Chemometric analysis of a detailed chemical reaction mechanism for methane oxidation

Chemometrics and Intelligent Laboratory Systems 44 Ž1998. 353–361

Chemometric analysis of a detailed chemical reaction mechanism for methane oxidation Anders Broe Bendtsen ) , Peter Glarborg, Kim Dam-Johansen Department of Chemical Engineering, Combustion and Harmful Emission Control Research Group, Technical UniÕersity of Denmark, Building 229, DK-2800 Lyngby, Denmark Received 19 August 1997; revised 4 May 1998; accepted 6 May 1998

Abstract A widely used detailed reaction mechanism for methane oxidation ŽGas Research Institute ŽGRI. mechanism 2.11. has been analysed, in order to evaluate if reactions were to be added to the mechanism. This mechanism consists of 279 reversible elementary reactions between 48 different species, each with a temperature dependence described by a modified Arrhenius expression. The mechanism was transformed to 558 irreversible reactions, and the rate constants were analysed at a fixed temperature, to reduce the complexity of the analysis. A partial least squares ŽPLS. model was generated, which estimated reaction rate constants as a function of a reaction descriptor vector. This vector characterized the different chemical bonds in the reactants and products of a chemical reaction. The model was validated through full cross validation. The original mechanism was unable to correctly predict oxidation of methane in a natural gas engine exhaust manifold: Oxidation of 2300 ppm methane in the presence of 300 ppm NO, 9% oxygen and 2% water. Therefore, these conditions were used for evaluation of the reaction mechanism. The potential reactions for expanding the mechanism were selected among reactions with one or two reactants and one or two products. A stepwise analysis combining rate of production ŽROP. analysis with sensitivity analysis was used to reduce 2138 potential elementary reactions to nine important reactions, which were added to the mechanism. The analysis was based on PLS estimates of the reaction rate constants, but in the final model, literature values were included where available. This modification of the mechanism improved model predictions. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Chemometrics; Partial least squares ŽPLS.; Chemical kinetics; Elementary reactions; Detailed reaction mechanism; Methane oxidation; Combustion

1. Introduction The reporting of a chemical reaction may have different levels of detail. At the level with fewest details is the ‘global reaction’. For methane oxidation, the global reaction is CH 4 q 2O 2 | CO 2 q 2H 2 O. )

Corresponding author. E-mail: [email protected]

The global reaction is mainly a description of the species consumed and produced; i.e., an element balance of the reaction. In some cases, this is identical to the reaction path and may be used in a mathematical model of the rate of production ŽROP.. However, in many cases, the mechanism of the reaction is much more complex than the global reaction. For example, methane oxidation does not take place through a si-

0169-7439r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 7 4 3 9 Ž 9 8 . 0 0 1 1 5 - 4

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multaneous collision of one methane molecule and two oxygen molecules. Therefore, a more detailed description of the reaction may be needed for modelling the reaction. One such description is the mechanism given in Table 1 w1x, which describes methane oxidation based on 23 reactions and 13 species. The reactions of this mechanism can be generalized into initiation reactions, which produce the initial radicals from reactions involving the stable reactants, propagation and branching reactions, which enhance reaction by production of radicals, which may attack methane, and termination reactions, which inhibit reaction. The 23 reactions occur simultaneously and the fate of a combustion system is determined by the balance between initiation and propagation on one side and termination on the other. The ROP Žor removal. is the contribution to the production Žor removal. of a species from an individTable 1 A simplified reaction mechanism for methane oxidation w1x Initiation Žproduction of radicals from non-radicals. CH 4 qŽM. |CH 3 qHqŽM. Propagation Žmaintenance of radical concentration. CH 4 qOH |CH 3 qH 2 O CH 4 qH |CH 3 qH 2 CH 3 qO 2 |CH 2 OqOH CH 2 OqOH |CHOqH 2 O CH 2 OqH |CHOqH 2 CHOqO|COqOH CHOqŽM. |COqHqŽM. COqOH |CO 2 qH H 2 qOH | HqH 2 O HqHO 2 |OHqOH Branching Žnet production of radicals involving intermediates as reactants. CH 4 qO|CH 3 qOH CH 2 OqO|CHOqOH CH 2 OqŽM. |CHOqHqŽM. H 2 qO|HqOH HqO 2 |OqOH Termination Žnet consumption of radicals. OHqOH | H 2 OqO HqO 2 qŽM. | HO 2 qŽM. CH 3 qO|CH 2 OqH CHOqOH |COqH 2 O HqOHqAr |H 2 OqAr HqOHqH 2 O|H 2 OqH 2 O CHOqH |COqH 2 ŽM. designate a third body, i.e., a molecule used for draining energy from the activated complex.

ual elementary reaction ŽR 1 q R 2 | P1 q P2 . and is calculated ŽEq. Ž1.. from the reaction rate constant k and the concentrations of the reacting species wR 1 x and wR 2 x. r s k P wR 1 x P wR 2 x

Ž 1.

The rate ‘constant’ varies with temperature T, and is determined from the modified Arrhenius expression ŽEq. Ž2.., where A, b and Ea typically are determined experimentally and R is the universal gas constant. y

ksAPT b Pe

Ea RPT

Ž 2.

The rate constants may be used as parameters in a system of coupled differential equations, which are solved for a prediction of the fate of a reaction system. Through integration the concentrations of reactants are continuously calculated, for use in Eq. Ž1.. ŽThe reader is referred to a text-book on chemical kinetics w2x for an in-depth discussion of reaction rates.. A reaction mechanism such as the one described in Table 1 corresponds to 13 coupled differential equations, when simulating reaction in an isothermal and isobaric plug flow reactor. In spite of the apparent complexity of a system of 13 coupled differential equations, more than just 23 reactions and 13 species are usually required for a correct model of methane combustion, especially if the model is to be used across a wide range of conditions, which is often the reality in combustion studies. Assuming that only carbon, hydrogen and oxygen are active elements in the combustion process, Ranzi et al. w3x reported a mechanism with 78 species and more than 1600 reactions. The detailed chemical kinetic model of methane combustion, Gas Research Institute (GRI) mechanism 2.11 w4x, which we have studied, consists of 277 reactions and 48 active species plus the inactive collision partner argon, and includes the active elements carbon, hydrogen, oxygen and nitrogen. Construction of such detailed reaction mechanisms is a complex task. Traditionally the approach has been to judge how the reactants could react with each other under the relevant conditions. The result-

A.B. Bendtsen et al.r Chemometrics and Intelligent Laboratory Systems 44 (1998) 353–361

ing products have then been included in the analysis, and the possible reactions in this new system were evaluated. During this process the resulting mechanism was evaluated against experimental data, and if the mechanism was found to be in correspondence with experiments, it was considered successful. However, with an increasing number of species and reactions, it is difficult to maintain this intuitive approach, and systematic alternatives must be found. One such systematic approach to construction of reaction mechanisms is exemplified by pyrolysis of ethane, based on one initial species Žethane. and six predefined reaction patterns Že.g., bond fission, Habstraction. w5x. If possible, the initial species are then assumed to undergo all the reaction patterns, and the corresponding products are included in the set of active species. This is then iterated with the products as species which may react, to expand the basis of species. This method for construction of a reaction mechanism is efficient, especially since the method makes it possible to employ a set of semi-empirical rules classified by reaction type w6x. However, when the complexity of species increase Že.g., by expanding the aim of the model from pyrolysis to oxidation and interactions with nitrogen species., the number of reaction patterns should also increase, and there is thus a risk that not all reaction types are included. Furthermore, only few rules are suggested for, e.g., nitrogen species.

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An alternative approach is to construct a ‘reaction grid’ by evaluating all combinations with balance in elements between reactants and products w7x. From 25 species Žcontaining C, H and O. 311 different irreversible reactions are suggested. Reaction rate constants may then be determined from experiments, semi-empirical rules and analogies with similar reactions. While all possible reactions are considered, an examination shows that some are left out. This is also confirmed by the fact that an odd number of irreversible reactions is presented. We assume that this selection to some extent is based on intuition and experience as well as the lack of available rules for rate constant estimation. The two approaches described above are fundamentally different in that the concept of a reaction grid w7x specifies the species and allow all reactions, while the concept of reaction patterns w5x specifies reaction types, and allow all species. When the species undergoing reaction are similar, the reaction types may be assumed to fit the patterns, e.g., for studies of pyrolysis of hydrocarbons. However, as species become increasingly complex, e.g., by including nitrogen as an element, the number of reaction patterns will increase. In this case, the reaction grid approach may be better, since it does not limit the reactions occurring. However, a successful construction of a reaction mechanism based on the reaction grid requires a sound initial set of species.

Fig. 1. GRI mech. 2.11 predictions Žfull line. and the expanded mechanism Ždashed lines. compared to experimental results w7x, under the conditions described in Table 2.

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As the number of species increases, and especially when the variation of species structure increases with the addition of nitrogen to the system, the number of possible reactions will increase dramatically, causing a need for a more efficient method for estimation of rate constants. With the 48 active species included in GRI mech. 2.11 the number of reactions which satisfies the element balance is 5378 and this number of reactions will require significant time for manual evaluation. Therefore, an automated method which will screen out irrelevant reactions and provide rate constant estimates will be of value. The background for this work was experiments in our laboratory w8x investigating the oxidation of methane at engine exhaust conditions, i.e., moderate temperatures in the presence of NO Žsee Fig. 1 and Table 2.. The experiments showed that methane oxidation is facilitated by the presence of NO, but this behaviour was not predicted by GRI mech. 2.11. However, a recent publication w9x suggested the addition of the reaction CH 3 q NO 2 | CH 3 O q NO, which resulted in a much better model prediction. Our present work is an attempt to find a more general way to assess the reactions to include a reaction mechanism. Since the motivation of our work was to describe the interactions between nitrogen and hydrocarbon oxidation chemistry, we chose to use the reaction grid to expand the existing mechanism, as a set of reaction patterns may be difficult to define for the combined system. The reaction grid was used in combination with a detection of non-elementary reactions,

Table 2 The conditions used for construction and evaluation of the model, corresponding to combustion of methane in an engine exhaust manifold w7x

O2 CO 2 H 2O NO CH 4 C2 H6 Temperature Pressure Residence time

Experiment

ROP screening and sensitivity analysis

9.11% 5.67% 2.2% 308 ppm 2297 ppm 130 ppm 1000–1186 K 1.2 atm 120 KrT ms

9.11%

308 ppm 2297 ppm 1000 K 1.2 atm 0–200 ms

and a regression model for estimation of rate constants.

2. The modelling approach The aim of this work was to find a method for selection of relevant reactions to include in a reaction mechanism. Therefore, a modelling approach with maximum generality was chosen. It was also chosen that the modelling should assume a minimum of a priori knowledge. As selection is made in several steps, a name Žin italics . has been assigned for each selected set of reactions. In steps 2–4c, the selection of reactions is made from those remaining selected in the previous step. The outline of the modelling approach is: Ž1. Estimate a regression model of reaction rate constants as a function of structural descriptor vectors. Ž2. Find all balancing reactions. Ž3. Determine all potential reactions, which fulfill overall demands for elementary reactions. Ž4a. Determine the selected reactions which are important in the ROP of species under the conditions investigated. Ž4b. Identify the important reactions using sensitivity analysis. Ž4c . Select the added reactions, by judging whether they fulfill detailed demands to elementary reactions. Ž5. Modify the mechanism by adding these reactions. If available use literature rate constants, otherwise use estimates. Ž6. Verify the mechanism against experiments. 2.1. A regression model of reaction rate constants We decided that the model was to be limited to operate at constant temperature and pressure only. However, it may be possible to estimate model parameters at different temperatures, and use the estimated rate constants to calculate the parameters of the Arrhenius expression from these rate constants. The reaction rate constants k i were modelled as a function of a reaction descriptor vector x i . For simplicity all reversible reactions were converted into two irreversible reactions each. As a consequence of

A.B. Bendtsen et al.r Chemometrics and Intelligent Laboratory Systems 44 (1998) 353–361 Table 3 The concept of species descriptors shown for only the species containing O and H atoms H) H2 H O O2 OH H 2O HO 2 H 2 O2

H–H

O)

O-1p

2

2 4 2 2 4 4

O–O

O5O

O–H

1 1

1 1

1

1 1

1 2 1 2

The header row is a description of electron configuration, e.g., H–H is a single bond between two hydrogen atoms. O) is an unpaired electron on an oxygen atom and O-1p is an oxygen lone pair. Blank cells correspond to zero.

bondrgroup theory w6x the reaction descriptor was built from the molecular structure of the reactants in a reaction in the following way: each bond-type ŽH–H, O–H, O–O, O5O, etc.. and other species characteristic ŽH-unpaired electron, O-unpaired electron, O-lone-pair, etc.. were assigned a position in a vector. In Table 3, an example of descriptors for the simplified OrH system is shown. The characteristics of a species were counted, and the vector was filled accordingly. These species vectors Ž z sp . were then combined to correspond with a given reaction. For reactions with either a single reactant or product the corresponding species vector Ž z sp . was replaced with a zero-vector. For example, for the reaction between H and O forming OH the x i-vector was formed as w z H z O z OH 0x. To ensure that the model was insensitive to the order of respectively reactants and products, reactants and products were permuted pairwise, yielding all together four vectors as illustrated in Table 4. The CHEMKIN w10x package has been used in the study of kinetics. CHEMKIN is a FORTRAN li-

brary, with functions for calculation of kinetic parameters from input data. From the Arrhenius parameters specified in the GRI mechanism w4x, CHEMKIN functions calculate rate constants in accordance with Eq. Ž2.. SENKIN w11x which is distributed with the CHEMKIN package is designed for simulation of plug flow reactors. SENKIN uses the CHEMKIN library during integration of the differential equations defined by the reaction mechanism and an isothermal plug flow reactor. During integration, sensitivity analysis may be made. The reaction rate constants were obtained at a fixed temperature, from the GRI mechanism’s database of Arrhenius parameters w4x. To provide a linear correlation of k and X, logarithmic transformation of the k vector of rate constants was used. The correlation between X Žas built from individual x i . and k Žas built from individual k i . was modelled with a PLS model w12x. An upper limit of 10 14 cm3 moly1 sy1 corresponding roughly to a generic collision frequency was assigned to all rate constant estimates. An alternative approach in which the descriptors were expanded with the elemental composition of each species did not improve predictions. Other potential modifications of the method which were not tried include addition of thermodynamic data of the reactants and products, and a representation of the relation between forward and reverse reaction, e.g. by modelling only the exothermal reactions, and estimating the reverse rate constant from this value and an equilibrium constant. 2.2. Selection of potential elementary reactions An elementary reaction is a reaction which proceeds through a single intermediate configuration of

Table 4 An example of the permutation of respectively reactants and products in the description of a reaction Reaction

H q O | OH q _ O q H | OH q _ H q O | _ q OH O q H | _ q OH

x zR 1

zR 2

z P1

z P2

1000000 0022000 1000000 0022000

0022000 1000000 0022000 1000000

0012001 0012001 0000000 0000000

0000000 0000000 0012001 0012001

"_" describes ‘no product’ to illustrate that the zero-vector is used.

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the species. Reactants collide, re-configure into an activated complex, and separate as products. For a reaction to be considered as elementary, Ž1. the elements in reactants and products must balance and Ž2. the transformation of the activated complex must be simple, e.g., the number of bonds formed and destroyed must be limited. In this study, we define the maximum number of allowable bond changes as the formation of one bond and the destruction of one bond. The matrix of potential reactions was established as follows: for all combinations of two reacting species, it was investigated whether any combination of products would match the elements in the reactants. If this was the case, a second step was taken, in which the difference in the sums of bonds of the reactants and products were calculated. To avoid too narrow restrictions a change of the multiplicity of bonds Že.g., from single bond to double bond. was not considered a change of the number of bonds. 2.3. Selection of important reactions to be added For all the potential reactions, the reaction rate constant was estimated. These potential reactions with estimated rate constants were then appended to the original mechanism. This expanded mechanism was then considered a basis for further optimization. This optimization was based on sensitivity analysis, which is the study of important reactions, under a given set of conditions. Sensitivity analysis w13x is an integrated part of the SENKIN w11x software package, but the calculation time of sensitivity analysis increases dramatically with the size of a mechanism. We therefore decided to perform the initial screening by an alternative method, based on the ROP and removal of each reaction. This so-called ROP screening was based on the assumption that for an elementary reaction to be important for the overall reaction it must participate with more than 1% of the production or removal of any species at any time. The reactions meeting this criteria were called selected reactions. The ROP is calculated for each integration step as shown in Eq. Ž1. as an integral part of the model integration, so this evaluation added only minimum calculation time. The draw-back of ROP screening was that all species were considered, even those

which are not active in reaction. This resulted in an overestimation of the importance of some reactions. This may be minimized by keeping the conditions used for ROP screening as simple as possible. Furthermore, the screening was quite efficient, so the remaining selected reactions could be evaluated using sensitivity analysis. This sensitivity analysis aimed at selecting the truly important reactions. Finally, the important reactions were examined manually, to determine if they really are elementary reactions. Only those which were considered to be elementary remained in the mechanism. This final set of reactions is termed the added reactions. 2.4. Modification and Õerification of the mechanism The final step was then to evaluate the reaction rate constants of the added reactions. A search in literature for the reaction rate constants was made, and these were added to the mechanism. At this step experimental determination of rate constants may also be necessary.

Fig. 2. A plot of observed vs. cross-validation predicted rates. The two axes are logarithmic Žbase 10. transformed. r 2 s 0.89. The circles correspond to classification in two classes of rates Žabove and below 10 5 cm3 moly1 sy1 .. Eighty-eight percent are classified correctly Žthe two circles on the diagonal..

A.B. Bendtsen et al.r Chemometrics and Intelligent Laboratory Systems 44 (1998) 353–361 Table 5 The number of important reactions Žcounted as irreversible reactions., as suggested by different types of sensitivity analysis Sensitivity analysis

Original mechanism

‘New’ reactions

None ROP sensitivity analysis Traditional sensitivity analysis Elementary reactions

558 142 47

2138 164 19 9

After replacing the estimated rate constants with experimental rate constants, the final mechanism was compared to experimental data.

3. Results The method outlined above was used to construct a model and modify the reaction mechanism accordingly. ROP screening and sensitivity analysis a set of physical and chemical conditions. These conditions match those found in an exhaust manifold of a natural gas lean-burn engine, and are described in Table 2. As mentioned above, ROP screening was im-

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proved by simplifying the conditions in order to focus the screening. The reaction mechanism included 279 reversible reactions each of which were modelled as two irreversible reactions. As mentioned, to provide a linear correlation of k and X, logarithmic transformation of the k vector of rate constants was used. An attempt using rank transform w14x as an alternative method for pre-treatment was not successful. The fit of the PLS model is acceptable, as shown in Fig. 2, where fit is evaluated by full cross-validation. A systematic underestimation of 0.34 and a standard deviation of 3.5 are seen. As Fig. 2 is a double logarithmic plot these values may be considered as a systematic underestimation by a factor 0.45 in combination with a random variation corresponding to a factor 3000. The correlation coefficient between the log-transformed true values and estimates is 0.89. When attempting to classify reactions as active or not active, by the arbitrary limit 10 5 cm3 moly1 sy1 88% of the reactions are classified correctly. In Table 5, the results of sensitivity analysis are presented. In all cases, sensitivity analysis was performed under the conditions reported in Table 2. The 2138 potential reactions are reduced first to 164 se-

Table 6 The important reactions, which were detected after ROP and traditional sensitivity analysis Literature rate NO 2 H CH 3 ™ NO H CH 3 O w15x C 2 H 6 H HO 2 ™ C 2 H 5 H H 2 O 2 w16x CH 3 H O ™ CH 3 O w17x NO H CH 3 O ™ HNO H CH 2 O w18x CH 2 H O 2 ™ CH 2 O H O w19x NO 2 H CO ™ NO H CO 2 w20x CH 3 H HO 2 ™ CH 3 OH H O CH 3 H H 2 O 2 ™ CH 3 OH H OH HO 2 H H ™ H 2 O 2

13

1.3)10 4.44)10 8 1.44)10 4 1.91)10 10 4)10 10 3.74)10 6

PLS estimate 14

10 1.36)10 13 10 14 4.14)10 13 7.94)10 12 1.22)10 11 10 14 10 14 10 14

Ratio 8 30,000 7)10 9 2200 200 32,000

NO2 q H2 O ™ NO q H2 O2 CH4 q OH ™ CH3 OH q H CH4 q O ™ CH3 O q H H2 O2 q O ™ H2 O q O2 C2 H6 q O ™ CH2 O q CH4 CH4 q CH2 ™ C2 H6 H2 O q O ™ H2 O2 C2 H4 q O ™ CO q CH4 CO q H2 O2 ™ CO2 q H2 O CH3 q H2 O2 ™ CH3 O q H2 O The reactions in italics below the dashed line were found to be non-elementary, so the bold faced added reactions were the only reactions which finally were added to the mechanism.

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lected reactions by ROP screening, and then through sensitivity analysis to 19 important reactions. The 19 important reactions were examined in detail, revealing that according to our criteria only nine were true elementary reactions, as shown in Table 6. From Table 5, it is seen that the number of important reactions in the original mechanism was significantly higher than among the ‘new’ reactions. This is not surprising as both intuitive and deliberate selection of reactions already has taken place in the design of the model. That, on the other hand, a major part of the original mechanism was considered irrelevant for this problem is not surprising either, since Ž1. the reactions are pairs of irreversible reactions and Ž2. the mechanism is designed for a wide range of conditions. Rate constants for the added reactions were found in literature when available w15–20x, and were included instead of the PLS estimate, and the model’s ability to predict the temperature dependency of methane oxidation in the presence of NO was demonstrated in Fig. 1.

were simple to remove, in the last part of the investigation. The separation of active and inactive reactions in the both ROP screening and sensitivity analysis was very distinct, so the risk that relevant reactions were hidden by the assumed activity of nonelementary reactions is considered low. However, the algorithm may be expanded by an iterative step, where the assumed important non-elementary reactions, are removed, before a new ROP screening and sensitivity analysis is made. There is a potential for improving the model estimates by developing a method of characterisation of the reacting species structure. Such a structure must give a unique representation of the reaction. The bond and electron matrix representation of reactions w5,21,22x include the necessary information, but they are designed for an approach, where reactions are formed based on six standard reactions, instead of the present approach where all potential reactions are evaluated. A suitable modification of the bond electron matrix approach may be possible, but this will not be a simple task.

4. Discussion

5. Conclusion

When evaluating the fit of the model, it is important to keep the purpose of the model in mind. In this study, the purpose has not been to estimate values which were to be included in simulations; instead it has been to provide a method for estimation of the importance of a reaction. Furthermore, the inclusion of reactions must be considered as the equivalent of modifying estimates from a rate constant of zero, to a non-zero value. For example, when evaluating the error of the PLS estimates for the reactions listed in Table 6, the alternatives are the value 0, which are included in the original mechanism Žby the absence of the reaction.. Still some estimates Že.g., the fifth reaction. may be so poor that they actually will be worse than the zero estimate, so improvements of the regression model will still be relevant. The characterisation of a reaction through the sum of bonds, lone pairs and unpaired electrons was chosen for simplicity. It has the drawback that the physical structure of a species was not characterised fully. As a consequence, there were some non-elementary reactions among the potential reactions. We do not consider this a major problem, since these reactions

We have analysed the GRI mech. ver. 2.11 and shown the possibility of modelling the rate constants of elementary reactions based on a simplified structure of reactant and product species. Each species’ structure was characterised by a descriptor summing bond types, lone pair electrons and unpaired electrons. The estimation of reaction rate constants was performed from descriptors of reactants and products using a PLS regression model, and the estimated rate constants were used to determine the importance of the potential reactions in the mechanism. An improved prediction quality of the reaction rate model would require a better representation of the reaction structure or a combination with other estimation principles. The evaluation of the reaction mechanism was made under fixed conditions, using ROP screening and sensitivity analysis. ROP screening was computationally efficient in selecting reactions which were to be included in sensitivity analysis. Since GRI mech. 2.11 did not correctly predict oxidation of methane under conditions corresponding to the exhaust manifold of a natural gas engine, these

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conditions were chosen for evaluation of the consistency of the mechanism. Two thousand one hundred thirty eight potential new reactions were added to GRI mech. 2.11, based on the species already included in the mechanism. Sensitivity analysis of these reactions under conditions corresponding to oxidation of methane in engine exhaust, pointed out that nine reactions, which were not included in the original mechanism, was of relevance for these conditions. The inclusion of these nine reactions improved the model predictions significantly. The modified reaction mechanism predicted NO enhanced methane oxidation well. The promising results of this method for analysis of a reaction mechanism suggest that PLS modelling of reaction mechanisms may in the future also be used for other conditions and reaction mechanisms.

Acknowledgements We thank the Danish Ministry of Energy and the CHEC research programme, for financial support. CHEC is co-sponsored by The Danish Ministry of Energy, The Danish Technical Research Council and the two Danish energy consortia Elsam and Elkraft.

w8x

w9x

w10x

w11x

w12x w13x

w14x w15x

w16x

w17x

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