(54d) One Approach to Kinetic Modeling of Combustion in Gaseous Composite Fuels

Combustion of gaseous composite fuels is normally modeled using either (a) macrokinetic formulations or (b) with detailed account of the complex kinetics of chain-branching reactions using a huge standard database. Approach (a), requiring the use of some experimental data obtained in some specific conditions, can describe the system behavior under the above conditions, but is inapplicable for its prediction under other conditions. At the same time, the use of approach (b) not always affords elucidating the role of individual reactions over a wide range of process conditions. In order to eliminate the above drawbacks, in this communication we suggest a novel approach to kinetic modeling of combustion in gaseous composite fuels, using the combustion of hydrogen and methane as illustrative examples.

Our approach is based on selecting the rate-controlling fragments from the large kinetic scheme and their analysis. For combustion of gaseous-fuel composites, these are the branching cycles of oxidation. Each of these cycles can control the process within its own range of system parameters. Identification of these ranges and their analysis can be expected to provide useful information about the kinetic features influencing practically important process parameters.

In qualitative analysis of the kinetic scheme we used the method previously suggested in [1] and its subsequent modifications [2, 3], allowing determine the boundaries of chain ignition region (CIR).

Method [1] affords a separation of branching cycles. These cycles provide negative contributions into the determinant D of the Jacobian matrix of the kinetic scheme while others being non-critical fragments, positive contributions. At the boundary of CIR, D = 0. Inside of the CIR, eigenvalue λ of the Jacobian matrix is positive, which ensures an exponential growth in the concentration of the species responsible for chain propagation within critical cycles. A procedure for determining the boundaries of CIR involves linearization of the kinetic scheme at initial conditions. Behavior of the system inside of the CIR isle can be characterized by matching different time moments with system position in a respective parametric point. Taking into account the effect of non-linear reactions at this point, one can perform the linearization. Inequality

A ? B ≥ 0 (1)

(where A and B are the sums of contributions from the critical and non-critical cycles) defines CIR and can be regarded as a generalization of Semenov' criterion for ignition φ ≥ 0 for a branching reaction with one reactive center. An algorithm for deriving analytical expressions for Aand Bhas been implemented as a computer program.

Analysis of criterion. The magnitudes of Aand Bin (1) are expressed in terms of the reaction rates for reactive species and their combinations, which affords to analyze a contribution from each reactive species into the dependence of A and Bon system parameters. The combinations that lead to an increase in A and Bwill define the group of reactions responsible for the accelerating or decelerating influence, of a given parameter on the overall process [2].

Representation of CIR on a two-parametric plane is obtained by finding out the roots of Eq. (1) at other parameters kept constant. Such a representation can be used to estimate the kinetic parameters of the process in different points near the CIR boundary. Within the closed CIR areas (domains), one can distinguish several ones (at least four) with characteristic behavior [3].

Analysis of system behavior inside of the domains is possible due to the fact the values of A ? B inside of a domain grow from zero, attain their maximum value, and then go down to zero again.

Kinetic model of superadiabatic filtration combustion (SFC) wave in methane?oxygen?steam mixtures involves two linear schemes as basic for partial oxidation of methane: the so-called peroxide mechanism (PM) and formaldehyde mechanism (FM). Their key role in low- and high-temperature conditions is outlined below.

In PM, a key role is played by the peroxide radicals CH₃O₂ formed upon oxidation of methyl radicals without activation threshold. Their reaction with methane yields methyl-hydro-peroxide CH₃OOH decomposing into the OH and CH₃O. Reactions of these radicals with methane and of CH₃O with oxygen result in recover of methyl radicals, thus giving rise to several branching cycles with formation of main intermediates, CH₂O and CH₃OOH, which reactions with peroxide radical also yield methyl-hydro-peroxide, starting the non-linear branching cycles. The role of all peroxide cycles decreases with temperature rise due to CH₃O₂O reverse decomposition.

In FM, the oxidation of methyl radicals proceeds in another route, with CH₂O direct formation and some activation threshold. Here the recover of methyl radicals (i.e. branching cycles) takes place only in high-temperature reactions of CH₂O (yielding the syngas). This is direct oxidation of CH₂O giving HCO and HO₂ and two CH₂O decomposition processes into H, HCO, and H₂, CO, the latter one being chain termination process The reactions of H and HO₂ with methane and water, decomposition of H₂O₂ into 2OH, the reaction of OH with methane, and decomposition and oxidation of HCO radicals form the cycles closely similar to those taking place during the oxidation of hydrogen.

Analysis of the above mechanisms (using our procedure) allowed us to characterize the parametric ranges of their individual and combined influence on the process kinetics. Combined use of both linear mechanisms (together with taking into consideration concomitant non-linear reactions as well as homogeneous/heterogeneous stages of water methane reforming) made it possible to simulate a traveling SFC wave, including its propagation rate, temperature profile in gas and solid, and concentration profiles for reagents, intermediates, and final products [4].

Domains in the T?α plane (α signs fuel excess)

These data can shed light on the relationship between a location of the upper and lower boundary of the domain and such significant characteristics of steady combustion as the maximum temperature and preheating, respectively.

For the hydrogen oxidation system the domain was obtained firstly for P = 1 atm. in reactor d = 1.0?7.4 cm using the linear part of the model developed in [5] but with allowance for reverse decomposition of HO₂ radicals, which just as the one of CH₃O₂ radicals in the methane oxidation system [3], may lower the upper temperature boundary of the domain. In the absence of inhibitors, very high (physically meaningless) temperatures of the upper limit have been obtained only for super-lean and super-rich mixtures. The respective exceedingly high reaction rates sooner correspond to detonation rather than to steady combustion. Apparently, this is a reason for the absence of SFC waves in stoichiometric and rich mixtures [6]. While, the formation of SFC waves in hydrogen-lean mixtures [6] correlates with a high activation energy (E_lean = 80?90 kcal/mol) at the lower boundary of the domain. Indeed, an initially slow heat release rate favors heat exchange of heating solid with oncoming cool gas, thus providing gas preheating.

The methane oxidation systems. The typical domains controlled by PM for methane oxidation neglected of CH₂O reactions (P = 1.0?1.2 atm, d = 1.7?3.6 cm) [3] exhibited four kinds of behavior at the lean and rich zones of the upper and lower temperature boundaries. Temperature difference between the maximum (α ≈ 1) and minimum (α ≈ 6) points ≈ 1200 ? 700 = 500 K.

The domains controlled by PM and combined PM + FM mechanism was investigated for filtration combustion (FC) of methane?oxygen?steam mixtures (P = 1 atm). At the pore size of solid (d_p = 0.4?0.8 cm) added water decreases the domains sizes due to lower concentrations of reagents, and, acting as efficient third body, results to widen PM-controlled domains due to intensified generation of peroxide radicals.

An elongated rich zone characterizes the domains controlled by PM including oxygen-less reactions of CH₃O radicals (decomposition into CH₂O + H, and interaction with methane), and also the domains controlled by PM + FM compozition. These radicals, being not formed in FM, react with softening of a sharp decline of the upper boundary typical for rich zone in FM-controlled domains, and thus, ensuring a dipper conversion herein.The lower boundary is basically PM-controlled . In case of the FM-controlled domains the activation energy is markedly lower on ≈ 15 kcal/mol in compare to PM one (Е _rich ≈ 75-80 kcal/mol). It can be concluded that a higher superadiabatic effect can be obtained when the lower boundary is PM-controlled .

1. Ivanova A.N., Tarnopol'skii B.L., Kinet. Katal, 1979, vol. 20, no. 6, pp. 1541?1548.

2. Ivanova A.N., Tarnopol'skii B.L., Karnaukh A.A., Kinet. Katal, 1997, vol. 38, no. 4, pp. 485?494.

3. Karnaukh A.A., Ivanova A.N., Kinet. Katal, 2005, vol. 46, no. 1, pp. 14?25. [Engl. transl. Kinet. Catal., 2005, vol. 46, no. 1, pp. 10?20].

4. Kostenko S.S., Ivanova A.N., Karnaukh A.A., Polianchik E.V., Manelis G.B., Dokl. Akad. Nauk, 2009, vol. 426, no. 6, in proof.

5. Azatyan V.V., Andrianova Z.S., Ivanova A.N., Zh. Fiz. Khim., 2006, vol. 80, pp. 1194?2000.

6. Kakutkina N.A., Korzhavin A.A., Mbarawa M, Fiz. Goreniya Vzryva, 2006, vol. 42, no. 4, pp. 8?20.