A combustion reaction can be defined as a fast chemical reaction between a fuel and an oxidizer that releases heat. Traditionally, the fuels used in the majority of practical combustion applications have been hydrocarbons, mainly due to their high energy density and easy availability (till recently). In most practical applications, combustion becomes a study of chemically reacting flows with rapid exothermic reactions, and involves a strong interplay between fluid mechanics, thermodynamics, chemical kinetics and transport processes.1 To describe a combustion event completely, one must be able to model these four phenomena simultaneously. This usually involves solving the Navier - Stokes equations coupled with chemical kinetics equations which describe species evolution, heat release and system temperature as a function of time. It is obvious that adequate knowledge of rate constants and reaction mechanisms for a particular fuel-oxidizer pair is needed before a more elaborate chemical kinetics-fluid mechanics coupling is attempted. During a combustion reaction, a variety of chemical species exist in the system, which can all react with each other. The reaction mechanism must thus be able to describe the rate constants for all these reactions occurring at the molecular level (called elementary steps) accurately. This paper describes the role of kinetics in one such article2 which attempts to compute the experimental and theoretical rate constants for an elementary reaction in methane oxidation viz. CH4 + O2 ïƒ CH3 + HO2.
2. Methane oxidation
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Methane oxidation has been extensively studied,3 both because it is the simplest hydrocarbon and because its reaction mechanism would serve as the subset of the reaction mechanisms of bigger hydrocarbons. Like all combustion reactions, methane combustion takes place through a branching-chain mechanism in which the products of one step serve as the reactants of the next and the reactive chain centers are free radicals.4 There are four main steps involved in a branched chain mechanism, which are chain initiation (in which radicals are produced from stable species), chain branching (in which the number of radicals are increased), chain propagation (in which the number of radicals are conserved) and chain termination (in which radicals are quenched to form stable products). The initiation of methane oxidation can happen via two reactions:
CH4 + M ïƒ CH3 + H + M (R1)
CH4 + O2 ïƒ CH3 + HO2 (R2)
where M is an inert third body that collides with CH4 and provides it with enough energy to dissociate into CH3 and H. R1 has a large activation energy, and as such is favored only at high temperatures.1 R1 is also a well studied reaction, so R2 forms the focus of the article2, as mentioned earlier.
3. Experimental and theoretical techniques
The article uses both experimental and theoretical techniques to study the rate constant of reaction R2. The shock tube technique was used for the experiments, with electronic detection absorption to monitor the OH-radical concentration in the reflected shock regime. The experimental details can be found in the article2. The initial mole fractions of methane and oxygen were 6-7 x 10-5 and 0.12-0.14 respectively, the remaining being Krypton gas. This low [CH4]:[O2] starting ratio was maintained to favor oxidation reaction R2 over dissociation reaction R1. R2 leads to the formation of unstable HO2 radicals, which dissociate to H and O2. The H radicals are readily oxidized in the presence of excess O2 to form OH radicals.2 Nineteen runs were conducted within the temperature range 1655-1822 K, and [OH](t) was measured in each run. For the theoretical aspect, ab initio electronic structure calculations were used to determine the potential energy surface of the reaction and to identify the transition states, and variational transition state theory (VTST) to figure out the rate constant of R2.
Figure 1. (a) 43-reaction mechanism used to simulate chemical system of methane and oxygen. (b) Results of the simulation to find k2. Figures reproduced from Srinivasan et al.2
For the experimental aspect of the study, a reduced 43-reaction mechanism was used to simulate the chemical system, because other elementary reactions were also expected to contribute to the formation and destruction of OH radicals (apart from HO2 ïƒ H + O2 ïƒ OH + O as mentioned earlier). This mechanism included all the species and elementary reactions that were considered relevant in the methane oxidation happening in this particular configuration. Particularly, a lot of the secondary chemistry leading to the formation of OH radicals can be neglected when [OH] is much greater than [CH4], allowing for the use of a reduced mechanism shown in Fig 1a. The only unknown rate constant in the mechanism is k2 (rate constant of the title reaction), which can be varied so that the predicted [OH](t) replicates the experimental concentration profile to the desired accuracy (Fig 1b). Fig 1b also provides insight into the importance of the title reaction in the methane combustion chemistry, as can be seen by the effect of varying the value of k2 to ±50% on the OH radical concentration profile.
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Figure 2. a) Arrhenius plot comparing the rate constants of experimental (filled circles) and theoretical (blue dotted line) aspects of the article, with other values in literature. Figures reproduced from Srinivasan et al.2
The values of the rate constants found at different temperatures (from 1655 K to 1822 K) are shown in an Arrhenius plot as filled circles (Fig 2a). Similarly, the energies of the reactants, products and the transition state found from the theoretical study are shown in Fig 2b, and the rate constant values at various temperatures are shown in Fig 2a (blue dotted line).
5. Conclusion and personal critique
The article computes rate constants for the reaction CH4 + O2 ïƒ CH3 + OH, which is an important initiator for methane combustion at low to moderate temperatures. The authors found rate constants values which were higher than those documented in literature, and that their values explained the ignition delay times of methane better. Personally, I thought this was a solid paper with good agreement between experimental and theoretical values. However, there were some places where I thought the authors could have better justified what they did. For instance, they did not explain how they narrowed down their choice of the 43-reaction mechanism that they used to find the rate constant from the experimentally measured [OH](t) data. The authors also do not explain why their values are higher than literature values, which is strange considering that it is their main result. An interesting study for future work can be to use comparable starting ratios for [CH4] and [O2] (a stoichiometric ratio for instance) and use an extended mechanism to see if the predicted OH radical concentration (or any suitable product concentration for that matter) matches the experimentally observed concentration as a function of time. This can act to serve as a validation of the rate constant found in this work, and also to observe the competition between reactions R1 and R2 for the initiation of methane oxidation.