Estimation of the Upper Flammability Limits of Hydrocarbons in Air at

Article pubs.acs.org/IECR

Estimation of the Upper Flammability Limits of Hydrocarbons in Air at Elevated Temperatures and Atmospheric Pressure Xin Wan,†,‡ Qi Zhang,*,† and Zheng Lian† †

State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, 100081 Beijing, China School of Chemistry and Chemical Engineering, BOHAI University, 121031 Jinzhou, China

‡

ABSTRACT: An approach is presented for predicting the upper flammability limits of hydrocarbons in air. The upper flammability limits of paraffin/air and olefin/air mixtures were determined using calculated adiabatic flame temperatures at initial temperatures of up to 500 K under atmospheric pressure. The explosion products of the various mixtures and their changes are discussed to improve the accuracy of the predicted upper flammability limits. It is found that the predicted upper flammability limits with temperature dependence agree with the experimental data. The relative error for the predicted upper flammability limits of the hydrocarbon/air is 0.13−3.40%. Moreover, the estimated upper flammability limits increase significantly with initial temperature at atmospheric pressure, which indicates that the examined hydrocarbon/air mixtures at high temperature have higher risk of explosion.

1. INTRODUCTION An understanding of the material safety properties is essential for handling and processing flammable gases, where the flammability limit is one of the most important factors for evaluating fire and explosion hazards. Consequently, flammability limit data is important in ascribing to determine preventive measures for technological processes. The flammability limits provide the range of fuel concentration, within which a combustible gas/air mixture can ignite and burn. The upper flammability limit (UFL) is usually expressed in volume percentage, which is the maximum concentration of fuel in air that will support flame propagation.1−3 In actual industrial processes or operations, the mixtures of combustible substances with oxidizing gases exist in different conditions, such as elevated temperatures. Some fuel/air mixtures are flammable even though their concentrations are outside the prescribed flammability limits. The probable reason for this is that the initial operating temperature directly affects the heat balance of a propagating flame, so that the threshold of the flammability limit is altered, resulting in an abnormal condition. When compared with a lower flammability limit, the upper flammability is more sensitive to the influence of temperature and pressure.4,5 However, experimenting with fuel/air mixtures at elevated temperatures or pressures is greatly difficult and potentially dangerous. Only a limited number of experimental studies on UFL of hydrocarbon are found in the literature.6−11 Therefore, it is necessary to develop mathematical models to predict the UFL. Several methods for the prediction of flammability limits have been proposed. However, most of these primarily provide possibilities for evaluating the UFL under ambient temperature and atmospheric pressure. Albahri12 developed a group contribution method to estimate © XXXX American Chemical Society

the UFLs of pure hydrocarbons using a total of 30 structural groups, and Gharagheizi13 used a quantitative structure− property relationship to predict the UFLs of pure compounds at ambient temperature and atmospheric pressure. Mashuga and Crowl14 performed calculations of the flammability zone of methane and ethylene using calculated adiabatic flame temperatures, where the results indicated a slight underestimation in the UFL region. However, these data were also determined at ambient temperature and normal pressure. Moreover, other methods studied the temperature dependence of the UFL, which were focused primarily on methane/air mixtures, and very little data exist for other hydrocarbon mixtures. The predicted values presented large discrepancies when compared to experimental values. Van den Schoor et al.15 estimated the temperature and pressure dependences of the UFL of methane/air mixtures using planar flame, spherical flame, limiting burning velocity, and limiting flame temperature models, respectively. Large discrepancies were found between the calculated and experimental values at elevated conditions. Benedetto16 proposed a thermal-thermodynamic theory to evaluate the adiabatic flammability limits, but the flammability region was wider than the experimental values. Therefore, this study proposed a method for predicting the upper flammability limits of paraffins (methane, ethane, propane, n-butane, and n-pentane) and olefins (ethylene, propylene, and butene-1) in air using adiabatic flammability temperatures based on thermodynamic equilibrium at initial temperatures of up to 500 K and atmospheric pressure. The Received: March 13, 2016 Revised: July 13, 2016 Accepted: July 21, 2016

A

DOI: 10.1021/acs.iecr.6b01012 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

In this expression, C̅ P is the average constant pressure heat capacity from the initial temperature to the final temperature. The CP value is normally obtained from a database at ambient temperature and atmospheric pressure.21 At other temperatures, we use

combustion product distributions of the various mixtures and their changes are discussed to improve the accuracy of the predicted UFLs.

2. NUMERICAL METHODS The flame temperature is calculated by assuming no heat loss and that it has reached chemical equilibrium. The temperature of this type of flame can be termed the calculated adiabatic flame temperature (CAFT). The CAFT is the maximum temperature of a system attained at chemical equilibrium at a fixed enthalpy and pressure. The flammability limit is associated with a specific critical reaction temperature, which can be assumed to be equivalent to the adiabatic flame temperature.14 The flammability limit can be estimated as a function of the CAFT.14,17,18 This method is well established for estimation of the lower flammability limits (LFL) of fuel/air mixtures at high temperatures and pressures.19 In the present work, the upper flammability limits of fuel in air under different conditions are determined using this method. When compared to the prediction of LFLs, the burning mechanism of the combustible gases at the UFL composition is more complicated, so various issues need to be considered for an accurate prediction. It is well-known that the products of the fuel/air combustion are widely varied, and include CO2 and H2O, but also H2 and CO which result from the incomplete combustion of the fuels in air.16 An assumption that the oxygen will react completely when the combustion occurs at UFL composition is suggested. Based on these described analyses, the combustion reaction for hydrocarbons occurring at UFL can be described as follows:

C P/R = a0 + a1T + a 2T 2 + a3T 3 + a4T 4

where a0 to a4 are the correlation coefficients, which are taken from Poling et al.21 The average constant pressure heat capacity can be obtained from eq 5. CP =

∫T

i

Tad

Cp

dT Tad − Ti

(5)

The equilibrium compositions of the combustion products can be determined by a minimization of the overall Gibbs free energy.22 It should be illustrated that an iterative procedure can be applied to these calculations by the compiled programs. So long as the adiabatic flame temperature under various initial conditions is determined, the UFL can be obtained from the balance of energy.

3. RESULTS AND DISCUSSION 3.1. Distribution of Combustion Products. The product distribution of the combustible gases at UFL composition is very complex. Moreover, the overall Gibbs free energy method depends on the equilibrium composition, and small changes in its value can cause large changes in the predicted UFL results. So it is necessary to investigate the product distribution in various hydrocarbon/air mixtures. The main products including CO2, H2O, H2, and CO were studied at the UFL composition when the combustion occurred at ambient temperature and atmospheric pressure (represented as UFLNTP). The results of the simulation illustrate the variation in the combustion products, which are plotted in Figures 1-2. The experimental UFLNTP values6,15,23 and calculated adiabatic flame temperatures at 298 K and 0.1 MPa resulting from this method are presented in Table 1.

CnHm + νao(O2 + 3.76N2) → nCO2CO2 + n H2OH 2O + nCOCO + n H2 H 2 + 3.76νao N2

(4)

(1)

where νa0 is the number of moles of air per mole of fuel in the mixture at the upper flammability limit. In addition, the dissociation of products should be considered.18 Moreover, CH4, C2H2, and C2H4 will be taken into account in assessing the combustion products that result from the thermal decomposition of each fuel.16 Therefore, the combustion products are composed of CO, CO2, H2O(ν), H2, CH4, C2H2, C2H4, N2, NO, OH, O, H, and N. This approach is based on the premise that the UFL is primarily thermal behavior and not highly dependent on kinetics.20 Based on these assumptions, the energy balance is given by eq 2. For a fuel-air combustion, the final reaction temperature can be determined from thermal balance:

∑ Hreac, i(Ti , P) = ∑ Hprod,j(Tad , P) i

(2)

j

Figure 1. Distribution of combustion products for paraffin/air mixtures at their UFLNTP.

where Hreac,i is the enthalpy of formation of the reactant, Hprod,j is the absolute enthalpy of the product, and Ti and Tad are the initial temperature and the adiabatic flame temperature, respectively. The absolute enthalpy and the enthalpy of formation of the product are related as follows:

As shown in Figure 1, the main products include CO2, H2O, CO, and H2 which are obtained from the combustion of methane, ethane and propane/air mixtures. However, we found that the composition of the combustion products from these fuel/air mixtures are not identical at equilibrium. For methane, the mole fractions of CO2 and H2O are obviously higher than that from ethane and propane. In addition, larger variations in

∑ Hprod,j(Tad , P) = ∑ ΔHfprod,j(Ti , P) + C̅P,j(Tad − Ti) j

j

(3) B


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Figure 2. Distribution of combustion products for olefin/air mixtures at their UFLNTP.

Figure 3. Distribution of products for methane/air mixtures at different fuel concentration, UFLNPT presents the upper flammability limit at room temperature and atmospheric pressure.

Table 1. Values for the Experimental UFLNTP and CAFT at 298 K and 0.1 MPa fuel

UFLNTPexp./vol %

literature

CAFT/K

methane ethane propane n-butane n-pentane ethylene propylene butene-1

16.0 15.3 10.4 9.6 7.8 34.7 12.7 10.0

15 6 6 6 23 6 6 23

1675 1066 1186 936 960 1426 1284 1242

inflections can be seen in the plot where the methane concentration is around 9.6 vol %, and CO and H2 are simultaneously formed by partial combustion of methane with oxygen. (ii) If the concentration of the methane is greater than 9.6 vol %, an incremental increase in methane concentration will result in higher mole fractions of CO and H2 and lower mole fractions of CO2 and H2O. This result indicates that the composition of H2 rises very rapidly for a small increase of 1% in methane concentration. When the methane concentration in air is increased to 25 vol %, the compositions of CO and H2 will reach the peak (the second inflection point), and the compositions of H2O and CO2 will nearly decline to minimum values. (iii). The mole fractions of CO and H2 appear to continuously decrease with increasing methane concentrations from 25 to 80 vol %, while the compositions of CO2 and H2O appear to be nearly constant under the same conditions. Therefore, it appears evident that the concentration of fuel in air has significant impact on the composition of resulting combustion products. Furthermore, the experiment results showed that the higher initial temperatures results in higher UFL.6−9 This indicates that the flammable fuel concentration in air will increase as the initial temperature increases. To obtain the accurate UFLs under elevated temperatures, the variations of the product composition when the methane concentration in air is more than UFLNTP composition must be considered. Similar results have occurred with other combustible mixtures including ethane and propane, as shown in Figure 4. It can be seen that the mole fractions of CO and H2 increase, and compositions of CO2 and H2O decrease markedly to the bottom when the ethane concentration is increased from its UFLNTP (15.3 vol %) to 18 vol %. A similar phenomenon occurred with the propane/air system, where the marginal changes are from UFLNTP (10.4 vol %) to 12 vol %. After estimation and analysis, it can be ascertained that the similar results are obtained if the fuel concentration in air is increased. However, it should be emphasized that an increase in the number of carbon atoms in the fuel will result in a smaller region from its UFLNTP to the second inflection point. Figure 5 shows the distributions of CO2, H2O, CO, and H2 for n-butane/air and n-pentane/air mixtures as a function of fuel concentration in air. Although the results have similar characteristics to the C1−C3 paraffin/air mixtures, there are obvious differences when used for UFL predictions.

CO and H2 content are predicted than for CO2 and H2O in the combustion of ethane and propane. However, in variance from the C1−C3 paraffin/air mixtures, the results for n-butane and n-pentane/air mixtures indicate that partial combustion to CO and H2 prevails and no CO2 and H2O form in the combustion. Likewise, discrepancies in the composition of the combustion products obtained from different fuel/air mixtures are also found. It appears that the H2/CO ratio for n-butane is 1.25, which is higher than that for n-pentane. In Figure 2, the product distributions are shown as obtained for ethylene, propylene, and butene-1 in air. It can be seen that the results have similar characteristics to C4−C5 paraffin/air mixtures. The oxidation products of C2−C4 olefin/air mixtures are CO and H2 without CO2 and H2O. However, it is worth noting that that the H2/CO ratio is the same for the investigated fuels. It is found that if the UFLs of the flammable gases are estimated using the CAFT method based on the described analysis, the variation in the equilibrium composition should be considered in determining the UFLs under different conditions. Furthermore, since this discussion has only focused on the distribution of products at the UFLNTP composition, the influence of the concentration of fuel in air on the product equilibrium composition was studied at room temperature and atmospheric pressure to obtain a clear understanding between the concentration of fuel and the resulting product distribution. The varieties of the product distributions as computed for paraffins and olefins in air at different initial concentrations of fuel are shown in Figures 3−6. Using the example of the methane/air mixture, we can observe from Figure 3 that the plot seems to form three distinct regions. (i) At low fuel concentration, the products are CO2 and H2O, the composition of which increases with the increasing methane concentration. It should be noted that C


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Figure 4. Distribution of products for ethane/air and propane/air mixtures at different fuel concentration.

Figure 5. Distribution of products for n-butane/air and n-pentane/air mixtures at different fuel concentrations.

For the n-butane/air mixture, if the fuel concentration in air is UFLNTP, the mole fractions of CO and H2 reach their maximum. Then, the compositions of products drop rapidly with increasing n-butane concentration. Thus, to estimate the UFLs of n-butane/air mixtures at elevated temperatures, when the fuel concentration occurs in the right region of the second inflection, the variations of product composition should be considered. This phenomenon is similar to what is found in npentane/air mixtures. Figure 6 presents the results for the mole fractions of combustion products for the olefin/air mixtures. Similarly, the variations of CO and H2 exhibit a decrease with an increase in fuel concentration, with nearly a constant tangent slope of the curves when the fuel concentration in air is more than UFLNTP for all the investigated combustibles. In fact, disregarding ethylene, the changes in the combustion behavior of propylene and butene-1 exhibit a similarity to the C4−C5 paraffin fuels. However, it has been observed that the mole fraction for every product of ethylene at the UFLNTP is lower than that at 20 vol % where the second inflection appears. As a result, these analyses should be applied to improve the accuracy of the predicted upper flammability limits. Consequently, the influence of temperature on the equilibrium composition of the products at the same fuel concentration was studied. It is found that the effect is so slight that it can be ignored; the results at ambient temperature and atmospheric pressure are shown to ensure a more effective calculation of the UFLs. 3.2. Calculated Adiabatic Flame Temperature. When predicting the UFLs using this proposed method, the most important parameter to consider is the calculated adiabatic

flame temperature. The relationship between CAFT and fuel concentration at elevated initial temperature and atmospheric pressure was studied, because the values of CAFT are influenced by initial operating conditions. The calculated results show that the CAFT decreases with increasing fuel concentration at the same initial temperature and it increases with increasing initial temperature at the same fuel concentration. Under the same conditions, the variations in the curves for methane, n-butane, n-pentane and all the olefins are very similar, but the results for ethane and propane are not. As an example, the plots for methane/air mixtures are displayed in Figure 7a. It has been previously shown that the slope of all these lines is the same regardless of the initial temperature, and the intervals are quite regular. So, from the basis of the influence of temperature and fuel concentration, a constant CAFT is assumed to ensure more accurate and effective UFL predictions. However, in Figure 7b, we can observe that the plot seems to form two distinct regions for ethane. It appears that the curves decrease rapidly with the increase in fuel concentration and then decrease slightly to lower values. This demonstrates that the CAFT exhibits a slight decrease under the same interval of fuel concentration when compared to the result of methane/air mixtures. A similar phenomenon occurs with propane as shown in Figure 7c. However, determining accurately the variation of the CAFT for the UFL predictions is very difficult. So we assume that the slight decrease can be ignored, the CAFT for ethane and propane can maintain a constant value at temperatures from 298 to 500 K so as to predict the UFLs more simply and effectively. The CAFT values at ambient D


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mixtures under various initial temperatures indicate that this assumption appears reasonable. 3.3. Estimation of the UFL. The UFLs of paraffin fuels including methane, ethane, propane, n-butane, and n-pentane in air were numerically calculated using adiabatic flame temperature modeling as a function of temperature at atmospheric pressure. It should be emphasized that the pyrolysis products of CH4, C2H2 and C2H4 were considered for the UFL calculation, where the composition of CH4 was the highest, C2H4 was considered as second and C2H2 appeared to be the least. Figure 8 shows a comparison of the predicted UFL values with several previously reported data,6,15 where the individual

Figure 8. Comparison of the experimental UFLs and temperature dependence calculated based on the numerical method for methane/ air, ethane/air and propane/air mixtures.

points show the experimental values and the lines show the calculated values. It can be seen that the predicted values for the UFL of the methane/air mixture are highly accurate compared with the experimental data at temperature of 298, 373, and 473 K, where the relative error is 0.13%, 1.41%, and 2.98% respectively. For ethane/air mixtures, it appears that the UFL values are also consistent with the reported values, where the region of relative error is 1.96−2.47% when the temperature is altered from 298 to 473 K. For propane/air mixtures, this approach results in a maximum relative error of 3.39%, and exhibits the minimum relative error of 1.92%. Thus, the proposed algebraic method appears to be reasonable for estimating the UFLs of paraffin fuels in air, with an average relative error of 2.05%. There are several numerical methods on the temperature dependence of UFLs using the concept of flame temperature, while the predicted modeling and principles are different and UFL estimations are concentrated on methane/air mixtures. Van den schoor et al.15 predicted the UFLs of methane/air

Figure 6. Distribution of products for ethylene/air, propylene/air and butene-1/air mixtures at different fuel concentration.

temperature and atmospheric pressure are listed in Table 1. In the section 3.3, the predicted UFLs for ethane and propane/air

Figure 7. Influence of temperatures on the CAFT for methane, ethane, and propane in air at different fuel concentration. E


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Industrial & Engineering Chemistry Research mixtures using a limiting flame temperature with considering heat loss and chemical kinetics by CHEM1D. The result showed that the difference between the calculated and experimentally determined values was approximately 1.1 mol % at high temperature of 200 °C, and the maximum relative error was around 5.8%. Benedetto16 applied ignition temperature as the threshold temperature for the flammability limits estimation under an adiabatic condition using a thermal/ thermodynamic modeling. The results indicated that the adiabatic UFL value was 33% at ambient temperature and pressure, while the experimental value of UFL is 16%. Therefore, the region of calculated UFLs became much higher with the increase of temperatures, which was changed from 33% to 40% at temperatures from 300 to 500 K. The UFL variations for the combustible olefin compounds are determined at high temperatures, but at atmospheric pressure. Figure 9 shows a comparison between the calculated

In Table 2, the experimental UFLs obtained from other literature8,9,22,24−26 are compared at the atmospheric pressure. Table 2. Comparison of Experimental UFLs for Hydrocarbon/Air Mixtures at Atmospheric Pressure and Elevated Temperatures UFLexp/vol % fuel

room temperature

373 K

473 K

literature

methane

15.7 16.0 15.7 15.8 10.4 9.8 9.5 10.0 34.7 30.5 31.4 36.0 12.7 10.3 11.0

16.8 17.0 16.5

18.1 18.8

11.8 10.04

13.6

38.5 34.0

45.1

14.4 10.7

15.6

9 15 8 24 6 8 25 26 6 8 24 25 6 8 22

propane

ethylene

propylene

It is found that the experimental UFLs for the same fuel are quite different at ambient temperature and atmospheric pressure. Vanderstraeten et al.9 and Zlochower and Green24 pointed out that the experimental values are different based on different explosion criterion. In addition, Zlochower and Green24 also showed that the difference among these measured data could be attributed to the differences in tested apparatus. Therefore, the variations of UFLs with temperature dependence differ from test conditions. In this paper, the calculation of CAFT for all investigated fuels is based on the UFLNTP values listed in Table 1, and thus the predicted values are compared with those reported by literature data6,15 at elevated temperatures. At atmospheric pressure, the theoretical predictions of the UFLs for other hydrocarbon fuel/mixtures including n-butane, n-pentane, and butene-1 were studied in the initial temperature range of 298−500 K. A graphical summary of the calculated values for combustible mixtures is shown in Figure 10.

Figure 9. Comparison of the experimental UFLs and temperature dependence calculated based on the numerical method for ethylene/ air, and propylene/air mixtures.

theoretical UFLs for ethylene and propylene in air, represented by the lines and the experimental data, represented by the individual points. It appears that the predicted UFLs at various temperatures are in agreement with the results published in the literature.6 At atmospheric pressure, the calculated UFL for ethylene/air mixtures changed from 34.96 vol % at ambient temperature to 43.74 vol % at 473 K. A maximum relative error of 3.02% is found, and the minimum relative error is 0.75% with respect to the experimental data. For propylene/air mixtures, at temperatures of 298, 373, and 473 K, the relative error between calculated and experimental UFL is 0.24%, 3.40%, and 1.54%, respectively. Therefore, the high accuracy of calculated values for ethylene and propylene validates that the proposed approach can be used for estimating UFLs for olefin fuels in air under elevated temperatures. In addition, it can also be seen from Figures 8 and 9 that the UFLs are sensitive to the changes of the temperature at atmospheric pressure, in that the UFLs increase rapidly for every 100 K increase in initial temperature for the paraffin and olefin/air mixtures considered. However, these variations in the calculated UFLs vary with type of mixture, with a change of 2.68 vol % for methane, 3.14 vol % for ethane, 3.74 vol % for propane, 10.62 vol % for ethylene, and 3.13 vol % for propylene from 298 to 500 K. However, the relationship between the UFL and initial temperature is nearly linear, indicating that the flammability and explosion hazard in the process of operation would be high.

Figure 10. Effect of temperature on upper flammability limits at atmospheric pressure for n-butane/air, n-pentane/air, and butene-1/air mixtures. F



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As is clearly shown, an increase in temperature will result in higher UFLs, which will increase the flammability envelope. Meanwhile, it can still be seen that the calculated UFLs are found to be linear for given initial temperatures. The values for n-butane/air mixtures have an increment of 2.51 vol % at UFL when the temperature is increased to 500 K. Similar results are observed for the butene-1/air mixture. However, the plot of the predicted UFLs for n-pentane/air mixtures shows a smaller decrease in slope than the other two mixtures, which varies from 7.77 to 9.61 vol % under the same condition. Figure 11 presents a comparison between experimental and calculated values of the UFLs for hydrocarbon/air mixtures. It

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AUTHOR INFORMATION

Corresponding Author

*[email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research presented in this paper was supported by the National Natural Science Foundation of China (No. 11372044).

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REFERENCES

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Figure 11. Comparison of predicted and reported UFL values for methane/air, ethane/air, propane/air, ethylene/air and propylene/air mixtures.

appears that the UFLs are mostly slightly underestimated compared to reported values6,15 and their discrepancies mainly increase with increasing temperatures. The probable reason is that the predicted UFLs are dependent on the CAFT based on this proposed method. Using the constant CAFT to estimate the UFLs would lead to slight underestimations at elevated temperatures. Actually, it seems that the CAFT for UFL prediction is dependent on the initial temperature, which slightly decreases with increasing temperature.

4. CONCLUSION In this study, an approach for predicting the UFL of flammable gases in air based on the calculation of adiabatic flame temperature is proposed. The UFLs are determined for paraffin/air and olefin/air mixtures in the temperature range from ambient temperature to 500 K at atmospheric pressure. In addition, the product distributions resulting from combustion of the various mixtures at UFLNTP composition and the influence of fuel concentration in air on the product equilibrium compositions are studied to improve the accuracy of the UFL prediction. The combustion products and their compositions vary with the variation in gas mixtures. Furthermore, the variations in the product composition are applied when the fuel concentration in air is more than UFLNTP composition. The predicted UFL values with temperature dependence agree well with the experimental UFL data. This prediction approach results in a maximum relative error in the UFL of 3.40% and minimum relative error of 0.13% for all fuel/air mixtures considered, validating the proposed prediction method. G


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Estimation of the Upper Flammability Limits of Hydrocarbons in Air at

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