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Estimation of LOC (limiting oxygen concentration) of fuel–air–inert mixtures at elevated temperatures by means of adiabatic flame temperatures
Chemical Engineering and Processing 45 (2006) 193–197
Estimation of LOC (limiting oxygen concentration) of fuel–air–inert mixtures at elevated temperatures by means of adiabatic flame temperatures Domnina Razus a,∗ , Maria Molnarne b , Codina Movileanu a , Adriana Irimia a a
Romanian Academy, “I.G. Murgulescu” Institute of Physical Chemistry, Spl. Independentei 202, P.O. Box 12-194, 060021 Bucharest, Romania b BAM (Federal Institute for Materials Research and Testing), Unter den Eichen 87, 12205 Berlin, Deutschland, Germany Received 23 September 2004; accepted 2 June 2005 Available online 28 September 2005
Abstract The limiting values of fuel concentration in a flammable fuel–air mixture are the LEL (lower explosion limit) and UEL (upper explosion limit). The addition of an inert component to fuel/air mixtures determines the increase of LEL and decrease of UEL, until these values finally merge at the inerting point. The maximum oxygen amount of a non-flammable fuel–air–inert mixture is the LOC (limiting oxygen concentration), an important safety characteristics. The investigation of a comprehensive set of flammability data at elevated temperatures and ambient pressure taken from literature sources was made for systems containing nitrogen, carbon dioxide and water(vapour) as inert components, at 100◦ , 200◦ and 250 ◦ C. The adiabatic flame temperatures at LEL (CAFTLEL ) and LOC (CAFTLOC ) were calculated by taking into account the dissociation of gases within the flame. A linear correlation of CAFTLOC versus CAFTLEL was empirically derived for the examined systems. The slope and intercept of the correlation are dependent on temperature and on nature of the inert gas. The correlation allows the development of a simple procedure for estimating LOC, when the LEL of fuel–air and the equivalence ratio of the fuel–air–inert mixture at the inerting point are known. Knowing the scarce information concerning the flammability of fuel–air–inert mixtures at temperatures higher than ambient, the proposed procedure brings about an useful tool for estimation of LOC. © 2005 Elsevier B.V. All rights reserved. Keywords: Limiting oxygen concentration; Lower explosion limit; Calculated adiabatic flame temperature; Explosion of gases; Flammability
1. Introduction The limiting oxygen concentration (LOC) of a fuel–air–inert system is defined as the maximum allowed oxygen concentration of the fuel–air–inert mixture in which an explosion will not occur [1–3]. Together with the lower and upper explosion limits, the limiting oxygen concentration (or, in a wider sense, the MOC—maximum oxidizer content) is an important parameter for safety recommendations and loss prevention, in all human activities based on use of fuel–air or fuel–air–inert mixtures. Usually, the limiting oxygen concentration is determined from flammability diagrams of fuel–air–inert mixtures, shown in Fig. 1. Such diagrams are obtained by measuring the lower and upper flammability limits for fuel–air–inert mixtures containing
∗
Corresponding author. Tel.: +40 21 2249204; fax: +40 21 3121147. E-mail addresses: [email protected] (D. Razus), [email protected] (M. Molnarne). 0255-2701/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2005.06.010
various amounts of inert additive, by adequate methods [4]. This approach is accurate, but it is a time- and material-consuming procedure. Alternative methods for LOC determination have been recently developed. A method based on group contributions [5–7] allows calculation of composition for limit mixtures (including the mixture at the inertisation point) assuming a constant CAFT (calculated adiabatic flame temperature). Another method, based on numerical simulation of flame propagation in flammable mixtures, allows the calculation of limit mixtures composition assuming zero burning velocity in such mixtures [8–10]. In a recent study, we proposed a simple and reliable method for LOC estimation from values of the LEL of fuel–air mixtures, based on use of adiabatic flame temperatures. The method was tested for fuel–air–nitrogen [11] and fuel–air–carbon dioxide [12] mixtures, at ambient initial pressure and temperature. A linear correlation was empirically derived for each of the studied inert gases between CAFTLOC , corresponding to limit fuel–air–inert mixtures at LOC and CAFTLEL , corresponding to
D. Razus et al. / Chemical Engineering and Processing 45 (2006) 193–197
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of the TRIANGLE software, which applied cubic vector splines for interpolation of the explosion curve [14]. The adiabatic flame temperatures of fuel–air and fuel–air–diluent mixtures were computed with the program ECHIMAD [15] assuming that chemical equilibrium is reached within the flame. Fifteen compounds (Cgraphite , CH4 , CO, CO2 , H2 O, H2 , O2 , N2 , NO, C2 H2 , C2 H4 , C3 H8 , H, OH and O) were considered as combustion products. Their heat capacities (expressed as function of temperature with the form: Cp = a + b·T + c·T2 + d·T−2 ), the standard enthalpies of formation at 298 K and the standard entropies at 298 K were taken from the collections of Stull et al. [16] and Knacke et al. [17]. 3. Results and discussion Fig. 1. Explosion area for methane–air–carbon dioxide gaseous mixture at 100 ◦ C [2].
fuel–air mixtures at the lower explosion limit. Using this correlation, the experimentally measured LEL and an assumed constant value of the equivalence ratio for fuel–air–inert mixtures at LOC, the composition of mixture at LOC can be computed by means of the adiabatic flame temperatures at LOC and LEL. For mixtures at ambient initial conditions, containing nitrogen and carbon dioxide, the method allowed LOC predictions within errors of experimental values. The method excludes however fuels such as acetylene or ethylene oxide (substances with high intramolecular energies) or fuels that have a steep upper branch of the flammability curve (between the inerting point and the upper explosion limit)[3]. In the present paper, the method is further tested by using flammability data at elevated initial temperatures (100–250 ◦ C) and ambient initial pressure. Several sets of flammability data from a recent publication [2] were used, referring to systems that contain nitrogen, carbon dioxide or water(vapour) as inert gases.
3.1. Correlation of CAFTLOC versus CAFTLEL for fuel–air–inert mixtures at elevated initial temperatures and p0 = 1 bar A representative set of data referring to mixtures at 100 ◦ C is given in Table 1. It is seen that the amount of diluent gas (N2 , CO2 , or H2 O(v)) necessary for complete inerting of various fuel–air mixtures varies significantly, at constant temperature. Typical concentrations of nitrogen at LOC range between 48 and 60 mol% and of water(vapour) between 33 and 48 mol%. Similar results were collected for 200 and 250 ◦ C. Unfortunately, for systems diluted with CO2 , the measurements are scarce and only data for 100 ◦ C were analyzed, in comparison with those at ambient initial temperature. An example of CAFTLOC against CAFTLEL plot, at two initial temperatures, is given in Fig. 2, for fuel–air–water(vapour) mixtures. For each set of data, a linear correlation was found: 100 ◦ C : CAFTLOG = −(160 ± 289) + (1.272 ± 0.215) × CAFTLEL ;
2. Computing procedure
rn = 0.960 (five points)
(1)
200 ◦ C : CAFTLOG = (566 ± 357) + (0.851 ± 0.291)
The flammability limits of fuel–air and fuel–air–inert mixtures, measured at atmospheric pressure by DIN 51649-1 method [13], were given in Ref. [2] both as tables and diagrams. The LOC concentrations of these systems were calculated by means
×CAFTLEL ;
rn = 0.825 (six points)
(2)
Further examples are shown in Figs. 3 and 4, where data evaluated for fuel–air–inert mixtures at 100 ◦ C are plotted together
Table 1 Composition of limit mixtures and adiabatic flame temperatures at the lower explosion limit (LEL) and at the inertisation point (LOC); initial temperature of mixtures: 100 ◦ C Fuel
LEL
LOC
LEL (%)
CAFT (K)
Diluent
[Fuel] at LOC (%)
LOC (%)
[Diluent] (%)
ϕ
CAFT (K)
CH4
4.0 4.0 4.0
1342 1342 1342
N2 CO2 H2 O
4.70 6.1 6.4
9.9 13.0 12.4
48.4 32.0 34.6
0.949 0.938 1.032
1497 1580 1681
C3 H8
1.7 1.6
1397 1344
N2 H2 O
1.9 2.8
9.1 11.7
54.0 41.5
1.044 1.197
1450 1539
C2 H4
2.3 2.4
1299 1335
N2 H2 O
3.1 3.8
8.0 10.2
58.5 47.6
1.163 1.118
1395 1534
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Table 2 Correlation equations for adiabatic flame temperatures in limit mixtures Diluent CAFTLOC
T0 (K)
α (K)
= α + β × CAFTLEL
± ± ± ±
β
rn
n
N2
298 373 473 523
683.8 356.1 −(4903 −(2227
197.1 323.5 3014) 1712)
0.512 ± 0.136 0.823 ± 0.244 4.929 ± 2.351 2.816 ± 1.370
0.574 0.833 0.903 0.899
31 7 3 3
CO2
298 373
735.4 ± 241.7 −(6555 ± 1844)
0.513 ± 0.163 6.142 ± 1.390
0.534 0.975
27 3
H2 O
373 473
−(159.6 ± 288.9) 566.3 ± 356.7
1.272 ± 0.215 0.851 ± 0.291
0.956 0.825
5 6
rn —Correlation coefficient; n—number of available points.
Fig. 2. Adiabatic flame temperatures for limit mixtures at LEL and LOC; inert: water (vapour); t0 = 100 ◦ C and 200 ◦ C.
Fig. 3. Adiabatic flame temperatures for limit mixtures at LEL and LOC; inert: nitrogen; t0 = 25 ◦ C and 100 ◦ C.
with data evaluated for fuel–air–inert mixtures at 25 ◦ C, previously given [11,12]. The slopes α and intercepts β of equations which correlate CAFTLOC with CAFTLEL , for several fuel–air–inert mixtures at various initial temperatures, are given in Table 2. They are strongly influenced by the initial temperature of flammable mixture and the nature of inert gas. The deviations in slope and intercept of these correlations are quite important, as shown already for fuel–air–water mixtures (Eqs. (1) and (2)). Small uncertainties in values of fuel and oxygen concentration either at LEL or at LOC (unavoidable in measurements of limit compositions at temperatures higher than ambient) explain the large scattering of calculated CAFT and the relatively large deviations in coefficients α and β. The trend is however identical for all examined systems and it shows clearly a dependency between the adiabatic flame temperatures of limit mixtures at LEL and at LOC. 3.2. Procedure for LOC estimation by using the adiabatic flame temperatures After determination of CAFTLOC against CAFTLEL correlation parameters, a further step for LOC estimation is the calcu¯ the average equivalence ratio1 of limit fuel–air–inert lation of ϕ, mixtures at LOC. In the previous cases (fuel–air–inert systems at 25 ◦ C), the mixtures at LOC were rich (ϕ¯ = 1.25 for nitrogen containing systems [12] and 1.28 for carbon dioxide containing systems [11]). The mixtures at elevated initial temperatures are characterized by a wide range of equivalence ratio values, between 0.9 and 1.3, as seen in Table 3. The raise of the initial temperature of fuel–air–inert systems is accompanied by the decrease of their equivalence ratio at LOC, excepting the fuel–air–nitrogen mixtures at 523 K. Doubtless, the availability of new measurements may lead to revision and completion of the actual values of ϕ¯ at 523 K. Using this information, the LOC estimation can be made using the algorithm previously given in [11,12]. It consists of:
[fuel]/[O2 ] The equivalence ratio is defined as ϕ = [fuel]/[O ; the subscript “stoich” 2 ]stoich refers to fuel–oxidant mixtures where the fuel/oxygen ratio corresponds to the stoichiometric combustion reaction, forming only CO2 and H2 O. 1
Fig. 4. Adiabatic flame temperatures for limit mixtures at LEL and LOC; inert: carbon dioxide; t0 = 25 ◦ C and 100 ◦ C.
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Table 3 Average equivalence ratio ϕ¯ of mixtures at the inertisation point Diluent
N2
T0 (K) ϕ¯
298 1.25
CO2 373 1.08
473 0.93
523 1.29
(i) measurement of LEL of fuel–air mixture, at elevated initial temperatures; (ii) calculation of CAFTLEL with any program able to provide adiabatic flame temperatures; (iii) calculation of CAFTLOC by means of the equation
valid for the temperature of interest; (iv) calculation of inert concentration and subsequently, of fuel and air concentrations for the mixture which is characterized by the value of CAFTLOC determined at step (iii). For this evaluation, one has to perform a supplementary computation of adiabatic flame temperatures, for fuel–air–inert systems with a constant fuel/oxygen ratio (identical to the ratio corresponding to the equivalence ratio) and various inert concentrations. Such values allow to calculate the fuel, air and inert composition at LOC, by interpolation. An exemplification of the algorithm is given below, for methane–air–water(vapour) mixtures, at 100 ◦ C and 1 bar.
Step 2 Step 3
At 100 ◦ C, the LEL of CH4 –air is 4.0 mol%. The corresponding CAFT at 1 bar is 1342 K According to Eq. (1), the CAFTLOC of the CH4 –air–water(v) at 100 ◦ C and 1 bar is 1547 K The average equivalence ratio of fuel–air–water mixtures at 100 ◦ C is 1.23; five CH4 –air–water gaseous mixtures with this equivalence ratio and various water contents have the CAFT listed below
Number
[H2 O] (mol%)
[O2 ] (mol%)
[N2 ] (mol%)
[CH4 ] (mol%)
CAFT (K)
1 2 3 4 5
32.0 34.0 36.0 38.0 40.0
12.65 12.28 11.91 11.53 11.16
47.57 46.17 44.77 43.38 41.97
7.78 7.55 7.32 7.09 6.87
1627.0 1592.9 1558.8 1523.3 1488.3
Step 4
Step 5 Step 6
373 1.18
373 1.23
473 1.00
For all examined systems, the calculated LOC agree with measured LOC within errors provided by the measuring methods themselves, supporting thus the validity of the proposed procedure for LOC estimation. More experimental support may offer a further development of the present method. 4. Conclusions
CAFTLOC = α + β × CAFTLEL ,
Step 1
298 1.28
H2 O
Their correlation of adiabatic flame temperatures vs. water(v) concentration has the form: CAFT (K) = (2146.5 ± 18.2) − (16.36 ± 0.53) × [H2 O] (mol%) The CAFT value computed in step 2 (1547 K) corresponds to [H2 O] = 36.6 mol%. The relative deviation between calculated and measured LOC (34.6 mol%) is 5.8%
For other fuel–air–water(vapour) mixtures, the relative deviations of calculated LOC to measured LOC range between 5 and 10% at 100 ◦ C, which is satisfactory. In a similar way, one could calculate LOC for systems diluted with N2 or CO2 , at the listed temperatures.
The usually available collections of recommended flammability data at elevated temperatures indicate only the LEL and UEL values of fuel–oxidant gaseous mixtures, at various initial pressures. Knowledge of the limiting oxygen concentration (LOC) is also required, when an inert component is added to fuel–oxidant systems. Few experimental data are available for LOC of gaseous mixtures at pressures and temperatures different from ambient, in spite of the fact that most industrial processes involving flammable mixtures are running at elevated temperatures. This scarce information can be completed by using the present method of estimating the fuel and the oxygen concentration at LOC, based upon the values of LEL and the calculated adiabatic flame temperatures, both at LEL and LOC. The method makes use of a linear relationship empirically found between CAFTLOC and CAFTLEL for fuel–air–inert mixtures, at temperatures between 25 and 250 ◦ C, when various gases (N2 , CO2 , H2 O(v)) were used as inert components. The procedure is simple and delivers limiting oxygen concentrations with relative errors within 5 and 10% in respect to experimentally measured values. Better predictions could be obtained by extending the number of investigated systems. It is important to notice the difficulty to use the present method to compounds which are unstable or may decompose even in the absence of an oxidant (e.g. C2 H2 ) or to compounds that have a steep upper branch of the flammability curve, between the inerting point and UEL. In such conditions, LOC should be determined by experiment. Acknowledgements This work was financed partially by the Contract No. 88/2002–2004, within the CERES-2 National Research Programme of the Romanian Ministry of Education and Research and partially by the BAM, Berlin, Germany. Appendix A. Nomenclature a, b, c, d coefficients of the dependency Cp = f(T) CAFT calculated adiabatic flame temperature (K) Cp specific heat (kJ/K) LEL lower explosion limit (mol%) LOC limiting oxygen concentration (mol%)
D. Razus et al. / Chemical Engineering and Processing 45 (2006) 193–197
MOC rn UEL
maximum oxidizer content (mol%) correlation coefficient upper explosion limit (mol%)
Greek letters α and β coefficients of the correlation CAFTLOC = f(CAFTLEL ) ϕ stoichiometric ratio for complete combustion to CO2 and H2 O Superscript LEL referring to the lower explosion limit LOC referring to the limiting oxygen concentration Subscript p referring to pressure stoich referring to a stoichiometric mixture References [1] E. Brandes, W. M¨oller, Sicherheitstechnische Kenngr˝oßen, Band 1 (Brennbare Fl¨ussigkeiten und Gase), Wirtschaftsverlag NW, Bremerhaven, 2003. [2] M. Molnarne, Th. Schendler, V. Schr¨oder, Sicherheitstechnische Kenngr˝oßen Band 2 (Explosionsbereiche von Gasgemischen), Wirtschaftsverlag NW, Bremerhaven, 2003. [3] prEN 14756, Determination of the limiting oxygen concentration (LOC) for gases and vapours, CEN/TC 305 (2003). [4] EN 1839, Determination of Explosion Limits of Gases and Vapours, Beuth Verlag GmbH, 2003. [5] O. Fuß, M. Molnarne, V. Schr¨oder, A. Sch¨onbucher, Determination of new group contributions to calculate limiting oxygen concentrations, Chem. Eng. Technol. 26 (2003) 428–433.
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[6] O. Fuß, M. Molnarne, A. Sch¨onbucher, V. Schr¨oder, Limiting oxygen concentrations of combustible gases and vapours, Chem. Ing. Technik 75 (2003) 101–104. [7] O. Fuß, M. Molnarne, A. Sch¨onbucher, V. Schr¨oder, Determination of new increments for the calculation of limiting oxygen concentrations, Chem. Ing. Technik 74 (6) (2002) 827–832. [8] D. Markus, H. Schildberg, W. Wildner, G. Krzdalic, U. Maas, Flammability limits of premixed methane/methanol/air flames, Comb. Sci. Technol. 175 (2003) 2095–2105. [9] D. Markus, U. Maas, Calculation of explosion limits with detailed reaction kinetics, Chem. Ing. Technik 76 (2004) 289–292. [10] G. Melhem, A detailed method for estimating mixture flammability limits using chemical equilibrium, Proc. Safety Progr. 16 (1997) 203. [11] D. Razus, M. Molnarne, O. Fuß, Limiting oxygen concentration evaluation in flammable gaseous mixtures by means of calculated adiabatic flame temperatures, Chem. Eng. Process. 43 (2004) 775– 784. [12] D. Razus, M. Molnarne, O. Fuß, Evaluation of limiting oxygen concentration of fuel/air/inert gaseous mixtures by means of calculated adiabatic flame temperatures and measured fuel/air lower explosion limits, Chem. Eng. Trans. 3 (2003) 69–74. [13] DIN 51649-1, Bestimmungen der Explosionsgrenzen von Gasen und Gasgemischen in Luft, Beuth Verlag GmbH, 1987. [14] G. Viczi´an, M. Moln´arn´e-Jobb´agy, J. Heszberger, K. Koll´ar-Hunek, Explosion areas of flammable substances and their numerical approximation, Hungarian J. Ind. Chem. 29 (2001) 143–147. [15] D. Geana, D. Popescu, M. Mihai, L. Adomnica, Computation of equilibrium temperature and composition during adiabatic combustion, Rev. Chim. (Bucuresti) 36 (1985) 708–714. [16] D. Stull, E. Westrum Jr., G. Sinke, The Chemical Thermodynamics of Organic Compounds, Wiley and Sons, New York and London, 1969. [17] O. Knacke, O. Kubaschewski, K. Hesselman, Thermochemical Properties of Inorganic Substances, 2nd ed., Springer Verlag, Berlin, Heidelberg and New York, 1991.
Estimation of LOC (limiting oxygen concentration) of fuel–air–inert mixtures at elevated temperatures by means of adiabatic flame temperatures Domnina Razus a,∗ , Maria Molnarne b , Codina Movileanu a , Adriana Irimia a a
Romanian Academy, “I.G. Murgulescu” Institute of Physical Chemistry, Spl. Independentei 202, P.O. Box 12-194, 060021 Bucharest, Romania b BAM (Federal Institute for Materials Research and Testing), Unter den Eichen 87, 12205 Berlin, Deutschland, Germany Received 23 September 2004; accepted 2 June 2005 Available online 28 September 2005
Abstract The limiting values of fuel concentration in a flammable fuel–air mixture are the LEL (lower explosion limit) and UEL (upper explosion limit). The addition of an inert component to fuel/air mixtures determines the increase of LEL and decrease of UEL, until these values finally merge at the inerting point. The maximum oxygen amount of a non-flammable fuel–air–inert mixture is the LOC (limiting oxygen concentration), an important safety characteristics. The investigation of a comprehensive set of flammability data at elevated temperatures and ambient pressure taken from literature sources was made for systems containing nitrogen, carbon dioxide and water(vapour) as inert components, at 100◦ , 200◦ and 250 ◦ C. The adiabatic flame temperatures at LEL (CAFTLEL ) and LOC (CAFTLOC ) were calculated by taking into account the dissociation of gases within the flame. A linear correlation of CAFTLOC versus CAFTLEL was empirically derived for the examined systems. The slope and intercept of the correlation are dependent on temperature and on nature of the inert gas. The correlation allows the development of a simple procedure for estimating LOC, when the LEL of fuel–air and the equivalence ratio of the fuel–air–inert mixture at the inerting point are known. Knowing the scarce information concerning the flammability of fuel–air–inert mixtures at temperatures higher than ambient, the proposed procedure brings about an useful tool for estimation of LOC. © 2005 Elsevier B.V. All rights reserved. Keywords: Limiting oxygen concentration; Lower explosion limit; Calculated adiabatic flame temperature; Explosion of gases; Flammability
1. Introduction The limiting oxygen concentration (LOC) of a fuel–air–inert system is defined as the maximum allowed oxygen concentration of the fuel–air–inert mixture in which an explosion will not occur [1–3]. Together with the lower and upper explosion limits, the limiting oxygen concentration (or, in a wider sense, the MOC—maximum oxidizer content) is an important parameter for safety recommendations and loss prevention, in all human activities based on use of fuel–air or fuel–air–inert mixtures. Usually, the limiting oxygen concentration is determined from flammability diagrams of fuel–air–inert mixtures, shown in Fig. 1. Such diagrams are obtained by measuring the lower and upper flammability limits for fuel–air–inert mixtures containing
∗
Corresponding author. Tel.: +40 21 2249204; fax: +40 21 3121147. E-mail addresses: [email protected] (D. Razus), [email protected] (M. Molnarne). 0255-2701/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2005.06.010
various amounts of inert additive, by adequate methods [4]. This approach is accurate, but it is a time- and material-consuming procedure. Alternative methods for LOC determination have been recently developed. A method based on group contributions [5–7] allows calculation of composition for limit mixtures (including the mixture at the inertisation point) assuming a constant CAFT (calculated adiabatic flame temperature). Another method, based on numerical simulation of flame propagation in flammable mixtures, allows the calculation of limit mixtures composition assuming zero burning velocity in such mixtures [8–10]. In a recent study, we proposed a simple and reliable method for LOC estimation from values of the LEL of fuel–air mixtures, based on use of adiabatic flame temperatures. The method was tested for fuel–air–nitrogen [11] and fuel–air–carbon dioxide [12] mixtures, at ambient initial pressure and temperature. A linear correlation was empirically derived for each of the studied inert gases between CAFTLOC , corresponding to limit fuel–air–inert mixtures at LOC and CAFTLEL , corresponding to
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of the TRIANGLE software, which applied cubic vector splines for interpolation of the explosion curve [14]. The adiabatic flame temperatures of fuel–air and fuel–air–diluent mixtures were computed with the program ECHIMAD [15] assuming that chemical equilibrium is reached within the flame. Fifteen compounds (Cgraphite , CH4 , CO, CO2 , H2 O, H2 , O2 , N2 , NO, C2 H2 , C2 H4 , C3 H8 , H, OH and O) were considered as combustion products. Their heat capacities (expressed as function of temperature with the form: Cp = a + b·T + c·T2 + d·T−2 ), the standard enthalpies of formation at 298 K and the standard entropies at 298 K were taken from the collections of Stull et al. [16] and Knacke et al. [17]. 3. Results and discussion Fig. 1. Explosion area for methane–air–carbon dioxide gaseous mixture at 100 ◦ C [2].
fuel–air mixtures at the lower explosion limit. Using this correlation, the experimentally measured LEL and an assumed constant value of the equivalence ratio for fuel–air–inert mixtures at LOC, the composition of mixture at LOC can be computed by means of the adiabatic flame temperatures at LOC and LEL. For mixtures at ambient initial conditions, containing nitrogen and carbon dioxide, the method allowed LOC predictions within errors of experimental values. The method excludes however fuels such as acetylene or ethylene oxide (substances with high intramolecular energies) or fuels that have a steep upper branch of the flammability curve (between the inerting point and the upper explosion limit)[3]. In the present paper, the method is further tested by using flammability data at elevated initial temperatures (100–250 ◦ C) and ambient initial pressure. Several sets of flammability data from a recent publication [2] were used, referring to systems that contain nitrogen, carbon dioxide or water(vapour) as inert gases.
3.1. Correlation of CAFTLOC versus CAFTLEL for fuel–air–inert mixtures at elevated initial temperatures and p0 = 1 bar A representative set of data referring to mixtures at 100 ◦ C is given in Table 1. It is seen that the amount of diluent gas (N2 , CO2 , or H2 O(v)) necessary for complete inerting of various fuel–air mixtures varies significantly, at constant temperature. Typical concentrations of nitrogen at LOC range between 48 and 60 mol% and of water(vapour) between 33 and 48 mol%. Similar results were collected for 200 and 250 ◦ C. Unfortunately, for systems diluted with CO2 , the measurements are scarce and only data for 100 ◦ C were analyzed, in comparison with those at ambient initial temperature. An example of CAFTLOC against CAFTLEL plot, at two initial temperatures, is given in Fig. 2, for fuel–air–water(vapour) mixtures. For each set of data, a linear correlation was found: 100 ◦ C : CAFTLOG = −(160 ± 289) + (1.272 ± 0.215) × CAFTLEL ;
2. Computing procedure
rn = 0.960 (five points)
(1)
200 ◦ C : CAFTLOG = (566 ± 357) + (0.851 ± 0.291)
The flammability limits of fuel–air and fuel–air–inert mixtures, measured at atmospheric pressure by DIN 51649-1 method [13], were given in Ref. [2] both as tables and diagrams. The LOC concentrations of these systems were calculated by means
×CAFTLEL ;
rn = 0.825 (six points)
(2)
Further examples are shown in Figs. 3 and 4, where data evaluated for fuel–air–inert mixtures at 100 ◦ C are plotted together
Table 1 Composition of limit mixtures and adiabatic flame temperatures at the lower explosion limit (LEL) and at the inertisation point (LOC); initial temperature of mixtures: 100 ◦ C Fuel
LEL
LOC
LEL (%)
CAFT (K)
Diluent
[Fuel] at LOC (%)
LOC (%)
[Diluent] (%)
ϕ
CAFT (K)
CH4
4.0 4.0 4.0
1342 1342 1342
N2 CO2 H2 O
4.70 6.1 6.4
9.9 13.0 12.4
48.4 32.0 34.6
0.949 0.938 1.032
1497 1580 1681
C3 H8
1.7 1.6
1397 1344
N2 H2 O
1.9 2.8
9.1 11.7
54.0 41.5
1.044 1.197
1450 1539
C2 H4
2.3 2.4
1299 1335
N2 H2 O
3.1 3.8
8.0 10.2
58.5 47.6
1.163 1.118
1395 1534
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Table 2 Correlation equations for adiabatic flame temperatures in limit mixtures Diluent CAFTLOC
T0 (K)
α (K)
= α + β × CAFTLEL
± ± ± ±
β
rn
n
N2
298 373 473 523
683.8 356.1 −(4903 −(2227
197.1 323.5 3014) 1712)
0.512 ± 0.136 0.823 ± 0.244 4.929 ± 2.351 2.816 ± 1.370
0.574 0.833 0.903 0.899
31 7 3 3
CO2
298 373
735.4 ± 241.7 −(6555 ± 1844)
0.513 ± 0.163 6.142 ± 1.390
0.534 0.975
27 3
H2 O
373 473
−(159.6 ± 288.9) 566.3 ± 356.7
1.272 ± 0.215 0.851 ± 0.291
0.956 0.825
5 6
rn —Correlation coefficient; n—number of available points.
Fig. 2. Adiabatic flame temperatures for limit mixtures at LEL and LOC; inert: water (vapour); t0 = 100 ◦ C and 200 ◦ C.
Fig. 3. Adiabatic flame temperatures for limit mixtures at LEL and LOC; inert: nitrogen; t0 = 25 ◦ C and 100 ◦ C.
with data evaluated for fuel–air–inert mixtures at 25 ◦ C, previously given [11,12]. The slopes α and intercepts β of equations which correlate CAFTLOC with CAFTLEL , for several fuel–air–inert mixtures at various initial temperatures, are given in Table 2. They are strongly influenced by the initial temperature of flammable mixture and the nature of inert gas. The deviations in slope and intercept of these correlations are quite important, as shown already for fuel–air–water mixtures (Eqs. (1) and (2)). Small uncertainties in values of fuel and oxygen concentration either at LEL or at LOC (unavoidable in measurements of limit compositions at temperatures higher than ambient) explain the large scattering of calculated CAFT and the relatively large deviations in coefficients α and β. The trend is however identical for all examined systems and it shows clearly a dependency between the adiabatic flame temperatures of limit mixtures at LEL and at LOC. 3.2. Procedure for LOC estimation by using the adiabatic flame temperatures After determination of CAFTLOC against CAFTLEL correlation parameters, a further step for LOC estimation is the calcu¯ the average equivalence ratio1 of limit fuel–air–inert lation of ϕ, mixtures at LOC. In the previous cases (fuel–air–inert systems at 25 ◦ C), the mixtures at LOC were rich (ϕ¯ = 1.25 for nitrogen containing systems [12] and 1.28 for carbon dioxide containing systems [11]). The mixtures at elevated initial temperatures are characterized by a wide range of equivalence ratio values, between 0.9 and 1.3, as seen in Table 3. The raise of the initial temperature of fuel–air–inert systems is accompanied by the decrease of their equivalence ratio at LOC, excepting the fuel–air–nitrogen mixtures at 523 K. Doubtless, the availability of new measurements may lead to revision and completion of the actual values of ϕ¯ at 523 K. Using this information, the LOC estimation can be made using the algorithm previously given in [11,12]. It consists of:
[fuel]/[O2 ] The equivalence ratio is defined as ϕ = [fuel]/[O ; the subscript “stoich” 2 ]stoich refers to fuel–oxidant mixtures where the fuel/oxygen ratio corresponds to the stoichiometric combustion reaction, forming only CO2 and H2 O. 1
Fig. 4. Adiabatic flame temperatures for limit mixtures at LEL and LOC; inert: carbon dioxide; t0 = 25 ◦ C and 100 ◦ C.
D. Razus et al. / Chemical Engineering and Processing 45 (2006) 193–197
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Table 3 Average equivalence ratio ϕ¯ of mixtures at the inertisation point Diluent
N2
T0 (K) ϕ¯
298 1.25
CO2 373 1.08
473 0.93
523 1.29
(i) measurement of LEL of fuel–air mixture, at elevated initial temperatures; (ii) calculation of CAFTLEL with any program able to provide adiabatic flame temperatures; (iii) calculation of CAFTLOC by means of the equation
valid for the temperature of interest; (iv) calculation of inert concentration and subsequently, of fuel and air concentrations for the mixture which is characterized by the value of CAFTLOC determined at step (iii). For this evaluation, one has to perform a supplementary computation of adiabatic flame temperatures, for fuel–air–inert systems with a constant fuel/oxygen ratio (identical to the ratio corresponding to the equivalence ratio) and various inert concentrations. Such values allow to calculate the fuel, air and inert composition at LOC, by interpolation. An exemplification of the algorithm is given below, for methane–air–water(vapour) mixtures, at 100 ◦ C and 1 bar.
Step 2 Step 3
At 100 ◦ C, the LEL of CH4 –air is 4.0 mol%. The corresponding CAFT at 1 bar is 1342 K According to Eq. (1), the CAFTLOC of the CH4 –air–water(v) at 100 ◦ C and 1 bar is 1547 K The average equivalence ratio of fuel–air–water mixtures at 100 ◦ C is 1.23; five CH4 –air–water gaseous mixtures with this equivalence ratio and various water contents have the CAFT listed below
Number
[H2 O] (mol%)
[O2 ] (mol%)
[N2 ] (mol%)
[CH4 ] (mol%)
CAFT (K)
1 2 3 4 5
32.0 34.0 36.0 38.0 40.0
12.65 12.28 11.91 11.53 11.16
47.57 46.17 44.77 43.38 41.97
7.78 7.55 7.32 7.09 6.87
1627.0 1592.9 1558.8 1523.3 1488.3
Step 4
Step 5 Step 6
373 1.18
373 1.23
473 1.00
For all examined systems, the calculated LOC agree with measured LOC within errors provided by the measuring methods themselves, supporting thus the validity of the proposed procedure for LOC estimation. More experimental support may offer a further development of the present method. 4. Conclusions
CAFTLOC = α + β × CAFTLEL ,
Step 1
298 1.28
H2 O
Their correlation of adiabatic flame temperatures vs. water(v) concentration has the form: CAFT (K) = (2146.5 ± 18.2) − (16.36 ± 0.53) × [H2 O] (mol%) The CAFT value computed in step 2 (1547 K) corresponds to [H2 O] = 36.6 mol%. The relative deviation between calculated and measured LOC (34.6 mol%) is 5.8%
For other fuel–air–water(vapour) mixtures, the relative deviations of calculated LOC to measured LOC range between 5 and 10% at 100 ◦ C, which is satisfactory. In a similar way, one could calculate LOC for systems diluted with N2 or CO2 , at the listed temperatures.
The usually available collections of recommended flammability data at elevated temperatures indicate only the LEL and UEL values of fuel–oxidant gaseous mixtures, at various initial pressures. Knowledge of the limiting oxygen concentration (LOC) is also required, when an inert component is added to fuel–oxidant systems. Few experimental data are available for LOC of gaseous mixtures at pressures and temperatures different from ambient, in spite of the fact that most industrial processes involving flammable mixtures are running at elevated temperatures. This scarce information can be completed by using the present method of estimating the fuel and the oxygen concentration at LOC, based upon the values of LEL and the calculated adiabatic flame temperatures, both at LEL and LOC. The method makes use of a linear relationship empirically found between CAFTLOC and CAFTLEL for fuel–air–inert mixtures, at temperatures between 25 and 250 ◦ C, when various gases (N2 , CO2 , H2 O(v)) were used as inert components. The procedure is simple and delivers limiting oxygen concentrations with relative errors within 5 and 10% in respect to experimentally measured values. Better predictions could be obtained by extending the number of investigated systems. It is important to notice the difficulty to use the present method to compounds which are unstable or may decompose even in the absence of an oxidant (e.g. C2 H2 ) or to compounds that have a steep upper branch of the flammability curve, between the inerting point and UEL. In such conditions, LOC should be determined by experiment. Acknowledgements This work was financed partially by the Contract No. 88/2002–2004, within the CERES-2 National Research Programme of the Romanian Ministry of Education and Research and partially by the BAM, Berlin, Germany. Appendix A. Nomenclature a, b, c, d coefficients of the dependency Cp = f(T) CAFT calculated adiabatic flame temperature (K) Cp specific heat (kJ/K) LEL lower explosion limit (mol%) LOC limiting oxygen concentration (mol%)
D. Razus et al. / Chemical Engineering and Processing 45 (2006) 193–197
MOC rn UEL
maximum oxidizer content (mol%) correlation coefficient upper explosion limit (mol%)
Greek letters α and β coefficients of the correlation CAFTLOC = f(CAFTLEL ) ϕ stoichiometric ratio for complete combustion to CO2 and H2 O Superscript LEL referring to the lower explosion limit LOC referring to the limiting oxygen concentration Subscript p referring to pressure stoich referring to a stoichiometric mixture References [1] E. Brandes, W. M¨oller, Sicherheitstechnische Kenngr˝oßen, Band 1 (Brennbare Fl¨ussigkeiten und Gase), Wirtschaftsverlag NW, Bremerhaven, 2003. [2] M. Molnarne, Th. Schendler, V. Schr¨oder, Sicherheitstechnische Kenngr˝oßen Band 2 (Explosionsbereiche von Gasgemischen), Wirtschaftsverlag NW, Bremerhaven, 2003. [3] prEN 14756, Determination of the limiting oxygen concentration (LOC) for gases and vapours, CEN/TC 305 (2003). [4] EN 1839, Determination of Explosion Limits of Gases and Vapours, Beuth Verlag GmbH, 2003. [5] O. Fuß, M. Molnarne, V. Schr¨oder, A. Sch¨onbucher, Determination of new group contributions to calculate limiting oxygen concentrations, Chem. Eng. Technol. 26 (2003) 428–433.
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