An updated detailed reaction mechanism for syngas combustion

Abstract

Detailed reaction mechanisms for syngas combustion are analyzed in the present work. The exhaustive list of reactions within different reaction mechanisms is summarized and the differences among these mechanisms are presented. Detailed comparisons of the contemporary choices of the reaction rate coefficients are analyzed in detail, and an updated reaction mechanism for syngas combustion together with the recommended rate coefficients with minimal uncertainties have been proposed. The importance of the listed reactions and their corresponding rate constant uncertainties are analyzed according to a detailed survey of the sources of the rate constants together with sensitivity analysis and rate-of-production (ROP) analysis. It is found that with the development of advanced experimental and computational methods, the rate constant uncertainties of a large number key reactions are minimized. However, large uncertainties still exist for hydrogen peroxide (H₂O₂) and hydroperoxyl radical (HO₂) related reaction sequences, which play a key role for syngas combustion at high-pressure and low-to-intermediate temperature conditions. The updated detailed mechanism is validated against standard targets, including ignition delay time and laminar flame speeds over a wide range of conditions. The present work not only provides an updated detailed mechanism for syngas combustion, but also provides fundamental information to further develop a universal core reaction mechanism which is the foundation to the development of combustion mechanisms of all the other hydrocarbon fuels.

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1. Introduction

As the world's energy demands and environmental concerns continue to grow, syngas (composed of varying amounts of hydrogen (H₂) and carbon monoxide (CO) as the fuel components) is expected to play an important role in future energy supplies, especially for stationary power generation using coal-based Integrated Gasification Combined Cycle (IGCC) systems. The improvement of combustion efficiency and reduction of pollutant emissions in gas turbines introduce significant scientific and technological challenges and require robust fluid dynamic models and chemical kinetic models in computational fluid dynamics (CFD) simulations.^1,2 Currently, it is well-recognized that the accuracy of chemical kinetic models is critical for the design of clean and efficient gas turbine combustors.^1,2 The development of detailed combustion mechanism for syngas is not only essential to understand combustion properties of H₂ and CO themselves, but also the fundamental hierarchical systems upon which to understand combustion chemistry of all the other hydrocarbon fuels.^3–7 Several detailed mechanisms are now available for syngas combustion under practical conditions.^8–13 However, uncertainties in the reaction rates, thermo-chemical data and reaction pathways among different mechanisms still exist, which further causes uncertainties in the predictions of combustion properties, e.g., low-temperature (below 950 K) auto-ignition processes at elevated pressure and laminar flame propagation at high pressure (above 10 atm) fuel-rich conditions.^14–18 Further, although syngas is composed of H₂ and CO as the fuel components, minor constituents such as N₂, CO₂, H₂O, and H₂S may be included depending on the fuel source from which syngas is derived. The presences of these constituents will affect the combustion properties. Therefore, considerable studies have been performed to investigate the combustion properties of syngas over a wide range of compositions and with the presence of minor constituents. For example, the effects of CO₂ and H₂O on the laminar flame speeds of syngas have been studied,^29–31 and it is found that discrepancies between the experimental measured and predicted flame speeds by using existing detailed mechanisms still exist possibly due to the inaccurate representation of reaction rates of certain reactions under certain conditions. Consequently, comprehensive assessment of existing chemical kinetic mechanisms is required. For syngas combustion mechanisms, the list of reactions, reaction rate coefficients and thermo-chemical data exhibit large discrepancies. Detailed comparison of kinetic mechanisms can be helpful to the continued development and refinement of high-fidelity mechanisms. Generally, the evaluation of detailed combustion reaction mechanisms is on the basis of their performances in the predictions of combustion properties, including ignition delay times, species profiles, and laminar flame speed, etc. For example, Ströhle et al.¹⁹ assessed six detailed reaction mechanisms for hydrogen combustion under gas turbine conditions, while Xu and Konnov²⁰ performed an evaluation of four reaction mechanisms for ethylene combustion. However, in essence, it should be noted that the underlying reason for the different predictability of combustion properties from various detailed mechanisms is mainly caused by the different species and reactions embodied in reaction mechanisms and their corresponding thermo-chemical and kinetic parameters. Thus, detailed comparisons of the reaction lists, reaction rates and thermo-chemical data are essential to refine these reaction mechanisms.

On the basis of the above considerations, the major objective of the present work is to analyze the detailed mechanisms for syngas combustion in detail. The paper is organized as following: in Section 2, the exhaustive list of reactions in different reaction mechanisms is summarized and detailed comparison of the list of reactions in different reaction mechanisms is presented; comparisons of the reaction rate constants in different mechanisms are carried out, and an updated reaction mechanism for syngas combustion together with the recommended rate coefficients have been proposed. The updated reaction mechanism is validated through a series of simulations including ignition delay time and laminar flame speeds in Section 3. The main conclusions and concluding remarks are briefly summarized in Section 4.

2. Reaction mechanisms for syngas combustion

2.1 Analysis of different reaction mechanisms

A number of detailed mechanisms for syngas combustion can be found in the literatures. Some of these mechanisms have been developed for the combustion of H₂ and CO, but most of them are dedicated to the combustion of large hydrocarbon fuels by taking H₂–CO chemistry as sub-mechanisms. In the present work, six detailed reaction mechanisms for syngas combustion including the optimized H₂–CO mechanism by Davis et al.,⁸ the San Diego mechanism,⁹ the C₁ model developed by Li et al.,¹⁰ the Ranzi mechanism,¹¹ the H₂–CO model proposed by Sun et al.,¹² and the recently refined mechanism by Kéromnès et al.¹³ are selected on the basis of the degree of validation and the frequency of being referred to. Besides the above mechanisms, popular reaction mechanisms for H₂ combustion including the Konnov mechanism,²¹ the Hong mechanism,²² and the updated mechanism by Burke et al.²³ are also considered, since the combustion properties of syngas are mainly dominated by the hydrogen part. Since the six reaction mechanisms for syngas have been widely tested against experimental results, thus, we do not try to compare the performances of the six above detailed mechanisms for syngas. Particular attention has been focused on the underlying differences of these mechanisms, including the reactions and their rate coefficients. First, the exhaustive list of reactions in the six mechanisms is summarized in table 1. There are totally 14 species and 35 elementary reactions, and 27 reactions exist in all the six mechanisms. It should be noted that in the Sun and Li mechanisms, formaldehyde (CH₂O) also exists. However, it is found that this species and its corresponding reaction (HCO + HCO = CH₂O + CO) show little effect on the performance of the mechanisms for syngas combustion. Therefore, this reaction and CH₂O are not considered in the present work. The reactions in the six mechanisms for the H₂ part exhibit very small discrepancy, and the differences are caused by reactions R7, R9 and R13. The difference between the Davis and the San Diego mechanisms is very small, and the Davis mechanism only lacks reaction R9 compared with the San Diego mechanism. The recently developed mechanism by Kéromnès et al.¹³ is based on the Li mechanism. Thus, the reaction lists in the two mechanisms are identical. From Table 1, major differences between the six mechanisms are owing to the HCO related reactions.

Table 1 Reaction list in reaction mechanisms for syngas combustion

No.	Reaction	Davis	San Diego	Li	Ranzi	Sun	Kéromnès	Present	Uncertainty^a	Importance^b
a L, M, and S represent the uncertainty factor of the reaction rate constant is large, medium and small, respectively.b V, G, and L represent the importance of the reaction is very important, general important, and less important, respectively.
1	H + O2 = O + OH	√	√	√	√	√	√	√	S	V
2	O + H2 = H + OH	√	√	√	√	√	√	√	M	V
3	OH + H2 = H + H2O	√	√	√	√	√	√	√	M	V
4	OH + OH = O + H2O	√	√	√	√	√	√	√	S	G
5	H + H + M = H2 + M	√	√	√	√	√	√	√	M	L
6	O + O + M = O2 + M	√	√	√	√	√	√	√	M	L
7	O + H + M = OH + M	√	√	√	×	√	√	√	L	V
8	H + OH + M = H2O + M	√	√	√	√	√	√	√	M	V
9	O + OH + M = HO2 + M	×	√	×	√	×	×	√	S	L
10	H + O2(+M) = HO2(+M)	√	√	√	√	√	√	√	S	V
11	HO2 + O = OH + O2	√	√	√	√	√	√	√	M	L
12	H2 + O2 = HO2 + H	√	√	√	√	√	√	√	S	V
13	HO2 + H = O + H2O	√	√	×	×	√	×	√	L	L
14	HO2 + H = OH + OH	√	√	√	√	√	√	√	L	V
15	HO2 + OH = O2 + H2O	√	√	√	√	√	√	√	S	V
16	OH + OH(+M) = H2O2(+M)	√	√	√	√	√	√	√	S	V
17	HO2 + HO2 = O2 + H2O2	√	√	√	√	√	√	√	M	V
18	H2O2 + H = HO2 + H2	√	√	√	√	√	√	√	L	V
19	H2O2 + H = OH + H2O	√	√	√	√	√	√	√	L	G
20	H2O2 + OH = HO2 + H2O	√	√	√	√	√	√	√	M	V
21	H2O2 + O = OH + HO2	√	√	√	√	√	√	√	L	G
22	CO + O(+M) = CO2(+M)	√	√	√	√	√	√	√	M	V
23	CO + OH = CO2 + H	√	√	√	√	√	√	√	S	V
24	CO + O2 = CO2 + O	√	√	√	√	√	√	√	S	G
25	CO + HO2 = CO2 + OH	√	√	√	√	√	√	√	S	V
26	HCO + M = CO + H + M	√	√	√	√	√	√	√	M	V
27	HCO + O2 = CO + HO2	√	√	√	√	√	√	√	L	V
28	HCO + H = CO + H2	√	√	√	√	√	√	√	S	V
29	HCO + O = CO + OH	√	√	√	×	√	√	√	S	G
30	HCO + O = CO2 + H	√	√	√	√	√	√	√	S	G
31	HCO + OH = CO + H2O	√	√	√	√	√	√	√	S	G
32	HCO + HO2 = CO2 + OH + H	×	×	√	√	√	√	√	S	L
33	HCO + HCO = H2 + CO + CO	×	×	√	×	√	√	√	S	L
34	CO + H2O = CO2 + H2	×	×	×	√	×	×	√	S	L
35	HCO + HO2 = H2O2 + CO	×	×	×	√	×	×	√	S	L

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In order to identify the effects of reaction rate constants on the results of combustion simulations, sensitivity analysis is first performed for ignition and laminar flame speed, because they are crucial characteristics of fuel combustion from both fundamental and practical considerations and often used as key parameters for mechanism validation. In the present work, the brute-force sensitivity analysis method^24,25 has been adopted. The percent sensitivity coefficient is defined by the following:^24,25

where k_i is the rate constant of reaction i, τ_ign(2k_i) is the ignition delay time when the rate constant of reaction i is doubled, and τ_ign(k_i) is the original ignition delay time. For laminar flame speed, similar approach is used. Sensitivity analysis is performed during ignition delay time and laminar flame speed simulations by employing the Chemkin packages.^26–28 Fig. 1 and Fig. 2 give the sensitivity analysis results for ignition and laminar flame speed by using the Davis mechanism. It is found that the ignition properties of syngas are mainly affected by reactions R1, R10, R16, R17, R18 and R25 listed in Table 1. It is found that as the temperature decreases, the effects of reactions R16, R17, and R18 on the ignition properties increases. The reactions of HCO nearly show no obvious effect on ignition. However, it should be noted that the small sensitivity coefficient of a reaction does not mean the reaction is not important, and it only demonstrates that changing of the rate constant of a certain reaction would greatly affect the prediction of the mechanism when the sensitivity coefficient is large. Particular attention should be focused on these reactions, since large uncertainty factor of these reaction rate constants will significantly affect the predictions of the reaction mechanisms.

Fig. 1 Sensitivity analysis of ignition delay time to rate constants for H₂–CO–air mixture at equivalence ratio of 0.5, p = 20 atm and various temperatures. The mole fractions of reactants are 7.33% H₂, 9.71% CO, 1.98% CO₂, 17.01% O₂, and 63.97% N₂.

Fig. 2 Sensitivity of laminar flame speed to rate constants for premixed H₂–CO–air flames at initial temperature T_u = 298 K, p = 2 atm and various equivalence ratios computed by using the Davis mechanism.

The sensitivity analysis results for laminar flame speed display larger discrepancies compared with the results for ignition. From Fig. 2, it is obvious that the laminar flame speed are mainly controlled by reactions involving H radical, e.g., R1, R2, R3, R7, R8, R14 and R15. It is obvious that reaction R7 excluded in the Ranzi mechanism plays an important role in laminar flame speed, indicating the necessity to have an exhaustive list of reactions for comprehensive analysis of the mechanisms. Besides, the reaction of CO and OH to the formation of CO₂ and H also plays a key role.

2.2 Updated reaction scheme for syngas combustion

Before the evaluations of individual reaction rate constants, the overall reaction scheme needs to be chosen. The H₂ sub-mechanisms in different mechanisms are nearly identical, even for pure H₂ combustion mechanisms, except reactions R7, R9 and R13. Based on sensitivity analysis, reaction R7 demonstrates large effect on laminar flame speed, and this reaction is recommended in the updated reaction mechanisms. Although reaction R9 is only included in the San Diego and Ranzi mechanisms, the reaction has been adopted, since it still exhibits small influence on ignition at low temperatures. Compared with the rate constant of reaction R14 (HO₂ + H = OH + OH), the rate constant of R13 (HO₂ + H = O + H₂O) is very small due to the large activation energy. However, this reaction still shows some effect on ignition and laminar flame speed at high temperatures (above 1200 K), and has been included in the Davis, San Diego and Sun mechanisms. Further, in the recently developed mechanism for H₂ combustion, this reaction is also recommended by Burke et al.²³ Consequently, the three reactions R7, R9 and R13 are both contained in the updated reaction mechanism. For CO related reactions, reaction R34 (CO + H₂O = CO₂ + H₂) only contained in the Ranzi mechanism exhibits high activation energy and demonstrates little effect on ignition and laminar flame speed. However, this reaction may become important when syngas combustion is at elevated temperatures or in presence of water addition.^29–31 Thus, it is included in the updated mechanism. For the reactions of HCO, sensitivity analysis and rate-of-production (ROP) analysis are performed by using different mechanisms to identify their importance. It is shown that the production and consumption of HCO are dominated by the reaction of HCO with H, O, OH, and O₂. The reactions of HCO with HO₂, HCO, and H₂O demonstrate very small effect on the performance of different reaction mechanisms. However, these reactions are still included in the updated mechanism for completeness.

2.3 Development of the reaction mechanism

In order to further identify the importance of different reactions, ROP analysis has been performed. ROP analysis determines the contribution of a certain reaction to the net production or destruction rates of a species, and can provide useful information for mechanism analysis at low computational cost. In the present work, the ROP analysis of H, OH, HO₂, H₂O₂, CO and HCO are selected since these are the key species for syngas combustion. And based on this, we have divided the discussion on the rate constants into four parts: reactions involving H and OH; reactions of HO₂; H₂O₂ related reactions; and the CO sub-mechanism.

2.3.1 Reactions involving H and OH radicals. Fig. 3 and Fig. 4 display the ROP analysis of H and OH radicals during the simulations of ignition and laminar flame speed. It is obvious that the relative importance of the reactions to the production and consumption rates of H and OH radicals are similar in ignition and laminar flame simulations. However, the relative total ROP of H radical is larger in laminar flame speed than that in ignition, indicating that the H radical and its corresponding reactions play a critical role in flame speed as revealed by sensitivity analysis. It is also noted that the relative contribution from reaction R14 (HO₂ + H = OH + OH) to the production or consumption rates of H and OH radicals increases in laminar flame speed simulations. This coincides with sensitivity analysis for ignition that increasing its rate constant increases reactivity at high temperatures, because flame speed is mainly controlled by high temperature combustion chemistry.

Fig. 3 ROP analysis of H and OH radicals by using the Davis mechanism during ignition simulations. The mole fractions of reactants are 7.33% H₂, 9.71% CO, 1.98% CO₂, 17.01% O₂, and 63.97% N₂, and following analysis is performed under the same conditions.

Fig. 4 ROP analysis of H and OH radicals by using the Davis mechanism during laminar flame speed simulations.

2.3.1.1 H + O₂ = O + OH. The chain-branching reaction is one of the most important elementary reactions in combustion. This reaction not only is extremely important in hydrogen combustion, but also it controls the high-temperature combustion properties of all fuels. Consequently, it has been studied extensively. Fig. 5 displays the rate constant of the reaction as a function of temperature. Although the rate coefficients used in different mechanisms are various, the discrepancies of the rate constants are small at temperatures above 1000 K except for the Ranzi mechanism, in which earlier rate coefficient proposed by Baulch et al.³² was employed. At low temperatures, large discrepancies exist among different mechanisms. However, this will not affect the performances of the mechanisms because this reaction mainly dominates the high-temperature combustion properties of fuels. In the present work, the recently proposed rate constant by Hong et al.³³ have been adopted and recommended. This rate coefficient was proposed by combining the experimental result³³ with those previously reported by Masten et al.³⁴ (employed in the San Diego mechanism) over a temperature range of 1450–3370 K. The two experimental results show good agreement in the overlapping temperature range. Therefore, the new rate constant covers a temperature range of 1100–3370 K with a small uncertainty of less than 10% on the basis of these two datasets. From Fig. 5, it is evident that the new rate constant also exhibits good agreements with the other sources used in various mechanisms, e.g., the rate coefficient in the Davis mechanism (adopted from the GRI mechanism³⁵), the calculated rate by Hessler³⁶ used in the Li mechanism, and the experimental measurement by Hwang et al.³⁷ employed in the Sun mechanism. Further, it also demonstrates good agreement with the rate constant recommended by Baulch et al.³⁸ Thus, the new rate coefficients are widely used in recently published reaction mechanisms, and recommended in the present work.

Fig. 5 The rate constants of H + O₂ = O + OH as a function of temperature.

2.3.1.2 O + H₂ = H + OH and OH + H₂ = H + H₂O. On the basis of sensitivity analysis, it is shown that the two hydrogen-abstraction reactions of H₂ by O and OH radicals exhibits great effects on laminar flame speed and small effects on high-temperature ignition properties. For reaction O + H₂ = H + OH, four typical sets of rate coefficients have been adopted in various reaction mechanisms. The rate constant of the reaction as a function of temperature has been plotted in Fig. 6. It is obvious that the rate coefficients used in the Ranzi mechanism³⁹ deviate largely compared with the other data. The experimental results measured by Sutherland et al.⁴⁰ from 504 to 2495 K were widely adopted in many combustion mechanisms, e.g., the Li, Kéromnès, and Konnov mechanisms. The rate coefficients used in the Davis mechanisms (from the GRI mechanism³⁵) are slightly changed compared with that by Sutherland.⁴⁰ However, the actual rate constant is nearly identical to that by Sutherland.⁴⁰ In order to improve the expression for low-temperature measurement results (600–950 K), Baulch et al.³⁸ proposed to use duplicate parameters for this reaction and fitted new rate coefficients. The duplicate rate expression has been adopted in the Sun and Hong mechanisms. As shown in Fig. 6, this fit is very close to the high-temperature measurements by Sutherland.⁴⁰ However, it significantly underestimates the rate constants compared with the measurements and previous evaluations at temperatures around 1000 K, even though this wouldn't affect the performance of the two mechanisms because low-temperature combustion simulations are not sensitive to this reaction. Consequently, the expression of Sutherland⁴⁰ is recommended and adopted in the updated mechanism.

Fig. 6 The rate constants of O + H₂ = H + OH as a function of temperature.

For reaction OH + H₂ = H + H₂O, it is one of the key reactions in the production or consumption of H, OH and H₂. However, at low temperatures, this reaction is not important. Fig. 7 shows various rate constants of this reaction as a function of temperature. It can be seen that little discrepancy exists at temperatures above 1000 K. The rate constant of this reaction measured by Michael et al.⁴¹ was adopted in the Li, Sun, Hong and Konnov mechanisms, while it was slightly reduced by multiplying a factor of 0.8 in the Davis mechanism. The San Diego mechanism employed the rate constant that previously adopted by Smooke in premixed laminar flame simulations.⁴² Although the rate coefficients is different from that by Michael et al.,⁴¹ the actual rate constants are nearly identical at high temperatures and only small deviations are observed as shown in Fig. 7. Most recently, Lam et al.⁴³ have used UV laser absorption of OH radicals behind reflected shock waves to measure the rate constant of this reaction over a temperature range of 902–1518 K and a pressure range of 1.15–1.52 atm, and re-estimated the rate constant and its uncertainty within 17%. From Fig. 7, it is found that their recommendation is consistent with previous works at temperatures above 900 K. Although their recommendation shows large deviations compared with previous work at low temperatures, however, this is not important since this reaction hardly affects ignition simulations at temperatures below 900 K. Therefore, the recently experimental result by Lam et al.⁴³ has been adopted in this work.

Fig. 7 The rate constants of OH + H₂ = H + H₂O as a function of temperature.

2.3.1.3 OH + OH = O + H₂O. Although both ignition and laminar flame speed are not sensitive to the rate constant of this reaction on the basis of sensitivity analysis, this reaction plays an important role in the production of OH radical at high temperatures on the basis of ROP analysis. Currently, two sets of rate coefficients for this reaction suggested by Wooldridge et al.⁴⁴ and Baulch et al.³⁸ are adopted in different reaction mechanisms. This reaction exhibits strong non-Arrhenius dependence, which is supported by experimental measurements at high temperature⁴⁵ and at low temperature.⁴⁶ However, the two sets of rate coefficients are almost indistinguishable at temperatures above 1000 K, and the uncertainty factor estimated by Baulch et al.³⁸ is 1.5.
2.3.1.4 H₂ + M = H + H + M, O + O + M = O₂ + M, and O + H + M = OH + M. The radical self-recombination reactions of H and O with different third bodies seem to be not important in most practical combustion conditions. However, flame speeds are sensitive to the reaction rates of the recombination reaction of H and O to the formation of OH. Further, it is also demonstrated that these slow free-radical or atom recombination rates may play an important role in the investigation of supersonic combustion process.⁴⁷ However, experimental and theoretical studies on the above three reactions are limited.

The self-recombination reaction of H atom to the formation of H₂ with different third body enhancements was employed in the Davis, San Diego and Konnov mechanisms, while the other reaction mechanisms employed the thermal decomposition reaction formulation of H₂. The rate constants combined with the third body efficiencies for both the reverse and forward reaction formulations exhibit large uncertainties. Fortunately, the large uncertainties do not greatly affect the predictions of various reaction mechanisms. A comprehensive review for the reaction rate constants have been performed by Baulch et al.³⁸ The recommendation for the decomposition reaction formulation by Baulch et al.³⁸ for the third bodies M = H₂ and Ar has been adopted in the present work, since the rate constant data for M = H₂ and Ar are the most extensively studied and reliable up to now. However, the data for other third bodies are still very uncertain, and further investigations are required.

For the oxygen atom self-recombination reaction, the reaction rate constant expression k = 6.165 × 10¹⁵ × T^−0.5 cm³ mol⁻¹ s⁻¹ recommended by Tsang and Hampson⁴⁸ has been widely adopted, e.g., in the Li, Sun, San Diego, Kéromnès, and Hong mechanisms. The recommendation of Warnatz⁴⁹ k = 1.0 × 10¹⁷ × T^−1.0 cm³ mol⁻¹ s⁻¹ was adopted in the Konnov mechanism, and it was slightly increased by 20% when used in the Davis mechanism. The rate constant by Tsang and Hampson⁴⁸ is about a factor of 2–3 times higher than that recommended by Warnatz.⁴⁹ Recent experimental results from Javoy et al.⁴⁷ introduced a new rate constant with N₂ as the third body, k = 3.6 × 10¹⁷ × T^−1.0 cm³ mol⁻¹ s⁻¹ with the relative collisional efficiency as N₂ : Ar = 2 : 1. The relative collisional efficiency obtained by Javoy et al.⁴⁷ is close to that proposed by Warnatz.⁴⁹ However, the rate constant by Javoy et al.⁴⁷ is much close to the one proposed by Tsang and Hampson.⁴⁸ Thus, in the present work, we have employed the reaction rates proposed by Tsang and Hampson,⁴⁸ but with some modification of the collisional efficiency.

The reaction of H and O radicals to the formation of OH with third body enhancements is included in most reaction mechanisms except that the Ranzi mechanism excluded this reaction. Flame speed simulations are sensitive to this reaction, and the reaction is recommended to include in the updated mechanism. However, determinations of the rate for this reaction are very limited. The recommendation of this reaction rate expression by Tsang and Hampson⁴⁸ is widely adopted. The rate constant is also in good agreement with the only experimental results by Naudet et al.⁵⁰ in the temperature range 2950–3700 K from the study of OH radical dissociation. The uncertainty of the rate constant by Tsang and Hampson⁴⁸ is evaluated to be about 3. In the Davis mechanism, the rate constant was optimized to be multiplied by a factor of 2 in order to gain better prediction of flame speed, which is also within the uncertainty factor estimated by Konnov.²¹ In the present work, we have employed the optimized rate expression by Davis et al.⁸ to obtain better performance of the updated mechanism.

2.3.1.5 H + OH + M = H₂O + M. On the basis of sensitivity analysis, it is shown that laminar flame speed is very sensitive to the rate constant of this reaction, and increasing the recombination rate of OH with H to the formation of water will significantly decrease reactivity as a result of the consumption of H radical. In most reaction mechanisms, the recombination reaction formulation with the rate constant proposed by Tsang and Hampson⁴⁸ have been employed, while the reverse reaction formulation, H₂O + M = H + OH + M was used in the Hong and Konnov mechanisms with the rate recommended by Srinivasan and Michael⁵¹ based on their shock tube study of the reaction at high temperature (2196–2792 K) and low pressure (0.0079 and 0.0145 atm) conditions by using Kr as the diluted gas. The authors concluded that the accuracy of their rate expression is to be ±18%. However, discrepancies for the rate of this reaction still exist. Recently, Sellevåg et al.⁵² performed theoretical investigations on this reaction based on high-level quantum chemistry methods combined with variable reaction coordinate transition state theory. The computed results showed good agreement with the experimental data of Srinivasan and Michael.⁵¹ However, when the experimental expression is adopted in reaction mechanisms, laminar flame speed is overestimated compared with experimental results. The rate expression recommended by Tsang and Hampson⁴⁸ for the recombination reaction formulation have been employed in the Sun mechanism without modification, while it has been increased by a factor of about 2 when used in the other mechanisms in order to gain better predictions of laminar flame speed. Although Sellevåg et al.⁵² argued that such an increase in the rate coefficient is not warranted at temperatures below 1000 K, however, they still cannot completely rule out that the rate coefficients can be a factor of 2 times larger at higher temperatures. Since this reaction is not important at low temperatures, thus, we have adopted the optimized rate together with the third body enhancements in the Davis mechanisms for this reaction.

2.3.2 HO₂ related reactions. The HO₂ related reactions play a critical role in combustion mechanisms not only for syngas, but also for other fuels with large molecular size at low-to-intermediate temperatures (950–1200 K) and high pressures. Fig. 8 and Fig. 9 demonstrate the ROP analysis of HO₂ by using the Davis mechanism during ignition and flame speed simulations. It can be seen that the production of HO₂ are completely dominated by the pressure-dependent reaction H + O₂(+M) = HO₂(+M), which competes with the major chain-branching reaction H + O₂ = O + OH. The HO₂ is quickly consumed via the reactions with H and OH radicals. Thus, the total ROP of HO₂ is small. Sensitivity analysis results reveal that ignition is very sensitive to the pressure-dependent reaction H + O₂(+M) = HO₂(+M), while laminar flame speed is much sensitive to the reactions of HO₂ with H and OH radicals.

Fig. 8 ROP analysis of HO₂ by using the Davis mechanism during ignition simulations.

Fig. 9 ROP analysis of HO₂ by using the Davis mechanism during laminar flame speed simulations.

2.3.2.1 O + OH + M = HO₂ + M. This reaction is less important in the production of HO₂, and only included in the San Diego and Ranzi mechanisms. The rates in the two mechanisms are independent of temperature, and a constant rate k = 1 × 10¹⁶ cm³ mol⁻¹ s⁻¹ was employed in the Ranzi mechanism, while the rate has been slightly reduced by 20% in the San Diego mechanism. On the basis of sensitivity analysis and ROP analysis by using the two mechanisms, it is demonstrated that this reaction hardly exhibits any influence on ignition and laminar flame speed simulations. However, a recent study by Burke et al.¹⁶ indicated that this reaction may exhibit some effect on the predictions in very lean high-pressure flames. Thus, this reaction has been considered in the updated mechanism. The uncertainty factor of this reaction rate is very small, and the rate coefficient used in the Ranzi mechanism has been employed.
2.3.2.2 H + O₂(+M) = HO₂(+M). This chain propagation reaction competes with the chain-branching reaction H + O₂ = OH + O, and controls the low-temperature ignition properties. Because of its critical importance in combustion mechanisms, this reaction has been studied by many groups, and various rate coefficients have been recommended. A complete review on experimental studies before 2005 for this reaction at the low-pressure limiting conditions can be found in ref. 38. In the recently developed mechanisms for H₂ by Hong et al.,²² they also discussed recent studies of this reaction, and both high-pressure and low-pressure limiting rate constants have been analyzed in detail. The high- and low-pressure limiting rate constants together with the center broadening factors are significantly different. However, from the view of combustion simulations, much attention should be paid to the actual rate constants. Fig. 10 demonstrates the actual rate constants of this reaction as a function of temperature at a fixed pressure of 10 atm in different reaction mechanisms, while Fig. 11 shows the actual rate constants as a function of pressure at a fixed temperature of 1150 K. It is shown that the actual rate constants used in different mechanisms are nearly identical below 100 atm at the same temperature. However, the actual rate constants at different temperatures used in the Ranzi and Li mechanisms show slightly discrepancies compared with the other expressions at fixed pressures. Based on a detailed analysis of the sources of the high- and low-pressure limiting rate constants employed in different mechanisms, we found that the high- and low-pressure limiting rate proposed by Troe⁵³ has been used in the San Diego mechanism and in the Konnov mechanism, while the rate has been increased by a factor of 1.1 in the optimized Davis mechanism. The Sun mechanism employed earlier rate also proposed by Troe,⁵⁴ which is nearly identical to the rate constant came out two years later. The Ranzi mechanism used the high-pressure limiting rate by Troe,⁵³ while it adopted the result from Davidson et al.⁵⁵ as the low-pressure limiting rate. Most recently, a new rate constant expression for this reaction has been determined by Fernandes et al.⁵⁶ over a pressure range of 1.3–938 atm and in the temperature range 300–900 K based on experiment and theoretical analysis. The new expression has been used in the Kéromnès mechanism with some modification on the low-pressure limiting rate in order to improve the performance of the mechanism in the predictions of mass burning rate in He. In the updated reaction mechanism by Hong et al.,²² they employed earlier experimental rate constants measured by Bates et al. for M = Ar, N₂, and H₂O.⁵⁷ For M = O₂ and H₂, the expressions for the low-pressure limit rate constants are taken from the work by Michael et al.⁵⁸ The low-pressure limiting rate constant by Michael et al.⁵⁸ combined with earlier measured high-pressure limiting constant by Cobos et al.⁵⁹ has been used in the Li mechanism. However, as pointed out previously, the actual pressure- and temperature-dependent rate constants do not exhibit large discrepancies under practical combustion conditions. Based on the above considerations and the comparisons of the actual rate constants shown in Fig. 10 and 11, we have employed the same rate coefficients proposed by Hong et al.,²² and this set of rate coefficients show good agreements with the others.

Fig. 10 The rate constants of H + O₂(+M) = HO₂(+M) as a function of temperature at a fixed pressure of 10 atm.

Fig. 11 The rate constants of H + O₂(+M) = HO₂(+M) as a function of pressure at a fixed temperature of 1150 K.

2.3.2.3 HO₂ + O = OH + O₂. Compared with the reactions of HO₂ with H and OH radicals, the effect of this reaction on the performance of detailed mechanisms is very small. Further, the uncertainty of the rate constant is not large. Currently, two sets of rate coefficients are used. The rate constant expression k = 3.25 × 10¹³ exp(445/RT) cm³ mol⁻¹ s⁻¹ within 220–400 K recommended by Atkinson et al.⁶⁰ was employed in the Sun, Hong and Konnov mechanisms. In the other mechanisms, the rate is defined as a constant, and the rate constant k = 3.25 × 10¹³ cm³ mol⁻¹ s⁻¹ recommended in ref. 61 has been adopted in the Li, Ranzi and Kéromnès mechanisms, while the Davis and San Diego mechanisms employed k = 4 × 10¹³ and 2 × 10¹³ cm³ mol⁻¹ s⁻¹ for this reaction, respectively. A comparison between the two sets reaction rates indicates that the difference is not large. Further, because this reaction is not important in most combustion conditions, we have employed k = 3.25 × 10¹³ cm³ mol⁻¹ s⁻¹ as the rate in the current mechanism.
2.3.2.4 Reactions channels of HO₂ with H. Currently, the reaction between HO₂ and H has three product channels: HO₂ + H = H₂ + O₂, HO₂ + H = O + H₂O, and HO₂ + H = OH + OH. The two channels, HO₂ + H = H₂ + O₂ and HO₂ + H = OH + OH, which are important in capturing species time-histories from flow reactor studies and laminar flame speeds, have been included in different mechanisms, while the channel HO₂ + H = O + H₂O was only included in the Davis, San Diego and Sun mechanisms. However, Konnov pointed out that it may be necessary to include all three product channels of the reaction between H and HO₂. Thus, all the three channels are adopted in the present work.

For the reaction HO₂ + H = H₂ + O₂, the reverse reaction together with the reaction H₂ + O₂ = OH + OH constitute chain initiation reactions for H₂–O₂ mixtures, which has been a subject of controversy for a long time. Generally, the reaction rate of H₂ + O₂ = OH + OH is very low, and nearly shows no competition with the reverse reaction rate of HO₂ + H = H₂ + O₂. Thus, it is usually neglected in most reaction mechanisms except in the Konnov mechanism. Another reason for neglecting of this reaction may be due to the lack of accurate reaction rate. Therefore, we have also excluded this reaction in the present work. Based on the assumption that the initiation reaction H₂ + O₂ = OH + OH can be neglected, Michael et al.⁶² obtained the reverse reaction rate of HO₂ + H = H₂ + O₂ between 400 and 2300 K via reflected shock tube experiments combined with ab initio calculations. The theoretical calculated rate constant⁶³ was also in good agreement with the measurements and calculations by Michael et al.⁶² Thus, this rate expression has been widely used, e.g. in the Sun and Hong mechanism, while it has been reduced by 20% and 30% in the Davis and Kéromnès mechanisms to reduce the reactivity at low temperature and to keep the same reactivity at high temperature. In the Li, San Diego and Ranzi mechanisms, the reverse reaction formulation H + HO₂ = H₂ + O₂ was used. The rate recommended by Tsang and Hampson⁴⁸ was employed in the Li and San Diego mechanisms, while the Ranzi mechanism adopted the rate recommended in ref. 61. Hong et al.²² employed the reverse rate expression based on the equilibrium constant given by Michael et al.⁶² and compared the rate with the expressions used in the Li, San Diego, Ranzi, and Konnov mechanisms. It is demonstrated that the rate recommended by Michael et al.⁶² tends to be the best fitted expression compared with experiments up to now. Consequently, the rate has been adopted in the updated mechanism, but it is also reduced by 20% in order to improve the mechanism performance, which is similar to that in the Davis mechanism.

The reaction channel of HO₂ with H to the formation of two OH radicals is highly sensitive for laminar flame speed, and begins to sensitive for ignition at high temperatures. The rate constant recommended by Tsang and Hampson⁴⁸ has been adopted in the Li, San Diego, Kéromnès, and Hong mechanisms without modification, while it has been slightly increased by 8% and reduced by 15% when used in the Davis and Sun mechanisms, respectively. The Ranzi mechanism has adopted the evaluated data for this reaction by LIoyd.⁶⁴ In the Konnov mechanism, the rate was taken from Baulch et al.⁶⁵ and slightly scaled up to fit the room temperature evaluation of the IUPAC. Fig. 12 demonstrates the three rate constant expressions as a function of temperature together with theoretical calculation results by Mousavipour.⁶⁶ In the present work, the widely used rate recommended by Tsang and Hampson⁴⁸ has been adopted.

Fig. 12 The rate constants of HO₂ + H = OH + OH as a function of temperature.

Compared with the above two channels discussed, the third channel of HO₂ with H to produce O and H₂O is less important, and is only considered in the Davis, San Diego and Sun mechanisms. Fig. 13 displays the rate constants as a function of temperature in the three mechanisms. Although large discrepancies exist, however, this hardly affects the mechanism performances since this reaction is not sensitive for ignition and flame simulations. However, this channel is still included in the present mechanism for completeness, and the rate constant adopted in the Sun mechanism proposed by Baulch et al.³⁸ has been adopted.

Fig. 13 The rate constants of HO₂ + H = O + H₂O as a function of temperature.

2.3.2.5 HO₂ + OH = O₂ + H₂O. The reaction of HO₂ with OH to the formation of O₂ and H₂O is a chain termination reaction. It is shown that both ignition and laminar flame speed are very sensitive to this reaction, and this reaction also demonstrates great contributions to the consumption of HO₂, especially during ignition. Thus, this reaction has been studied experimentally and theoretically by many authors. However, large discrepancy still exists for the rate constants of this reaction. The rate constant expression fitted by Keyser et al.⁶⁷ based on experimental results from 254 to 382 K has been widely adopted without modification in the Li, San Diego, and Hong mechanisms. However, anomalous temperature dependence of this reaction (the deep and unusually narrow rate constant minimum close to 1250 K) was observed by Hippler et al.⁶⁸ and subsequently confirmed, but at notably shifted temperature by Kappel et al.⁶⁹ The high-temperature rate of Hippler et al.⁶⁸ was adopted by Baulch et al.³⁸ as a recommendation over the temperature range 1300–2000 K, and it was combined with the low-temperature part rate by Keyser et al.⁶⁷ to describe the rate for this reaction, which was employed in the Davis and Konnov mechanisms. In the work by Kappel et al.,⁶⁹ they found it is difficult to combine their results with the low-temperature rate expression by Keyser et al.,⁶⁷ and a new expression as a sum of two Arrhenius expressions was proposed, which was employed in the Sun mechanism. Most recently, Hong et al.⁷⁰ re-investigated this reaction experimentally, and they found that there is only a weak temperature dependence of this reaction, which is in good agreement with the earlier study by Srinivasan et al.⁷¹ in 2006. The rate expression by Keyser et al.⁶⁷ was recommended, and was employed in the Hong mechanism. The weak temperature-dependence of this reaction was also supported by recent theoretical calculations by Burke et al.²³ Fig. 14 illustrates the rate constants as a function of temperature used in various mechanisms. The rate expression employed in the Davis and Konnov mechanisms tends to overestimate the rate constant at high temperatures, while the rate expressions used in the Ranzi and Sun mechanisms tends to underestimate the rate constant. Therefore, the rate constant defined by Keyser et al.⁶⁷ has been adopted in the current work without modification.

Fig. 14 The rate constants of HO₂ + OH = O₂ + H₂O as a function of temperature.

Fig. 15 ROP analysis of H₂O₂ by using the Davis mechanism during ignition simulations.

Fig. 16 ROP analysis of H₂O₂ by using the Davis mechanism during laminar flame speed simulations.

2.3.3 H₂O₂ related reactions. The recombination reaction of two OH radicals to the formation of H₂O₂ is the dominant chain-branching reaction that controls hydrocarbon ignition in the intermediate temperature regime (950–1200 K). For H₂ and most fuels, at intermediate temperatures and high pressure conditions, the H-abstraction reaction of the fuel by HO₂ to the formation of H₂O₂ and its corresponding radical is important in the prediction of ignition delay times. Sensitivity analysis demonstrates that although laminar flame speed is hardly affected by H₂O₂ related reactions, ignition delay time is very sensitive to H₂O₂ related reactions, especially the three reactions, OH + OH(+M) = H₂O₂(+M), HO₂ + HO₂ = H₂O₂ + O₂, and H₂O₂ + H = HO₂ + H₂ (reverse reaction: abstraction reaction of H₂ by HO₂). Moreover, the sensitivity coefficients of ignition to the three reactions increase as the temperature decreases. We have also performed ROP analysis of H₂O₂ during ignition and laminar flame speed simulations. It is clearly shown that the H₂O₂ is mainly produced by the recombination reactions of OH and HO₂ radicals, respectively, while it is mainly consumed by the reactions with H and OH radicals.
2.3.3.1 H₂O₂(+M) = OH + OH(+M). On the basis of sensitivity analysis, it is demonstrated that ignition delay times are very sensitive to this chain-branching reaction under high-pressures and low-to-intermediate temperature conditions. This reaction is often regarded as the central kinetic feature in engine knock.⁷² However, due to experimental challenges, data for this reaction's rate constant is still limited. In contemporary mechanisms, some mechanisms including the Li, Sun, Kéromnès and Hong mechanisms employed the thermal decomposition reaction of H₂O₂, while the other mechanisms employed the reverse OH recombination reaction. For the reverse OH recombination reaction rate coefficients, the high-pressure limiting rate measured by Zellner et al.⁷³ was adopted in the San Diego and Ranzi mechanisms, while the pre-exponential factor was slightly increased by a factor of about 1.5 in the Davis and Konnov mechanisms. The low-pressure limiting reaction rate used in the San Diego and Ranzi mechanisms was obtained from those for N₂ of Baulch et al.⁷⁴ by use of equilibrium constants from the thermal decomposition reaction, while the rate coefficients used in the Konnov mechanism was recommended by Baulch el al.³⁸ The rate constants from those by Zellner et al.⁷³ and Baulch et al.⁶¹ were refitted in the Davis mechanism. Although the high-pressure and low-pressure rate coefficients used in various mechanisms are different, the actual rate constants under typical combustion conditions are nearly identical. And the rate constants for the OH recombination reaction also show good correlation with that for the thermal decomposition reaction proposed by Baulch el al.³⁸ via equilibrium constants. The rate coefficients for the thermal decomposition formula proposed by Baulch el al.³⁸ was employed in the Sun and Li mechanisms without modification. The rate constants for the forward and reverse reaction formulas discussed above are mostly based on old measurements or theoretical calculations. With the development of experimental techniques and theoretical/computational methods, continuous research on this reaction still proceeds due to its critical role in combustion chemistry. Recently, shock tube study for this reaction at 1.8 atm over a temperature range of 1020–1460 K has been performed by Hong et al.,⁷⁵ and a new low-pressure limiting rate constant combined with a high-pressure limiting rate constant from Sellevåg et al.⁷⁶ was recommended. The rate expressions was adopted in the Hong mechanism. Recently, Troe⁷⁷ performed a systematic review of the experimental data, and derived a new set of pressure-dependent rate coefficients for this reaction by combining the experimental data with systematic theoretical analysis. The rate coefficients by Troe⁷⁷ was employed in the Kéromnès mechanism. Kéromnès et al. also compared the two sets of rate coefficients by implementing the two rate expressions separately in the Kéromnès mechanism and performing ignition delay time simulations. They found that using the rate coefficients by Hong et al.²² can accurately predict the ignition delay times at 14.8 atm but will underestimate the ignition delay time when the pressure increases to 29.6 and 49 atm. Therefore, they recommended to use the rate expression by Troe⁷⁷ since this set of rate constants covers a wider range of pressure and temperature, and the use of this rate coefficient accurately predicts the pressure dependence of the ignition delay times. Fig. 17 demonstrates the actual rate constants of this reaction from the two sets of rate coefficients together with the recommendations by Baulch el al.³⁸ as a function of temperature at a fixed pressure of 10 atm, while Fig. 18 shows the actual rate constants as a function of pressure at fixed temperatures of 850, 950, 1050, and 1250 K. It can be seen that the actual rate constants by the two sets of rate expressions by Hong et al.²² and Troe⁷⁷ are nearly identical when temperature is above 800 K at fixed pressures. However, from Fig. 18, it is evident that the actual rate constants by the two sets of rate expressions by Hong et al.²² and Troe⁷⁷ show large differences when the pressure is above 10 atm. The rate constants by using the rate coefficients by Hong et al.²² is larger than that by Troe,⁷⁷ which will increase the reactivity of the system and result in the underestimation of the ignition delay time as revealed by Kéromnès et al.¹³ Therefore, the rate coefficients proposed by Troe⁷⁷ has been adopted in the updated mechanism.

Fig. 17 The rate constants of H₂O₂(+M) = OH + OH(+M) as a function of temperature at a fixed pressure of 10 atm.

Fig. 18 The rate constants of H₂O₂(+M) = OH + OH(+M) as a function of pressure at various temperatures.

2.3.3.2 HO₂ + HO₂ = O₂ + H₂O₂. The self-recombination reaction of HO₂ to the production of H₂O₂ and O₂ inhibits reactivity under low-temperature, high-pressure ignition conditions as revealed by sensitivity analysis. It requires the sum of two Arrhenius rate expressions to accurately describe the temperature dependence of this reaction. The rate constant defined as a sum of two Arrhenius expressions proposed by Hippler et al.⁷⁸ for the reaction has been adopted in many combustion mechanisms, e.g., in the Li and Sun mechanisms, while it has been slightly reduced by 13% when used in the Davis and Kéromnès mechanisms. Kappel et al.⁶⁹ improved the accuracy of the measurements and re-evaluated the rate expression for this reaction via extending the temperature ranges. The new expression has been used in the Konnov mechanism. Most recently, Zhou et al.⁷⁹ performed theoretical study on this reaction by using statistical rate theory in conjunction with high level ab initio electronic structure calculations. This reaction shows slightly pressure-dependence at very low temperatures, and the pressure-dependence disappears quickly when temperature is large than 500 K. The authors also generated new theoretical rate coefficients which are appropriate for both high and low temperature regimes. On the basis of theoretical study on this reaction, Som et al.⁸⁰ studied the effect of quantum tunneling of this reaction on the performance of a compression-ignition engine. Fig. 19 illustrates the different rate constants as a function of temperature. The San Diego mechanism used a single Arrhenius rate expression to describe this reaction,⁸¹ while a constant was employed in the Ranzi mechanism.⁸² Both the two expressions cannot accurately reproduce the temperature-dependence of this reaction. The other three rate expressions defined as a sum of two Arrhenius expressions exhibits large differences at high temperatures. However, the differences tend to decrease as the temperature decreases. The expression proposed by Hippler et al.⁷⁸ tends to overestimate the experimental results,⁶⁹ while the theoretical calculations tend to slightly overestimate the experimental results at temperatures around 700 K.^69,78 Therefore, the rate expression proposed by Kappel et al.⁶⁹ has been adopted in the present work.

Fig. 19 The rate constants of HO₂ + HO₂ = O₂ + H₂O₂ as a function of temperature.

2.3.3.3 H₂O₂ + H = HO₂ + H₂ and H₂O₂ + H = OH + H₂O. For the reaction between H₂O₂ and H radical, two reaction channels are considered. The product channel to the formation of HO₂ and H₂ (the reverse reaction is the H-abstraction of H₂ by HO₂) is very sensitive to ignition delay time at high pressure and low temperature conditions, while the other channel to the formation of H₂O and OH hardly exhibits any influence on ignition and laminar flame speed. Fig. 20 displays the rate constants for H₂O₂ + H = HO₂ + H₂ as a function of temperature proposed in various literatures. For this reaction, the rate constants proposed by Tsang and Hampson⁴⁸ and Baulch et al.³⁸ show large differences, especially at high temperature conditions. The rate expression recommended by Tsang and Hampson⁴⁸ has been adopted in the Li mechanism, and slightly reduced or increased when used in the San Diego and Ranzi mechanisms. The one proposed by Baulch et al.³⁸ was employed in the Sun and Konnov mechanisms. The rate originally used in GRI Mech³⁵ was adopted in the Hong mechanism, and was optimized to be reduced by 50% when used in the Davis mechanism. It can be seen that the difference between this rate and the one by Tsang and Hampson³⁸ is not large. Due to the large difference and uncertainty of this reaction's rate constant, Ellingson et al.⁸³ reported theoretical investigations on this reaction by using canonical variational transition state theory with multidimensional tunneling combined with reaction barrier height from a variety of ab initio methods. Based on a detailed evaluation of experimental results and the benchmark theoretical calculations, they recommended a new rate coefficient for this reaction,⁸³ which was employed in the Kéromnès mechanism. The rate constant is closed to the one proposed by Tsang and Hampson.⁴⁸ Therefore, the theoretical calculated rate by Ellingson et al.⁸³ has been employed in the present work. However, large uncertainty remains exist for this reaction. As pointed out previously, the reverse reaction of it is the H-abstraction of H₂ by HO₂, and it greatly affects the predictions of ignition at low temperature conditions. Cavaliere et al.⁸⁴ tried to modify the rate constant of this reaction artificially to obtain better agreement with low-temperature ignition data. Although good agreement was obtained, however, the actual rate constant of this reaction is still unknown. Thus, reliable experimental results are badly needed for this reaction.

Fig. 20 The rate constants of H₂O₂ + H = HO₂ + H₂ as a function of temperature.

For the reaction of H₂O₂ with H to the formation of H₂O and OH, it is less sensitive to the predictions of ignition and laminar flame speed. Two sets of rate coefficients were adopted in different mechanisms: the rate constant proposed by Tsang and Hampson⁴⁸ was employed in the Davis, Li, Ranzi, and Kéromnès mechanisms, while the rate recommended by Baulch et al.³⁸ was used in the San Diego, Sun, Hong and Konnov mechanisms. Fig. 21 illustrates the two sets of rate constants as a function of temperature, together with theoretical calculated results by Ellingson et al.⁸³ and Koussa et al.⁸⁵ The theoretical results by Koussa et al.⁸⁵ significantly overestimated the rate constant, while the results by Ellingson et al.⁸³ cannot correctly describe experimental results by different authors. The rate constants proposed by Baulch et al.³⁸ seems to be the good candidate up to now.

Fig. 21 The rate constants of H₂O₂ + H = OH + H₂O as a function of temperature.

2.3.3.4 H₂O₂ + OH = HO₂ + H₂O. Although the predictions of ignition and laminar flame speed are not sensitive to the rate constant of this reaction, the reaction shows great contributions to the consumption of H₂O₂ as shown in Fig. 15 and Fig. 16. However, due to the difficulty in detecting H₂O₂ and HO₂, fewer studies of this reaction have been performed. Generally, the reaction requires a sum of two Arrhenius rate expressions to accurately describe the temperature dependence of the reaction rate. Initially, Hippler et al.⁸⁶ investigated this reaction over a temperature range from 1000 to 1250 K, and obtained a rate expression of this reaction, which was employed in the Li mechanism. Subsequently, the authors extended the experimental temperature ranges (930–1680 K), and derived a new rate for this reaction over the range 240 ≤ T ≤ 1700 K.⁸⁷ The new rate expression has been used in the Davis (refitted at high temperatures), Sun, and Konnov mechanisms. Most recently, an experimental research on this reaction was performed by Hong et al.,⁷⁵ and the authors declared that a better rate constant expression than that used in previous mechanisms has been derived by combining their high-temperature data with previous studies at low to intermediate temperatures. This expression has been employed in the subsequently developed Hong and Kéromnès mechanisms. Fig. 22 demonstrates rate constants used in various mechanisms. It should be noted that the San Diego mechanism used a single Arrhenius expression taken from earlier literature,⁸¹ while the Ranzi mechanism also employed a single Arrhenius expression but split the reaction as a forward and a reverse reaction.⁸⁸ The rate proposed by Hong et al.⁷⁵ shows the best performance compared with the recent experimental results, and this updated rate expressions have been employed in the present work. Further, it is also noted that the above experiments were performed by shock tube devices, and consequently lacks an accurate descriptions of the reaction rate from 500 to 1000 K, where a significant change in the activation energy could exist as pointed out by Hong et al.⁷⁵

Fig. 22 The rate constants of H₂O₂ + OH = HO₂ + H₂O as a function of temperature.

2.3.3.5 H₂O₂ + O = OH + HO₂. Compared with the reactions of H₂O₂ with H and OH radicals, this reaction is less important. Experimentally, the rate constant of this reaction was measured mostly under low-to-medium temperatures. Baulch et al.³⁸ recommended a rate expression for this reaction as k = 8.43 × 10¹¹ exp(−16595/RT) cm³ mol⁻¹ s⁻¹ within the temperature range from 283 to 500 K. This rate expression has been adopted in the Sun and Hong mechanisms. Although this expression is in good agreement with the low-temperature experimental data,⁸⁹ it cannot accurately reproduce the medium-temperature experiments of Albers et al.⁹⁰ Earlier rate expression k = 9.63 × 10⁶ T^2.0 exp(−16595/RT) cm³ mol⁻¹ s⁻¹ proposed by Tsang and Hampson⁴⁸ correctly describes both the low-temperature data and the rate values of Albers et al.⁹⁰ via introduction of the temperature exponent in the modified Arrhenius rate expression. This rate has been adopted in the Davis, Li, San Diego, Konnov, and Kéromnès mechanisms. Fig. 23 shows the two rate constants, together with the rate used in the Ranzi mechanisms, which was taken from earlier ref. 88 The rate used in the Ranzi mechanism exhibits similar tendency as the rate proposed by Tsang and Hampson,⁴⁸ however, it underestimates the rate from medium-to-high temperatures. Thus, in the present work, the rate proposed by Tsang and Hampson⁴⁸ has been employed.

Fig. 23 The rate constants of H₂O₂ + O = OH + HO₂ as a function of temperature.

2.3.4 CO sub-mechanism. As a fuel, CO by itself is difficult to ignite and burn, because it lacks a free radical chain branching and propagation mechanism to facilitate the combustion processes. For pure CO oxidation in air, the reaction mechanism includes two reactions: the first one is the chain initiation reaction CO + O₂ = CO₂ + O, and the other one is the chain termination reaction CO + O(+M) = CO₂(+M), which converts CO to CO₂. However, for mixture of CO and H₂, the oxidation of CO to CO₂ is greatly accelerated due to the existence of OH radical, and the oxidation of CO is dominated by the reaction of CO with OH: CO + OH = CO₂ + H. Fig. 24 and Fig. 25 display the ROP analysis of HCO and CO during ignition and flame speed simulations. It is evident that the transformation between CO and CO₂ are completely dominated by the single reaction, CO + OH = CO₂ + H. Moreover, on the basis of sensitivity analysis, this reaction greatly affects laminar flame speed simulations, and significantly increases reactivity by increasing its rate constant. The reaction of CO with O₂ and HO₂ demonstrates large effect on ignition delay times. The effect of HCO related reactions on ignition is small, while they show some effect on laminar flame speed simulations. ROP analysis reveals that the HCO chemistry is mainly controlled by the three reactions: HCO + M = CO + H + M, HCO + H = CO + H₂, and HCO + O₂ = CO + HO₂.

Fig. 24 ROP analysis of HCO and CO by using the Davis mechanism during ignition simulations. It should be noted that the reaction CO + OH = CO₂ + H is duplicated in the Davis mechanism, and their contributions to ROP of CO have been separated in this figure and Fig. 25.

Fig. 25 ROP analysis of HCO and CO by using the Davis mechanism during laminar flame speed simulations.

2.3.4.1 CO + O(+M) = CO₂(+M). This reaction is one of the three pressure-dependent reactions in H₂–CO mechanism. The most popular reaction rate was described with a Lindemann fall-off expression, which employed the low-pressure limiting rate from Westmoreland et al.⁹¹ and the high-pressure limiting rate from Troe.⁹² This formulation has been used in the Li and San Diego mechanisms without modification, while the rate has been reduced by 13% and 25% for the low- and high-pressure limiting in the Davis mechanism. In the recently developed Kéromnès mechanism, they have shown that the optimized reaction rates in the Davis mechanism exhibits the best agreement over a wide range of experimental results, especially at high-pressure and fuel rich, high-CO-content conditions. The Sun mechanism employed the rate formulation proposed by Baldwin et al.⁹³ However, this rate cannot accurately capture the inhibiting effect of CO addition as revealed by Kéromnès. In the Ranzi mechanism, they have employed a different rate constant expression by adopting the fitted modified Arrhenius expression in NIST combined with the low-pressure parameters of Kondratiev using the Lindemann formulation.⁹⁴ The high-pressure rate constant in the Ranzi mechanism is about 2–3 times faster than the one proposed by Troe⁹² at a temperature range from 700 to 2000 K, while the low-pressure rate constant is about 50% lower than that by Troe⁹² by averaged from 700 to 2000 K. Thus, this also affects the performance of the mechanism at high-CO-content conditions. Based on the above considerations, the optimized rate coefficients in the Davis mechanism together with the third body efficiencies has been recommended and used in the updated mechanism.
2.3.4.2 CO + OH = CO₂ + H. The reaction of OH radical with CO plays a crucial role in hydrocarbon combustion and is regarded as the second most important reaction in hydrocarbon combustion, because H₂ is always abundantly available in hydrocarbon fuels and it is also the main mechanism of converting CO into CO₂ and responsible for a major fraction of the heat release. Sensitivity analysis suggests that changing the rate constant of the reaction hardly affect ignition delay times, while it exhibits significant effect on predictions of laminar flame speeds. Therefore, this reaction has been studied extensively. In the Davis mechanism, the rate constant for this reaction was refitted by the sum of two modified Arrhenius expressions, and this formulation was used in the Ranzi mechanism. The refitted rate expression can describe the high temperature data of Wooldridge et al.⁹⁵ and the data in ref. 96 more accurately. And the authors concluded that it was impossible to accurately obtain good predictions of the high-temperature H₂ ignition delay time and the H₂–CO laminar flame speeds without this revision.⁸ The Li and San Diego mechanisms employed a single modified Arrhenius expression to represent the rate constant. In the Li mechanism, they have used the method of weighted least squares to fit the rate constant over a wide range of experimental results,¹⁰ while the San Diego mechanism employed an earlier expression for this reaction.⁹⁷ In 1998, Troe analyzed the temperature and pressure dependence of this reaction.⁵⁴ Based on an in-depth theoretical analysis for this reaction by Joshi and Wang,⁹⁹ it is demonstrated that the rate constants of this reaction only deviate from its low-pressure limit rate constants by 2% even at elevated pressures (above 100 atm). Therefore, the pressure dependence of this reaction was unimportant under most practical combustion conditions, and the low pressure limiting rate constant expression can be applicable for most combustion conditions. The low pressure limiting rate constant represented by the sum of three modified Arrhenius expressions by Troe⁵⁴ was used in the Sun mechanism. Senosiain et al.⁹⁸ performed a complete statistical analysis of the reaction by taking the influences of electron-rotation coupling, angular momentum conservation, and tunneling into account. The calculated rates are in excellent agreement with the experimental data. Nearly at the same time, Joshi and Wang⁹⁹ analyzed the reaction by using RRKM/master equation and Monte Carlo simulations based on high-level potential energy surfaces of Yu et al.,¹⁰⁰ and the calculated rate was adopted in the Kéromnès mechanism to replace the single reaction rate constant in the Li mechanism. Quantum tunneling effect for this reaction was also analyzed recently.¹⁰¹ Fig. 26 displays various rate constants of this reaction. It can be seen that the differences among different rate expressions are not large when temperature is above 1200 K. The calculated rate constant by Joshi and Wang⁹⁹ shows well agreement with the optimized rate in the Davis mechanism. Consequently, the rate calculated by Joshi and Wang⁹⁹ has been adopted in the present work. Further, as pointed out by Joshi and Wang,⁹⁹ from the view of combustion modeling application, as long as the bi-exponential characteristics of this reaction is captured and implemented in detailed mechanisms, this should not be a severe problem. It should be also noted that uncertainty factor and discrepancies of this reaction rate at high temperature is small, indicating that the predictions of different mechanisms are not greatly affected by this reaction since the reaction is mainly sensitive to high temperature combustion properties as revealed by sensitivity analysis.

Fig. 26 The rate constants of CO + OH = CO₂ + H as a function of temperature.

2.3.4.3 CO + O₂ = CO₂ + O. This reaction shows some influence on ignition delay times. However, the uncertainty of this reaction rate constant is small. The rate constant proposed by Tsang and Hampson,⁴⁸ has been widely adopted. In the Davis mechanism, the rate constant has been optimized to multiply by a factor of 0.44 to improve the performance of the mechanism, and this refinement has been adopted in the Kéromnès mechanism. Based on sensitivity analysis, this change would not affect the performance of the mechanisms. However, in order to gain better performance of the current mechanism, the refined rate parameter has been employed in the present work.
2.3.4.4 CO + HO₂ = CO₂ + OH. On the basis of sensitivity analysis, ignition delay times are very sensitive to the reaction of CO and HO₂ both at low and high temperatures. Recent experimental and modeling investigations also demonstrate that large uncertainty factor of this reaction may still exist, which may be a major reason of the discrepancies between experimental data and model predictions.¹⁰² However, no direct determinations have been reported of the rate constant for this reaction at temperatures above 800 K. Atri et al.¹⁰³ suggested a rate expression based on their results at 713–773 K. Later, theoretical calculated activation energy by Allen et al.¹⁰⁴ shows good agreement with that from Atri et al.¹⁰³ However, in the development of reaction mechanisms, a 50% reduction of the rate by Atri et al.¹⁰³ is often used since the practical applications support the lower reaction rate above 1000 K, e.g., in the Davis and Ranzi mechanisms. The San Diego mechanism employed this expression by multiplying a factor of 1/3. In the Sun mechanism, they have employed high-level ab initio methods to refine the rate constant of this reaction based on potential energy surfaces proposed by Allen et al.¹⁰⁴ over a temperature range of 300–2500 K. This refinement has been supported by Mittal et al.¹⁰⁵ You et al.¹⁰⁶ also performed theoretical study on this reaction by combining ab initio electronic structure theory, transition state theory, and master equation modeling, and found that the overall rate coefficient is independent of pressure up to 500 atm for temperature ranging from 300 to 2500 K. A rate expression was recommended for 300 < T < 2500 K with the uncertainty factor equal to 8, 2, and 1.7 at temperatures of 300, 1000, and 2000 K, respectively. This rate coefficient was adopted in the Li and Kéromnès mechanisms. Fig. 27 gives the rate constants as a function of temperature from various resources. The rate constant by You et al.¹⁰⁶ is about a factor of 0.8 lower than that recommended in the Sun mechanism within the temperature range of 800–2500 K, while the rate constants used in the other mechanisms is slightly larger than that in the Sun mechanism. Considering the underlying uncertainties in different rate constants, the rate constant expression proposed in the Sun mechanism seems to be the best candidate up to now, and has been adopted in the present work. The last reaction of CO considered in the present work is CO + H₂O = CO₂ + H₂, which only existed in the Ranzi mechanism. This reaction exhibits high activation energy and demonstrates little effect on ignition and laminar flame speed. Due to the lack of accurate rate constants for this reaction, the rate coefficient used in the Ranzi mechanism is employed without modification.

Fig. 27 The rate constants of CO + HO₂ = CO₂ + OH as a function of temperature.

2.3.4.5 HCO + M = CO + H + M. The reaction is one of the most important reactions controlling the ignition of hydrocarbon oxidation as revealed by computational singular perturbation analysis.²⁵ This dissociation reaction competes strongly with the H-abstraction reactions from HCO by H, OH, and O₂ as a result of the weakly bond of the H atom in HCO. The first experiment to measure the rate constant of this reaction was performed by Timonen et al.¹⁰⁷ The fitted rate constant has been used in the Davis and San Diego mechanisms, and has been multiplied by a factor of 0.65 when used in the Ranzi mechanism. In 2002, Friedrichs et al.¹⁰⁸ detected HCO in shock tube experiment for the first time by using frequency-modulated spectroscopy, and the rate constant was estimated by fitting the experimental HCO profiles at 835–1230 K. The expression was used in the Sun mechanism, and the rate estimated by Friedrichs et al.¹⁰⁸ is about two times lower than the measurements of Timonen et al.¹⁰⁷ Krasnoperov et al.¹⁰⁹ then investigated the reaction by using pulsed laser photolysis coupled to transient UV-vis absorption spectroscopy in a heatable high-pressure flow reactor. The low-pressure data were combined with those from a high-temperature shock tube study and the low-temperature data on the reverse reaction to derive a rate expression over an extended temperature range from 298 to 1229 K. This expression is close to the result reported by Friedrichs et al.¹⁰⁸ Fig. 28 displays typical rate constants as a function of temperature. In the Li and Kéromnès mechanisms, they have used a new rate expression by using a weighted least-squares fitting to all experimental data available in the literatures. The new fitted expression is about 2 times higher than that recommended by Friedrichs et al.¹⁰⁸ in the temperature range from 1500 to 2500 K, while it begins to approach to the formulation recommended by Friedrichs et al.¹⁰⁸ within 50% at temperature below 1500 K. The new expression also shows good correlation with the rate expressions in the Ranzi mechanism. Thus, this fitted formulation is adopted in the present work, since it covers a wide range of available experimental results.

Fig. 28 The rate constants of HCO + M = CO + H + M as a function of temperature.

2.3.4.6 Other HCO related reactions. The reactions of HCO with O₂, O, H, OH, H₂O, and HO₂ in various mechanisms are all considered in the present work to make the reaction mechanism as complete as possible. On the basis of ROP analysis, it is shown that the reactions of HCO with O₂ and H control the consumption of HCO. For HCO + O₂ = CO + HO₂ (the reverse reaction can be considered as another chain initiation reaction of CO by HO₂ when CO is burn in presence of H₂, etc.), earlier experimental result by Timonen et al.¹¹⁰ was adopted in the Li, San Diego and Kéromnès mechanisms. Quantum chemical calculation results performed by Hsu et al.¹¹¹ have been used in the Davis and Sun mechanisms. However, based on various channels of this reaction,¹¹¹ they have used different formulations, which show large discrepancy. The Ranzi mechanism employed a constant as the rate constant, which is contrary to experimental result that the reaction reveals slightly positive temperature dependence.^112,113 The experiment performed by Nesbitt et al.¹¹² is not considered in the present work, since the temperature is very low (200–398 K). Recently, Colberg et al.¹¹³ used shock tube to determine the rate constant of this reaction. The experimental result behind reflected shock waves was over a wide range of temperature from 739 to 1108 K, and a new expression was fitted. Fig. 29 demonstrates the rate constants from different sources. Although large discrepancies exist among various rate coefficients, fortunately, both ignition and laminar flame speed simulations are not very sensitive to the rate constants of this reaction. According to the temperature ranges of different experiments, the rate coefficients by Colberg et al.¹¹³ should be the best candidate for this reaction, and is used in the present work.

Fig. 29 The rate constants of HCO + O₂ = CO + HO₂ as a function of temperature.

For the reactions of HCO with H, O, OH, and HO₂, the reaction rate constants are independent of temperature, and the uncertainty of the rate constants are small. Further, mechanism performances are not sensitive to the reaction rates of these reactions. In different mechanisms discussed in this work, the rate constant for HCO + H = CO + H₂ shows slightly discrepancy. The experimental result, k = 1.1 × 10¹⁴ cm³ mol⁻¹ s⁻¹ by Friedrichs et al.¹⁰⁸ was adopted in the Davis, Sun and Ranzi mechanisms, while earlier experimental result, k = 7.3 × 10¹³ cm³ mol⁻¹ s⁻¹ by Timonen et al.¹¹⁴ was adopted in the Li and Kéromnès mechanisms. Recent theoretical calculations¹¹⁵ revealed that the experimental result by Friedrichs et al.¹⁰⁸ tends to be more accurate. However, the difference between the two sets of rate coefficients is very small. The rate constant by Friedrichs et al.¹⁰⁸ has been adopted in this work. For the two reaction channels of HCO with O to produce H and CO₂ or CO and OH, the rate constants are identical in all the mechanisms, and the rate constant, k = 3.0 × 10¹³ cm³ mol⁻¹ s⁻¹ recommended by Tsang and Hampson⁴⁸ is used. For the reaction HCO + OH = CO + H₂O, the rate constant, k = 3.0 × 10¹³ proposed by Tsang and Hampson⁴⁸ was used in the Davis, Li, and San Diego mechanisms. The uncertainty factor was estimated to be 3. Later, Baulch et al.⁶¹ re-evaluated the rate constant to be k = 1.0 × 10¹⁴ cm³ mol⁻¹ s⁻¹ with a uncertainty factor of 2, and this rate constant was adopted in the Sun and Kéromnès mechanism. This rate constant agreed well with earlier experimental result by Temps et al.¹¹⁶ Thus, this rate constant has been recommended in the present mechanism. Two channels are considered for the reaction of HCO with HO₂. For HCO + HO₂ = CO₂ + OH + H, the rate constant proposed by Tsang and Hampson⁴⁸ was employed in all mechanisms. The other channel HCO + HO₂ = CO + H₂O₂ only exists in the Ranzi mechanism, and the reaction rate is very slow compared with the reaction HCO + HO₂ = CO₂ + OH + H. The self-recombination reaction of HCO to the formation of H₂ and two CO included in the Li, Sun and Kéromnès mechanisms employed the rate proposed by Tsang and Hampson,⁴⁸ and this rate is adopted in the present mechanism.

On the basis of the above detailed discussions on the rate constants of the reactions listed in Table 1 together with sensitivity analysis and ROP analysis, the importance of the reactions and uncertainties of their corresponding rate constants are given in Table 1. However, the uncertainty factors of different reactions are not explicitly shown. In contrast, we have divided the rate constant uncertainties into three classes: large, medium, and small, while the importance of different reactions also into three classes: very important, general, and less important. According to detailed comparisons of various rate constants for certain reactions, it is demonstrated that with the development of advanced experimental devices and theoretical methods, the uncertainties of a large number of important reactions are greatly reduced. And we anticipate that future experimental and theoretical studies should pay particular attention to the important reactions still with large uncertainties to further refine the reaction mechanism.

2.4 Thermo-chemical data and transport parameters

In most reaction mechanisms for combustion, to maintain thermodynamic consistency, the rate coefficients for a reaction is often specified in one direction (e.g., the forward rate) and the reverse rate coefficients are computed from the equilibrium constant. Thus, the accuracy of the reverse rate is limited by the accuracy of the free energy of reaction, which is directly relevant to the thermo-chemical parameters for the species in the reaction. Consequently, it is essential that the relevant thermo-chemical parameters for each species should be known as accurately as possible. The species included in the reaction mechanism for syngas combustion are all small molecules. With the development of experimental techniques and accurate quantum chemistry methods, thermo-chemical parameters can be obtained as accurately as possible. A large number of databases that cover a lot of species in combustion are available, such as those by NIST,¹¹⁷ PrIMe,¹¹⁸ and Active Thermo-chemical Tables (ATcT).¹¹⁹ Moreover, new data and experimental measurements are produced continuously, and these data should be evaluated and incorporated in the reaction mechanisms to obtain better performance of reaction mechanisms. Most recently, Goldsmith et al.¹²⁰ developed a database of small molecule thermo-chemistry for combustion based on high accuracy ab initio calculations employing the RQCISD(T)/cc-PV ∞ QZ//B3LYP/6-311++G(d, p) method, and the thermo-chemical parameters have been employed in the current mechanism. It is demonstrated that the values by Goldsmith et al.¹²⁰ are the most accurate and comprehensive numbers available based on comparison with benchmark data and uncertainty analysis. Fig. 30 shows a representative comparison of enthalpy of OH radical as a function of temperature used in typical mechanisms. It is found that the thermo-chemical data for the species presented in reaction mechanism for syngas is nearly indistinguishable at low temperatures, while slightly discrepancies appear when temperature is above 1500 K, which may be induced by the fitting procedures that the thermo-chemical parameters of Chemkin polynomial format are mostly fitted based on standard-state enthalpy and entropy combined with heat capacity values at temperatures below 1500 K. This may have some impact on the flame speed simulations. Overall, the thermo-chemical parameters used in different mechanisms is similar. The Chemkin-compatible polynomial format parameters fitted by Goldsmith et al.¹²⁰ are based on calculated thermo-chemical values in 10 K increments from 300 to 3000 K, and should be more accurate at high temperatures. Thus, the set of thermo-chemical parameters have been employed in the current mechanism.

Fig. 30 Enthalpy of OH radical as a function of temperature used in typical mechanisms.

Besides kinetic and thermo-chemical data, transport parameters exhibit large sensitivity to flame speed simulations. The parameters for the 14 species used in different mechanisms are identical after careful comparisons. However, it should be noted that updated description of diffusive transport properties involving H radical has been compiled and distributed by Wang and coworkers,^121,122 e.g., in the Davis mechanism. The updated transport properties result in some differences in some flame speed targets, sometimes slightly faster at some conditions and sometimes slightly slower at others. However, the overall performance of the updated transport properties and the traditional transport treatments is very similar. Therefore, in the present work, we have employed the traditional treatments of transport properties for simplicity. Since the thermo-chemical parameters and transport properties are nearly identical, it can be concluded that the different performances of the reaction mechanisms are mainly affected by chemical reactions and their corresponding rate constants.

3. Validation of the present reaction mechanism

This section dedicates to validate the current mechanism for standard targets, including ignition delay times and laminar flame speeds. It should be noted that we do not try to validate the mechanism against all available experimental results, because too many experiments have been conducted for syngas combustion, and such a validation is beyond the scope of the current work. However, standard targets, including ignition delay times and laminar flame speeds under typical conditions are validated. As mentioned previously, ignition delay time and laminar flame speed are crucial characteristics of fuel combustion and often used as key parameters for mechanism validations. Ignition delay times for homogeneous adiabatic ignition computations in an isobaric reactor, are compared with results of shock-tube measurements by Kalitan et al.¹²³ for CO–H₂–air mixtures with equivalence ratio of 0.5 and different CO–H₂ ratios representative of typical syngas mixtures. The conditions considered include near-atmospheric and elevated pressure. As can be seen from Fig. 31, the agreement between the computations and the experiments is reasonably good.

Fig. 31 Experimental ignition delay times¹²³ and modeling results for lean H₂–CO fuels in air.

Fig. 32 displays the experimental measurements of the laminar flame speeds for CO–H₂–air and CO–H₂–O₂–He (helium) mixtures as a function of equivalence ratio at different mixing ratios and pressures,¹² with comparisons to the calculated flame speeds by using the updated mechanism. It is found that the laminar flame speeds decrease with decreasing H₂ content in the CO–H₂ mixtures, and they decrease with increasing pressure for the He diluted mixtures. It should be noted that practical combustion processes wouldn't be happened in a He system. Experimentally, laminar flame speeds at high pressures are usually measured based on outwardly propagating flames. However, the outwardly propagating flame becomes cellularly unstable at higher pressures above 5 atm.^12,124 The use of He instead of N₂ can increase the Lewis number of the mixture, thereby suppressing the formation of wrinkles over the flame surface, which makes the flame stable.^12,124 Overall, the calculated results by using the updated mechanism agree well with the experimental data at different fuel mixtures and pressures. Further, as the laminar flame speed is determined by chemical reaction rates and heat release coupled with molecular diffusion, thus, it can be concluded that the different performances of these mechanisms in the predictions of laminar flame speeds are ascribed to the discrepancies of the elementary rate constants in various mechanisms since the thermo-chemical and transport data in all mechanisms are nearly identical in contemporary reaction mechanisms as shown in Section 2.4.

Fig. 32 Calculated laminar flame speeds by using the current mechanism and experimental measurements¹² for different CO–H₂ mixtures at various pressures and equivalence ratios.

4. Concluding remarks

In spite of its apparent simplicity, detailed reaction mechanisms for syngas combustion developed by different authors often differ by the list reactions and their rate coefficients. Generally, the evaluation of reaction mechanism is on the basis of their performances in the predictions of combustion properties. However, in essence, the underlying reason for the different performance of different mechanisms is caused by the differences of species, reactions and their thermo-chemical and kinetic data embodied in the mechanisms. Thus, detailed comparisons of the reaction lists, reaction rates and thermo-chemical data are essential to refine reaction mechanisms.

In the present work, detailed mechanisms for syngas combustion are analyzed. The exhaustive list of reactions in different mechanisms is summarized and the differences between these mechanisms are presented. Detailed comparisons of the choices of the reaction rate coefficients are analyzed in detail and an updated reaction mechanism together with the recommended rate coefficients have been proposed. The importance of the listed reactions and their corresponding uncertainties are analyzed on the basis of sensitivity analysis and ROP analysis. The importance and uncertainty analysis results are summarized in Table 1. It is demonstrated that with the development of advanced experimental and computational methods in chemical kinetics, the rate constant uncertainties of a large number key reactions in reaction mechanisms for syngas combustion have been reduced. However, large uncertainties still exist for H₂O₂ and HO₂ related reaction sequence, which are found to play a key role for syngas combustion at high-pressure and low-to-intermediate temperature conditions and deserve to investigate deeply. The present work provides detailed survey on the rate coefficients employed in detailed mechanisms, which can be very helpful to further reduce the uncertainty of the reaction mechanism in combustion simulations. Finally, the current mechanism is validated against standard targets for mechanism validation. The present work not only provides detailed survey into reaction mechanisms for syngas combustion, but also provides fundamental information towarding to the development of a universal core reaction mechanisms upon which to the development of reaction mechanisms of all the other hydrocarbon fuels.

Acknowledgements

This work is supported by the Fundamental Research Funds for the Central Universities of China (no. 2013QNA08).

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Footnote

† Electronic supplementary information (ESI) available: Reaction mechanism, thermo-chemical and transport parameters in Chemkin format for syngas combustion. See DOI: 10.1039/c3ra45959d

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