lable at ScienceDirect Energy 118 (2017) 414e424 Contents lists avai Energy journal homepage: www.elsevier .com/locate/energy Flammability limits temperature dependence of pure compounds in air at atmospheric pressure Andr�es Z. Mendiburu a, *, Jo~ao A. de Carvalho Jr. a, Christian R. Coronado b, Justo J. Roberts a a S~ao Paulo State University - UNESP, Campus of Guaratinguet�a - FEG, Av. Ariberto P. da Cunha, 333 - Guaratinguet�a, SP, CEP 12510410, Brazil b Federal University of Itajub�a e UNIFEI, Mechanical Engineering Institute e IEM, Av BPS, 1303 - Itajub�a, MG, CEP 37500903, Brazil a r t i c l e i n f o Article history: Received 19 May 2016 Received in revised form 10 November 2016 Accepted 10 December 2016 Available online 22 December 2016 Keywords: Combustion Flammable properties Semi-empirical method * Corresponding author. E-mail address: andresmendiburu@yahoo.es (A.Z. http://dx.doi.org/10.1016/j.energy.2016.12.036 0360-5442/© 2016 Elsevier Ltd. All rights reserved. a b s t r a c t The objective of the present work is to study the temperature dependence of the flammability limits for pure compounds, and to develop a methodology to determine these limits in air at atmospheric pressure and at different initial temperatures of the mixture. A method to determine the lower flammability limits in those conditions was developed and compared with other methods available in the literature. The developed method shows an average absolute relative error of 3.25% and a squared correlation coefficient of 0.9928. Particularly, in the case of compounds with more than 5 carbon atoms, the method presents better accuracy than other available methods. Likewise, a method to determine the upper flammability limits was developed and compared with other widely accepted method. In this case, the developed methodology shows an average absolute relative error of 3.60% and a squared correlation coefficient of 0.9957, showing better accuracy than the available method. © 2016 Elsevier Ltd. All rights reserved. 1. Introduction A flammable gas forming amixturewith air can be flammable or non-flammable in the presence of an ignition source. In a flam- mable mixture a flame can propagate through it while in a non- flammable mixture a flame cannot propagate. Given certain con- ditions of temperature and pressure, the key parameter that defines the flammability condition of a mixture is its composition. A stoichiometric mixture of a flammable compound and air is always flammable. By slightly increasing the air to flammable gas ratio above the stoichiometric condition, a flammable lean mixture is obtained; this process can be repeated until the mixture becomes non-flammable. At this condition the mixture would be too lean as to sustain flame propagation. The leaner composition of the mixturewhich can sustain flame propagation is known as the lower flammability limit (LFL) and it is characterized by the mole per- centage of the flammable gas in that mixture. On the other hand, by slightly decreasing the air to flammable gas ratio below the stoichiometric condition, a flammable rich mixture is obtained; this process can be repeated until the mixture Mendiburu). becomes non-flammable. At this point the mixture is too rich to sustain flame propagation. The richest composition of the mixture which can sustain flame propagation is known as the upper flam- mability limit (UFL) and it is also characterized by the mole per- centage of the flammable gas in that mixture. Other parameters that affect the flammability limits are the temperature and pressure conditions at which the process occurs. If one of these parameters is held constant and the other is varied, the values of the LFL and UFL will change. The importance of determining the flammability limits (FL) of a flammable gas relies on the safety operation of several industrial processes; the knowledge of the FL is used to adopt safety mea- sures. Experimental data on the FL for several compounds is available on the literature, mainly at atmospheric pressure and reference temperature conditions. However, there are a large number of flammable compounds for which experimental data of the FL are not known. Furthermore, the FL depends on the pressure and temperature conditions, in which cases fewer experimental data is available. In the present work the temperature dependence of the flam- mability limits is studied considering atmospheric pressure. The aim of the study is to develop an accurate methodology to deter- mine the LFL and UFL in air at atmospheric pressure and at different initial mixture temperatures. There are several methods for the mailto:andresmendiburu@yahoo.es http://crossmark.crossref.org/dialog/?doi=10.1016/j.energy.2016.12.036&domain=pdf www.sciencedirect.com/science/journal/03605442 http://www.elsevier.com/locate/energy http://dx.doi.org/10.1016/j.energy.2016.12.036 http://dx.doi.org/10.1016/j.energy.2016.12.036 http://dx.doi.org/10.1016/j.energy.2016.12.036 Abbreviations FL Flammability limit LFL Lower flammability limit UFL Upper flammability limit ARE Absolute value of the relative error AARE Average of the absolute values of the relative errors Symbols cp Heat capacity at constant pressure, kJ/mol-K cp Average heat capacity at constant pressure, kJ/mol-K h 0 f ;i Formation enthalpy at standard conditions in molar base, kJ/mol hi Absolute enthalpy in molar base, kJ/mol Dhi Specific sensible enthalpy, kJ/mol HC Heat of combustion, kJ HFL;0 Heat released at the flammability limit at the temperature T0, kJ HFL;T Heat released at the flammability limit at the temperature T, kJ I Parameter defined in section 6 LT Heat losses in the combustion process for the initial temperature T, kJ kUFL Slope of a straight line representing qUFL;T=qUFL;0 Mi Molecular weight, g/mol m Slope of a straight line ni Number of moles of species i, mol R2 Squared correlation coefficient T Temperature, K or �C T0 Temperature considered as reference, K or �C TUFL;T Adiabatic flame temperature at the UFL for an initial temperature T, K Tstq;T Adiabatic flame temperature at the stoichiometric composition for an initial temperature T, K var Number of moles of oxygen at the FL composition, mol vsar Number of moles of oxygen at the stoichiometric composition, mol vUFLar Number of moles of oxygen at the UFL composition, mol xC Number of moles of carbon in the molecule of the flammable compound, mol xH Number of moles of hydrogen in the molecule of the flammable compound, mol xO Number of moles of oxygen in the molecule of the flammable compound, mol f Equivalence ratio qUFL;T Ratio Tstq;T=TUFL;T qUFL;0 Ratio Tstq;0=TUFL;0 Subscripts 0 Variable taken at a temperature considered as reference ar Variable related to air calc Calculated value of a variable or parameter exp Experimental value of a variable or parameter F Variable related to the flammable compound P Products R Reactants T Variable taken at some temperature T A.Z. Mendiburu et al. / Energy 118 (2017) 414e424 415 determination of the LFL available in the specialized literature, those with wider application were implemented and compared with themethod developed in the presentwork. On the other hand, fewer methods are available to determine the UFL and only one is widely accepted; this method was implemented and compared with the method developed in the present work. In order to develop and test the methods proposed in the present study, a set of experimental data of the FL at atmospheric pressure and different initial temperature was obtained from the literature. 2. The behavior of the flammability limits with different initial temperatures Consider nF moles of a flammable gas forming a mixture with nar moles of air. If the mixture corresponds to one of the FL, such limit would be determined by Eq. (1). FL ¼ nF nF þ nar ¼ 1 1þ ðnar=nFÞ ¼ 1 1þ 4:76var (1) Therefore, the number of moles of air per mole of flammable gas ð4:76varÞ, defines the value of the FL. The number of moles of ox- ygen in the air is given by var. The values of the FL depend on the pressure and temperature conditions. When the initial pressure of the mixture is held constant the FL of a flammable gas will vary with the initial mixture temperature. From the experimental data, the following behavior is observed: i) The lower flammability limit (LFL) decreases with the in- crease of the initial mixture temperature. That is, the ratio nar=nF increases in value. ii) The upper flammability limit (UFL) increases with the in- crease of the initial mixture temperature. In other words, the ratio nar=nF decreases in value. iii) The flammability limits vary linearly with the increase of the mixture initial temperature. The slope of the function is negative for the LFL and positive for the UFL. Eq. (2) repre- sents this behavior: FL FL0 ¼ 1þmðT � T0Þ (2) 3. The modified Burgess e Wheeler Law The energy conservation equation for the combustion process at constant pressure of 1 mol of flammable gas in air and at an initial temperature T is shown in Eq. (3). h 0 f ;F þ DhF;T þ narDhar;T ¼ X T nih 0 f ;i þ X T niDhi þ LT (3) Dividing by the total number of moles of the reactants ð1þ narÞ and rearranging: FLT$DhF;T þ ð1� FLT ÞDhar;T þ FLT$HFL;T ¼ FLT X T niDhi þ LT ! (4) where HFL;T is the heat released at the FL, given by Eq. (5), and LT represents the heat losses at the initial temperature. A.Z. Mendiburu et al. / Energy 118 (2017) 414e424416 HFL;T ¼ h 0 f ;F � X T nih 0 f ;i (5) It can be observed in Eq. (4) that the sum of the sensible en- thalpies of the reactants and the heat liberated in the combustion process is used to increase the sensible enthalpies of the products and overcome the heat losses. The modified Burgess e Wheeler Law, proposed by Zabetakis et al. [1] for the LFL, can de stated as follows: “For a flammable gas the sum of the heat liberated at the LFL and the sensible enthalpies of the reactants is a constant”. This state- ment is represented by Eq. (6). FLT h� DhF;T � Dhar;T � þ HFL;T i þ Dhar;T ¼ FLT X T niDhi þ LT ! ¼ K (6) The term between brackets on the left hand side of Eq. (6) is dominated by the heat liberated, HFL;T . The maximum amount of heat which can be released corresponds to the complete combus- tion of the flammable gas. As the mixture initial temperature increases, the heat liberated at the LFL will also increase because there is less fuel which, being at a higher initial temperature, can react more efficiently towards complete combustion. As the mixture initial temperature increases, the heat released at the UFL will decrease, since there is more fuel in excess and the product distribution contains more species of incomplete combustion. The flammability limit FL0 at some temperature T0 is considered as a known variable. The temperature T0 can be selected as the reference temperature without losing generality. In consequence, the enthalpies of formation are determined at T0. Therefore, Eq. (6) becomes: FL0HFL;0 ¼ FL0 X T0 niDhi þ LT0 ! ¼ K (7) For simplicity in the formulation, the sensible enthalpies will be represented by using the average heat capacities at constant pres- sure, as shown in Eqs. (8) And (9). Also the temperature difference is expressed asDT ¼ T � T0. cp;ar;T ¼ 1 T � T0 ZT T0 cp;ardT (8) cp;R;T ¼ 1 T � T0 ZT T0 � cp;F � cp;ar � dT (9) Dividing the left hand side of Eq. (6) by that of Eq. (7), using Eqs. (8) and (9), and rearranging, the expression shown in Eq. (10) is obtained. FLT FL0 ¼ HFL;0 HFL;T þ cp;R;TDT � 1� cp;ar;T FL0HFL;0 DT � ¼ 1þmDT (10) Solving Eq. (10) to find the slope yields Eq. (11). m ¼ HFL;0 HFL;T þ cp;R;TDT � 1 DT � 1 DT HFL;T þ cp;R;TDT HFL;0 � cp;ar;T FL0HFL;0 � (11) Therefore, for the determination of m, it would be necessary to know the heat liberated at different initial temperatures of the flammable mixture. Some assumptions must be made in order to express Eq. (11) in simpler terms: � The heat liberated at the LFL is constant at different initial temperatures of the mixture. Furthermore, it is equal to the heat of combustion as shown below: HC ¼ h 0 f ;F � xCh 0 f ;CO2 � xH 2 h 0 f ;H2O (12) � The average heat capacities at constant pressure of the reactants can be represented by the heat capacity of air. Therefore, cp;R;T ¼ 0. � The slope of the function at the UFL and at the LFL presents the same value, but with different sign. Considering these assumptions in Eq. (11) and replacing the results in Eq. (10): LFLT LFL0 ¼ 1� cp;ar;T FL0HC ðT � T0Þ (13) UFLT UFL0 ¼ 1þ cp;ar;T FL0HC ðT � T0Þ (14) According to Zabetakis [2], the slope of Eqs. (13) and (14) can be obtained by considering that the heat capacity at constant pressure of air is constant and equal to 0.0075 kcal/mol-K, and that the product LFL0HC is constant and equal to 10.4 kcal/mol, then: LFLT LFL0 ¼ 1� 0:000721ðT � T0Þ (15) UFLT UFL0 ¼ 1þ 0:000721ðT � T0Þ (16) In the present work, Zabetakis' equations will be validated with experimental data and compared with two developed methods. 4. Methods to determine the FL at different initial temperatures Most of the methods available in the literature were developed to determine the LFLs, such as the works of Catoire and Nauder [3], Rowley et al. [4], Britton [5], Britton and Frurip [6], Mendiburu et al. [7], Zlochower [8], Mendiburu et al. [9] and Liaw and Chen [10]. Fewer studies are devoted to determine the UFLs at different initial temperatures, among them the works of Mendiburu et al. [11] and Liaw and Chen [10]. Some of these works ([7] [8], and [10]), are based on the assumption that the adiabatic flame temperature at the LFL is constant with respect to the initial mixture temperature. Such consideration gives good results for the case of hydrocarbons; however, the theoretical results deviate from the experimental data for CHO compounds. The method developed by Liaw and Chen [10] was applied to predict both FL by considering heat losses in the processes. The authors [10] concluded that the differences in the LFLs predictionwere negligible with respect to the heat losses; also, A.Z. Mendiburu et al. / Energy 118 (2017) 414e424 417 the predicted UFLs based on adiabatic conditions were more ac- curate than those predicted by considering heat losses. Some of the above cited works [2e4,6] are considered for comparison with the results obtained by using Eqs. (15) and (16) and with the methods developed in the present study. 5. Empirical equations for FLs at different initial temperatures There are several studies which have developed empirical equations to represent experimental data. A list of such works is presented in Table 1, along with other relevant information. The slope of Eq. (2) can be determined for each compound of the experimental data set compiled for the development of the present work. The slopes determined by directly adjusting the straight lines to the experimental data are represented by mLFL;exp and mUFL;exp, for the LFL and UFL, respectively. The resulting values for mLFL;exp and mUFL;exp are presented in Tables 2 and 3, respectively. Other parameters are also shown in Tables 2 and 3, these will be intro- duced later. The use of the experimentally determined slopes allows the estimation of the FL at different initial temperatures for the com- pounds presented in Tables 2 and 3 6. Method for estimating the LFL at different initial temperatures The method for the determination of the LFL's at different mixture initial temperatures is based on a procedure that adjusts a correlation function to approximate the value of the slope deter- mined with the experimental data. Therefore, a calculated slope for the LFLs is obtained, mLFL;calc. In the method proposed by Zabetakis [2], there are no means to differentiate among flammable gases because the slope is the same for all compounds. In order to differentiate among flammable gases the parameter I is introduced. In the works of Kondo et al. [17] and Rowley et al. [28], a spherical vessel of 12 L volume was used in the experiments. Assuming that the mixture behaves as an ideal gas, at atmospheric pressure, with a 12 L volume, and knowing the initial temperature, the number of moles of the mixture can be determined ðnT Þ. The value of nT will change with the initial temperature; however, for the determination of parameter I, the value of nT corresponds to the initial mixture temperature T0. Also, since at the initial temperature T0, the lower flammability limit LFL0 is known, the number of moles of the flammable gas ðnFÞ can be easily determined. Taking into account these considerations, the value of the parameter I can be Table 1 Works which present experimental data accompanied by empirical correlations. Reference Studied compounds Flammabilit Goethals et al. [12] Toluene LFL, UFL Liu and Zhang [13] Hydrogen LFL, UFL Vanderstraeten et al. [14] Methane UFL Van den Schoor [15] Ethane UFL Propane UFL n-Butane UFL Ethylene UFL Propylene UFL Hustad and Sonju [16] Methane LFL Commercial Butane LFL Hydrogen LFL Carbon Monoxide LFL a The temperature range was 20e230 from 1500 to 2500 kPa and it was 20e200 for 3 b The temperature range was 20e200 for 1000 kPa. determined by Eq. (17). I ¼ MF nFHC (17) The parameter I is the combination of the molecular weight of the flammable gasðMFÞ, its heat of combustion ðHCÞ , given by Eq. (12), and the number of moles of the flammable gas ðnFÞ, when the mixture is at T0, atmospheric pressure and occupies a volume of 12 L. By applying a multiple linear regression, the following correla- tion was obtained for the calculated slope: mLFL;calc ¼ 8:3959 104 þ 9:6643 105 I þ 2:6402 106 I2 þ 8:3413 1010 HC$I (18) The values of the parameters I, HC and mLFL;calc for the studied compounds are presented in the last three columns of Table 2. The validation of the proposed method is presented in Section 8 of Results and Discussions. 7. Method for estimating the UFL at different initial temperatures The method to determine the UFL's at different initial temper- atures of the mixture is based on the calculated adiabatic flame temperature. Additionally, some considerations are assumed to determine this temperature: i) A fraction of the flammable gas undergoes complete combustion, ii) The unreacted flammable gas is treated as an inert and its sensible enthalpy is represented by the sensible enthalpy of an equal mass of air, iii) The sensible enthalpies of the flammable gases are deter- mined by considering average heat capacities at constant pressure. The global combustion reaction is, then, given by Eq. (19). CxCHxHOxO þ vUFLar ðO2 þ 3;76N2Þ/f�1 � xCCO2 þ xH 2 H2O � þ 3;76vUFLar N2 þ � 1� f�1 � CxCHxHOxO (19) where vUFLar is the number ofmoles of oxygen at the UFL composition and f is the equivalence ratio given by Eq. (20). y limits Temperature range (�C) Pressure range (kPa) 60e225 100e500 21e90 100e400 20e200 100e5500 20e250 100e3000 20e250 100e1000 20e250 100e300 20e260a 100e3000 20e250b 100e1000 25e450 101.325 25e450 101.325 25e450 101.325 25e450 101.325 000 kPa. Table 2 Values of parameters for the determination of the LFL at different initial temperatures of the mixture. References Compounds Formula CAS# mLFL;exp ð1=�CÞ HC ðkJÞ I ðg=mol:kJÞ mLFL;calcð1=�CÞ Kondo et al. [17] Dimethyl ether C2H6O 115-10-6 0.000957 1328.42 2.0745 0.001054 Kondo et al. [17] Methyl formate C2H4O2 107-31-3 0.000825 933.80 2.4318 0.001092 Kondo et al. [17] Methane CH4 74-82-8 0.000658 802.30 0.8121 0.000920 Wierzba and Wang [18] Methane CH4 74-82-8 0.000850 802.30 0.8315 0.000922 Li et al. [19] Methane CH4 74-82-8 0.000609 802.30 0.8200 0.000921 White [20] Methane CH4 74-82-8 0.000658 802.30 0.6359 0.000903 Kondo et al. [17] Propane C3H8 74-98-6 0.000810 2043.17 2.1098 0.001059 Kondo et al. [17] iso-Butane C4H10 75-28-5 0.000915 2649.02 2.6170 0.001116 Kondo et al. [17] Propylene C3H6 115-07-1 0.000915 1926.45 2.0078 0.001048 Kondo et al. [17] Ethylene C2H4 74-85-1 0.000823 1323.17 1.5453 0.000997 Craven and Foster [21] Ethylene C2H4 74-85-1 0.000836 1323.17 1.6344 0.001006 White [20] Ethylene C2H4 74-85-1 0.000745 1323.17 1.2317 0.000964 White [20] Acetylene C2H2 74-86-2 0.000913 1255.60 1.4325 0.000985 Kondo et al. [17] Carbon Monoxide CO 630-08-0 0.000791 282.99 1.6125 0.001003 Wierzba and Wang [18] Carbon Monoxide CO 630-08-0 0.000882 282.99 1.4832 0.000989 Karim et al. [22] Carbon Monoxide CO 630-08-0 0.000801 282.99 1.4663 0.000987 White et al. [20] Carbon Monoxide CO 630-08-0 0.000844 282.99 1.2168 0.000961 Kondo et al. [17] Ammonia NH3 7664-41-7 0.000575 316.80 0.6950 0.000908 White [23] (downward) Ammonia NH3 7664-41-7 0.000970 316.80 0.5706 0.000896 White [23] (horizontal) Ammonia NH3 7664-41-7 0.000582 316.80 0.5878 0.000897 White [23] (upward) Ammonia NH3 7664-41-7 0.000559 316.80 0.6645 0.000905 Ciccarelli et al. [24] Ammonia NH3 7664-41-7 0.000861 316.80 0.6528 0.000904 Chang et al. [25] Methanol CH4O 67-56-1 0.001500 672.17 2.2808 0.001075 Coronado et al. [26] Ethanol C2H6O 64-17-5 0.001213 1278.52 1.9264 0.001038 Goethals [12] Toluene C7H8 108-88-3 0.001327 3772.06 4.7745 0.001376 White et al. [20] n-Pentane C5H12 109-66-0 0.000696 3271.77 2.8878 0.001149 Chang et al. [25] Benzene C6H6 71-43-2 0.000909 3169.51 5.7145 0.001493 Wierzba and Wang [18] Hydrogen H2 1333-74-0 0.001460 241.83 0.4343 0.000882 Ciccarelli et al. [24] Hydrogen H2 1333-74-0 0.000848 241.83 0.3701 0.000876 Karim et al. [22] Hydrogen H2 1333-74-0 0.003358 241.83 0.4100 0.000880 White et al. [20] Hydrogen H2 1333-74-0 0.000872 241.83 0.1772 0.000857 Wierzba et al. [27] Hydrogen H2 1333-74-0 0.001034 241.83 0.3454 0.000873 Rowley et al. [28] Methanol CH4O 67-56-1 0.001149 672.17 1.3951 0.000980 Rowley et al. [28] 1-hexine C6H10 693-02-7 0.001603 3692.56 5.2554 0.001437 Rowley et al. [28] Butanol C4H10O 71-36-3 0.001310 2506.22 3.9705 0.001273 Rowley et al. [28] Methyl benzoate C8H8O2 93-58-3 0.002212 3846.18 8.7010 0.001908 Rowley et al. [28] 1-Octanol C8H18O 111-87-5 0.001820 4968.61 8.1929 0.001843 Rowley et al. [28] Phenetole C8H10O 103-73-1 0.002015 4255.71 7.3406 0.001717 Rowley et al. [28] 4-Methyl-2-pentanol C6H14O 108-11-2 0.001584 3709.81 5.7482 0.001500 Rowley et al. [28] Dibutyl amine C8H19N 111-92-2 0.002210 3882.81 9.6620 0.002051 Rowley et al. [28] 2-penteno C10H16 80-56-8 0.001979 5853.43 8.2118 0.001851 Rowley et al. [28] 2-methyl-1,3-propanediol C4H10O2 2163-42-0 0.001750 2277.32 6.9605 0.001653 Rowley et al. [28] Hexyl Formate C7H14O2 629-33-4 0.001763 3928.95 7.7408 0.001771 Rowley et al. [28] Octyl formate C9H18O2 112-32-3 0.002056 5151.68 10.1597 0.002138 Rowley et al. [28] Di iso butyl phthalate C16H22O4 84-69-5 0.004312 7869.14 22.0334 0.004395 Rowley et al. [28] Ethyl Lactate C5H10O3 97-64-3 0.001754 2481.66 6.9838 0.001658 A.Z. Mendiburu et al. / Energy 118 (2017) 414e424418 f ¼ vsar vUFLar (20) The number of moles of oxygen at the stoichiometric compo- sition ðvsarÞ is determined as follows: vsar ¼ xC þ xH 4 � xO 2 (21) Since the mass of air is equal to that of the unreacted flammable gas, the equivalent number of moles of air is determined using the following relation: neqar ¼ � 1� f�1 � MF Mar (22) vUFLar ¼ vsarMm � har;P � har;R � hF � xChCO2 � xH 2 hH2O þMm � har;P � har;R �þ vsar � har;R � 3;76hN The molecular weight of air ðMarÞ was considered as 28.96 g/ mol. The energy conservation law is given by Eq. (23). f�1hF þ h vUFLar þ � 1� f�1 � Mm i har;R ¼ f�1 � xChCO2 þ xH 2 hH2O � þ 3;76vUFLar hN2 þ � 1� f�1 � Mmhar;P (23) where Mm represents the ratio Mm ¼ MF=Mar , the subscripts R and P refer to reactants and products, respectively. Isolating the number of moles of oxygen at the UFL Eq. (24) is obtained. 2 � (24) Table 3 Values of parameters for the determination of the UFL at different initial temperatures of the mixture. References Composto F�ormula mUFL;exp ð1=ºCÞ h 0 f ;F ðkJ=molÞ I ðg=mol:kJÞ Kondo et al. [17] Methane CH4 0.000633 �74.9 0.2560 Wierzba and Wang [18] Methane CH4 0.000719 �74.9 0.2910 Li et al. [19] Methane CH4 0.000532 �74.9 0.2611 Van Den Schoor [15] Methane CH4 0.000941 �74.9 0.2504 Vanderstraeten et al. [14] Methane CH4 0.000854 �74.9 0.2552 White [20] Methane CH4 0.000740 �74.9 0.3106 Kondo et al. [17] Propane C3H8 0.000314 �104.7 0.4413 Van Den Schoor [15] Propane C3H8 0.001470 �104.7 0.4240 Kondo et al. [17] iso-Butane C4H10 0.000025a �134.2 0.5565 Kondo et al. [17] Propylene C3H6 0.000469 20.4 0.4250 Van Den Schoor [15] Propylene C3H6 0.001413 20.4 0.3502 Kondo et al. [17] Ethylene C2H4 0.001284 52.5 0.1393 White [20] Ethylene C2H4 0.000808 52.5 0.3102 Van Den Schoor [15] Ethylene C2H4 0.001522 52.5 0.1218 Kondo et al. [17] Ammonia NH3 0.000695 �45.9 0.3645 Ciccarelli et al. [24] Ammonia NH3 0.000770 �45.9 0.3714 White [23] (downward) Ammonia NH3 0.001038 �45.9 0.5412 White [23] (horizontal) Ammonia NH3 0.000680 �45.9 0.4196 White [23] (upward) Ammonia NH3 0.00633 �45.9 0.4022 Goethals [12] Toluene C7H8 0.000506 50.1 0.6829 Wierzba and Wang [18] Hydrogen H2 0.000397 0.0 0.0227 Ciccarelli et al. [24] Hydrogen H2 0.000379 0.0 0.0222 White [20] Hydrogen H2 0.000367 0.0 0.0233 Wierzba et al. [27] Hydrogen H2 0.000339 0.0 0.0213 Chang et al. [25] Benzene C6H6 0.001667 82.9 1.0477 Van Den Schoor [15] Ethane C2H6 0.000694 �84.0 0.2556 Van Den Schoor [15] n-Butane C4H10 0.001165 �125.6 0.4613 White [20] n-pentane C5H12 0.000678 �146.8 0.9819 White [20] Acetylene C2H2 0.002551 226.7 0.0755 Kondo et al. [17] Dimethyl ether C2H6O 0.002928 �184.1 0.2758 Kondo et al. [17] Methyl formate C2H4O2 0.000928 �336.9 0.5754 Chang et al. [25] Methanol CH4O 0.002584 �205.0 0.3142 Coronado et al. [26] Ethanol C2H6O 0.004661 �234.0 0.4139 Kondo et al. [17] Carbon Monoxide CO 0.000390 �110.5 0.2728 Wierzba and Wang [18] Carbon Monoxide CO 0.000569 �110.5 0.3033 White [20] Carbon Monoxide CO 0.000268 �110.5 0.2833 a The UFL variation for this compound was small. A.Z. Mendiburu et al. / Energy 118 (2017) 414e424 419 The adiabatic flame temperature for the UFL at any initial tem- perature T was determined by solving Eq. (23); this temperature is denoted by TUFL;T . Also, the adiabatic flame temperature at the stoichiometric composition and at any initial temperature T was determined and denoted by Tstq;T . The value of the upper flammability limit at T0 was used to determine the adiabatic flame temperature denoted by TUFL;0, the adiabatic flame temperature at the stoichiometric composition and at T0 was determined and is denoted by Tstq;0. The ratio of the adiabatic flame temperature at the stoichio- metric composition to that at the UFL composition is represented by qUFL;T . At the initial temperature T0 the value of this ratio is denoted by qUFL;0. The following equation shows that the quotient qUFL;T=qUFL;0 increases its value linearly as the initial temperature difference increases. qUFL;T qUFL;0 ¼ Tstq;T � TUFL;T Tstq;0 � TUFL;0 ¼ 1þ kUFLðTT � T0Þ (25) In order to approximate the value of TUFL;T , it is necessary to determine the factor kUFL. In themethod here proposed, this is done by means of a correlation. Once the value of the adiabatic flame temperature has been approximated, the number of moles of ox- ygen can be determined using Eq. (24). In the present work, a total of 18 flammable compounds were studied, obtaining two correla- tion functions: For CeH compounds, hydrogen and ammonia. kUFL ¼ 3:7611 104 � 3:0500 104 I þ 2:5988 106 h 0 f ;F þ 2:0798 108 � h 0 f ;F �2 (26) For CeHeO compounds and carbon monoxide kUFL ¼ �5:8362 10�3 � 3:8838 104 I � 6:7817 105 h 0 f ;F � 1:4430 107 � h 0 f ;F �2 (27) The value of the parameter I is calculated with Eq. (17), and the number of moles of the flammable gas is determined by consid- ering UFL0. The other parameter used was the enthalpy of forma- tion of the flammable gas ðh0f ;FÞ. Once the ratio qUFL;T=qUFL;0 has been approximated, Eq. (28) is employed to determine the desired adiabatic flame temperature: TUFL;T ¼ Tstq;T qUFL;0 � qUFL;T qUFL;0 ��1 (28) To perform the calculations, the flammable compounds' heat capacities at constant pressure were obtained from the NIST Chemistry Web Book [29]. The data were then adjusted to two degree polynomials as a function of temperature ranging from 100 to 1500 K. An analogous expression to that shown in Eq. (8) was used setting the integration interval from T0 to T . The other species' absolute enthalpies were determined by using the NASAeGlenn coefficients given byMcBride et al. [30]. The values of the necessary parameters are presented in Table 3. Table 4 Results and comparison of the method for determining the LFL at different initial temperatures of the mixture. Method N AARE (%) R2 Britton and Frurip [6] 161 4.44 0.9946 Catoire and Naudet [3] 140 14.64 0.9003 Rowley et al. [4] 109 5.95 0.9857 Zabetakis [2] 180 4.82 0.9948 This work 180 3.25 0.9928 Table 5 Further comparison of the method for the LFL at different initial temperatures. Set N Zabetakis [2] Britton and Frurip [6] This work AARE (%) R2 AARE (%) R2 AARE (%) R2 xC � 5 110 2.36 0.9978 2.75 0.9955 2.73 0.9972 xC >5 30 11.74 0.6844 10.33 0.7553 2.01 0.9851 NH3 21 4.70 0.8593 4.88 0.8499 5.76 0.7649 H2 19 8.28 0.9439 e e 5.47 0.9639 Fig. 1. Calculated and experimental flammability limits of methane (CH4) at different initial temperatures of the mixture and atmospheric pressure. Experimental data by: (a) Wierzba and Wang [18] and (b) White [20]. A.Z. Mendiburu et al. / Energy 118 (2017) 414e424420 8. Results and discussions The method proposed in the present study was implemented along with the methods available in the literature. The results are compared in terms of the absolute relative error (ARE), for an in- dividual flammable gas; in terms of the average absolute relative error (AARE), for a set of flammable gases; and in terms of the squared correlation coefficient (R2), also for a set of flammable gases. The subscripts “exp” and “calc” refer to experimental and calculated data, respectively. The absolute relative error, ARE, is determined using Eq. (29). The average absolute relative error, AARE, is determined using Eq. (30), where N is the number of experimental data. ARE ¼ LIexp � LIcalc LIexp 100% (29) AARE ¼ 1 N XN i¼1 AREi (30) According to Montgomery [31], the squared correlation Fig. 2. Calculated and experimental flammability limits of ethylene (C2H4) at different initial temperatures of the mixture and atmospheric pressure. Experimental data by: (a) White [20], (b) Craven and Foster [21] and (c) Van Den Schoor [15]. A.Z. Mendiburu et al. / Energy 118 (2017) 414e424 421 coefficient, R2, is calculated with Eq. (31). R2 ¼ 1� SSE SST (31) where the sum of squares of the errors (SSE) and the total sum of squares (SST) are calculated using Eq. (32) and Eq. (33), respectively. SSE ¼ XN i¼1 � LIexp � LIcalc �2 (32) SST ¼ XN i¼1 � LIexp �2 �PN i¼1 LIexp N (33) 8.1. Results of the method for LFL at different initial temperatures The results obtained by applying the methods for estimating the LFL at different initial temperatures and at atmospheric pressure are presented in this section. In total, 180 experimental points were Fig. 3. Calculated and experimental flammability limits of (a) dimethyl ether (C2H6O) and (b) methyl formate (C2H4O2) at different initial temperatures of the mixture and atmospheric pressure. Experimental data by Kondo et al. [17]. assessed, aside from the reference points. For the sake of compar- ison, Table 4 presents the results derived from the methods pro- posed by Britton and Frurip [6], Catoire and Naudet [3], Rowley et al. [4], and Zabetakis [2], along with the method proposed in this study. The method developed in the present work presents better re- sults in terms of AARE. Whereas in terms of correlation coefficient R2, the method presents better results than those by Catoire and Naudet [3] and by Rowley et al. [4]; and a slightly lower value of R2 with respect to the methods of Zabetakis [2] and Britton and Frurip [6]. Further comparison with the methods of Zabetakis [2] and Britton and Frurip [6] is presented in Table 5. Here, the data is classified into flammable gases with up to 5 carbon atoms ðxC � 5Þ, flammable gases with more than 5 carbon atoms ðxC >5Þ, ammonia ðNH3Þ and hydrogen ðH2Þ. When determining the LFLs of flammable gases with up to 5 carbon atoms, all the methods present similar values of R2. The method proposed by Zabetakis [2] is slightly more accurate. The method developed in the present work presents a higher value of R2 (0.9851) when applied to determine the LFLs of Fig. 4. Calculated and experimental flammability limits of carbon monoxide (CO) at different initial temperatures of the mixture and atmospheric pressure. Experimental data by: (a) Wierzba and Wang [18] and (b) White [20]. A.Z. Mendiburu et al. / Energy 118 (2017) 414e424422 flammable gases with more than 5 carbon atoms. Therefore, the present method is more accurate for flammable gases with higher molecular weights. In the case of ammonia, the three methods present unsatisfac- tory values of R2; the method of Zabetakis [2] presents the highest R2 (0.8593). From these results, it is recommended to use the experimental values ofmLFL;exp for ammonia, as reported in Table 2, instead of any of the empirical methods tested here. In the case of hydrogen, the method developed in this work presents the higher accuracy, with R2 of 0.9639, which is consid- ered satisfactory. The analysis of the results reveals that the proposed method should be used for estimating the LFL at different initial tempera- tures of heavier flammable gasesðxC >5Þ. On the other hand, for lighter flammable gases ðxC � 5Þ, the method proposed by Zabe- takis [2] is recommended due to its higher accuracy and simplicity of implementation. The LFLs calculated for some flammable gases using the method proposed here are presented in Figs. 1e8; the experimental data from the different sources are also presented in the figures. A good agreement between the experimental data and the estimated values using the method proposed in the present study is observed. Fig. 5. Calculated and experimental flammability limits of hydrogen (H2) at different initial temperatures of the mixture and atmospheric pressure. Experimental data by: (a) Ciccarelli et al. [24]. and White [20]. Fig. 6. Calculated and experimental flammability limits of (a) 2-methyl-1,3- propanediol (C4H10O2) and (b) hexyl formate (C7H14O2) at different initial tempera- tures of the mixture and atmospheric pressure. Experimental data by Rowley et al. [28]. Fig. 7. Calculated and experimental flammability limits of (a) 4-methyl-2-pentanol (C6H14O) and (b) phenetole (C8H10O) at different initial temperatures of the mixture and atmospheric pressure. Experimental data by Rowley et al. [28]. The results for all the considered compounds are presented in Table S1 of the supplementary material. 8.2. Results of the method for the UFL at different initial temperatures The results obtained with the methods to determine the UFLs in air at different initial temperatures and at atmospheric pressure are Fig. 8. Calculated and experimental flammability limits of (a) ethyl lactate (C5H10O3), (b) octyl formate (C9H18O2) and (c) di iso butyl phthalate (C16H22O4) at different initial temperatures of the mixture and atmospheric pressure. Experimental data by Rowley et al. [28]. Table 6 Results and comparison of the method for determining the UFL at different initial temperatures of the mixture. Reference N AAER (%) R2 Zabetakis [2] 129 5.01 0.9748 This work 129 3.60 0.9957 A.Z. Mendiburu et al. / Energy 118 (2017) 414e424 423 presented in Table 6. Without considering the reference points, a total of 129 experimental points were assessed. The method developed in the present work was compared with the method proposed by Zabetakis [2], resulting in AARE values of 3.60% and 5.01%, respectively. The coefficients of determination, R2, resulted 0.9957 for the method developed in the present work and 0.9748 for the method of Zabetakis [2]. This result implies a better accuracy of the here proposed method. The UFLs for some flammable gases calculated with the devel- oped method are presented in Fig. 1 through 5, along with the experimental data. The results suggest a good agreement between the experimental data and the calculated values of UFLs at different initial temperatures of mixture. The results for all the considered compounds are presented in Table S2 of the supplementary material. 9. Conclusions In the present work, a method to determine the lower flam- mability limits (LFL) and upper flammability limits (UFL) of pure compounds in air at atmospheric pressure and at different initial temperatures was developed. The method to determine the LFL was compared with other available methods by Zabetakis [2], Catoire and Naudet [3], Rowley et al. [4] and Britton and Frurip [6]. The method by Zabetakis [2] shows slightly better accuracy when predicting the LFL of compounds with 5 or less carbon atoms; whereas the method proposed here presents better accuracy when predicting the LFL of compounds with more than 5 carbon atoms. For the method pro- posed here, the average absolute relative error (AARE) is 3.25% and the squared correlation coefficient (R2) results equal to 0.9928. With respect to method proposed here to determine the UFL, it was compared with the method presented by Zabetakis [2]. In this case, the method developed here shows better accuracy, presenting an AARE of 3.60% and a R2 of 0.9957. Acknowledgment The authors are grateful to FAPESP (Fundaç~ao de Amparo �a Pes- quisa do Estado de S~ao Paulo) for support of this work through Project 2015/23351-9. Appendix A. 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Introduction 2. The behavior of the flammability limits with different initial temperatures 3. The modified Burgess – Wheeler Law 4. Methods to determine the FL at different initial temperatures 5. Empirical equations for FLs at different initial temperatures 6. Method for estimating the LFL at different initial temperatures 7. Method for estimating the UFL at different initial temperatures 8. Results and discussions 8.1. Results of the method for LFL at different initial temperatures 8.2. Results of the method for the UFL at different initial temperatures 9. Conclusions Acknowledgment Appendix A. Supplementary data References