Analysis of the Autoignition Process under the Industrial Partial

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Analysis of the Autoignition Process under the Industrial Partial Oxidation Conditions Using Detailed Kinetic Modeling Yefei Liu and Tiefeng Wang* Department of Chemical Engineering, Tsinghua University, Beijing 100084, China ABSTRACT: In the noncatalytic partial oxidation process, autoignition of the heated premixed combustible gases is a major source of reactor damage, unstable operation, and even explosion accidents. The knowledge of the autoignition behavior is of great importance to risk assessment and loss prevention in the partial oxidation reactors. The large experimental effort could be reduced if a reliable modeling procedure is available to identify the safe operating conditions. In this work the reliability of the detailed kinetic modeling method was investigated by comparing the simulated results with the experimental data reported in the literatures. It was found that the USC II mechanism gave the best predictions on the ignition delay times for the methane/air mixtures with equivalence ratios of 3.33 and 6.67. This mechanism was used to extrapolate the ignition delay times in the industrial partial oxidation process. The effects of initial temperature and equivalence ratio on ignition delay times were also investigated. The species concentration profiles were analyzed to understand the underlying ignition chemistry. The sensitivity analysis was carried out for the identification of the main reactions affecting the autoignition process.

1. INTRODUCTION As crude oil deposits dwindle and the cost of naphtha-derived olefins increases, the use of natural gas is becoming more important. Industry and academia have been pursuing the conversion of natural gas to higher valued products. The noncatalytic partial oxidation (NCPOX) technique converts natural gas into acetylene and synthesis gas via combustion of fuel-rich natural gas/ oxygen mixtures.1,2 Compared with the conventional production of synthesis gas or hydrogen alone from natural gas by the NCPOX method without flame quenching technique,3
5 the NCPOX method with rapid flame quenching can achieve the coproduction of acetylene and thus is more economically attractive. The process does not require a catalyst, thus it is not limited by the catalyst lifetime and the cost of the catalytic materials. In the NCPOX process, methane and oxygen are heated separately, mixed in the premixing section, and then ignited in the combustion chamber. Preheating the mixture of methane and oxygen to high temperatures is a necessary step in the production of acetylene.6 However, the methane/oxygen mixture at such high temperatures lies within the explosive region and is liable to autoignition. In the premixing combustors autoignition must be avoided at all costs.7 The autoignition in the industrial premixer can damage the apparatus and lead to unstable combustion in the downstream region. Furthermore, the uncontrolled autoignition may trigger the explosion accident. The ignition delay time, also called induction time, is the time interval needed by a certain mixture of reactants to spontaneously ignite without external energy supply.8 For safety considerations, the homogeneous premixed gas mixtures must enter the reaction zone before the autoignition process is completed. Hence, the ignition delay time in the industrial NCPOX process should be studied quantitatively. Kovalivnich et al.6 studied autoignition in the partial oxidation process for acetylene production. The ignition delay times in a narrow range of operating r 2011 American Chemical Society

conditions were calculated using the empirical relations. Our previous work evaluated the available detailed kinetic mechanisms based on the reported experimental data of ignition delay time.9 However, the initial or preheat temperatures used in our previous work were still much higher than those in realistic scenarios. The reliability of the detailed kinetic mechanisms for predicting ignition delay times in the NCPOX process should be further investigated. A large number of ignition delay time data of methane or natural gas mixtures has been experimentally determined by the shock tubes and rapid compression machines.10
13 However, most of them focused on the autoignition processes in the fuel-lean, stoichiometric or slightly fuel-rich combustion devices such as gas turbines, internal combustion engines, and industrial furnaces. Moreover, these laboratory experiments usually did not exactly reproduce the operating conditions in the industrial NCPOX apparatus. Therefore, the experimental data similar to the industrial ones should be found, and some detailed kinetic mechanisms should be further validated to give more accurate predictions. The ignition delay time is determined by the underlying chemical kinetics. If the detailed kinetic mechanism is known, the ignition delay time can be predicted using detailed kinetic modeling. The detailed kinetic mechanisms, based on a complex interaction among elementary reactions, are increasingly applied to simulate oxidation or ignition processes of many simple gaseous species.14,15 The strong point of detailed kinetic modeling over the simple empirical relation is its wider application ranges for predicting the ignition phenomena. Moreover, only detailed kinetic mechanisms can provide the information of the

Received: December 12, 2010 Accepted: March 29, 2011 Revised: March 25, 2011 Published: March 29, 2011 6009

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Table 1. The Detailed Kinetic Mechanisms Used in This Work number of species Leeds 1.5

37

number of reactions

Table 2. The Methane/Air Mixtures Studied by Giua and Pasman26 CH4

O2

N2

mixture

(vol %)

(vol %)

(vol %)

φ

(atm)

1.63 3.33

1 1

reference 16

175

Hughes et al.

18

initial pressure

GRI 3.0 USC II

53 111

325 784

Smith et al. Wang et al.19

A B

14.0 25.0

17.2 15.0

68.8 60.0

Petersen

118

665

Petersen et al.20

C

40.0

12.0

48.0

6.67

1

Healy (08)

289

1580

Healy et al.21

D

90.0

2.0

8.0

90.00

1

Healy (10)

293

1593

Healy et al.13

concentrations of the stable and radical species involved in the ignition processes.15 In the present study, the predictions of ignition delay times under the industrial NCPOX conditions were carried out using the appropriate detailed kinetic mechanism. First, some typical detailed kinetic mechanisms were evaluated and the best mechanism was selected. Second, the ignition delay times under the industrial conditions were calculated using the selected mechanism. Some extrapolations to the industrial operating conditions were obtained to analyze the effects of initial temperature and equivalence ratio φ on the ignition delay time. The sensitivity analysis was used to identify the primary reaction pathways that affect the autoignition process.

2. METHODOLOGY 2.1. Detailed Kinetic Mechanisms. The development of a new detailed kinetic mechanism was very complicated so this laborious work was avoided in the present study by evaluating and selecting the reported hydrocarbon oxidation mechanisms. The detailed kinetic mechanisms evaluated in this work are listed in Table 1. Among these mechanisms, the Leeds methane oxidation mechanisms were published in various electronic versions (1.1
1.5) and available on the Web site.16 The overall performance of the Leeds mechanisms was similar to that of GRI 3.0 and other earlier GRI mechanisms, although many of the most important reactions differed significantly.17 The latest version Leeds 1.5 mechanism was used in the present study. The GRI 3.0 mechanism was optimized for the calculation of the natural gas oxidation process, and it contained 53 species and 325 elementary reactions.18 The application ranges of the GRI 3.0 mechanism were reported as 1000
2500 K in temperature, 1.0
1000 kPa in pressure and 0.1
5.0 in equivalence ratio. The USC II mechanism with 111 species and 784 reactions incorporated the recent thermodynamic, kinetic, and species transport data updates relevant to high-temperature oxidation of hydrogen, carbon monoxide, and C1
C4 hydrocarbons.19 This mechanism was subjected to validation against reliable combustion data and applicable to a wide variety of combustion scenarios. Petersen et al.20 developed a combustion kinetic mechanism (118 species and 665 reactions) including the CH3O2 radical and its reactions. The reactions involving the CH3O2 radical were very important at a variety of conditions typical for methane combustion in turbines. The Petersen mechanism has been further extended by Healy et al.21 to include 289 species and 1580 reactions. This larger Healy (08) mechanism was used in the simulation of the oxidation of methane/ethane/propane mixtures at high, intermediate, and low temperatures. Recently Healy et al.13 studied the oxidation of the mixtures of CH4/C2H6/C3H8/n-C4H10/ n-C5H12 under the conditions of temperatures of 630
1550 K,

pressure at 8
30 bar, and equivalence ratios of 0.5, 1.0, and 2.0 in “air”. A detailed kinetic mechanism was developed to simulate these experimental results and approximate the similar fuels. This mechanism consisted of 293 species and 1593 reactions and was named as Healy (10) mechanism in this work. 2.2. Experimental Data of Ignition Delay Time. To the authors’ knowledge, no special experimental work has been reported on the autoignition under the industrial NCPOX conditions. Asaba et al.22 conducted the autoignition experiments for methane/oxygen mixtures with equivalence ratios between 0.2 and 6.0 and temperatures between 800 and 2200 K. The tested initial pressures ranged from 7 to 10 bar. Since the pressures had a significant effect on the ignition delay time23 and the industrial NCPOX reactor was operated at atmospheric pressure or slightly elevated pressure,24 the above experimental data were not suitable for the modeling validation. Seery et al.10 reported the ignition delay time data for methane/oxygen mixtures diluted in argon at temperatures between 1350 and 1900 K, equivalence ratios between 0.20 and 5.0, and pressures between 1.5 and 4 atm. Since the initial temperatures in the industrial NCPOX process usually ranged from 823 to 973 K,24 these data were also not appropriate to the modeling validation. Many ignition delay time data were reported by the SAFEKINEX project.25 This project aimed at fundamentally improving the understanding, risk assessment, efficiency, and safety of hydrocarbon oxidation processes. In this project, the experiments on ignition delay times of methane/air mixtures were carried out in a 500 cm3 quartz glass spherical flask (semiopen).26 The details of the tested methane/air mixtures are listed in Table 2. The initial temperatures and pressures of the mixtures were very close to the corresponding parameters in the industrial NCPOX process. The initial temperatures ranged from 745 to 931 K. The range of equivalence ratios for the mixtures covered the values of equivalence ratios in the industrial NCPOX process. The measured ignition delay times for 14% (φ = 1.63), 25% (φ = 3.33), and 40% (φ = 6.67) methane/air mixtures were used for the modeling validation. The main component of natural gas was methane (e.g., 98% vol.) in many oil and gas areas,27 so the effect of ethane and propane on the ignition delay time was not considered in the present study. 2.3. Simulation Methods. The ignition delay times measured in the autoignition apparatus of the SAFEKINEX project were calculated using a detailed kinetic modeling method. The autoignition apparatus is shown in Figure 1.28 A loose quartz cover was placed on the inlet of the flask. This semiopen quartz glass flask was modeled as a constant pressure reactor at atmospheric pressure. In the autoignition process, heat losses usually played an important role in the gas temperature profile. On the time scale of the experiments (seconds and minutes) the influence of the heat losses on ignition delay times was discussed in Section 3.1. 6010

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Figure 1. Cross section of the autoignition apparatus.28

Figure 3. The calculated temperature profiles of the 40% methane/air mixture using (a) GRI 3.0, (b) USC II, (c) Leeds 1.5. Figure 2. Schematic of the industrial NCPOX reactor.29

The schematic of the industrial NCPOX reactor is shown in Figure 2.29 The gas premixing zone was open to the reaction zone. To calculate ignition delay times in the industrial process, the premixing zone was also modeled as a constant pressure system at atmospheric pressure, which allowed the temperature and gas volume to change simultaneously during the autoignition process. The premixing zone of the industrial NCPOX reactor was covered by heat insulating materials, therefore the heat losses to the containing wall were not considered in the simulations. All of the ignition delay times were calculated with a closed homogeneous constant pressure reactor model in the CHEMKIN 4.1 software30 based on detailed kinetic modeling. This

reactor model was appropriate to the transient simulation of autoignition processes according to the CHEMKIN manual. It was found that the ignition delay time predicted with a constant volume reactor model was very similar to that predicted by a constant pressure reactor model.

3. RESULTS AND DISCUSSION 3.1. Heat Losses in the Autoignition Apparatus. For the simulation of the quartz glass flask, the influence of heat losses on ignition delay times should be first investigated. The heat losses from gas mixture to the vessel wall were calculated from the heat transfer coefficient h and temperature difference ΔT. However, the realistic heat transfer coefficient was variable and very difficult 6011

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Figure 4. The calculated and measured ignition delay times for fuel-rich mixture A.

Figure 5. The calculated and measured ignition delay times for fuel-rich mixture B.

to be determined. For simplicity, the averaged heat transfer coefficient was used in the present study. In the experiments performed in the 500 cm3 quartz glass flask, the averaged heat transfer coefficient was experimentally determined as 6.9 W/(m2 3 K).28 In the calculations, the heat transfer coefficients of 10, 30, and 50 W/(m2 3 K) were investigated. Figure 3 shows the calculated temperature profiles with the different heat transfer coefficients. The simulations were conducted using the GRI 3.0, USC II, and Leeds 1.5 mechanisms. In the experiments using quartz glass flask, the ignition delay times were determined with the temperature curve by the intersection of the line of initial temperature with the tangent at the point of maximum rate of temperature rise. This method was also used in the calculations, as shown in Figure 3. The effects of heat transfer coefficient on the temperature profile and calculated ignition delay time are shown in Figure 3. As expected, the heat losses had a notable effect on the temperature profile in both peak height and slope. However, the effect of heat losses on the calculated ignition delay time was insignificant. This conclusion was also confirmed with the results by other mechanisms. In Section 3.2, the value of 10 W/(m2 3 K) for the overall heat transfer coefficient was used to calculate the ignition delay times of different methane/air mixtures.

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Figure 6. The calculated and measured ignition delay times for fuel-rich mixture C.

3.2. Modeling Validation. Before using detailed kinetic mechanisms to predict ignition delay times in the industrial NCPOX process, the validation of the modeling method is needed. Figures 4
6 show the comparisons between the calculated and measured ignition delay times of methane/air mixtures in the quartz glass flask. In this section the calculated ignition delay times were determined according to the ignition criterion used in the quartz glass flask experiments as discussed in Section 3.1. The ignition delay times of the methane (14 vol %)/air mixture are shown in Figure 4. All the mechanisms failed to agree with the experimental data well. The GRI 3.0 mechanism overpredicted the ignition delay times at the low temperatures and underpredicted the ignition delay times at the high temperatures. The other mechanisms underpredicted the ignition delay times in the whole temperature range. Figure 5 shows the calculated and measured ignition delay times of the methane (25 vol %)/air mixture. This mixture was more fuel-rich and outside the flammable range at ambient temperature and atmospheric pressure. As shown in Figure 5, the GRI 3.0 mechanism overpredicted the ignition delay times in the whole temperature range, while Leeds 1.5 mechanism still underestimated the ignition delay times of the methane/air mixture. The Petersen, Healy (08), and Healy (10) mechanisms underpredicted the ignition delay times in the low temperature range. The Petersen and Healy (10) mechanisms gave good predictions at high temperatures. Although the predictions of the USC II mechanism had some discrepancy with the experiment data at high temperatures, the overall prediction performance of this mechanism was better than that of the other tested mechanisms. The ignition delay times of the methane (40 vol %)/air mixture are shown in Figure 6. The results were very similar to those of the methane (25 vol %)/air mixture. It could be seen that the USC II mechanism still gave the best agreement with the experimental data in the whole temperature range. The Petersen, Healy (08), and Healy (10) mechanisms only gave reasonable predictions at high temperature range. This limited the application of these three mechanisms to predict the ignition delay time in the conditions relevant to the industrial NCPOX process. The reason for the better predictions of the USC II mechanism was partially due to the updated rate parameters of COþOH, OHþHO2, and COþHO2,19 which were important in the ignition process. In Figure 4, there is a negative temperature coefficient (NTC) region between 897 and 907 K. In this region, the increase of 6012

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Figure 8. Predicted profiles of major species concentrations and temperature for CH4/O2 mixture. Figure 7. The calculated ignition delay times at different temperatures and equivalence ratios.

temperature slowed down the reaction and thus increased the ignition delay time. For the methane/air mixtures of φ = 3.33 and 6.67, the NTC region was not distinguishable, as shown in Figures 5 and 6. All the tested mechanisms did not successfully reproduce the NTC region, although the results of the Petersen, Healy (08), and Healy (10) mechanisms predicted similar trends to the NTC region. This special region will be studied in the future work. In the industrial reactor, the pure oxygen was used and there was no diluent in the combustible mixtures. Lifshitz et al.31 confirmed that dilution had no effect on the ignition delay time. So the modeling method can be used to investigate the methane/ oxygen mixtures besides the methane/air mixtures. The equivalence ratio in the premixing zone of the industrial NCPOX reactor is in the range 3.0
4.0, and the temperature is in the range 823 to 973 K. The USC II mechanism could give reliable predictions of the ignition delay times under such conditions, and was therefore used to further study the autoignition process under the industrial NCPOX conditions. 3.3. Autoignition in the Industrial Process. The NCPOX process produces acetylene and synthesis gas by burning hydrocarbons with oxygen to supply energy for pyrolysis of the residual hydrocarbons. Since acetylene is produced by the endothermic pyrolysis of methane, a higher initial or preheat temperature promotes more pyrolysis reactions to give a higher acetylene concentration. However, the initial or preheat temperatures of the gas mixtures must be controlled and limited to avoid uncontrolled autoignition in the mixing chamber and pyrolysis of methane in the preheater. The ignition delay times of methane/oxygen mixtures at different preheat temperatures were calculated using the USC II mechanism. As discussed in Section 2.3, the calculations were conducted in an adiabatic constant pressure reactor model. The preheat temperatures ranged from 823 to 973 K. For the calculations of ignition delay time in the industrial process, the ignition delay times were also determined by the intersection of the line of initial temperature with the tangent at the point of maximum rate of temperature rise. As shown in Figure 7, the ignition delay times were strongly affected by the preheat temperatures, showing an exponential decrease with an increase in temperature. At high preheat temperatures, the overall reactivity of the mixture was greatly enhanced, so the ignition delay

Figure 9. Predicted concentration profiles of typical intermdediate species for CH4/O2 mixture.

time was dramatically decreased. The ignition delay times of the mixtures with different equivalence ratios were also calculated and are shown in Figure 7. In these calculations, the equivalence ratio of 3.64 was widely used in the industrial NCPOX process.29 The results showed that an increased equivalence ratio resulted in a longer ignition delay time. The fuel-rich mixture with a higher equivalence ratio had a larger concentration of methane. As the methane concentration increased, methane molecules deactivated oxygen atoms.22 This was the primary reason for the increased ignition delay time with an increase in methane concentration. The preheat temperatures and mixture compositions widely used in the industrial process were enclosed by the dashed rectangle in Figure 7. The characteristic time of the ignition delay in the industrial process was about 2
3 s. The gas residence time should be below this value. When the preheat temperature was changed, the gas velocity or geometry of the premixing zone should be accordingly adjusted to avoid the preignition in the premixing zone. Although the autoignition behavior under realistic industrial conditions was more complicated due to the turbulence-chemistry interaction and solid impurity on the wall, a yardstick was provided by the detailed kinetic modeling. 3.4. Species Profiles and Sensitivity Analysis. The ignition delay time is a global parameter that only qualitatively indicates 6013

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Figure 10. Predicted concentration profiles of active intermediate species for CH4/O2 mixture.

the overall reaction activity, but it cannot give any detailed information of the underlying reactions.32 The species concentrations versus time are important for further study of the autoignition process. Figure 8 shows the profiles of the temperature and concentrations of CH4, O2, H2, CO, and H2O for the CH4/O2 mixture (φ = 3.64, T0 = 873 K, P0 = 1 atm) with USC II mechanism and adiabatic constant pressure reactor model. The equilibrium mole fractions were 57% for H2 and 28% for CO, consistent with the industrial data. This synthesis gas composition was suitable for methanol synthesis. The concentration profiles of typical intermediate species at the same conditions are shown in Figure 9. Before the ignition occurred, a small fraction of CH4 was converted to ethylene (C2H4), ethane (C2H6), and formaldehyde (CH2O). At the time of ignition most of the C2 species were converted to acetylene (C2H2). And then the formed acetylene was converted to other species that were not discussed in this work. The concentration profiles in Figure 9 were representative for methane/oxygen mixtures under the NCPOX conditions. The maximum mole fraction of C2H2 was about 7%, consistent with the measured data in an industrial reactor.33 This agreement further validated that the USC II mechanism was suitable for the simulation of the NCPOX process. The concentration profiles of the active intermediate species (H2O2, HO2, OH, O, and H) are shown in Figure 10. Autoignition was also indicated by a sharp increase in O, H, and OH concentrations. These highly reactive species initiated the ignition by the chain-branching reactions. The buildup of H2O2 and HO2 also indicated the preignition chemistry of methane. Because of the low oxygen concentration in the feed mixture, the O atom and OH radical had lower concentrations than the H atom. To study the main species and reactions that affect the autoignition process, the brute-force sensitivity analysis was performed for the methane/oxygen mixture (φ = 3.64, T0 = 873 K, P0 = 1 atm). The sensitivity coefficient of the ignition delay time to specific rate coefficient ki was evaluated by the following expression: Dtign tign ð2ki Þ
tign ðki Þ  Dki tign ðki Þ where tign(ki) is the ignition delay time corresponding to the reaction rate constant ki, tign(2ki) is the perturbed ignition delay

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Figure 11. Sensitivity coefficients of the ignition delay time with respect to the main reactions.

time, resulting from multiplying the reaction rate constant ki by a factor of 2. This analysis was carried out by using a closed constant pressure reactor model. Owing to a large number of reactions in the USC II mechanism, a rate-of-production analysis was previously made to determine the contribution of each reaction to the net reaction rate of the main propagating species (HO2, H2O2, H, OH, O) in the ignition process. The procedure of the sensitivity analysis was similar to the work of Hernandez et al.34 There were 37 elementary reactions as the most important ones to the autoignition process. The sensitivity coefficients for the 14 reactions are shown in Figure 11. The sensitivity coefficients were greater than 0.001 (this meaning a 0.1% change in the nonperturbed ignition delay time tign(ki)). The negative sensitivity coefficient indicated an increase in the overall reactivity and thus a decrease in the ignition delay time, and vice versa. In addition, a larger sensitivity coefficient indicated a stronger influence of the reaction on the autoignition. It could be seen from Figure 11 that the main ignition promoters at 873 K were the following reactions: H þ O2 ¼ O þ OH

ðR1Þ

CH2 O þ HO2 ¼ HCO þ H2 O2

ðR85Þ

CH2 O þ O2 ¼ HCO þ HO2

ðR86Þ

CH3 þ O2 ¼ O þ CH3 O

ðR93Þ

CH3 þ HO2 ¼ CH3 O þ OH

ðR96Þ

CH3 þ H2 O2 ¼ CH4 þ HO2

ðR97Þ

CH3 O þ O2 ¼ CH2 O þ HO2

ðR115Þ

The chain-branching steps (R1), (R86), and (R93) in the USC II mechanism greatly increased the radical pool. The ignition chemistry is driven by the radical pool. Close to ignition, reaction (R96) becomes the dominant step for methyl (CH3) oxidation.35 The CH3O radical produced from (R93) and (R96) is highly active and rapidly converted to formaldehyde. The formaldehyde subsequently reacts with HO2 and O2. 6014

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In Figure 11 the dominant ignition inhibiting reactions were as follows: HO2 þ HO2 ¼ O2 þ H2 O2

ðR18,19Þ

CH3 þ HO2 ¼ CH4 þ O2

ðR95Þ

CH4 þ H ¼ CH3 þ H2

ðR123Þ

The HO2 recombination reaction played an inhibiting role in the ignition process. The CH3 and HO2 radicals were converted to the stable species CH4 and O2 via the reaction (R95). The reaction (R123) converted the active H atoms to less active CH3 radicals. The species and sensitivity analysis revealed the detailed information of various species and main controlling reactions in the USC II mechanism. This information provides guidance to further improve the detailed chemical mechanisms to reproduce the NTC region. In addition, the methods to promote or inhibit the reactions relevant to the ignition process can be used to effectively control the global ignition and reduce the possibility of explosion.

4. CONCLUSIONS The autoignition behavior of methane/oxygen mixtures under industrial NCPOX conditions was predicted by using the detailed kinetic modeling. The results are helpful for the risk assessment and loss prevention in the industrial NCPOX process. The main conclusions are summarized as follows: (1) The reliability of the detailed kinetic modeling was investigated by using the reported data of fuel-rich methane/air mixtures. Among the mechanisms, the USC II mechanism was the best to predict the ignition delay times for the industrial NCPOX process. (2) The ignition delay times of methane/oxygen mixtures under the industrial NCPOX conditions were calculated by using the USC II mechanism. The ignition delay times were strongly affected by the preheat temperatures. The increase of the methane concentration in the feed reduced the overall reactivity of the mixture and increased the ignition delay time. (3) The species concentrations gave the microscopic information of the autoignition process. The acetylene was one of the main products in the partial oxidation of the fuel-rich methane/oxygen mixtures and this was the theoretical basis of the industrial NCPOX process. (4) The sensitivity analysis showed that the ignition delay time was very sensitive to the formaldehyde reactions: CH2O þ HO2 = HCO þ H2O2 and CH2O þ O2 = HCO þ HO2. The recombination reaction of the HO2 radicals played a main inhibiting role in the ignition process. ’ AUTHOR INFORMATION Corresponding Author

*Tel.: 86-10-62794132. E-mail: [email protected].

’ ACKNOWLEDGMENT The authors gratefully acknowledge the financial supports by the National Natural Science Foundation of China

(No. 20976090) and the Foundation for the Author of National Excellent Doctoral Dissertation of PR China (No. 200757).

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