Kinetic Analysis of the Gas-Phase Reactions of Methyl Tert-Butyl Ether with the OH Radical in the Presence of NO

Um mecanismo explícito para a reação do metil-terc-butil-éter (MTBE) com radicais OH, numa mistura NOx -ar, foi simulado resolvendo as equações diferenciais ordinárias usando o método Runge-Kutta-4-semi-implícito. Os resultados simulados são consistentes com os dados experimentais publicados e o modelo explica as principais vias de reação para a oxidação do MTBE com radicais OH na presença de NOx -ar. Usando uma análise dos autovetores e autovalores dos coeficientes de sensibilidade, para todas as espécies químicas envolvidas em diferentes tempos de reação, foi extraída informação cinética do sistema. Este método foi utilizado para reduzir o modelo cinético de forma objetiva. Foi utilizado, também, o método tradicional de análise de velocidade de produção (ROPA) para estudar a importância relativa das reações individuais. Usando a informação da análise de componente principal e da análise de velocidade de produção, foram identificadas as principais reações individuais.


Introduction
Numerical integration of the coupled differential equations, which describe a reaction system, is becoming an important tool in chemical kinetics.The results and conditions obtained from such kinetic models are largely dependent on the selection of the elementary steps and their rate coefficients.For complex models, it is frequently difficult to assess the relative importance of each step or to explain certain features of the system kinetic behavior.
In order to assess the relationship between the model results and kinetic parameters and to evaluate which parts of the model are of particular importance, some sensitivity analysis is usually required [1][2][3][4][5][6] .
In this work, the gas-phase reactions of methyl tert-butyl ether (hereafter MTBE, CH3OC(CH3)3) with OH radicals in NOx-air systems are simulated and the relative importance of the elementary processes is carried out by an eigenvalue-eigenvector analysis of the linear sensitivity coefficients called Principal Component Analysis 7 .
In this paper the initial conditions for the simulations were those of the laboratory smog chamber experiments from Tuazon et al. 19 in order to compare the calculated and experimental results.

Methodology
Numerical simulation and principal component analysis of kinetic models is fully described in the literature 6-7,33- 35 .Briefly, the kinetic model can be represented by a set of ordinary kinetic differential equations, where c(t) is the n-vector of species concentrations with c(t = 0) = c 0 and k is the m-vector of kinetic parameters.A change in the kinetic parameters from k 0 to k at time t1 causes a change in the solution of the system at a time t2 (with t2 > t1).The effect of the parameter change on the solution can be expressed through the first order local sensitivity coefficients defined as In the first order approximation, the concentration sensitivity defined above represents the magnitude of the deviation in the concentration of species i at time t2 due to the differential variation of the parameter of reaction j at time t1 from value kj 0 to kj.For the present model, the parameters kj are the thermal rate constants and photochemical coefficients.
Sensitivity coefficients are normalized in order to eliminate their dependence on the dimensions of the kinetic model.The sum of the squares of the normalized sensitivities is called overall sensitivity.A convenient way to understand the sensitivity results is in terms of the eigenvalues and eigenvectors of the matrix S T S, where S is the array of normalized sensitivity coefficients.The methodology of principal component analysis is fully discussed in the literature [5][6][7] .
The classic method for the study of the reactions relevance is the rate of production analysis called ROPA [36][37] .Although the combination of species reduction and rate sensitivity analysis 6 seems to be a more effective way for this purpose, the rate of production analysis is still an important method for the exploration of important reaction pathways.The rate of production analysis requires the calculation of the Pij matrix elements 38 , which show the contribution of reaction j to the rate of production of species i.

Results and Discussions
The full mechanism and rate constants are presented in Table 1.The reduced mechanism was obtained after elimination of the non-important reactions (denoted by # in Table 1) on the basis of the principal component analysis described below.The rank of reactions ordered by overall sensitivities and rates is shown in Table 2.We calculated normalized sensitivities for all species at time points 1, 2, 3, 4, 5 and 6 min.Eigenvalues of S T S and the corresponding eigenvectors are listed in Table 3.
In the conditions of the modelling, the main source of hydroxyl radicals is the reaction (5) (HO2 + NO → OH + NO2) which follows the photolysis of the ethyl nitrite (CH3CH2ONO + hν → CH3CH2O + NO) and the oxidation of the CH3CH2O radicals (CH3CH2O + O2 → CH3CHO + HO2).Reaction (5) accounts for ca.95% of OH radical formed and the only significant sources of NO are the photodecomposition of ethyl nitrite (46%) and NO2 (54%), reactions (27) and (10), respectively.Since we had no data on photolysis light intensities during the experiments, the ethyl nitrite photodecomposition coefficient was estimated from experimental data (Fig. 1) and values, which gave consistent results for other photodecompositions, were used.The photolysis rates were also consistent with the 2) OH + HNO3 → H2O + NO3 k2 = 1.50 x 10 -13 3) NO + OH → HONO k3 a = 1.12 x 10 -11  value reported in the literature 20 for NO2 photodecomposition.Also, photochemical reactions of other species, not including NO2 photodecomposition, are of negligible importance compared with other paths.As expected the set of reactions of Table 1 accounts for the formation of the main products, tert-butyl formate, formaldehyde, methyl acetate, and acetone.As shown in Figs. 2 and 3, the simulated results are in reasonable agreement with experimental data, both for MTBE and the main products concentrations.In this simulation conditions, formaldehyde is formed both from acetaldehyde, the initial product of ethyl nitrite photolysis, reaction (27) The rate of production analysis shows that 60% of formaldehyde is formed through reaction (13), CH3O + (O2) → HCHO + HO2 and 40% through the reaction sequence ( 20), ( 23) and ( 24), which involve the reaction of CH3OC(CH3)2CH2O2 with NO and O2.Under the modeling conditions, the secondary reactions of formaldehyde are of minor importance.As observed experimentally 19,23- 24 , the formed formaldehyde reacts essentially with OH radicals which are in relatively high concentrations (calculated values about 9 x 10 7 molecule cm -3 ).Nevertheless, the rate of this reaction path is 3.6% of the total formation rate and, in comparison with OH radical reaction (11)  (HCHO + OH + (O2) → HO2 + CO + H2O), the photochemical decompositions (39) and (40) (HCHO + (2 O2) + hν → 2 HO2 + CO and HCHO + hν → H2 + CO) are of negligible importance.
In the conditions of this simulation, the formation of acetaldehyde (Fig. 4) and peroxyacetyl nitrate (PAN) (Fig. 5) can be attributed to the photooxidation of ethyl nitrite 19- 20 .The main discrepancy between the experimental results and the model predictions is the much lower concentrations of calculated peroxyacetyl nitrate.The reasons for this discrepancy are not well established, but may be associated   to the large uncertainty in the related kinetic parameters.Also, other reactions which have not been considered in the present work, such as heterogeneous reactions, may be important to describe the whole system.In comparison with OH radical reaction (CH3CHO + OH + (O2) → CH3CO3 + H2O), the acetaldehyde photochemical decompositions (CH3CHO + (2 O2) + hν → CH3O2 +HO2 +CO) are of negligible importance, as shown by the principal component analysis.
The 1 st and 2 nd principal components in Table 3 show that ethyl nitrite photodecomposition, reaction (27), oxidation of MTBE, reaction (20), and OH/NO chemistry, reactions (3), ( 4) and ( 5), are strongly coupled and are the most influential reaction sequence in the mechanism.Thus a small deviation in k20 or j27 should largely affect the simulation results.
According to the magnitude of the eigenvalues and significant entries (≥ 0.20) of the corresponding eigenvec-tor, the individual reactions may be classified in three groups: 1) Eigenvalues λ1 to λ21 are much larger than the remaining ones.Note that λ j = 0.9976.Principal components ψ1 to ψ21 contain steps ( 3)-( 10), ( 12)-( 16), ( 18), ( 20)-( 27), ( 30)-( 34), ( 37) and (38), forming the ''basic'' part of the mechanism.According to ψ1, the most influential reaction sequence is formed by ( 27), ( 20), ( 3) and ( 4).This ''reaction kernel'' emphasizes that the largest effect is brought about by setting the parameters j27 and k20.Also the NO/NO2 ratio (Figs. 6 and 7) largely affects the simulated results.Due to the coupling of the individual reactions, this ratio not only depends on the rate of reactions ( 20) and ( 27) but also on all the reactions involving NOx.Since j27 is an estimated parameter, some deviations of the simulated results may be attributed to it.An uncertainty analysis of this parameter shows that a change of 10% in    j27 leads to a substantial change of all product concentrations (6.8% in TBF and about 7.5% in the minor products).The inclusion of another minor reaction path, such as the formation of alkylnitrates, might affect the NO/NOx ratios in a non-negligible amount.
2) According ψ22 to ψ27, reactions (1), ( 2), ( 11) and (35), are of ''transitional'' importance.As it will be shown, in spite of their small contributions they can not be removed from the mechanism.
As shown in Table 4, eliminating the last group of reactions causes small changes in concentrations.However, additional elimination of steps (1), ( 2), ( 11) and (35) (i.e.reactions of ''transitional'' importance) leads to large deviations (Table 4).That is, no further reduction of the mechanism is possible since all concentration changes should be small.Table 4 also shows that the importance or contribution of individual reactions changes as the overall reaction proceeds.
The rank of reactions by overall sensitivity (Table 2) suggests that reactions (11) and ( 35) may be eliminated.However, this elimination leads to large deviations (e.g. at t = 6 min the deviation for HCHO is about 20%).On the other hand, reactions ( 19) and ( 28) with larger overall sensitivities can be dropped.The probable reason for this is that reactions (11) and (35) are coupled with other important reactions (see ψ24-ψ27).
The rate reaction rank (Table 2) gives a different rank of reactions and is not an effective way of reducing a mechanism.Individual rates do not consider the interactions between reactions and may lead to incorrect conclusions about the relevance of individual reactions.Anyway, as previously shown the rate of production analysis is a good method for the exploration of the reaction pathways.

Conclusions
The mechanism of Table 1 is quite successful in reproducing chamber data for the oxidation of MTBE by OH radicals.The rate of production analysis gives useful information in determining the main reaction pathways.
Principal component analysis shows that reactions are strongly coupled and confirms that the most influential reactions paths are the ethyl nitrite photolysis, the MTBE oxidation and the chemistry of NOx and OH radical.On the basis of the calculated eigenvalues, the mechanism can be reduced to 33 reactions.No further reduction is possible since all concentration changes should be small.Certainly, the conclusions taken from the eigenvalue-eigenvector analysis are only valid for the rather narrow range of conditions of the smog chamber experiments.Anyway, the information seems useful to identify a minimal reaction set and to assess the relationships and dependencies among the parameters.

Figure 1 .
Figure 1.Simulated and experimental data for the ethyl nitrite photodecomposition as a function of reaction time.

Figure 2 .
Figure 2. Simulated and experimental data for the main products of the gas-phase reactions of MTBE with the OH radical in the presence of NOx as a function of reaction time.

Figure 3 .
Figure 3. Simulated and experimental data for the oxidation of the MTBE as a function of reaction time.

Figure 4 .
Figure 4. Simulated and experimental data for the acetaldehyde concentrations as a function of reaction time.

Figure 5 .
Figure 5. Simulated and experimental data for the peroxyacetyl nitrate (PAN) concentrations as a function of reaction time.

Figure 6 .
Figure 6.Simulated and experimental data for the NO concentrations as a function of reaction time.

Figure 7 .
Figure 7. Simulated and experimental data for the NO2 concentrations as a function of reaction time.

Table 1 .
Chemical mechanism for gas-phase reactions of MTBE with the OH radical in the presence of NOx.

Table 2 .
Rank of reactions by overall sensitivity and rates.