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Nitrogen and carbon dioxide dilution effect on upper flammability limits for organic compound containing carbon, hydrogen and oxygen atoms
Journal of the Taiwan Institute of Chemical Engineers 41 (2010) 453–464
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Nitrogen and carbon dioxide dilution effect on upper flammability limits for organic compound containing carbon, hydrogen and oxygen atoms TzuChi Wang a, ChanCheng Chen b,*, HuiChu Chen a a b
Department of Chemical and Materials Engineering, Chinese Culture University, Taipei 111, Taiwan Department of Safety, Health and Environmental Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung 811, Taiwan
A R T I C L E I N F O
A B S T R A C T
Article history: Received 31 December 2009 Received in revised form 27 February 2010 Accepted 2 March 2010
In this work semi-empirical models for predicating upper flammability limit (UFL) for flammable gases diluted with inert nitrogen and with carbon dioxide are developed, respectively. Experimental data for 20 flammable gases are collected and used to determine the unspecified parameter in our earlier theoretical model. It is found that if we divide these 20 organic compounds into three groups—CnHm, CnHmO, and CnHmO2, the coefficients of determination (R2) for these three categories for the case of inert nitrogen will be 0.9969, 0.9940 and 0.9971, respectively; and for the case of inert dioxide will be 0.9922, 0.9811 and 0.9877, respectively. If all the compounds are unified in a same model, it is found the R2 values are 0.9954 and 0.9897 for inert nitrogen and inert carbon dioxide, respectively. Experimental data of cyclopropane, ammonia, benzene, acetylene, carbon disulfide, carbon monoxide, diethyl ether, and hydrogen, which are not included in the original semi-empirical model, is used to validate the predictive ability for the proposed unified model, and it is found that the average predictive errors for each component are lower than 10% for inert gases of both nitrogen and carbon dioxide. ß 2010 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Keywords: Upper flammability limit Inert nitrogen Inert carbon dioxide Safety
1. Introduction Flammability limits are one of the important safety indicators for all who manufacture, process, transport and storage chemicals. To meet the practical requirements from the process industries, a bunch of literature has provided experimental data on the flammability limits of flammable gases and their mixtures (Coward and Jones, 1952; Kuchta, 1985; Zabetakis, 1963). Aside from experimental research, theoretical models have also been proposed by many researchers to investigate their applicability. Shimy, for example, estimated the flammability limits of hydrocarbons and alcohols by counting their carbon atoms and hydrogen atoms (Shimy, 1972). High and Danner (1987) proposed a group contribution method to estimate the flammability limits of combustible gases. Kondo et al. (2001), on the other hand, used F-number estimation method to achieve the same goal. As for Britton (2002), he constructed a model that can find the lower flammable limit (LFL) by using the combustion heat and oxygen usage of combustible gases. In case of estimating the flammability limits of a mixture of combustible gases, Le Chatelier equation is the most widely adopted method (Mashuga and Crowl, 2000; Kondo et al., 2007,
* Corresponding author. Tel.: +886 7 6011000x2311; fax: +886 7 6011061. E-mail address: [email protected] (C. Chen).
2008; Liekhus et al., 2000). However, combustible gases are not the only components that exist in industrial processes: inert gases may do too. For example, inerting is a common procedure in process industries before a vessel containing flammable gases is out of service or in service. In an inerting process, the flammable gases can be diluted with inert gases—mostly nitrogen or carbon dioxide, sometimes water vapor—to alter the flammability limit and in turn to reduce the possibility of explosion or catching fire (Crowl and Louvar, 2002; Planas-Cuchi et al., 1999). Although Le Chatelier equation is satisfactory in estimating the flammability limits of mixtures of flammable gases, it cannot be applied effectively in such kinds of inertized mixtures, which explains why many researchers devoted themselves to the topic of prediction of the flammability limit of the inertized mixtures. Because inert gas does not take part in the reaction in combustion, some of the researchers forecast the flammability limits of inertized mixture by calculating the adiabatic flame temperature. Vidal et al. (2006), employed the adiabatic flame temperatures of non-inertized methane and ethane to predict the LFL of the inertized mixtures. Shebeko et al. (2002), on the ground of kinetics of combustion, make use of the critical temperature of a combustion system to find the flammability limits of an inertized mixture of combustible gas via the calculation of adiabatic flame temperature. According to aforementioned results, in evaluating the flammability limits by means of the approach of adiabatic flame temperature, LFL is more accurate than the UFL.
1876-1070/$ – see front matter ß 2010 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jtice.2010.03.004
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Table 1 Calculated adiabatic flame temperatures in the UFL for methane, propane, and ethylene diluted with inert nitrogen gas (x = hydrocarbon/hydrocarbon + inert gas).
Nomenclature Cpf Cpinert n1 Tad U U1 x
FU q r s
mean molar heat capacities of the hydrocarbon mean molar heat capacities of the inert gas number of mole of oxygen needed in the combustion of one mole of pure fuel gas adiabatic flame temperature upper flammability limits of a fuel gas diluted with inert gas upper flammability limits of the pure fuel gas mole fraction of a fuel gas in the mixture (fuel and inert gas, but no air) parameter of the upper flammability limits prediction model parameter of the upper flammability limits prediction model parameter of the upper flammability limits prediction model parameter of the upper flammability limits prediction model
Besides the adiabatic flame temperature approach, Kondo et al. (2006a,b) revised the Le Chatelier equation and applied their result to find the flammability limits of either nitrogen mixture or carbon dioxide mixture. They theoretically proposed that xn1 xn1 ¼ 1 ðU=xÞ 1 U 1
(1)
where U is the UFL (in molar fraction) of a fuel gas diluted with inert gas; U1 is the UFL of the pure fuel gas; x is the mole fraction of a fuel gas in the mixture (fuel and inert gas, but no air); n1 is the number of mole of oxygen needed in the combustion of one mole of pure fuel gas. However, the prediction result from (1) do not fit the experimental result very well, so that Kondo et al., to enhance the accuracy, added to the equation a power series to obtain the semiempirical equation as shown in (2): xn1 xn1 ¼ þ qð1 xÞ þ rð1 xÞ2 þ sð1 xÞ3 1 ðU=xÞ 1 U 1
(2)
where q, r, and s are unspecified parameters whose values are determined by the contents of gases in a mixture. Although the accuracy can be improved by using this revised equation, it depends largely on the values of the unspecified parameters, that is, the amount of experimental data of the mixture. For those combustible gases with little discussion in literature, finding the suitable values of these unspecified parameters is still a job with challenge. We have proposed (3) as a theoretical model in previous research in which we integrate adiabatic temperature with the Le Chatelier equation to deal with UFL of combustible hydrocarbon mixture with either nitrogen or carbon dioxide as its inert gas (Chen et al., 2008, 2009a,b). 1 1 1 1 (3) ¼ FU U U1 x where
FU ¼
U 1 C p f þ ð1 U 1 ÞC pinert U1 C p f
(4)
Cpf and Cpinert are the mean molar heat capacities of the hydrocarbon and the inerted mixture, respectively, heated from
x
1.000 0.850 0.750 0.700 0.500 0.375 0.250 0.150
Methane
Propane
Ethylene
UFL (%)
Tad (K) (a = 0.8)
UFL (%)
Tad (K) (a = 2)
UFL (%)
Tad (K) (a = 2)
15.80 14.90 14.30 13.94 12.19 10.60 8.70 –
1937.4 1920.8 1902.7 1893.0 1838.1 1788.9 1690.6 –
10.00 – 9.10 – 8.20 7.53 – 4.96
1826.8 – 1830.6 – 1800.7 1768.7 – 1650.3
31.50 – 25.00 – 18.40 – 10.50 7.00
1433.9 – 1479.6 – 1508.2 – 1531.0 1495.1
25 8C to a specified adiabatic temperature. In deriving (3), one important assumption is that the adiabatic flame temperature does not change as inert gas is added to the combustible gas. However, this assumption seems to be effective in case of the calculation in LFL, but not in case of the calculation in UFL. To clearly illustrate this point, Table 1 lists the calculated adiabatic flame temperatures of nitrogen-inertized combustible gas mixture (methane, propane, and ethylene) in the condition of UFL from the experimental data. The data of UFL come from research results obtained by Kondo et al. (2006a). The parameter a in Table 1 denotes the number of mole of carbon monoxide generated in the course of burning one mole of combustible gas. This parameter is adopted to reflect that the combustible gas in an inertized mixture does not burn completely in UFL, and it is assumed the value of a does not change as inert gas is added to a combustible gas. It is obvious from Table 1 that the adiabatic flame temperature of a combustible gas does change in the inerting process. In addition, for different gas mixtures, the adiabatic flame temperatures in UFL vary widely, which also necessitates the need of experimental data to calculate FU instead of calculating it theoretically. However, as we know, most organic compounds of similar structure are of similar mean molar heat capacity and UFL, thus, according to (4), it seems possible that there is a unified value of FU if the organic compounds are properly grouped. In this research, we explore this possibility through the existing experimental data. In the course of the study, experimental data gleaned from literature on the UFL of organic combustibles inertized with nitrogen or carbon dioxide will be explored. This work is organized as follows. The data compilation is discussed in Section 2. The fitting performance of (3) for individual compounds is presented in Section 3. In Section 4, we discuss both the fitting and predictive performance in case the flammable gases are grouped according to their molecular structure. Finally, the conclusion of this work is presented in Section 5. 2. Data compilation The data of UFL collected in this study come either from official reports of Mineral Bureau of the USA or from research literature. It is widely known that the accuracy of experimental results of UFL is heavily depended on the experimental instrument and environmental conditions. To maintain the coherence of the data, most of them are collected from the Bulletin 503 and Bulletin 627 (Coward and Jones, 1952; Zabetakis, 1963). However, the bulk of the results listed in these two reports are showed in diagrams, so if there exist newer data obtained under similar experimental conditions and presented in numerical forms, the newer ones will supersede those in the official reports (Kondo et al., 2006a,b). Except for directly giving the numerical values, there are two types of presentation of the flammability limit data in Bulletin 503 and Bulletin 627 with the form of only curve description. The first one showed both the experimental data and the fitting curve, and the other showed only
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Table 2 The source, type, and number of data of the UFL for 20 compounds. No.
Compound name
Formula
Inert gas (N2) Source
Data no.
Data type
Source
Data no.
Data type
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether Methyl formate Isobutyl formate Methyl acetate
CH4 C2H6 C3H8 C4H10 C5H12 C6H14 C2H4 C3H6 C4H6 C4H8 C4H8 C5H10 CH4O C2H6O C3H6O C4H8O C2H6O C2H4O2 C5H10O2 C3H6O2
Kondo et al. (2006a) Zabetakis (1963) Kondo et al. (2006a) Zabetakis (1963) Coward and Jones (1952) Coward and Jones (1952) Kondo et al. (2006a) Kondo et al. (2006a) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Kondo et al. (2006a) Kondo et al. (2006a) Zabetakis (1963) Zabetakis (1963)
9 16 8 16 15 8 6 8 16 16 16 16 16 16 16 16 8 8 16 16
Value Curve Value Curve Curve Point Value Value Curve Curve Curve Curve Curve Curve Curve Curve Value Value Curve Curve
Kondo et al. (2006b) Zabetakis (1963) Kondo et al. (2006b) Zabetakis (1963) Coward and Jones (1952) Coward and Jones (1952) Kondo et al. (2006b) Kondo et al. (2006b) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Kondo et al. (2006b) Kondo et al. (2006b) Zabetakis (1963) Zabetakis (1963)
7 16 9 16 15 7 7 8 16 16 16 16 16 16 16 16 8 7 16 16
Value Curve Value Curve Curve Points Value Value Curve Curve Curve Curve Curve Curve Curve Curve Value Value Curve Curve
the fitting curve. In this work, if the experimental points are given on the curve, only the experimental points are adopted; otherwise, 15–16 evenly spaced points are read from the curve for later analysis. Therefore, there are three types of reference data in Table 2: value means numerical value is directly available, point means experimental points are read from the curve, and curve means the data are read from the fitting curve. Table 2 also lists the data source and number of the data used in later analyses. As showed in Table 2, inertized data for 20 compounds (with either nitrogen or carbon dioxide) are formulated here for later analyses. According to their functional structure, the compounds can be divided as alkane (methane, ethane, propane, n-butane, npentane, n-hexane), alkene (ethylene, propylene, 1,3-butadiene, isobutylene, 1-butene, 3-methyl-1-butene), alcohol (methyl alcohol, ethyl alcohol), ketone (acetone, methyl ethyl ketone), ether (dimethyl ether), and ester (methyl formate, isobutyl formate, methyl acetate). 3. Results In this section, the collected experimental data are studied to see whether or not they are well described by (3). The possibility that whether or not specific relations could be obtained if the flammable materials are properly grouped, is then explored in Section 4.
Inert gas (CO2)
3.2. Inertion with carbon dioxide as inert gas When the same procedure as is used in the previous subsection is applied to combustible gas mixture inertized with carbon dioxide, the regression results acquired through the use of the prediction model suggested by Chen et al., are listed in Table 4. As Table 4 shows, R2 values are all greater than 0.9762 for the 20 combustible organic compounds taken into consideration, saving that of dimethyl ether (0.9565). Furthermore, it is also found that the maximum errors between the experimental value of UFL and the prediction value obtained by using FU value are all lower than 10.7402%, except those for ethylene (21.2212%) and dimethyl ether (32.1252%). All the average errors, but those for ethylene (10.9083%) and dimethyl ether (14.1140%), are under 4.3646%. The regression results for the 20 combustible organic compounds are showed in Fig. 2. As these figure shows, experimental data are also well described by (3) in case that the inert gas is of carbon dioxide.
Table 3 The regression and UFL prediction results for 20 combustible organic compounds inertized with nitrogen. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether Methyl formate Isobutyl formate Methyl acetate
1.6592 1.6770 1.6321 1.6607 1.6271 1.6357 1.6767 1.6435 1.6684 1.6481 1.6197 1.6589 1.7064 1.7145 1.6976 1.7209 1.7225 1.5209 1.5688 1.5874
0.9968 0.9946 0.9965 0.9989 0.9983 0.9976 0.9933 0.9950 0.9953 0.9977 0.9973 0.9997 0.9989 0.9955 0.9987 0.9994 0.9798 0.9981 0.9965 0.9998
3.7332 3.8902 4.8918 1.8030 2.2438 3.0223 16.0774 7.0004 4.6385 1.9235 2.9039 1.0403 2.4117 4.6454 2.8076 1.3550 31.7726 2.6330 3.1353 0.9527
1.9433 2.3390 3.4447 0.7833 0.9987 1.5186 7.4877 4.3104 2.7685 1.2826 1.4045 0.3313 1.3662 2.6646 1.3548 0.6955 12.9415 1.4741 1.2965 0.2746
3.1. Inertion with nitrogen as inert gas Applying regression analysis to the data of inert nitrogen listed in Table 2 by using the prediction model suggested by Chen et al. (i.e. (3)) generated the results showed in Table 3. As is obvious in Table 3, for all the 20 combustible organic compounds, R2 values are greater than 0.9798. In all cases, the average estimating errors, but those for ethylene (7.4877%) and dimethyl ether (12.9415%), are under 4.3104%. The maximum estimating errors are lower than 7.04%, except those for ethylene (16.0774%) and dimethyl ether (31.7726%). The regression results are shown in Fig. 1 for these 20 compounds. The deviations in cases of ethylene and dimethyl ether might come from the fact that these two compounds are reported to generate cool flame instead of hot flame, which has been discussed in our earlier work. As it is seen from these results, most experimental results are well described by (3), thus the only parameter in (3) might be used to characterize their flammable characteristics.
456
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Fig. 1. The regression results of ((1/U) (1/U1)) vs. ((1/x) 1) for organic compounds inertized by nitrogen. The straight lines in the figures are forced to pass through the original point in regression; the dots in the figures are experimental data of UFL collected from various literature.
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457
Fig. 1. (Continued ).
4. Discussion As Section 3 shows, the UFLs of inertized mixture could be effectively described by (3) and there is only one parameter
(i.e. FU) in the proposed model, so we explore the possibility whether unified value of FU for each group of compounds could be found if the flammable compounds are properly grouped.
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Fig. 1. (Continued ).
4.1. Inertion with nitrogen as inert gas On the inspection of Table 3, it is plain that the FU values of alkane and alkene range from 1.6197 to 1.6770; those of alcohol, ketone, and ether, from 1.6976 to 1.7225; finally those of ester, from 1.5209 to 1.5874. Consequently, if the 20 compounds are classified into three groups—CnHm, CnHmO, and CnHmO2—it is feasible to procure FU values that are representative enough for each of these types of organic compounds. Table 5 shows the FU value and the coefficient of determination (R2) of compounds with the form CnHm, as well as maximum errors and average errors Table 4 The regression and UFL prediction results for 20 combustible organic compounds inertized with carbon dioxide. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether Methyl formate Isobutyl formate Methyl acetate
2.2836 2.1999 2.1741 2.1370 2.1004 2.2172 2.1970 2.1300 2.2361 2.3028 2.2058 2.2840 2.2358 2.3068 2.3634 2.1278 2.3840 1.8847 2.0203 2.1654
0.9939 0.9924 0.9923 0.9993 0.9971 0.9992 0.9796 0.9918 0.9899 0.9969 0.9931 0.9990 0.9968 0.9762 0.9963 0.9994 0.9565 0.9973 0.9915 0.9968
4.3967 3.9269 5.4661 1.2157 2.6089 2.0559 21.2212 10.7402 6.8937 2.7710 3.9660 2.7076 3.0838 7.9831 3.2171 1.1178 32.1252 2.9344 4.0487 2.4883
2.1788 2.3730 3.5215 0.3794 1.1282 0.5653 10.9083 4.3646 3.8491 0.9849 2.2091 1.1814 1.9305 4.3437 1.7931 0.1640 14.1140 1.7703 1.7231 1.4206
between the experimental UFL and the predicted value obtained by the use of FU value. According to Table 5, FU value is 1.6473 and R2, 0.9966; the maximum errors between experimental data and predicted values of UFL by using FU are all less than 6.9431% except that of ethylene (17.3388%); average errors are all smaller than 4.2694% saving that of ethylene (8.0291%). On the careful comparison between error values of various alkanes in Table 3 and those in Table 5, we find them within the tolerable ranges and make the conclusion that (5) can serve as the prediction model for the UFL of nitrogen-inertized organic gases with the form of CnHm. 1 1 1 1 ¼ 1:6473 U U1 x
(5)
In the same manner, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and experimental data for CnHmO-type compounds are listed in Table 6. According to Table 6, FU value is 1.7154 and R2, 0.9940; the maximum errors between experimental data and predicted values of UFL by using FU are all smaller than 4.6313% except that of dimethyl ether (31.9417%); average errors are all smaller than 2.6579% saving that of dimethyl ether (12.9660%). After drawing a detailed comparison between error values of the organic compounds with the form of CnHmO in Table 3 and those in Table 6, we find them within the tolerable ranges and reach the conclusion that (6) can serve as the prediction model for the UFL of nitrogeninertized organic compounds of alcohols, ketones, and ethers. 1 1 1 1 ¼ 1:7154 U U1 x
(6)
In the same way, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and
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Fig. 2. The regression results of ((1/U) (1/U1)) vs. ((1/x) 1) for organic compounds inertized by carbon dioxide. The straight lines in the figures are forced to pass through the original point in regression; the dots in the figures are experimental data of UFL collected from various literature.
experimental data for CnHmO2-type compounds are listed in Table 7. Based on the observation of Table 7, FU value is 1.5625 and R2, 0.9971; the maximum errors between experimental data and
predicted values of UFL by using FU are all smaller than 4.4754% for esters; average errors are smaller than 1.2750%. After comparing error values of the esters in Table 3 with those in Table 7, we deem that they are within the tolerable ranges and arrive at the conclusion
460
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Fig. 2. (Continued ).
that (7) can serve as the prediction model of the UFL for nitrogeninertized organic compounds with the form CnHmO2. 1 1 1 1 ¼ 1:5625 U U1 x
(7)
As can be seen from (5)–(7), in the prediction models of UFL for nitrogen-inertized CnHm, CnHmO, and CnHmO2, the FU value are very close. In the same way, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and experimental data for all 20 compounds are listed in Table 8.
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461
Fig. 2. (Continued ).
In Table 8, FU value is 1.6513; the maximum errors between experimental data and predicted values of UFL are all, except those for ethylene (17.1656%) and dimethyl ether (33.4884%), smaller than 8.3837%; average errors except those for ethylene (7.9548%) and dimethyl ether (13.7386%) smaller than 4.2263%. The comparison of maximum and average errors between Table 8 and other tables leads us to conclude that they are within the tolerable ranges and that (8) is suitable for being the prediction model of the UFL for nitrogen-inertized organic compounds, if no other useful information are available. 1 1 1 1 (8) ¼ 1:6513 U U1 x It should be noted that Kondo et al. has claimed (9) as the UFL prediction model to the same purpose. Their results were obtained Table 5 The regression and prediction results for 12 organic compounds with the form CnHm in nitrogen-inertized case. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene
1.6473
0.9966
3.9599 4.5742 4.7034 2.3470 2.8059 3.2570 17.3388 6.9431 5.2098 1.9343 2.9884 1.5548
2.0424 2.6653 3.2927 0.6528 1.1225 1.5537 8.0291 4.2694 3.0562 1.2830 1.2220 0.3146
Total average
2.4586
from five nitrogen-inertized organic compounds (methane, propane, propylene, methyl formate, and 1,1-difluoroethane). xn1 xn1 ¼ þ 0:122ð1 xÞ þ 0:187ð1 xÞ2 1 ðU=xÞ 1 U 1 0:242ð1 xÞ3
(9)
in which n1 is the number of mole of oxygen needed for the combustion of one mole of combustible gas at UFL. To examine the effectiveness of (8) and (9), eight compounds appearing neither in this research nor in Kondo et al.’s are selected as comparison basis. These compared components are cyclopropane, ammonia,
Table 6 The regression and prediction results for five organic compounds with the form CnHmO in nitrogen-inertized case. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether
1.7154
0.9940
2.2129 4.6313 2.6051 1.3987 31.9417
1.2801 2.6579 1.3728 0.7596 12.9660
Total average
3.8073
Table 7 The regression and prediction results for three organic compounds with the form CnHmO2 in nitrogen-inertized case. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methyl formate Isobutyl formate Methyl acetate
1.5625
0.9971
4.4754 3.3902 2.0351
1.2750 1.2245 0.3918
Total average
0.9638
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Table 8 The regression and prediction results of UFL for 20 organic compounds in nitrogeninertized case.
Table 10 The regression and prediction results for 12 organic compounds with the form CnHm in carbon dioxide-inertized case.
Compound
FU
R2
Max. error (%)
Ave. error (%)
Compound
FU
R2
Max. error (%)
Ave. error (%)
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether Methyl formate Isobutyl formate Methyl acetate
1.6513
0.9954
3.8836 4.4748 4.6675 2.1840 2.9295 3.3376 17.1656 6.8829 5.0983 1.8801 3.1518 1.3768 3.8144 5.6465 3.3382 3.6464 33.4884 8.3837 3.8615 2.8299
2.0091 2.6166 3.2529 0.6918 1.1513 1.5658 7.9548 4.2263 3.0015 1.2808 1.1976 0.3139 2.4118 3.5928 1.9643 2.0544 13.7386 2.7127 2.4081 1.4558
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene
2.2001
0.9922
5.1421 3.9242 5.2344 2.3927 4.2385 1.6826 21.1342 9.8005 7.5527 5.6221 4.0654 3.0620
2.3766 2.3720 3.4615 0.7888 1.7816 0.7733 10.8692 4.5486 4.1386 1.1938 2.2391 2.2188
Total average
2.9800
benzene, acetylene, carbon disulfide, carbon monoxide, diethyl ether, and hydrogen. The results are shown in Table 9. Table 9 shows that the maximum predictive errors and average predictive errors between experimental data and predicted values of the proposed equation (8) are smaller than 28.9628% and 14.8983%, respectively. Although Kondo et al.’s model (i.e. Eq. (9)) has up to three regression parameters, the predictive performance of their model is inferior to the proposed one which is of only one regression parameter. This result might imply that the proposed model structure is more suitable to represent the diluted effect on UFL. Moreover, it could be found that the grand average predictive error is about 6.0% for these eight testing compounds, thus if no experimental data are available, Eq. (8) might give an estimate with reasonable accuracy. 4.2. Inertion with carbon dioxide as inert gas When the same procedure as is used in the previous section is applied to combustible gas mixture inertized with carbon dioxide, it is plain that the FU values of alkane and alkene range from 2.1004 to 2.3028; those of alcohol, ketone, and ether from 2.1278 to 2.3840; finally those of ester, from 1.8847 to 2.1654 on the inspection of Table 4. The 20 compounds are classified into three groups—CnHm, CnHmO, and CnHmO2. Table 10 shows the FU values and coefficients of determination (R2) of compounds with the form CnHm, as well as Table 9 Comparison of predictive capability between this work and Kondo et al.’s model with inert gas of nitrogen. Compound
This work (8)
Total average
3.0635
maximum errors and average errors between the experimental UFL and the predicted value obtained by the use of FU value. According to Table 10, FU value is 2.2001 and R2, 0.9922; the maximum errors between experimental data and predicted values of UFL by using FU are all less than 9.8005% except that of ethylene (21.1342%); average errors are all smaller than 4.5486% saving that of ethylene (10.8692%). On the careful comparison between error values of various alkanes in Table 4 and those in Table 10, we find them within the tolerable ranges and make the conclusion that (10) can serve as the prediction model for the UFL of carbon dioxide-inertized organic gases with the form of CnHm. 1 1 1 1 ¼ 2:2001 U U1 x
(10)
In the same manner, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and experimental data for CnHmO-type compounds are listed in Table 11. According to Table 11, FU value is 2.2606 and R2, 0.9811; the maximum errors between experimental data and predicted values of UFL by using FU are all smaller than 8.5045% except that of dimethyl ether (34.1669%); average errors are all smaller than 4.5961% saving that of dimethyl ether (15.5702%). After drawing a detailed comparison between error values of the organic compounds with the form of CnHmO in Table 4 and those in Table 12, we find them within the tolerable ranges and reach the conclusion that (11) can serve as the prediction model for the UFL of nitrogen-inertized organic compounds of alcohols, ketones, and ethers. 1 1 1 1 ¼ 2:2606 U U1 x
(11)
In the same way, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and
Kondo et al. (9) Table 11 The regression and prediction results for five organic compounds with the form CnHmO in carbon dioxide-inertized case.
Max. error (%)
Ave. error (%)
Max. error (%)
Ave. error (%)
Cyclopropane Ammonia Benzene Acetylene Carbon disulfide Carbon monoxide Diethyl ether Hydrogen
2.6392 12.7073 13.5848 5.0374 8.5418 12.0324 28.9628 13.8184
1.5977 6.6717 10.4253 2.3509 2.5778 5.4485 14.8983 4.8629
9.8637 20.5565 30.8400 32.9217 17.3667 19.0773 51.3115 17.9982
7.0201 11.2871 24.3640 15.6815 9.4344 8.8863 22.4042 10.2305
Compound
FU
R2
Max. error (%)
Ave. error (%)
Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether
2.2606
0.9811
3.0093 8.5045 4.3265 4.0420 34.1669
1.7960 4.5961 2.7723 2.0276 15.5702
Grand average
12.2655
6.0141
24.9920
13.6635
Total average
5.3524
T.C. Wang et al. / Journal of the Taiwan Institute of Chemical Engineers 41 (2010) 453–464 Table 12 The regression and prediction results for three organic compounds with the form CnHmO2 in carbon dioxide-inertized case. Compound Methyl formate Isobutyl formate Methyl acetate
FU 2.0274
R2 0.9877
Max. error (%)
Ave. error (%)
4.7843 3.8570 4.1188
2.6173 1.7651 3.0427
Total average
2.4750
experimental data for CnHmO2-type compounds are listed in Table 12. Based on the observation of Table 12, FU value is 2.0274 and R2, 0.9877; the maximum errors between experimental data and predicted values of UFL by using FU are all smaller than 4.7843% for esters; average errors are smaller than 3.0427%. After comparing error values of the esters in Table 4 with those in Table 12, we deem that they are within the tolerable ranges and arrive at the conclusion that (12) can serve as the prediction model of the UFL for carbon dioxide-inertized organic compounds with the form CnHmO2. 1 1 1 1 ¼ 2:0274 U U1 x
(12)
As can be seen from (10)–(12), in the prediction models of UFL for carbon dioxide-inertized CnHm, CnHmO, and CnHmO2, the FU value are very close. In the same way, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and experimental data for all 20 compounds are listed in Table 13. In Table 13, FU value is 2.1975 and R2, 0.9897; the maximum errors between experimental data and predicted values of UFL are all, except those for ethylene (21.2072%) and dimethyl ether (35.2354%), smaller than 12.0243%; average errors except those for ethylene (10.9020%) and dimethyl ether (16.6708%), smaller than 5.1445%. The comparison of maximum and average errors between Table 13 and other tables leads us to conclude that they are within the tolerable ranges and that (13) is suitable for being the prediction model of the UFL for carbon dioxide-inertized organic Table 13 The regression and prediction results of UFL for 20 organic compounds in carbon dioxide-inertized case. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether Methyl formate Isobutyl formate Methyl acetate
2.1975
0.9897
5.1655 3.9584 5.1877 2.3352 4.1850 1.6256 21.2072 9.8350 7.6007 5.6963 4.1108 3.0784 3.7847 9.2248 5.0755 2.1743 35.2354 12.0243 4.8498 2.4598
2.3955 2.3858 3.4675 0.7547 1.7512 0.8102 10.9020 4.5339 4.1666 1.2226 2.2528 2.2593 2.2496 5.1445 3.6842 1.0814 16.6708 4.9625 3.2211 1.3849
Total average
3.7651
463
Table 14 Comparison of predictive capability between this work and Kondo et al.’s model with inert gas of carbon dioxide. Compound
This work (13)
Kondo et al. (14)
Max. error (%)
Ave. error (%)
Max. error (%)
Ave. error (%)
Cyclopropane Ammonia Benzene Acetylene Carbon disulfide Carbon monoxide Diethyl ether Hydrogen
2.9336 19.3991 15.3877 19.3741 18.8728 16.7407 17.9151 23.1552
1.1644 10.4194 10.4220 9.2636 7.8132 8.9139 9.9746 11.6591
13.5318 23.3330 33.1362 42.4802 27.3623 30.1289 62.1652 33.1622
10.0469 12.5983 25.7411 20.8385 14.7133 14.8204 26.4306 16.6180
Grand average
16.7229
8.7038
33.1625
17.7259
compounds. 1 1 1 1 ¼ 2:1975 U U1 x
(13)
On the other hand, Kondo et al., framed (14) as the UFL prediction model for five carbon dioxide-inertized organic compounds (methane, propane, propylene, methyl formate, and 1,1-difluoroethane), xn1 xn1 ¼ þ 0:105ð1 xÞ þ 0:106ð1 xÞ2 1 ðU=xÞ 1 U 1 0:156ð1 xÞ3
(14)
To examine the effectiveness of (13) and (14), eight compounds appearing neither in this research nor in Kondo’s are selected as comparison basis. These components are cyclopropane, ammonia, benzene, acetylene, carbon disulfide, carbon monoxide, diethyl ether, and hydrogen. The results are shown in Table 14. Table 14 shows that the maximum predictive errors and average predictive errors between experimental data and predicted values of the proposed equation (13) are smaller than 23.1152% and 11.6591%, respectively. Although Kondo et al.’s model (i.e. Eq. (14)) has up to three regression parameters, the predictive performance of their model is inferior to the proposed one which is of only one regression parameter. This result might imply that the proposed model structure is more suitable to represent the diluted effect on UFL. Moreover, it could be found that the grand average predictive error is about 8.70% for these eight testing compounds, thus if no experimental data are available, Eq. (13) might give an estimate with reasonable accuracy. 5. Conclusion In this work the theoretical models proposed in our earlier work (i.e. Eq. (3)) to predict the UFL for flammable gases are examined through the UFL experimental data of 20 organic compounds. These experimental data include both the case of inert nitrogen and the case of inert carbon dioxide. It is found that if we divide these 20 organic compounds into three groups—CnHm, CnHmO, and CnHmO2, the coefficients of determination (R2) for these three categories for the case of inert nitrogen will be 0.9969, 0.9940 and 0.9971, respectively; and for the case of inert dioxide will be 0.9922, 0.9811 and 0.9877, respectively. If all the compounds are unified in a same model, it is found the R2 values are 0.9954 and 0.9897 for inert nitrogen and inert dioxide, respectively. For convenience, the results are summarized in Table 15. In Table 15, the column titled with ‘No. of compounds’ means the number of compounds that are used to build the model and the column titled with ‘Ave. error’ means the grand average error of the average fitting error of individual compounds. Although the results seems
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References
Table 15 Summary of the predictive models in this work. Group
Inert gas
No. of compounds
FU
R2
Ave. error (%)
CnHm
N2 CO2
12 12
1.6473 2.2001
0.9966 0.9922
2.4586 3.0635
CnHmO
N2 CO2
5 5
1.7154 2.2606
0.9940 0.9811
3.8073 5.3524
CnHmO2
N2 CO2
3 3
1.5625 2.0274
0.9971 0.9877
0.9638 2.4750
Whole
N2 CO2
20 20
1.6513 2.1975
0.9954 0.9897
2.9800 3.7651
to be attractive, it should be noted that it is found that the substance which is of cool flame phenomena will result in larger predictive error. For example, the maximum fitting error is found to be 35.2354% of dimethyl ether, although the maximum fitting errors are below 5% for most compounds. Experimental data of cyclopropane, ammonia, benzene, acetylene, carbon disulfide, carbon monoxide, diethyl ether, and hydrogen, which are all not included in the procedure to determine the unspecified parameter in the proposed model, are used to validate the predictive ability for the proposed unified model, and it is found that the average predictive errors for each compound between the predictive value and the experimental one are lower than 14.8983% and 11.6591% for inert nitrogen and inert carbon dioxide, respectively; and the grand averages are about 6.01% and 8.70% for inert nitrogen and inert carbon dioxide, respectively. As compared to the models suggested by Kondo et al., the proposed models result in much better predictive performance both in the case of inert nitrogen and inert carbon dioxide. Acknowledgements The authors would like to thank the National Science Council of the ROC for supporting this study financially under grant #NSC 972221-E-039-006 and # NSC 98-2221-E-034-003.
Britton, L. G., ‘‘Using Heat of Oxidation to Evaluate Flammability Hazards,’’ Process Saf. Prog., 21, 31 (2002). Chen, C. C., H. J. Liaw, T. C. Wang, and C. Y. Lin, ‘‘Carbon Dioxide Dilution Effect on Flammability Limits for Hydrocarbons,’’ J. Hazard. Mater., 163, 795 (2009a). Chen, C. C., T. C. Wang, H. J. Liaw, and H. C. Chen, ‘‘Nitrogen Dilution Effect on the Flammability Limits for Hydrocarbons,’’ J. Hazard. Mater., 166, 880 (2009b). Chen, C. C., T. C. Wang, H. J. Liaw, and H.-C. Chen, ‘‘Upper Flammability Limit of Hydrocarbons Diluted with Nitrogen,’’ Prog. Safety Sci. Techno., 7, 1249 (2008). Coward, H. F. and G. W. Jones, ‘‘Limits of Flammability of Gases and Vapors,’’ US Bureau Mines Bull., 503 (1952). Crowl, D. A. and J. F. Louvar, Chemical Process Safety—Fundamentals with Applications, 2nd ed., , Prentice Hall, NJ, USA (2002). High, M. S. and R. P. Danner, ‘‘Prediction of Upper Flammability Limit by a Group Contribution Method,’’ Ind. Eng. Chem. Res., 26, 1395 (1987). Kondo, S., Y. Urano, K. Tokuhashi, A. Takahashi, and K. Tanaka, ‘‘Prediction of Flammability of Gases by Using F-number Analysis,’’ J. Hazard. Mater., 100, 113 (2001). Kondo, S., K. Takizawa, A. Takahashi, and K. Tokuhashi, ‘‘Extended Le Chatelier’s Formula for Nitrogen Dilution Effect on the Flammability Limits,’’ Fire Safety J., 41, 406 (2006a). Kondo, S., K. Takizawa, A. Takahashi, and K. Tokuhashi, ‘‘Extended Le Chatelier’s Formula for Carbon Dioxide Dilution Effect on Flammability Limits,’’ J. Hazard. Mater., 138, 1 (2006b). Kondo, S., K. Takizawa, A. Takahashi, K. Tokuhashi, and A. Sekiya, ‘‘Flammability Limits of Isobutane and its Mixtures with Various Gases,’’ J. Hazard. Mater., 148, 640 (2007). Kondo, S., K. Takizawa, A. Takahashi, K. Tokuhashi, and A. Sekiya, ‘‘A Study on Flammability Limits of Fuel Mixtures,’’ J. Hazard. Mater., 155, 440 (2008). Kuchta, J. M., ‘‘Investigation of Fire and Explosion Accidents in the Chemical, Mining, and Fuel-related Industries,’’ US Bureau Mines Bull., 680 (1985). Liekhus, K. J., I. A. Zlochower, K. L. Cashdollar, S. M. Djordjevic, and C. A. Loehr, ‘‘Flammability of Gas Mixtures Containing Volatile Organic Compounds and Hydrogen,’’ J. Loss Prevent. Proc., 13, 377 (2000). Mashuga, C. V. and D. A. Crowl, ‘‘Derivation of Le Chatelier’s Mixing Rule for Flammable Limits,’’ Process Saf. Prog., 19, 112 (2000). Planas-Cuchi, E., J. A. Vilchez, and J. Casal, ‘‘Fire and Explosion Hazards During Filling/ Emptying of Tanks,’’ J. Loss Prevent. Proc., 12, 479 (1999). Shebeko, Y. N., W. Fan, I. A. Bolodian, and V. Y. Navzenya, ‘‘An Analytical Evaluation of Flammability Limits of Gaseous Mixtures of Combustible–Oxidizer–Diluent,’’ Fire Safety J., 37, 549 (2002). Shimy, A. A., ‘‘Calculating Flammability Characteristics of Hydrocarbons and Alcohols,’’ Fire Techno., 6 (2), 135 (1972). Vidal, M., W. Wong, W. J. Rogers, and M. S. Mannan, ‘‘Evaluation of Lower Flammability Limits of Fuel–Air–Diluent Mixtures Using Calculated Adiabatic Flame Temperatures,’’ J. Hazard. Mater., 130, 21 (2006). Zabetakis, M. G., ‘‘Flammability Characteristics of Combustible Gases and Vapors,’’ US Bureau Mines Bull., 627 (1963).
Contents lists available at ScienceDirect
Journal of the Taiwan Institute of Chemical Engineers journal homepage: www.elsevier.com/locate/jtice
Nitrogen and carbon dioxide dilution effect on upper flammability limits for organic compound containing carbon, hydrogen and oxygen atoms TzuChi Wang a, ChanCheng Chen b,*, HuiChu Chen a a b
Department of Chemical and Materials Engineering, Chinese Culture University, Taipei 111, Taiwan Department of Safety, Health and Environmental Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung 811, Taiwan
A R T I C L E I N F O
A B S T R A C T
Article history: Received 31 December 2009 Received in revised form 27 February 2010 Accepted 2 March 2010
In this work semi-empirical models for predicating upper flammability limit (UFL) for flammable gases diluted with inert nitrogen and with carbon dioxide are developed, respectively. Experimental data for 20 flammable gases are collected and used to determine the unspecified parameter in our earlier theoretical model. It is found that if we divide these 20 organic compounds into three groups—CnHm, CnHmO, and CnHmO2, the coefficients of determination (R2) for these three categories for the case of inert nitrogen will be 0.9969, 0.9940 and 0.9971, respectively; and for the case of inert dioxide will be 0.9922, 0.9811 and 0.9877, respectively. If all the compounds are unified in a same model, it is found the R2 values are 0.9954 and 0.9897 for inert nitrogen and inert carbon dioxide, respectively. Experimental data of cyclopropane, ammonia, benzene, acetylene, carbon disulfide, carbon monoxide, diethyl ether, and hydrogen, which are not included in the original semi-empirical model, is used to validate the predictive ability for the proposed unified model, and it is found that the average predictive errors for each component are lower than 10% for inert gases of both nitrogen and carbon dioxide. ß 2010 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Keywords: Upper flammability limit Inert nitrogen Inert carbon dioxide Safety
1. Introduction Flammability limits are one of the important safety indicators for all who manufacture, process, transport and storage chemicals. To meet the practical requirements from the process industries, a bunch of literature has provided experimental data on the flammability limits of flammable gases and their mixtures (Coward and Jones, 1952; Kuchta, 1985; Zabetakis, 1963). Aside from experimental research, theoretical models have also been proposed by many researchers to investigate their applicability. Shimy, for example, estimated the flammability limits of hydrocarbons and alcohols by counting their carbon atoms and hydrogen atoms (Shimy, 1972). High and Danner (1987) proposed a group contribution method to estimate the flammability limits of combustible gases. Kondo et al. (2001), on the other hand, used F-number estimation method to achieve the same goal. As for Britton (2002), he constructed a model that can find the lower flammable limit (LFL) by using the combustion heat and oxygen usage of combustible gases. In case of estimating the flammability limits of a mixture of combustible gases, Le Chatelier equation is the most widely adopted method (Mashuga and Crowl, 2000; Kondo et al., 2007,
* Corresponding author. Tel.: +886 7 6011000x2311; fax: +886 7 6011061. E-mail address: [email protected] (C. Chen).
2008; Liekhus et al., 2000). However, combustible gases are not the only components that exist in industrial processes: inert gases may do too. For example, inerting is a common procedure in process industries before a vessel containing flammable gases is out of service or in service. In an inerting process, the flammable gases can be diluted with inert gases—mostly nitrogen or carbon dioxide, sometimes water vapor—to alter the flammability limit and in turn to reduce the possibility of explosion or catching fire (Crowl and Louvar, 2002; Planas-Cuchi et al., 1999). Although Le Chatelier equation is satisfactory in estimating the flammability limits of mixtures of flammable gases, it cannot be applied effectively in such kinds of inertized mixtures, which explains why many researchers devoted themselves to the topic of prediction of the flammability limit of the inertized mixtures. Because inert gas does not take part in the reaction in combustion, some of the researchers forecast the flammability limits of inertized mixture by calculating the adiabatic flame temperature. Vidal et al. (2006), employed the adiabatic flame temperatures of non-inertized methane and ethane to predict the LFL of the inertized mixtures. Shebeko et al. (2002), on the ground of kinetics of combustion, make use of the critical temperature of a combustion system to find the flammability limits of an inertized mixture of combustible gas via the calculation of adiabatic flame temperature. According to aforementioned results, in evaluating the flammability limits by means of the approach of adiabatic flame temperature, LFL is more accurate than the UFL.
1876-1070/$ – see front matter ß 2010 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jtice.2010.03.004
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Table 1 Calculated adiabatic flame temperatures in the UFL for methane, propane, and ethylene diluted with inert nitrogen gas (x = hydrocarbon/hydrocarbon + inert gas).
Nomenclature Cpf Cpinert n1 Tad U U1 x
FU q r s
mean molar heat capacities of the hydrocarbon mean molar heat capacities of the inert gas number of mole of oxygen needed in the combustion of one mole of pure fuel gas adiabatic flame temperature upper flammability limits of a fuel gas diluted with inert gas upper flammability limits of the pure fuel gas mole fraction of a fuel gas in the mixture (fuel and inert gas, but no air) parameter of the upper flammability limits prediction model parameter of the upper flammability limits prediction model parameter of the upper flammability limits prediction model parameter of the upper flammability limits prediction model
Besides the adiabatic flame temperature approach, Kondo et al. (2006a,b) revised the Le Chatelier equation and applied their result to find the flammability limits of either nitrogen mixture or carbon dioxide mixture. They theoretically proposed that xn1 xn1 ¼ 1 ðU=xÞ 1 U 1
(1)
where U is the UFL (in molar fraction) of a fuel gas diluted with inert gas; U1 is the UFL of the pure fuel gas; x is the mole fraction of a fuel gas in the mixture (fuel and inert gas, but no air); n1 is the number of mole of oxygen needed in the combustion of one mole of pure fuel gas. However, the prediction result from (1) do not fit the experimental result very well, so that Kondo et al., to enhance the accuracy, added to the equation a power series to obtain the semiempirical equation as shown in (2): xn1 xn1 ¼ þ qð1 xÞ þ rð1 xÞ2 þ sð1 xÞ3 1 ðU=xÞ 1 U 1
(2)
where q, r, and s are unspecified parameters whose values are determined by the contents of gases in a mixture. Although the accuracy can be improved by using this revised equation, it depends largely on the values of the unspecified parameters, that is, the amount of experimental data of the mixture. For those combustible gases with little discussion in literature, finding the suitable values of these unspecified parameters is still a job with challenge. We have proposed (3) as a theoretical model in previous research in which we integrate adiabatic temperature with the Le Chatelier equation to deal with UFL of combustible hydrocarbon mixture with either nitrogen or carbon dioxide as its inert gas (Chen et al., 2008, 2009a,b). 1 1 1 1 (3) ¼ FU U U1 x where
FU ¼
U 1 C p f þ ð1 U 1 ÞC pinert U1 C p f
(4)
Cpf and Cpinert are the mean molar heat capacities of the hydrocarbon and the inerted mixture, respectively, heated from
x
1.000 0.850 0.750 0.700 0.500 0.375 0.250 0.150
Methane
Propane
Ethylene
UFL (%)
Tad (K) (a = 0.8)
UFL (%)
Tad (K) (a = 2)
UFL (%)
Tad (K) (a = 2)
15.80 14.90 14.30 13.94 12.19 10.60 8.70 –
1937.4 1920.8 1902.7 1893.0 1838.1 1788.9 1690.6 –
10.00 – 9.10 – 8.20 7.53 – 4.96
1826.8 – 1830.6 – 1800.7 1768.7 – 1650.3
31.50 – 25.00 – 18.40 – 10.50 7.00
1433.9 – 1479.6 – 1508.2 – 1531.0 1495.1
25 8C to a specified adiabatic temperature. In deriving (3), one important assumption is that the adiabatic flame temperature does not change as inert gas is added to the combustible gas. However, this assumption seems to be effective in case of the calculation in LFL, but not in case of the calculation in UFL. To clearly illustrate this point, Table 1 lists the calculated adiabatic flame temperatures of nitrogen-inertized combustible gas mixture (methane, propane, and ethylene) in the condition of UFL from the experimental data. The data of UFL come from research results obtained by Kondo et al. (2006a). The parameter a in Table 1 denotes the number of mole of carbon monoxide generated in the course of burning one mole of combustible gas. This parameter is adopted to reflect that the combustible gas in an inertized mixture does not burn completely in UFL, and it is assumed the value of a does not change as inert gas is added to a combustible gas. It is obvious from Table 1 that the adiabatic flame temperature of a combustible gas does change in the inerting process. In addition, for different gas mixtures, the adiabatic flame temperatures in UFL vary widely, which also necessitates the need of experimental data to calculate FU instead of calculating it theoretically. However, as we know, most organic compounds of similar structure are of similar mean molar heat capacity and UFL, thus, according to (4), it seems possible that there is a unified value of FU if the organic compounds are properly grouped. In this research, we explore this possibility through the existing experimental data. In the course of the study, experimental data gleaned from literature on the UFL of organic combustibles inertized with nitrogen or carbon dioxide will be explored. This work is organized as follows. The data compilation is discussed in Section 2. The fitting performance of (3) for individual compounds is presented in Section 3. In Section 4, we discuss both the fitting and predictive performance in case the flammable gases are grouped according to their molecular structure. Finally, the conclusion of this work is presented in Section 5. 2. Data compilation The data of UFL collected in this study come either from official reports of Mineral Bureau of the USA or from research literature. It is widely known that the accuracy of experimental results of UFL is heavily depended on the experimental instrument and environmental conditions. To maintain the coherence of the data, most of them are collected from the Bulletin 503 and Bulletin 627 (Coward and Jones, 1952; Zabetakis, 1963). However, the bulk of the results listed in these two reports are showed in diagrams, so if there exist newer data obtained under similar experimental conditions and presented in numerical forms, the newer ones will supersede those in the official reports (Kondo et al., 2006a,b). Except for directly giving the numerical values, there are two types of presentation of the flammability limit data in Bulletin 503 and Bulletin 627 with the form of only curve description. The first one showed both the experimental data and the fitting curve, and the other showed only
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Table 2 The source, type, and number of data of the UFL for 20 compounds. No.
Compound name
Formula
Inert gas (N2) Source
Data no.
Data type
Source
Data no.
Data type
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether Methyl formate Isobutyl formate Methyl acetate
CH4 C2H6 C3H8 C4H10 C5H12 C6H14 C2H4 C3H6 C4H6 C4H8 C4H8 C5H10 CH4O C2H6O C3H6O C4H8O C2H6O C2H4O2 C5H10O2 C3H6O2
Kondo et al. (2006a) Zabetakis (1963) Kondo et al. (2006a) Zabetakis (1963) Coward and Jones (1952) Coward and Jones (1952) Kondo et al. (2006a) Kondo et al. (2006a) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Kondo et al. (2006a) Kondo et al. (2006a) Zabetakis (1963) Zabetakis (1963)
9 16 8 16 15 8 6 8 16 16 16 16 16 16 16 16 8 8 16 16
Value Curve Value Curve Curve Point Value Value Curve Curve Curve Curve Curve Curve Curve Curve Value Value Curve Curve
Kondo et al. (2006b) Zabetakis (1963) Kondo et al. (2006b) Zabetakis (1963) Coward and Jones (1952) Coward and Jones (1952) Kondo et al. (2006b) Kondo et al. (2006b) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Zabetakis (1963) Kondo et al. (2006b) Kondo et al. (2006b) Zabetakis (1963) Zabetakis (1963)
7 16 9 16 15 7 7 8 16 16 16 16 16 16 16 16 8 7 16 16
Value Curve Value Curve Curve Points Value Value Curve Curve Curve Curve Curve Curve Curve Curve Value Value Curve Curve
the fitting curve. In this work, if the experimental points are given on the curve, only the experimental points are adopted; otherwise, 15–16 evenly spaced points are read from the curve for later analysis. Therefore, there are three types of reference data in Table 2: value means numerical value is directly available, point means experimental points are read from the curve, and curve means the data are read from the fitting curve. Table 2 also lists the data source and number of the data used in later analyses. As showed in Table 2, inertized data for 20 compounds (with either nitrogen or carbon dioxide) are formulated here for later analyses. According to their functional structure, the compounds can be divided as alkane (methane, ethane, propane, n-butane, npentane, n-hexane), alkene (ethylene, propylene, 1,3-butadiene, isobutylene, 1-butene, 3-methyl-1-butene), alcohol (methyl alcohol, ethyl alcohol), ketone (acetone, methyl ethyl ketone), ether (dimethyl ether), and ester (methyl formate, isobutyl formate, methyl acetate). 3. Results In this section, the collected experimental data are studied to see whether or not they are well described by (3). The possibility that whether or not specific relations could be obtained if the flammable materials are properly grouped, is then explored in Section 4.
Inert gas (CO2)
3.2. Inertion with carbon dioxide as inert gas When the same procedure as is used in the previous subsection is applied to combustible gas mixture inertized with carbon dioxide, the regression results acquired through the use of the prediction model suggested by Chen et al., are listed in Table 4. As Table 4 shows, R2 values are all greater than 0.9762 for the 20 combustible organic compounds taken into consideration, saving that of dimethyl ether (0.9565). Furthermore, it is also found that the maximum errors between the experimental value of UFL and the prediction value obtained by using FU value are all lower than 10.7402%, except those for ethylene (21.2212%) and dimethyl ether (32.1252%). All the average errors, but those for ethylene (10.9083%) and dimethyl ether (14.1140%), are under 4.3646%. The regression results for the 20 combustible organic compounds are showed in Fig. 2. As these figure shows, experimental data are also well described by (3) in case that the inert gas is of carbon dioxide.
Table 3 The regression and UFL prediction results for 20 combustible organic compounds inertized with nitrogen. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether Methyl formate Isobutyl formate Methyl acetate
1.6592 1.6770 1.6321 1.6607 1.6271 1.6357 1.6767 1.6435 1.6684 1.6481 1.6197 1.6589 1.7064 1.7145 1.6976 1.7209 1.7225 1.5209 1.5688 1.5874
0.9968 0.9946 0.9965 0.9989 0.9983 0.9976 0.9933 0.9950 0.9953 0.9977 0.9973 0.9997 0.9989 0.9955 0.9987 0.9994 0.9798 0.9981 0.9965 0.9998
3.7332 3.8902 4.8918 1.8030 2.2438 3.0223 16.0774 7.0004 4.6385 1.9235 2.9039 1.0403 2.4117 4.6454 2.8076 1.3550 31.7726 2.6330 3.1353 0.9527
1.9433 2.3390 3.4447 0.7833 0.9987 1.5186 7.4877 4.3104 2.7685 1.2826 1.4045 0.3313 1.3662 2.6646 1.3548 0.6955 12.9415 1.4741 1.2965 0.2746
3.1. Inertion with nitrogen as inert gas Applying regression analysis to the data of inert nitrogen listed in Table 2 by using the prediction model suggested by Chen et al. (i.e. (3)) generated the results showed in Table 3. As is obvious in Table 3, for all the 20 combustible organic compounds, R2 values are greater than 0.9798. In all cases, the average estimating errors, but those for ethylene (7.4877%) and dimethyl ether (12.9415%), are under 4.3104%. The maximum estimating errors are lower than 7.04%, except those for ethylene (16.0774%) and dimethyl ether (31.7726%). The regression results are shown in Fig. 1 for these 20 compounds. The deviations in cases of ethylene and dimethyl ether might come from the fact that these two compounds are reported to generate cool flame instead of hot flame, which has been discussed in our earlier work. As it is seen from these results, most experimental results are well described by (3), thus the only parameter in (3) might be used to characterize their flammable characteristics.
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T.C. Wang et al. / Journal of the Taiwan Institute of Chemical Engineers 41 (2010) 453–464
Fig. 1. The regression results of ((1/U) (1/U1)) vs. ((1/x) 1) for organic compounds inertized by nitrogen. The straight lines in the figures are forced to pass through the original point in regression; the dots in the figures are experimental data of UFL collected from various literature.
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457
Fig. 1. (Continued ).
4. Discussion As Section 3 shows, the UFLs of inertized mixture could be effectively described by (3) and there is only one parameter
(i.e. FU) in the proposed model, so we explore the possibility whether unified value of FU for each group of compounds could be found if the flammable compounds are properly grouped.
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458
Fig. 1. (Continued ).
4.1. Inertion with nitrogen as inert gas On the inspection of Table 3, it is plain that the FU values of alkane and alkene range from 1.6197 to 1.6770; those of alcohol, ketone, and ether, from 1.6976 to 1.7225; finally those of ester, from 1.5209 to 1.5874. Consequently, if the 20 compounds are classified into three groups—CnHm, CnHmO, and CnHmO2—it is feasible to procure FU values that are representative enough for each of these types of organic compounds. Table 5 shows the FU value and the coefficient of determination (R2) of compounds with the form CnHm, as well as maximum errors and average errors Table 4 The regression and UFL prediction results for 20 combustible organic compounds inertized with carbon dioxide. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether Methyl formate Isobutyl formate Methyl acetate
2.2836 2.1999 2.1741 2.1370 2.1004 2.2172 2.1970 2.1300 2.2361 2.3028 2.2058 2.2840 2.2358 2.3068 2.3634 2.1278 2.3840 1.8847 2.0203 2.1654
0.9939 0.9924 0.9923 0.9993 0.9971 0.9992 0.9796 0.9918 0.9899 0.9969 0.9931 0.9990 0.9968 0.9762 0.9963 0.9994 0.9565 0.9973 0.9915 0.9968
4.3967 3.9269 5.4661 1.2157 2.6089 2.0559 21.2212 10.7402 6.8937 2.7710 3.9660 2.7076 3.0838 7.9831 3.2171 1.1178 32.1252 2.9344 4.0487 2.4883
2.1788 2.3730 3.5215 0.3794 1.1282 0.5653 10.9083 4.3646 3.8491 0.9849 2.2091 1.1814 1.9305 4.3437 1.7931 0.1640 14.1140 1.7703 1.7231 1.4206
between the experimental UFL and the predicted value obtained by the use of FU value. According to Table 5, FU value is 1.6473 and R2, 0.9966; the maximum errors between experimental data and predicted values of UFL by using FU are all less than 6.9431% except that of ethylene (17.3388%); average errors are all smaller than 4.2694% saving that of ethylene (8.0291%). On the careful comparison between error values of various alkanes in Table 3 and those in Table 5, we find them within the tolerable ranges and make the conclusion that (5) can serve as the prediction model for the UFL of nitrogen-inertized organic gases with the form of CnHm. 1 1 1 1 ¼ 1:6473 U U1 x
(5)
In the same manner, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and experimental data for CnHmO-type compounds are listed in Table 6. According to Table 6, FU value is 1.7154 and R2, 0.9940; the maximum errors between experimental data and predicted values of UFL by using FU are all smaller than 4.6313% except that of dimethyl ether (31.9417%); average errors are all smaller than 2.6579% saving that of dimethyl ether (12.9660%). After drawing a detailed comparison between error values of the organic compounds with the form of CnHmO in Table 3 and those in Table 6, we find them within the tolerable ranges and reach the conclusion that (6) can serve as the prediction model for the UFL of nitrogeninertized organic compounds of alcohols, ketones, and ethers. 1 1 1 1 ¼ 1:7154 U U1 x
(6)
In the same way, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and
T.C. Wang et al. / Journal of the Taiwan Institute of Chemical Engineers 41 (2010) 453–464
459
Fig. 2. The regression results of ((1/U) (1/U1)) vs. ((1/x) 1) for organic compounds inertized by carbon dioxide. The straight lines in the figures are forced to pass through the original point in regression; the dots in the figures are experimental data of UFL collected from various literature.
experimental data for CnHmO2-type compounds are listed in Table 7. Based on the observation of Table 7, FU value is 1.5625 and R2, 0.9971; the maximum errors between experimental data and
predicted values of UFL by using FU are all smaller than 4.4754% for esters; average errors are smaller than 1.2750%. After comparing error values of the esters in Table 3 with those in Table 7, we deem that they are within the tolerable ranges and arrive at the conclusion
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T.C. Wang et al. / Journal of the Taiwan Institute of Chemical Engineers 41 (2010) 453–464
Fig. 2. (Continued ).
that (7) can serve as the prediction model of the UFL for nitrogeninertized organic compounds with the form CnHmO2. 1 1 1 1 ¼ 1:5625 U U1 x
(7)
As can be seen from (5)–(7), in the prediction models of UFL for nitrogen-inertized CnHm, CnHmO, and CnHmO2, the FU value are very close. In the same way, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and experimental data for all 20 compounds are listed in Table 8.
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461
Fig. 2. (Continued ).
In Table 8, FU value is 1.6513; the maximum errors between experimental data and predicted values of UFL are all, except those for ethylene (17.1656%) and dimethyl ether (33.4884%), smaller than 8.3837%; average errors except those for ethylene (7.9548%) and dimethyl ether (13.7386%) smaller than 4.2263%. The comparison of maximum and average errors between Table 8 and other tables leads us to conclude that they are within the tolerable ranges and that (8) is suitable for being the prediction model of the UFL for nitrogen-inertized organic compounds, if no other useful information are available. 1 1 1 1 (8) ¼ 1:6513 U U1 x It should be noted that Kondo et al. has claimed (9) as the UFL prediction model to the same purpose. Their results were obtained Table 5 The regression and prediction results for 12 organic compounds with the form CnHm in nitrogen-inertized case. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene
1.6473
0.9966
3.9599 4.5742 4.7034 2.3470 2.8059 3.2570 17.3388 6.9431 5.2098 1.9343 2.9884 1.5548
2.0424 2.6653 3.2927 0.6528 1.1225 1.5537 8.0291 4.2694 3.0562 1.2830 1.2220 0.3146
Total average
2.4586
from five nitrogen-inertized organic compounds (methane, propane, propylene, methyl formate, and 1,1-difluoroethane). xn1 xn1 ¼ þ 0:122ð1 xÞ þ 0:187ð1 xÞ2 1 ðU=xÞ 1 U 1 0:242ð1 xÞ3
(9)
in which n1 is the number of mole of oxygen needed for the combustion of one mole of combustible gas at UFL. To examine the effectiveness of (8) and (9), eight compounds appearing neither in this research nor in Kondo et al.’s are selected as comparison basis. These compared components are cyclopropane, ammonia,
Table 6 The regression and prediction results for five organic compounds with the form CnHmO in nitrogen-inertized case. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether
1.7154
0.9940
2.2129 4.6313 2.6051 1.3987 31.9417
1.2801 2.6579 1.3728 0.7596 12.9660
Total average
3.8073
Table 7 The regression and prediction results for three organic compounds with the form CnHmO2 in nitrogen-inertized case. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methyl formate Isobutyl formate Methyl acetate
1.5625
0.9971
4.4754 3.3902 2.0351
1.2750 1.2245 0.3918
Total average
0.9638
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462
Table 8 The regression and prediction results of UFL for 20 organic compounds in nitrogeninertized case.
Table 10 The regression and prediction results for 12 organic compounds with the form CnHm in carbon dioxide-inertized case.
Compound
FU
R2
Max. error (%)
Ave. error (%)
Compound
FU
R2
Max. error (%)
Ave. error (%)
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether Methyl formate Isobutyl formate Methyl acetate
1.6513
0.9954
3.8836 4.4748 4.6675 2.1840 2.9295 3.3376 17.1656 6.8829 5.0983 1.8801 3.1518 1.3768 3.8144 5.6465 3.3382 3.6464 33.4884 8.3837 3.8615 2.8299
2.0091 2.6166 3.2529 0.6918 1.1513 1.5658 7.9548 4.2263 3.0015 1.2808 1.1976 0.3139 2.4118 3.5928 1.9643 2.0544 13.7386 2.7127 2.4081 1.4558
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene
2.2001
0.9922
5.1421 3.9242 5.2344 2.3927 4.2385 1.6826 21.1342 9.8005 7.5527 5.6221 4.0654 3.0620
2.3766 2.3720 3.4615 0.7888 1.7816 0.7733 10.8692 4.5486 4.1386 1.1938 2.2391 2.2188
Total average
2.9800
benzene, acetylene, carbon disulfide, carbon monoxide, diethyl ether, and hydrogen. The results are shown in Table 9. Table 9 shows that the maximum predictive errors and average predictive errors between experimental data and predicted values of the proposed equation (8) are smaller than 28.9628% and 14.8983%, respectively. Although Kondo et al.’s model (i.e. Eq. (9)) has up to three regression parameters, the predictive performance of their model is inferior to the proposed one which is of only one regression parameter. This result might imply that the proposed model structure is more suitable to represent the diluted effect on UFL. Moreover, it could be found that the grand average predictive error is about 6.0% for these eight testing compounds, thus if no experimental data are available, Eq. (8) might give an estimate with reasonable accuracy. 4.2. Inertion with carbon dioxide as inert gas When the same procedure as is used in the previous section is applied to combustible gas mixture inertized with carbon dioxide, it is plain that the FU values of alkane and alkene range from 2.1004 to 2.3028; those of alcohol, ketone, and ether from 2.1278 to 2.3840; finally those of ester, from 1.8847 to 2.1654 on the inspection of Table 4. The 20 compounds are classified into three groups—CnHm, CnHmO, and CnHmO2. Table 10 shows the FU values and coefficients of determination (R2) of compounds with the form CnHm, as well as Table 9 Comparison of predictive capability between this work and Kondo et al.’s model with inert gas of nitrogen. Compound
This work (8)
Total average
3.0635
maximum errors and average errors between the experimental UFL and the predicted value obtained by the use of FU value. According to Table 10, FU value is 2.2001 and R2, 0.9922; the maximum errors between experimental data and predicted values of UFL by using FU are all less than 9.8005% except that of ethylene (21.1342%); average errors are all smaller than 4.5486% saving that of ethylene (10.8692%). On the careful comparison between error values of various alkanes in Table 4 and those in Table 10, we find them within the tolerable ranges and make the conclusion that (10) can serve as the prediction model for the UFL of carbon dioxide-inertized organic gases with the form of CnHm. 1 1 1 1 ¼ 2:2001 U U1 x
(10)
In the same manner, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and experimental data for CnHmO-type compounds are listed in Table 11. According to Table 11, FU value is 2.2606 and R2, 0.9811; the maximum errors between experimental data and predicted values of UFL by using FU are all smaller than 8.5045% except that of dimethyl ether (34.1669%); average errors are all smaller than 4.5961% saving that of dimethyl ether (15.5702%). After drawing a detailed comparison between error values of the organic compounds with the form of CnHmO in Table 4 and those in Table 12, we find them within the tolerable ranges and reach the conclusion that (11) can serve as the prediction model for the UFL of nitrogen-inertized organic compounds of alcohols, ketones, and ethers. 1 1 1 1 ¼ 2:2606 U U1 x
(11)
In the same way, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and
Kondo et al. (9) Table 11 The regression and prediction results for five organic compounds with the form CnHmO in carbon dioxide-inertized case.
Max. error (%)
Ave. error (%)
Max. error (%)
Ave. error (%)
Cyclopropane Ammonia Benzene Acetylene Carbon disulfide Carbon monoxide Diethyl ether Hydrogen
2.6392 12.7073 13.5848 5.0374 8.5418 12.0324 28.9628 13.8184
1.5977 6.6717 10.4253 2.3509 2.5778 5.4485 14.8983 4.8629
9.8637 20.5565 30.8400 32.9217 17.3667 19.0773 51.3115 17.9982
7.0201 11.2871 24.3640 15.6815 9.4344 8.8863 22.4042 10.2305
Compound
FU
R2
Max. error (%)
Ave. error (%)
Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether
2.2606
0.9811
3.0093 8.5045 4.3265 4.0420 34.1669
1.7960 4.5961 2.7723 2.0276 15.5702
Grand average
12.2655
6.0141
24.9920
13.6635
Total average
5.3524
T.C. Wang et al. / Journal of the Taiwan Institute of Chemical Engineers 41 (2010) 453–464 Table 12 The regression and prediction results for three organic compounds with the form CnHmO2 in carbon dioxide-inertized case. Compound Methyl formate Isobutyl formate Methyl acetate
FU 2.0274
R2 0.9877
Max. error (%)
Ave. error (%)
4.7843 3.8570 4.1188
2.6173 1.7651 3.0427
Total average
2.4750
experimental data for CnHmO2-type compounds are listed in Table 12. Based on the observation of Table 12, FU value is 2.0274 and R2, 0.9877; the maximum errors between experimental data and predicted values of UFL by using FU are all smaller than 4.7843% for esters; average errors are smaller than 3.0427%. After comparing error values of the esters in Table 4 with those in Table 12, we deem that they are within the tolerable ranges and arrive at the conclusion that (12) can serve as the prediction model of the UFL for carbon dioxide-inertized organic compounds with the form CnHmO2. 1 1 1 1 ¼ 2:0274 U U1 x
(12)
As can be seen from (10)–(12), in the prediction models of UFL for carbon dioxide-inertized CnHm, CnHmO, and CnHmO2, the FU value are very close. In the same way, FU, coefficient of determination (R2), and the maximum and average errors between predicted UFL and experimental data for all 20 compounds are listed in Table 13. In Table 13, FU value is 2.1975 and R2, 0.9897; the maximum errors between experimental data and predicted values of UFL are all, except those for ethylene (21.2072%) and dimethyl ether (35.2354%), smaller than 12.0243%; average errors except those for ethylene (10.9020%) and dimethyl ether (16.6708%), smaller than 5.1445%. The comparison of maximum and average errors between Table 13 and other tables leads us to conclude that they are within the tolerable ranges and that (13) is suitable for being the prediction model of the UFL for carbon dioxide-inertized organic Table 13 The regression and prediction results of UFL for 20 organic compounds in carbon dioxide-inertized case. Compound
FU
R2
Max. error (%)
Ave. error (%)
Methane Ethane Propane n-Butane n-Pentane n-Hexane Ethylene Propylene 1,3-Butadiene Isobutylene 1-Butene 3-Methyl-1-butene Methyl alcohol Ethyl alcohol Acetone Methyl ethyl ketone Dimethyl ether Methyl formate Isobutyl formate Methyl acetate
2.1975
0.9897
5.1655 3.9584 5.1877 2.3352 4.1850 1.6256 21.2072 9.8350 7.6007 5.6963 4.1108 3.0784 3.7847 9.2248 5.0755 2.1743 35.2354 12.0243 4.8498 2.4598
2.3955 2.3858 3.4675 0.7547 1.7512 0.8102 10.9020 4.5339 4.1666 1.2226 2.2528 2.2593 2.2496 5.1445 3.6842 1.0814 16.6708 4.9625 3.2211 1.3849
Total average
3.7651
463
Table 14 Comparison of predictive capability between this work and Kondo et al.’s model with inert gas of carbon dioxide. Compound
This work (13)
Kondo et al. (14)
Max. error (%)
Ave. error (%)
Max. error (%)
Ave. error (%)
Cyclopropane Ammonia Benzene Acetylene Carbon disulfide Carbon monoxide Diethyl ether Hydrogen
2.9336 19.3991 15.3877 19.3741 18.8728 16.7407 17.9151 23.1552
1.1644 10.4194 10.4220 9.2636 7.8132 8.9139 9.9746 11.6591
13.5318 23.3330 33.1362 42.4802 27.3623 30.1289 62.1652 33.1622
10.0469 12.5983 25.7411 20.8385 14.7133 14.8204 26.4306 16.6180
Grand average
16.7229
8.7038
33.1625
17.7259
compounds. 1 1 1 1 ¼ 2:1975 U U1 x
(13)
On the other hand, Kondo et al., framed (14) as the UFL prediction model for five carbon dioxide-inertized organic compounds (methane, propane, propylene, methyl formate, and 1,1-difluoroethane), xn1 xn1 ¼ þ 0:105ð1 xÞ þ 0:106ð1 xÞ2 1 ðU=xÞ 1 U 1 0:156ð1 xÞ3
(14)
To examine the effectiveness of (13) and (14), eight compounds appearing neither in this research nor in Kondo’s are selected as comparison basis. These components are cyclopropane, ammonia, benzene, acetylene, carbon disulfide, carbon monoxide, diethyl ether, and hydrogen. The results are shown in Table 14. Table 14 shows that the maximum predictive errors and average predictive errors between experimental data and predicted values of the proposed equation (13) are smaller than 23.1152% and 11.6591%, respectively. Although Kondo et al.’s model (i.e. Eq. (14)) has up to three regression parameters, the predictive performance of their model is inferior to the proposed one which is of only one regression parameter. This result might imply that the proposed model structure is more suitable to represent the diluted effect on UFL. Moreover, it could be found that the grand average predictive error is about 8.70% for these eight testing compounds, thus if no experimental data are available, Eq. (13) might give an estimate with reasonable accuracy. 5. Conclusion In this work the theoretical models proposed in our earlier work (i.e. Eq. (3)) to predict the UFL for flammable gases are examined through the UFL experimental data of 20 organic compounds. These experimental data include both the case of inert nitrogen and the case of inert carbon dioxide. It is found that if we divide these 20 organic compounds into three groups—CnHm, CnHmO, and CnHmO2, the coefficients of determination (R2) for these three categories for the case of inert nitrogen will be 0.9969, 0.9940 and 0.9971, respectively; and for the case of inert dioxide will be 0.9922, 0.9811 and 0.9877, respectively. If all the compounds are unified in a same model, it is found the R2 values are 0.9954 and 0.9897 for inert nitrogen and inert dioxide, respectively. For convenience, the results are summarized in Table 15. In Table 15, the column titled with ‘No. of compounds’ means the number of compounds that are used to build the model and the column titled with ‘Ave. error’ means the grand average error of the average fitting error of individual compounds. Although the results seems
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References
Table 15 Summary of the predictive models in this work. Group
Inert gas
No. of compounds
FU
R2
Ave. error (%)
CnHm
N2 CO2
12 12
1.6473 2.2001
0.9966 0.9922
2.4586 3.0635
CnHmO
N2 CO2
5 5
1.7154 2.2606
0.9940 0.9811
3.8073 5.3524
CnHmO2
N2 CO2
3 3
1.5625 2.0274
0.9971 0.9877
0.9638 2.4750
Whole
N2 CO2
20 20
1.6513 2.1975
0.9954 0.9897
2.9800 3.7651
to be attractive, it should be noted that it is found that the substance which is of cool flame phenomena will result in larger predictive error. For example, the maximum fitting error is found to be 35.2354% of dimethyl ether, although the maximum fitting errors are below 5% for most compounds. Experimental data of cyclopropane, ammonia, benzene, acetylene, carbon disulfide, carbon monoxide, diethyl ether, and hydrogen, which are all not included in the procedure to determine the unspecified parameter in the proposed model, are used to validate the predictive ability for the proposed unified model, and it is found that the average predictive errors for each compound between the predictive value and the experimental one are lower than 14.8983% and 11.6591% for inert nitrogen and inert carbon dioxide, respectively; and the grand averages are about 6.01% and 8.70% for inert nitrogen and inert carbon dioxide, respectively. As compared to the models suggested by Kondo et al., the proposed models result in much better predictive performance both in the case of inert nitrogen and inert carbon dioxide. Acknowledgements The authors would like to thank the National Science Council of the ROC for supporting this study financially under grant #NSC 972221-E-039-006 and # NSC 98-2221-E-034-003.
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