarbons (It was through experimental observations). Therefore, the measured upper flammability limits of the saturated hydrocarbon mixtures can roughly fit Le Chatelier’s Law while unsaturated mixtures do not. Tables 4–9 show the experimental data and their absolute and relative deviations from the predictions of Le Chatelier’s Law at the lower and upper flammability limits for these binary hydrocarbon mixtures.
Numerical analysis of experimental data
Although Le Chatelier’s Law is still extensively used because of its simplicity and effectiveness to estimate the flammability limits of fuel mixtures at low pressures, its accuracy, however, can be unacceptably low when applied to the upper flammability limits of some fuel mixtures (Mashuga and Crowl, 2000). As demonstrated by experimental data from this research, modification of Le Chatelier’s Law is required when used to predict upper flammability limits for binary hydrocarbon mixtures
Table 10 – Correlations between the flammability limits and the stoichiometric concentrations for binary hydrocarbon mixtures LFLmix /Cst-mix a
Fuel1/fuel2 mixtures
CH4 /n-C4 H10 CH4 /C3 H8 CH4 /C2 H4 CH4 /C2 H2 C2 H4 /C3 H6 C2 H4 /C2 H2
aL
bL
aU
bU
LFLmix /Cst-mix LFLmix /Cst-mix 0.12 0.24 −0.08 0.12
≈0.55 ≈0.53 0.42 0.28 0.51 0.31
2.03 −0.17 −0.50 3.55 2.97 3.27
−5.25 −0.66 −0.52 −12.47 −0.37 −8.28
xfuel1 molar fractions (0–1) of fuel1 in fuel1 and fuel2 mixtures. LFLmix Cst,mix b UFLmix Cst,mix a
= aL xfuel1 + bL . 2 = aU xfuel1 + bU xfuel1 + cU .
UFLmix /Cst-mix b cU 4.84 2.50 2.69 10.30 2.27 9.89
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Fig. 17 – Best fitting curve for UFLs of methane and acetylene mixtures at standard conditions.
Fig. 15 – Lower flammability limits (top) and upper flammability limits (bottom) of ethylene and acetylene mixtures in air at standard conditions. Fig. 18 – Best fitting curve for UFLs of ethylene and propylene mixtures at standard conditions. curves to the experimental data, and Eqs. (5)–(8) represent the best fitting curves of the modified Le Chatelier’s Law for the hydrocarbon combinations of methane and ethylene, methane and acetylene, ethylene and propylene, and ethylene
Fig. 16 – Best fitting curve for UFLs of methane and ethylene mixtures at standard conditions. containing at least one unsaturated hydrocarbon (alkenes and alkynes). Based on maximum R-square values (close to 1), a simple way was applied to modify Le Chatelier’s Law by powering the fuel percentage concentrations. This empirical modification significantly increases the prediction accuracy for industrial purposes. Figs. 16–19 illustrate the best fitting
Fig. 19 – Best fitting curve for UFLs of ethylene and acetylene mixtures at standard conditions.
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and acetylene.
Acknowledgement 0.6
1 x1.3 (1 − x) = + UFLmethane/ethylene UFLmethane UFLethylene 1 UFLmethane/acetylene 1 UFLethylene/propylene 1 UFLethylene/acetylene
(5)
0.3
=
x2.1 (1 − x) + UFLmethane UFLacetylene
=
x0.3 (1 − x) + UFLethylene UFLpropylene
(6)
1.3
=
x UFLethylene
(7)
1.3
+
(1 − x) UFLacetylene
(8)
The flammability limits of the binary hydrocarbon mixtures can be correlated with the stoichiometric concentrations using the ratios of stoichiometric concentrations to lower/upper flammability limits and the fuel molar fractions. Table 10 shows the results expressed as a linear function for the subcategory of lower flammability limits, and a quadratic function for the upper flammability limits, in which different fuel combinations have different coefficients except saturated hydrocarbon mixtures (LFL/Cst approximates 0.55 for methane and n-butane mixtures, and 0.53 for methane and propane mixtures).
5.
This research was sponsored by the Mary Kay O’Connor Process Safety Center, Artie McFerrin Department of Chemical Engineering, Texas A&M University.
Conclusions
In this research, the lower flammability limits and upper flammability limits of binary hydrocarbon mixtures (methane and n-butane, methane and propane, methane and ethylene, methane and acetylene, ethylene and propylene, ethylene and acetylene) at standard conditions were estimated employing an innovative detection criterion, in which five thermistors worked as the flame propagation detector, and one dynamic transducer was used to record pressure change to confirm the occurrence of combustion. By comparing experimental data represented by Le Chatelier’s Law, we found that the lower flammability limits of binary hydrocarbon mixtures can be fit by Le Chatelier’s Law very well; for upper flammability limits of fuel mixtures that contain two saturated hydrocarbons, the experimental observations can be roughly fit by Le Chatelier’s Law; however, for upper flammability limits of fuel mixtures containing one unsaturated component at least, modification of Le Chatelier’s Law is needed based on the experimental data. Le Chatelier’s Law was modified by powering the percentage concentrations of fuels from maximum R-square values. For different fuel combinations, the powering values were different and there seems to be no direct connection among them. Moreover, the experimentally measured flammability limits were related to the stoichiometric concentrations, in which a linear function was preferred for the lower flammability limit quantifications. A quadratic function expression for the upper flammability limit conditions fit the measured data much better than a linear function.
References American Society of Heating., 1999, Refrigerating and Air-conditioning Engineers, Number designation of safety classification of refrigerants, proposed addendum to ANSI/ASHRAE 34-1997, In Proceedings of the 3rd Public Review Draft ASTM, 1999, Standard practice for determining limits of flammability of chemicals at elevated temperature and pressure, ASTM E 918-83. ASTM, 2001, Standard test methods for limiting oxygen (oxidant) concentration in gases and vapors, ASTM E 2079-01. Burgess, D.S., Furno, A.L., Kuchta, J.M., and Mura, K.E., 1982, Flammability of mixed gases, Bureau of Mines, Report of Investigations RI 8709. Cashdollar, K.L., Zlochower, I.A., Green, G.M., Thomas, R.A. and Hertzberg, M., 2000, Flammability of methane, propane, and hydrogen gases. Journal of Loss Prevention in the Process Industries, 13: 327–340. Coward, H.F. and Jones, G.W., (1952). Limits of Flammability of Gases and Vapors Bulletin 503. (Bureau of Mines, Washington, DC). De Smedt, G.D., De Corte, D., Notele, R. and Berghmans, J., 1999, Comparison of two standard test methods for determining explosion limits of gases at atmospheric conditions. Journal of Hazardous Materials, A70: 105–113. Ju, Y., Guo, H. and Maruta, K., 1999, Determination of burning velocity and flammability limit of methane/air mixture using counterflow flames. Japan Journal of Applied Physics, 38: 961–967. Kondo, S., Takizawa, K., Takahashi, A. and Tokuhashi, K., 2006, Extended Le Chatelier’s formula for carbon dioxide dilution effect on flammability limits. Journal of Hazardous Materials, A138: 1–8. Kuchta, J.M., (1985). Investigation of Fire and Explosion Accidents in the Chemical, Mining, and Fuel-related Industrial—A Manual Bulletin 680. (Bureau of Mines, Pittsburgh). Mashuga, C.V., 1999, Determination of the combustion behavior for pure components and mixtures using a 20 L sphere, Chemical Engineering, Ph.D. dissertation, Michigan Technological University, Michigan. Mashuga, C.V. and Crowl, D.A., 2000, Derivation of Le Chatelier’s mixing rule for flammability limits. Process Safety Progress, 19(2): 112–117. Wierzba, I., Karim, G.A. and Cheng, H., 1988, The flammability of rich gaseous fuel mixtures including those containing propane in air. Journal of Hazardous Materials, 20: 303–312. Wong, W.K., 2006, Measurement of flammability in a closed cylindrical vessel with thermal criterion, Ph.D. Dissertation, Artie McFerrin Department of Chemical Engineering, Texas A&M University. Zabetakis, M.G., (1965). Flammability Characteristics of Combustible Gases and Vapors Bulletin 627. (Bureau of Mines, Pittsburgh). Zabetakis, M.G. and Richmond, J.K., 1953, The determination and graphic presentation of the limits of flammability of complex hydrocarbon fuels at low temperature and pressure, In Proceedings of the 4th Symposium (International) on Combustion (Williams & Wilkins Co, Baltimore, MD), pp. 121–126.
Contents lists available at ScienceDirect
Process Safety and Environmental Protection journal homepage: www.elsevier.com/locate/psep
Experimental measurement and numerical analysis of binary hydrocarbon mixture flammability limits Fuman Zhao, William J. Rogers, M. Sam Mannan ∗ Mary Kay O’Connor Process Safety Center, Artie McFerrin Department of Chemical Engineering, Texas A&M University System, 3122 TAMU, College Station, TX 77843-3122, USA
a b s t r a c t The flammability limits of binary hydrocarbon mixtures in air were measured in a combustion apparatus using an innovative method developed for this apparatus. The experimental results were obtained at standard conditions (room temperature and ambient atmospheric pressure) with upward flame propagation. The experimentally determined flammability limits for pure hydrocarbons (methane and ethylene) were compared with existing data reported in the literature. Le Chatelier’s Law was fit to all experimental data to obtain LFLs and UFLs for various two-component combinations of saturated and unsaturated hydrocarbons (methane, ethylene, acetylene, propane, propylene, and n-butane). A modification of this law was used if experimental observations showed large deviations from Le Chatelier’s predictions. Also, experimentally measured flammability limit data of the binary hydrocarbon mixtures were analytically related to the stoichiometric concentrations. © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Flammability limits; Experimental measurement; Numerical analysis; Binary hydrocarbon mixtures; Le Chatelier’s Law
1.
Introduction
Flammability limits, sometimes referred to as explosion limits (De Smedt et al., 1999), are defined as the volume percentage concentration range in air in which a flammable substance can produce a fire or explosion when an ignition source (such as a spark or open flame) is present. Additionally, flammability limits are divided into two types: (i) the upper flammable limit (UFL) above which the fuel concentration is too rich (deficient in oxygen) to burn; (ii) the lower flammability limit (LFL) below which the fuel concentration becomes too lean (sufficient in oxygen) to be ignited. Usually, the limits are experimentally obtained by determining the limiting mixture compositions between flammable and non-flammable mixtures (Zabetakis and Richmond, 1953), that is, LFLT,P =
1 (Cg,n + Cl,f ) 2
(1)
UFLT,P =
1 (C + Cl,n ) 2 g,f
(2)
∗
where LFLT,P , UFLT,P are lower flammability limit and upper flammability limit at a specific temperature and pressure; Cg,n , Cl,n are the greatest concentration and the least concentration of a fuel in an oxidant that are nonflammable; Cl,f , Cg,f are the greatest concentration and the least concentration of a fuel in an oxidant that are flammable. Previously, flammability limits were determined by visual identification. This criterion for flammability limit estimation is flame propagation from the point of ignition to a certain distance. The best known experimental method using visual identification for measuring flammability limits of premixed gases is that developed by the Bureau of Mines (BM) (Coward and Jones, 1952). For a mixture to be declared flammable, propagation has to occur at least half way of a glass tube with 1.5 m length and 50 mm i.d. By using this method, BM generated a large body of flammability limits data for pure gases as well as some gas mixtures. Much of the work was done and summarized by Coward and Jones (1952), Zabetakis (1965), and Kuchta (1985) through BM Bulletin publications. In recent years, apparatus with closed, steel, spherical reaction vessels and center ignition also have been used for
Corresponding author. Tel.: +1 979 862 3985. E-mail address: [email protected] (M. Sam Mannan). Received 16 May 2008; Received in revised form 14 June 2008; Accepted 16 June 2008 0957-5820/$ – see front matter © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.psep.2008.06.003
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Fig. 1 – Flammability experimental apparatus. flammability limit measurement. Unlike a visual detection apparatus, the detection criterion is the relative pressure increase in a reaction vessel resulting from combustion. Burgess et al. published data from a 25,500 L sphere vessel that incorporated a 7% pressure rise criterion (Burgess et al., 1982), and Cashdollar et al. (2000) published data from 20 to 120 L chambers with 3% and 7% pressure rise criteria, respectively. Flammability limits also have been tested indirectly using counterflow burners, where twin gas jets of premixed fuel and oxidizer are released from opposing nozzles against each other, and ignited to produce twin, planar flames. The average gas exit velocity, often called stretch rate, is measured at different fuel concentrations. The fuel concentration is plotted as a function of stretch rate. The fuel concentration is extrap-
Fig. 3 – Temperature (top) and pressure (bottom) profiles for non-propagation combustion (1.5% methane in air at 25 ◦ C and 14.7 psi).
Fig. 2 – Reaction vessel.
olated linearly to a stretch rate of zero, and the intercept is taken as the flammability limit (Ju et al., 1999). Flammability data for pure fuels are usually available, while industrially, single phase or multiphase flammable mixtures are probably even more important than pure fuels. Unfortunately, our flammability knowledge of mixing fuels is approximately limited to Le Chatelier’s Law. Le Chatelier arrived at his mixture rule for lower flammability limits of gas mixtures (American Society of Heating, 1999). The proposed empirical mixing rule is expressed as Eq. (3). In addition, Kondo et al. (2006) showed that Le Chatelier’s Law
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Fig. 4 – Temperature (top) and pressure (bottom) profiles for flash combustion (4.35% methane in air at 25 ◦ C and 14.7 psi).
Fig. 5 – Temperature (top) and pressure (bottom) profiles for discontinuous flame propagation (5.10% methane in air at 25 ◦ C and 14.7 psi). satisfactory estimation.
can be extended to estimate upper flammability limit for some blended fuels with acceptable accuracy as in Eq. (4). Algebraically, Le Chatelier’s method states that the mixture flammability limit has a value between the maximum and minimum of the pure component flammability limits. Because Le Chatelier’s Law is an empirically summarized formula which is originated from the evaluation of mixing flammability at lower fuel concentrations (LFLs), its extended application at higher fuel concentrations (UFLs) is limited to certain fuel mixtures (Kondo et al., 2006). Mashuga and Crowl (2000) developed a theoretical derivation for this law with several pre-required assumptions. At lower fuel concentrations with greater inter-molecular separation, these assumptions are more consistent with real situations. Therefore, Le Chatelier’s Law can provide more reasonable estimation of lower flammability limits of fuel mixtures. At concentrations of upper flammability limits, the assumptions of this model deviate significantly from real conditions, and result in less
LFLmix =
N
UFLmix =
N
1
(3)
y /LFLi i=1 i 1
(4)
y /UFLi i=1 i
where yi is the mole fraction of the ith component considering only the combustible species; LFLi , UFLi are the lower and upper flammability limit of the ith component in volume percent; LFLmix , UFLmix are the lower and upper flammability limit of the fuel mixtures. In this paper, an innovative detection method was conducted to measure the lower and upper flammability limits of binary saturated/unsaturated hydrocarbon mixtures. The validity of Le Chatelier’s Law was evaluated for those fuel mixtures, and a modification of this law was developed from the experimental data.
Table 1 – Probabilities of continuous flame propagation at different concentrations of methane in air Methane conc. (molar %)a 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 a
Measurement times 10 10 10 10 10 10 10 10
Room temperature (25 ◦ C) and 1 atmospheric pressure.
Continuous flame propagation times 0 2 4 4 7 7 8 10
Probability of continuous propagation (%) 0 20 40 40 70 70 80 100
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Table 2 – Probabilities of continuous flame propagation at different concentrations of ethylene in air Ethylene conc. (molar %)a
Measurement times
2.78 2.79 2.80 2.81 2.82 2.83 2.84 a
Continuous flame propagation times
10 10 10 10 10 10 10
Probability of continuous propagation (%)
0 2 4 6 7 7 10
0 20 40 60 70 70 100
Room temperature (25 ◦ C) and 1 atmospheric pressure.
Table 3 – Low flammability limits of pure methane and pure ethylene in air (25 ◦ C and 1 atm) Methane LFL in air (%)
Ethylene LFL in air (%)
5.3 4.85 4.3 4.95 4.66 5.25 ± 0.05
Apparatus types
3.05 2.62 2.4 2.6 NA 2.81 ± 0.05
Vertical glass cylinder 20 L sphere, 7% pressure rise EN 1839 (T) EN 1839 (B) Counterflow burner This research
Table 4 – Flammability limit data from experimental measurements and Le Chatelier’s Law (methane and n-butane mixtures) xa (CH4 %)
LFLsb This research
0 12.5 25 37.5 50 62.5 75 87.5 100 a b
1.72 1.86 2.05 2.29 2.56 2.95 3.49 4.19 5.25
Le Chatelier’s 1.72 1.88 2.07 2.30 2.59 2.97 3.47 4.18 5.25
UFLsb Dev
Dev (%)
This research
Le Chatelier’s
Dev
Dev (%)
0.00 −0.02 −0.02 −0.01 −0.03 −0.02 0.02 0.01 0.00
0.00 0.96 0.86 0.43 1.22 0.57 0.58 0.28 0.00
8.46 8.91 9.48 10.11 10.83 11.82 12.71 14.12 15.80
8.46 8.98 9.57 10.24 11.02 11.92 12.98 14.25 15.80
0.00 −0.07 −0.09 −0.13 −0.19 −0.10 −0.27 −0.13 0.00
0.00 0.80 0.97 1.33 1.75 0.86 2.15 0.95 0.00
Percentage fractions of methane in methane and n-butane mixtures. Data obtained at room temperature and atmospheric pressure.
Table 5 – Flammability limit data from experimental measurements and Le Chatelier’s Law (methane and propane mixtures) xa (CH4 %)
LFLsb This research
0 12.5 25 37.5 50 62.5 75 87.5 100 a b
2.09 2.24 2.45 2.73 2.97 3.36 3.84 4.40 5.25
UFLsb
Le Chatelier’s
Dev
2.09 2.26 2.46 2.70 2.99 3.35 3.81 4.42 5.25
0.00 −0.02 −0.01 0.03 −0.02 0.03 0.03 −0.02 0.00
Dev (%) 0.00 0.89 0.41 1.11 0.67 0.89 0.78 0.45 0.00
Percentage fractions of methane in methane and propane mixtures. Data obtained at room temperature and atmospheric pressure.
This research
Le Chatelier’s
Dev
Dev (%)
10.09 10.44 10.85 11.47 12.03 12.77 13.46 14.59 15.80
10.09 10.57 11.09 11.67 12.32 13.03 13.84 14.76 15.80
0.00 −0.13 −0.24 −0.20 −0.29 −0.26 −0.38 −0.17 0.00
0.00 1.24 2.21 1.74 2.41 2.04 2.82 1.17 0.00
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Table 6 – Flammability limit data from experimental measurements and Le Chatelier’s Law (methane and ethylene mixtures) xa (CH4 %)
LFLsb This research
0 12.5 25 37.5 50 62.5 75 87.5 100 a b
Le Chatelier’s
2.81 3.01 3.20 3.37 3.68 4.01 4.30 4.71 5.25
2.81 2.98 3.18 3.40 3.66 3.96 4.31 4.74 5.25
UFLsb Dev
Dev (%)
This research
Le Chatelier’s
Dev
Dev (%)
0.00 0.03 0.02 −0.03 0.02 0.05 −0.01 −0.03 0.00
0.00 0.89 0.64 0.98 0.53 1.24 0.32 0.55 0.00
30.61 29.62 26.66 23.54 20.59 18.34 17.11 16.55 15.80
30.61 27.40 24.80 22.65 20.84 19.30 17.97 16.82 15.80
0.00 2.22 1.86 0.89 −0.25 −0.96 −0.86 −0.27 0.00
0.00 7.50 6.98 3.79 1.22 5.25 5.05 1.61 0.00
Percentage fractions of methane in methane and ethylene mixtures. Data obtained at room temperature and atmospheric pressure.
Table 7 – Flammability limit data from experimental measurements and Le Chatelier’s Law (methane and acetylene mixtures) LFLsb
xa (CH4 %) This research 0 12.5 25 37.5 50 62.5 75 87.5 100 a b
Le Chatelier’s
2.42 2.61 2.83 3.00 3.26 3.68 4.08 4.55 5.25
2.42 2.59 2.80 3.03 3.31 3.65 4.06 4.58 5.25
UFLsb Dev
Dev (%)
This research
Le Chatelier’s
Dev
Dev (%)
0.00 0.02 0.03 −0.03 −0.05 0.03 0.02 −0.03 0.00
0.00 0.58 1.17 1.10 1.62 0.83 0.43 0.67 0.00
77.31 72.12 60.53 51.24 46.07 31.45 22.38 19.46 15.80
77.31 52.00 39.18 31.43 26.24 22.52 19.72 17.54 15.80
0.00 20.12 21.35 19.81 19.83 8.93 2.66 1.92 0.00
0.00 27.89 35.27 38.66 43.05 28.40 11.87 9.84 0.00
Percentage fractions of methane in methane and acetylene mixtures. Data obtained at room temperature and atmospheric pressure.
2.
Experimental method
2.1.
Flammability apparatus
The reaction vessel (Fig. 2) is a closed cylinder with dimensions of 11.43 cm o.d., 10.22 cm i.d. and 100 cm length. At the central line of the reaction vessel, there are five evenly separated temperature sensors consisting of NTC thermistors (Thermometrics, FP07DB104N with fast response time 0.1 sec in still air and 100 K resistance at 25 ◦ C), which can detect a flame front in real time and locate a self-sustained frame propagation distance when fuel/air mixtures ignite and combust upwardly. The greatest distance from the ignition source to thermistor 5 is 75 cm. This design is consistent with the
The flammability apparatus used in this research was developed by Wong (2006) at Texas A&M University and is showed in Fig. 1. The apparatus consists of: (i) reaction vessel; (ii) gas feeding system; (iii) gas mixer; (iv) gas mixture ignition system; and (v) data acquisition system.
Table 8 – Flammability limit data from experimental measurements and Le Chatelier’s Law (ethylene and propylene mixtures) xa (C2 H4 %)
LFLsb This research
0 12.5 25 37.5 50 62.5 75 87.5 100 a b
2.28 2.32 2.43 2.41 2.52 2.55 2.64 2.75 2.81
Le Chatelier’s 2.28 2.34 2.39 2.45 2.52 2.58 2.66 2.73 2.81
UFLsb Dev
Dev (%)
This research
Le Chatelier’s
Dev
Dev (%)
0.00 −0.02 0.04 −0.04 0.00 −0.03 −0.02 0.02 0.00
0.00 0.65 1.53 1.81 0.10 1.36 0.59 0.70 0.00
10.25 10.38 11.66 12.81 14.04 17.31 22.64 27.23 30.61
10.25 11.18 12.29 13.66 15.36 17.54 20.45 24.52 30.61
0.00 −0.80 −0.63 −0.85 −1.32 −0.23 2.19 2.71 0.00
0.00 7.70 5.44 6.61 9.38 1.34 9.66 9.95 0.00
Percentage fractions of ethylene in ethylene and propylene mixtures. Data obtained at room temperature and atmospheric pressure.
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Table 9 – Flammability limit data from experimental measurements and Le Chatelier’s Law (ethylene and acetylene mixtures) xa (C2 H4 %)
LFLsb This research
0 12.5 25 37.5 50 62.5 75 87.5 100 a b
2.42 2.44 2.50 2.58 2.61 2.68 2.68 2.72 2.81
Le Chatelier’s 2.42 2.46 2.51 2.55 2.60 2.65 2.70 2.75 2.81
UFLsb Dev
Dev (%)
This research
Le Chatelier’s
Dev
Dev (%)
0.00 −0.02 −0.01 0.03 0.01 0.03 −0.02 −0.03 0.00
0.00 0.93 0.28 1.05 0.37 1.12 0.79 1.27 0.00
77.31 67.42 58.21 52.36 45.54 42.12 38.66 35.25 30.61
77.31 64.93 55.96 49.18 43.86 39.57 36.05 33.11 30.61
0.00 2.49 2.25 3.18 1.68 2.55 2.61 2.14 0.00
0.00 3.70 3.86 6.08 3.70 6.04 6.74 6.07 0.00
Percentage fractions of ethylene in ethylene and acetylene mixtures. Data obtained at room temperature and atmospheric pressure.
flammability apparatus of BM when visual observation is used as a flammability limit detection criterion (Coward and Jones, 1952). Thermistor 1 is located at a distance of 15 cm from the ignition source (at the bottom of reaction vessel). At the top of reaction vessel is a dynamic pressure transducer (Omega DPX 101, with a range of 0–250 psig pressure rise, 0–5 V nominal output signal, 1 s rise time, 1% amplitude linearity and temperature effect of 0.03%/F) mounted on the top plate and used to record the pressure variation when fuel/air mixtures ignite or explode. The gas feeding system includes a manifold that connects to chemical cylinders, a vacuum pump, the mixing vessel, and the reaction vessel. The gas mixtures used with the experimental apparatus are synthesized by loading the individual components from pressurized cylinders. Mixture composition is controlled through partial pressure gauging recommended by BM (Burgess et al., 1982). Theoretically, at the conditions of
Fig. 7 – Temperature (top) and pressure (bottom) profiles for violent and continuous flame propagation (6.53% ethylene in air at 25 ◦ C and 14.7 psi).
Fig. 6 – Temperature (top) and pressure (bottom) profiles for temperately continuous flame propagation (5.25% methane in air at 25 ◦ C and 14.7 psi).
room temperature and ambient pressure, the calculated compressibility factor is very close to 1, so that fuel/air mixtures at standard conditions can be treated as ideal gas mixtures. The feeding gas mixtures are prepared to be homogeneous using a gas mixer which consists of a cylinder containing a cylindrical Teflon block that slides along the length of the vessel. Gas mixing is obtained by rotating the mixer. The ignition source is a 10 mm piece of AWG 40 tinned copper wire, which is vaporized by a 500 VA isolation transformer (Hammond 171 E) at 115 V AC switched on with a zero-crossing solid-state relay (Omega, model #SSRL240DC 100). The gas mixture igniter system used in this research is similar to that outlined in ASTM E 918-83 (ASTM, 1999), which was demonstrated by Mashuga (1999) to be capable of inputting 10 J of energy with a repeatable power delivery.
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Fig. 8 – Determination of LFL of methane in air at standard conditions. Data acquisition is performed with a desktop computer equipped with a Keithley data acquisition card (Keithley KPCI3102, 8 differential inputs with total of 225 signals per second @ 0.05% accuracy), which measures differential voltages of the thermistors and the pressure transducer. The measurement process is controlled by a LabView® program.
2.2.
Calibration for flammability limit estimation
Combustion behavior in the reaction vessel was classified into five categories over a range of concentrations for fuel/air mixtures: (i) non-propagation: lacking flame propagation after ignition and with negligible temperature and pressure fluctuations in the flammability apparatus (Fig. 3); (ii) flash combustion: short distance of vertical flame propagation with little or no horizontal propagation, where flame terminates before reaching the position of thermistor 1 (Fig. 4); (iii) discontinuous flame propagation: flame propagates vertically and horizontally but terminates before reaching the top thermistor (Fig. 5); (iv) temperately continuous flame propagation: flame propagates vertically and horizontally and does not terminate until it reaches the top thermistor; fuel combusts smoothly and pressure varies temperately in the reaction vessel (Fig. 6); and (v) violent and continuous flame propaga-
Fig. 9 – Determination of LFL of ethylene in air at standard conditions.
Fig. 10 – Lower flammability limits (top) and upper flammability limits (bottom) of methane and n-butane mixtures in air at standard conditions. tion: flame propagates upward farther and dynamic pressure varies much more rapidly than the temperately continuous flame propagation (Fig. 7). Data of temperature and pressure profiles were acquired and interpreted to identify these combustion categories. An innovative criterion was developed for the flammability apparatus by matching combustion behavior with the signal vs. time curves of sensors. Wierzba et al. (1988) showed that the probability of flame propagation can vary from 0% to 100% when the fuel is within a certain concentration range near the flammability limits. ASTM (2001) recommended that the lower flammability limit can be estimated by averaging the lowest fuel concentration with flame propagation and the highest concentration in which flame will not propagate, and vice versa for the upper flammability limit. In this research a series of experiments were conducted to measure the probability of continuous flame propagation for a concentration (near the flammability limits) for a fuel/air mixture, and repeated measurements were made at different concentrations. The propagation probabilities were plotted against different fuel concentrations, and by regression a linear function was obtained, where a concentration with a 0.5 or 50% of probability of continuous flame propagation was identified as the lower flammability limit or upper flammability limit of the measured fuel/air mixture. For calibration purposes, the original experiments for flammability limit determination were performed using pure
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Fig. 11 – Lower flammability limits (top) and upper flammability limits (bottom) of methane and propane mixtures in air at standard conditions. hydrocarbons: methane and ethylene. Table 1 shows the probability of continuous flame propagation at different percentage concentrations of methane in air, where for every concentration the measurement was repeated 10 times, and the result of continuous flame propagation was recorded. Fig. 8 provides a graphical representation of the data presented in Table 1, and the lower flammability limit of methane in air at standard conditions was obtained by finding the concentration point with 0.5 or 50% probability of continuous flame propagation. The same procedure was used to determine the lower flammability limit of ethylene in air at standard conditions (Table 2 and Fig. 9). Using this novel criterion, the experimentally determined lower flammability limits of pure methane and pure ethylene were compared with some literature data from previous research with different experimental apparatus and detection criteria, and the data are shown in Table 3. Although the experimental data from this research differ slightly from previous measurements, differences are expected because flammability behavior changes with different experimental configurations and detection criteria.
3.
Experimental results
The hydrocarbons that were measured in this research consist of combinations of some typical hydrocarbons: saturated alkanes (methane, propane, and n-butane), double-bonded
101
Fig. 12 – Lower flammability limits (top) and upper flammability limits (bottom) of methane and ethylene mixtures in air at standard conditions. unsaturated alkenes (ethylene and propylene), and one triplebonded unsaturated alkyne (acetylene). The uncertainties for flammability estimation were calculated using error propagation from uncertainties of random gas feeding errors and gauging errors, and the magnitudes of uncertainties were indicated by error bars. The experimentally measured lower flammability limits and upper flammability limits (in air at standard conditions) of methane and n-butane, methane and propane, methane and ethylene, methane and acetylene, ethylene and propylene, and ethylene and acetylene are presented in Figs. 10–15, respectively, in which the theoretically calculated lower flammability limits were plotted also by applying Le Chatelier’s Law. As shown in these figures, the experimental data of lower flammability limits were fit very well by Le Chatelier’s Law. At the conditions of upper flammability limits, Le Chatelier’s Law can roughly fit the experimental data for the combinations of methane and n-butane, methane and propane. For the fuel mixtures of methane and ethylene, ethylene and propylene, ethylene and acetylene, the measured upper flammability limits show moderate deviations from Le Chatelier’s predictions, while large deviations are exhibited for the methane and acetylene mixtures. The probable reason for the deviation from Le Chatelier’s Law for the mixtures containing unsaturated hydrocarbon(s) is the even higher tendency of incomplete combustion (e.g. soot formation, cool flame or decomposition) compared with saturated
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Fig. 13 – Lower flammability limits (top) and upper flammability limits (bottom) of methane and acetylene mixtures in air at standard conditions.
Fig. 14 – Lower flammability limits (top) and upper flammability limits (bottom) of ethylene and propylene mixtures in air at standard conditions.
4. mixtures that can be approximated to complete combustion for lower-carbon hydrocarbons (It was through experimental observations). Therefore, the measured upper flammability limits of the saturated hydrocarbon mixtures can roughly fit Le Chatelier’s Law while unsaturated mixtures do not. Tables 4–9 show the experimental data and their absolute and relative deviations from the predictions of Le Chatelier’s Law at the lower and upper flammability limits for these binary hydrocarbon mixtures.
Numerical analysis of experimental data
Although Le Chatelier’s Law is still extensively used because of its simplicity and effectiveness to estimate the flammability limits of fuel mixtures at low pressures, its accuracy, however, can be unacceptably low when applied to the upper flammability limits of some fuel mixtures (Mashuga and Crowl, 2000). As demonstrated by experimental data from this research, modification of Le Chatelier’s Law is required when used to predict upper flammability limits for binary hydrocarbon mixtures
Table 10 – Correlations between the flammability limits and the stoichiometric concentrations for binary hydrocarbon mixtures LFLmix /Cst-mix a
Fuel1/fuel2 mixtures
CH4 /n-C4 H10 CH4 /C3 H8 CH4 /C2 H4 CH4 /C2 H2 C2 H4 /C3 H6 C2 H4 /C2 H2
aL
bL
aU
bU
LFLmix /Cst-mix LFLmix /Cst-mix 0.12 0.24 −0.08 0.12
≈0.55 ≈0.53 0.42 0.28 0.51 0.31
2.03 −0.17 −0.50 3.55 2.97 3.27
−5.25 −0.66 −0.52 −12.47 −0.37 −8.28
xfuel1 molar fractions (0–1) of fuel1 in fuel1 and fuel2 mixtures. LFLmix Cst,mix b UFLmix Cst,mix a
= aL xfuel1 + bL . 2 = aU xfuel1 + bU xfuel1 + cU .
UFLmix /Cst-mix b cU 4.84 2.50 2.69 10.30 2.27 9.89
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Fig. 17 – Best fitting curve for UFLs of methane and acetylene mixtures at standard conditions.
Fig. 15 – Lower flammability limits (top) and upper flammability limits (bottom) of ethylene and acetylene mixtures in air at standard conditions. Fig. 18 – Best fitting curve for UFLs of ethylene and propylene mixtures at standard conditions. curves to the experimental data, and Eqs. (5)–(8) represent the best fitting curves of the modified Le Chatelier’s Law for the hydrocarbon combinations of methane and ethylene, methane and acetylene, ethylene and propylene, and ethylene
Fig. 16 – Best fitting curve for UFLs of methane and ethylene mixtures at standard conditions. containing at least one unsaturated hydrocarbon (alkenes and alkynes). Based on maximum R-square values (close to 1), a simple way was applied to modify Le Chatelier’s Law by powering the fuel percentage concentrations. This empirical modification significantly increases the prediction accuracy for industrial purposes. Figs. 16–19 illustrate the best fitting
Fig. 19 – Best fitting curve for UFLs of ethylene and acetylene mixtures at standard conditions.
104
process safety and environmental protection 8 7 ( 2 0 0 9 ) 94–104
and acetylene.
Acknowledgement 0.6
1 x1.3 (1 − x) = + UFLmethane/ethylene UFLmethane UFLethylene 1 UFLmethane/acetylene 1 UFLethylene/propylene 1 UFLethylene/acetylene
(5)
0.3
=
x2.1 (1 − x) + UFLmethane UFLacetylene
=
x0.3 (1 − x) + UFLethylene UFLpropylene
(6)
1.3
=
x UFLethylene
(7)
1.3
+
(1 − x) UFLacetylene
(8)
The flammability limits of the binary hydrocarbon mixtures can be correlated with the stoichiometric concentrations using the ratios of stoichiometric concentrations to lower/upper flammability limits and the fuel molar fractions. Table 10 shows the results expressed as a linear function for the subcategory of lower flammability limits, and a quadratic function for the upper flammability limits, in which different fuel combinations have different coefficients except saturated hydrocarbon mixtures (LFL/Cst approximates 0.55 for methane and n-butane mixtures, and 0.53 for methane and propane mixtures).
5.
This research was sponsored by the Mary Kay O’Connor Process Safety Center, Artie McFerrin Department of Chemical Engineering, Texas A&M University.
Conclusions
In this research, the lower flammability limits and upper flammability limits of binary hydrocarbon mixtures (methane and n-butane, methane and propane, methane and ethylene, methane and acetylene, ethylene and propylene, ethylene and acetylene) at standard conditions were estimated employing an innovative detection criterion, in which five thermistors worked as the flame propagation detector, and one dynamic transducer was used to record pressure change to confirm the occurrence of combustion. By comparing experimental data represented by Le Chatelier’s Law, we found that the lower flammability limits of binary hydrocarbon mixtures can be fit by Le Chatelier’s Law very well; for upper flammability limits of fuel mixtures that contain two saturated hydrocarbons, the experimental observations can be roughly fit by Le Chatelier’s Law; however, for upper flammability limits of fuel mixtures containing one unsaturated component at least, modification of Le Chatelier’s Law is needed based on the experimental data. Le Chatelier’s Law was modified by powering the percentage concentrations of fuels from maximum R-square values. For different fuel combinations, the powering values were different and there seems to be no direct connection among them. Moreover, the experimentally measured flammability limits were related to the stoichiometric concentrations, in which a linear function was preferred for the lower flammability limit quantifications. A quadratic function expression for the upper flammability limit conditions fit the measured data much better than a linear function.
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