Detailed Kinetic Study of the Partial Oxidation of Methane over La2O3

ENSIC 1, Rue GrandVille, B.P. 20451 F-54001 Nancy Cedex, France. In the first part of this research, a detailed experimental study was conducted for t...
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Ind. Eng. Chem. Res. 2007, 46, 1069-1078

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Detailed Kinetic Study of the Partial Oxidation of Methane over La2O3 Catalyst. Part 2: Mechanism Matthieu Fleys, Yves Simon, and Paul-Marie Marquaire* Nancy-UniVersite´ , CNRSsDe´ partement de Chimie Physique des Re´ actions, ENSIC 1, Rue GrandVille, B.P. 20451 F-54001 Nancy Cedex, France

In the first part of this research, a detailed experimental study was conducted for the partial oxidation of methane (POM) over La2O3. It was shown that the interactions between gas-phase and surface reactions should be considered and that the POM is a homogeneous-heterogeneous reaction. In this second part of the study, a detailed mechanism is proposed that involves 450 elementary homogeneous reaction steps and 33 heterogeneous reactions. From this mechanism, simulations were performed using Chemkin software packages. Computed values are consistent with experimental results over a large range of temperatures (650-850 °C), residence times (0.7-6 s), and catalyst amounts (0.45-3.6 g). 1. Introduction The conversion of methane to syngas (CO + H2) has attracted much attention, because it is considered to be a possible method for a more-efficient use of abundant natural gas reserves. The development of a hydrogen economy based on the partial oxidation or reforming reactions demands a good understanding of the reactions that are involved. Much effort must be devoted to the catalyst formulation and the understanding of its behavior, with respect to the reactions. To do so, one of the requirements is the development of consistent mechanisms that can account for experimental observations under various operating conditions. The partial oxidation of methane (POM) typically operates at temperatures in the range of 700-900 °C. Under these conditions, significant numbers of homogeneous radical reactions can occur spontaneously in the gas phase. This phenomenon must be taken into account, especially for large gas volumes. In the presence of a catalyst, both homogeneous and heterogeneous reactions occur at the same time. It is important to consider the coupling effect for reliable mechanistic developments. Moreover, the prevailing role of the catalyst is to behave as a source of radicals that diffuse toward the gas phase.1-3 Under these conditions, the catalyst becomes the initiator of the homogeneous reactions. For these reasons, an empirical model that neglects the homogeneous reactions and considers only the surface reactions would be inherently incomplete, and it would be limited to a narrow range of operating conditions. Under these conditions, heterogeneous mechanistic studies must be performed by including a consistent homogeneous mechanism. Detailed investigation of the mechanism of the POM is a key step for future technological developments of syngas production. The modeling of reactors is a complex task and requires detailed kinetic modeling to obtain representative and reliable results. The present part of this study involves the simulation of the catalytic POM over lanthanum oxide (La2O3), based on the experimental results obtained in the first part of the study.4 The mechanism can be divided into two sub-mechanisms; one that is related to gas-phase reactions, and another that includes the surface reactions. Only elementary reactions or elementary steps were considered for both sub-mechanisms. The operating * To whom correspondence should be addressed. Tel.: +33 383 175 070. Fax: +33 383 378 120. E-mail address: [email protected].

conditions were those studied in the first part of the study.4 Simulations were performed using Chemkin and Chemkin Surface software packages. 2. The homogeneous mechanism 2.1. The Homogeneous Kinetics Database. The homogeneous mechanism is composed of 450 elementary reactions, whose kinetic parameters mainly come from the literature.5,6 These parameters were not changed to fit the experimental data. The mechanism itself, which is called “C0-C2”, was written in our laboratory.7,8 The C0-C2 reaction base mainly takes into account molecules or radicals that contain less than three carbons. Most of the sensitive and important gas-phase reactions involved in the POM are summarized in Table 1. In this table, 54 out of the 450 reactions are given. In this set of reactions, M designates the collision partner. The general expression for the kinetic constant is

( )

k ) ATn exp -

Ea RT

where A is given in units of (mol, cm-3, s) and Ea is expressed in units of kcal/mol. The role and the relative importance of the reactions in Table 1 may vary with the operating conditions, such as temperature and residence time. As an example, at very low residence times and low conversions, the main initiation reaction is that between methane and oxygen, which leads to the formation of radicals. As the conversion increases, the important consumption reactions are those between methane and radicals. 2.2. Experimental Results in the Absence of Catalyst and Comparison with Gas-Phase Simulations. Experiments without a catalyst were conducted at two temperatures, 810 °C and 875 °C, as a function of the residence time, which was in the range of 0.7-5 s. Simulations of the corresponding data in a perfectly stirred reactor were generated using the PSR-Chemkin software packages and are given in Figure 1. This figure shows that the major products are H2, CO, and CO2, whereas minor amounts of C2H4 and C2H6 were formed. It is noteworthy that C2H2 was not detected under these conditions. The ratio between the amounts of major compounds, with respect to the amount of minor compounds, is ∼10 when τ ) 3 s. Outlet concentra-

10.1021/ie060343r CCC: $37.00 © 2007 American Chemical Society Published on Web 01/18/2007

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Table 1. Most-Important Gas-Phase Reactions Used in the Homogeneous Kinetic Database for Methane Oxidation reaction number

A (mol, cm-3, s)

n

Ea (kcal/mol)

reference

0.0 -0.8 1.6 0.0

14.8 0.0 3.3 -1.6

5 5 5 5

C1 Sub-mechanism without Oxygen 3.6 × 1013 3.0 × 1013 1.7 × 1014 1.3 × 104

0.0 0.0 0.0 3.0

0.0 13.5 0.0 8.0

5 5 5 5

C1 Sub-mechanism with Oxygen 1.3 × 1014 3.0 × 1030 4.0 × 1013 5.1 × 1013 2.0 × 1013 8.4 × 1013 7.2 × 108 4.1 × 1011 6.0 × 1013 1.6 × 107 6.3 × 106 3.4 × 109 1.6 × 1014 1.2 × 1014 7.3 × 103 1.3 × 108 1.8 × 1013 9.0 × 1012 1.5 × 1014 3.0 × 1013 3.0 × 1012 1.5 × 1013 1.8 × 1011 5.0 × 1012

0.0 -4.69 0.0 0.0 0.0 0.0 1.56 0.57 0.0 1.83 1.5 1.18 0.0 0.0 2.85 1.62 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

31.3 36.6 56.7 1.7 38.8 0.0 8.4 2.7 0.0 2.7 -0.5 -0.4 15.7 0.0 22.4 2.1 0.0 24.6 23.6 0.0 13.0 47.0 18.5 -1.4

5 27 5 6 6 5 5 5 5 5 5 5 5 6 6 5 5 5 6 6 45 28 6 29

reaction

1 2 3 4

O2 + H ) OH + O O2 + H (+ M) ) HO2 (+ M) OH + H2 ) H + H2O 2HO2 ) H2O2 + O2

5 6 7 8

2CH3 (+ M) ) C2H6 (+ M) 2CH3 ) C2H5 + H H + CH3 (+ M) ) CH4 (+ M) CH4 + H ) CH3 + H2

C0 Sub-mechanism 9.8 × 1013 6.2 × 1017 1.0 × 108 1.3 × 1011

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

O2 + CH3 ) CH3O + O O2 + CH3 ) HCHO + OH O2 + CH4 ) CH3 + HO2 O2 + CHO ) CO + HO2 O2 + HCHO ) CHO + HO2 O + CH3 ) HCHO + H O + CH4 ) CH3 + OH O + HCHO ) CHO + OH OH + CH3 (+ M) ) CH3OH (+ M) OH + CH4 ) CH3 + H2O OH + CO ) CO2 + H OH + HCHO ) CHO + H2O CHO (+ M) ) H + CO (+ M) CHO + CH3 ) CH4 + CO CHO + CH4 ) HCHO + CH3 HCHO + H ) CHO + H2 HO2+ CH3 ) CH3O + OH HO2 + CH4 ) CH3 + H2O2 HO2 + CO ) CO2 + OH HO2 + CHO ) OH + H + CO2 HO2 + HCHO ) CHO + H2O2 CH3O2 ) HCHO + OH CH3O2 + CH4 ) CH3O2H + CH3 CH3O2 + CH3 ) 2CH3O

33 34 35 36 37 38 39 40

C2H6 (+ M) ) C2H4 + H2 (+ M) C2H6 + H ) C2H5 + H2 C2H6 + CH3 ) C2H5 + CH4 C2H5 (+ M) ) C2H4 + H (+ M) C2H4 (+ M) ) C2H2 + H2 (+ M) C2H4 + H ) C2H3 + H2 C2H4 + CH3 ) CH4 + C2H3 C2H2 + H (+ M) ) C2H3 (+ M)

41 42 43 44 45 46 47 48 49 50 51 52 53 54

O2 + C2H5 ) C2H4 + HO2 O2 + C2H3 ) HCHO + CHO O2 + C2H3 ) C2H2 + HO2 O2 + C2H2 ) 2CHO O + C2H6 ) C2H5 + OH O + C2H4 ) CH3 + CHO O + C2H4 ) HCHO + CH2 O + C2H4 ) CH2CO + H2 O + C2H4 ) CH2CHO + H O + C2H4 ) OH + C2H3 OH + C2H4 ) C2H3 + H2O OH + C2H4 ) CH3 + HCHO OH + C2H6 ) C2H5 + H2O HO2 + C2H6 ) C2H5 + H2O2

C2 Sub-mechanism without Oxygen 2.3 × 1017 1.4 × 109 1.5 × 10-7 8.2 × 1013 1.0 × 1017 5.1 × 107 6.3 × 1011 8.4 × 1012

0.0 1.5 6.0 0.0 0.0 1.93 0.0 0.0

67.4 7.4 5.8 40.0 71.6 12.9 16 2.61

30 5 5 5 5 31 32 5

C2 Sub-mechanism with Oxygen 8.4 × 1011 3.0 × 1012 1.2 × 1011 7.0 × 108 1.0 × 109 8.1 × 106 4.0 × 105 6.6 × 105 4.7 × 106 1.5 × 107 2.0 × 1013 2.0 × 1012 7.2 × 106 1.3 × 1013

0.0 0.0 0.0 1.8 1.5 1.88 1.88 1.88 1.88 1.91 0.0 0.0 2.0 0.0

3.9 -0.3 0.0 30.6 5.8 0.2 0.2 0.2 0.2 3.7 5.9 0.9 0.9 20.4

6 27 6 33 5 5 5 5 5 34 5 35 5 5

tions of the products increased with temperature and residence time, except for C2H6, which can decompose to C2H4 or react with oxygen to form oxygenated compounds, such as formaldehyde or the formyl radical. Comparison between the experiments and the simulations clearly shows that there is a good agreement. This homogeneous component of the kinetic scheme will be associated with the catalytic heterogeneous mechanism in the following sections.

3. The Heterogeneous Mechanism 3.1. Estimation of the Kinetic Parameters. The heterogeneous mechanism is a set of 33 elementary reactions and is given in Table 2. The activation energies were chosen to be equal to analogous gas-phase reactions that have been found in the literature. For instance, the activation energy of reaction 3a in Table 2, CH4 + O(s) f CH3 + OH(s), was chosen equal to the activation energy of the following homogeneous reaction:

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Figure 1. Comparison between experiments (symbols) and simulations (solid lines) at 810 and 875 °C, as a function of the residence time without a catalyst: (a) H2 molar fraction, (b) CO molar fraction, (c) CO2 molar fraction, (d) C2H4 molar fraction, (e) C2H6 molar fraction, and (f) XCH4-methane conversion.

CH4 + CH3O• f CH3• + CH3OH that is, Ea ) 8.84 kcal/mol. The pre-exponential factors were calculated by methods derived from Benson’s techniques.9 They were estimated using partition functions of reactants and transition state. The general reaction between gaseous species A and surface species B(s) can be written as

q* AB qB(s)

≈ q* ABv

so that

( )

* kBT NqABv A) h qA

A + B(s) f AB* f products The pre-exponential factor is given by the equation

A)

( )

kBT Nq* AB h qAqB(s)

where qA, qB(s), and q* B are the partition functions of A, B, and the activated complex AB*. The partition functions of gas-phase molecules, such as species A, are calculated using equations described in the following example. On the other hand, the determination of the partition function of absorbed species [B(s), AB*(s)] requires some assumptions. Therefore, we suppose that the difference between the partition functions of these two species is only due to the vibrational contribution qv

Hence, a vibrational analysis of adsorbed species has been conducted to estimate the vibrational partition function qv. The frequency values used are those given by Benson.9 As an example, the calculation of the pre-exponential factor of the heterogeneous reaction C2H4 + O(s) f C2H3• + OH(s) is explained in the following discussion. The C2H4 partition function, qC2H4, can be calculated according to

qC2H4 ) qCt 2H4qCr 2H4qCe 2H4qCv 2H4 where the translational component (qt), the rotational component (qr), the electronic component (qe), and the vibrational

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Table 2. Set of Heterogeneous Reactions for the Partial Oxidation of Methane reaction number

surface reactions

A (mol, cm-3, s)

Ea (kcal/mol)

1a -1a 2a -2a 3a 4a 5a 6a 7a 8a 9a 10a 11a 12a 13a 14a 15a 16a 17a 18a 19a 20a 21a -21a 22a 23a 24a 25a 26a 27a 28a 29a 30a

O2 + s f O2(s) O2(s) f O2 + s O2(s) + s f 2O(s) 2O(s) f O2(s) + s CH4 + O(s) f CH3 + OH(s) CH4 + s f CH3 + H(s) C2H6 + O(s) f C2H5 + OH(s) C2H6 + s f H(s) + C2H5 C2H4 + O(s) f C2H3 + OH(s) C2H4 + s f H(s) + C2H3 C2H5 + O(s) f C2H4 +OH(s) C3H7 + O(s) f C3H6 + OH(s) CH3 + O(s) f CH2 + OH(s) CH2 + O(s) f CH + OH(s) CH + O(s) f C + OH(s) CH3 + O(s) f CH3O(s) CH3O(s) + O(s) f HCHO + OH(s) + s HCHO + O(s) f CHO + OH(s) CHO + O(s) f CO + OH(s) C2H5 + O(s) f C2H5O(s) C2H5O(s) + O(s) f CH3CHO + OH(s) + s CO + O(s) f CO2 + (s) CO2 + (s) f CO2(s) CO2(s) f CO2 + (s) C + O(s) f CO(s) C+O(s) f CO + s CO(s) + O(s) f CO2(s) + s H + s f H(s) H(s) + H(s) f H2 + 2s OH(s) + H(s) f H2O + 2s OH(s) + OH(s) f H2O + O(s) + s H2 + s f 2H(s) H2 + O(s) f OH(s) + H

3.0 × 106 2.3 × 1013 5.3 × 1023z 1.3 × 1023z 3.0 × 108 9.49 × 107 2.0 × 109 8.5 × 106 2.5 × 109 6.0 × 106 5.5 × 107 6.1 × 107 1.9 × 109 3.6 × 1011 8.9 × 108 9.9 × 108 1.2 × 1023z 3.4 × 107 6.9 × 107 1.0 × 109 6.6 × 1021z 8.31 × 108 6.2 × 108 2.3 × 1013 1.1 × 1011 1.1 × 1011 1.1 × 1023z 2.3 × 1013 4.0 × 1023z 1.0 × 1022z 3.0 × 1023z 6.1 × 1016 1.0 × 109

1.5 45.0 25.0 33.0 8.84 9.85 0.0 0.0 0.0 0.0 0.0 0.0 2.8 11.9 4.7 0.6 0.0 3.0 0.0 0.6 0.0 0.0 0.0 43.58 0.0 0.0 0.0 0.0 0.0 0.0 2.4 0.0 0.0

component (qv) are estimated using the following equations:

qt )

(2πmkBT)3/2 h3

( )

2 π1/2 8π kBT qr ) σext h2

3/2

R1/2

qe ) 2s + 1 qv )

∏i qv,i

(ω ) 1650 cm-1), one CdC torsion (ω ) 1000 cm-1), three C-H stretches (ω ) 3100 cm-1), one H‚‚‚C-H bend (ω ) 1000 cm-1), one H-C-H bend (ω ) 1450 cm-1), three H-Cd C bends (ω ) 1150 cm-1), one H‚‚‚CdC bend (ω ) 800 cm-1), two out-of-plane vibrations (ω ) 700 cm-1), one C‚‚‚H stretch (reaction coordinate), one O‚‚‚H stretch (reaction coordinate), two C‚‚‚H‚‚‚O bends (nontabulated), and one internal rotation of the C2H3- group. The partition function of the internal rotation is calculated using the equation

qint.rot )

where

qv,i )

1 1 - exp[-1.44(ωi/T)]

Knowledge of the vibrational frequencies, ωi (expressed in units of cm-1), is required to calculate qv. The number of vibrational degrees of freedom for a nonlinear molecule is 3n - 6, where n represents the number of atoms in the molecule considered. In the case of C2H4, we have n ) 6; therefore, 3n - 6 ) 12 vibrations. These vibrations include one CdC bond stretching (ω ) 1650 cm-1), one CdC bond torsion (ω ) 1000 cm-1), four C-H bond stretchings (ω ) 3100 cm-1), two bending vibrations of the H-C-H angle (ω ) 1450 cm-1), and four bending vibrations of the H-CdC angle (ω ) 1150 cm-1). The frequencies of these vibrations have been tabulated by Benson.9 From these values, we determined that qCv 2H4 ) 6.36 and qC2H4 ) 3 × 1031 cm-3 at 1100 K. Similarly, there are 18 vibrational degrees of freedom for the activated complex, and the vibrations include one CdC stretch

T 3.6 I σint red 100

1/2

[ ( )]

where σint is the internal symmetry number (σint ) 1) and Ired is the reduced moment of inertia for the considered rotation. Benson’s table gives this moment of inertia for the rotation of a C2H5 group, with respect to an infinite mass: Ired ) 17 amu A2. Finally, we determined the following values: qint.rot ) 49, qv ) 25, and q* v ) qint.rot × qv ) 1215. Now, we can determine the pre-exponential factor:

A)

kBT q* v ) 5.5 × 108 cm3 mol-1 s-1 h qC2H4

(at 1100 K)

We have not taken into account the nontabulated vibration (C‚‚‚H‚‚‚O)bend. As a consequence, the pre-exponential factor A is probably slightly higher than this estimation. Another example is the reaction that involves two surface reactants, such as

H(s) + H(s) f H2 + 2s

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The pre-exponential factor A is given by the expression

A)

( )

kBT q* h q2H

where q* and q2H are the partition functions for the transition state and the double site H, respectively. In this case, there are not many vibrational degrees of freedom, and there are no internal rotations, so we can consider the partition functions of the reactant and the activated complex to be approximatively the same. Therefore, the Arrhenius factor can be written as

A)

kBT ) 2 × 1013 s-1 h

The rate becomes

( )

r ) A exp -

Ea [H(s)-H(s)] RT

where [H(s)-H(s)] is the double sites concentration. The Chemkin Surface formalism uses the following expression:

( )

r ) A′ exp -

Ea [H(s)]2 RT

where

A′ (mol, cm3, s) ) A

(2Lz ) ) 1.3 × 10

23

z

In this expression, z represents the number of nearest-neighbor sites and L stands for the concentration of sites over the surface of the catalyst (L ) 9 10-11 mol.cm-2). This explains the typically high values of the rate constants for reactions that involve two adsorbed species. Because of the fact that a precise value of z could not be found in the literature, the value of z was chosen to be equal to 1 in our simulations. It is noteworthy that the calculated values of the preexponential factors give only an estimation of the theoretical values. For some heterogeneous reactions, the pre-exponential factors were changed to fit the experimental data. In this case, the preexponential factor (calculated by the Benson’s techniques, see section 3.1) was multiplied or divided by a factor inferior to 10 which is in the order of magnitude of the estimation accuracy. Table 3 summarizes the modified preexponential factors. In this table, A(fitted) refers to the modified values and A(calc) refers to the calculated values from Benson’s techniques.9 In regard to the heterogeneous reactions that do not appear in Table 3, no fitting was done. Moreover, the activation energies were not changed to fit the experimental data. Hence, in the heterogeneous-homogeneous kinetic model, only some of the preexponential factors of the heterogeneous reactions were changed to fit the experimental data. 3.2. Development of the Heterogeneous Mechanism. The exact nature of the active sites on the lanthanum oxide catalyst remains unclear. Different studies suggested that O2- ions may be the active sites or the precursor of the active oxygen species for methane activation.10 Hutchings et al.11,12 suggested that Ois the oxidizing species that is responsible for CH3· production and that O22- could lead to the formation of CH2: radicals. Lacombe et al.13 identified various active sites; the basic sites are associated with oxygen vacancies, which would be respon-

sible for dissociating gaseous oxygen into atomic species that are able to activate methane molecules, and the localized lowcoordinate atoms on which methyl radicals would react to be further oxidized to CO2. The main conclusion of these different authors is that there should be at least two different active species or two different active sites on the catalyst surface, with respect to the POM reaction. In the proposed heterogeneous mechanism, two different sites were considered: these are denoted “s” and “O(s)”. The first abbreviation refers to an undefined site, whereas the second abbreviation represents an oxygenated site. The oxygenated sites are produced by decomposition of the reactant oxygen on an active site s, as illustrated by reactions 2a and -2a:

O2(s) + s f 2O(s)

(2a)

2O(s) f O2(s) + s

(-2a)

In this mechanism, an O2 molecule dissociates into two active adsorbed oxygens, in agreement with previous experimental studies of oxygen chemisorption.14 The interaction between gaseous oxygen and lattice atoms, which involves the formation of active surface species that are able to activate C-H bonds, is believed to be fast.15 Overall, the mechanism is written by considering possible reactions between the main products, or main radicals, with the different sites, s and O(s). For example, methane activation can follow two reactions: 3a or 4a.

CH4 + O(s) f CH3• + OH(s)

(3a)

CH4 + s f CH3• + H(s)

(4a)

Both reactions produce CH3‚ radicals in the gas phase and adsorbed H(s) or OH(s) species. Similarly, C2H6 and C2H4 can react with both sites to produce not only C2H5‚ and C2H3‚ radicals, respectively, but also adsorbed hydrogenated and oxygenated compounds. The reaction of CH4 with an active site(s) and an oxygenated site, O(s), was already taken into account successfully by Toops et al.16 This is a key point in the mechanism development, because it provides two different adsorbed species, H(s) and OH(s), which can further react according to reactions 26a, 27a, and 28a, which leads to the formation of hydrogen and water via surface steps: 26a

H(s) + H(s) 98 H2 + 2s 27a

OH(s) + H(s) 98 H2O + 2s 28a

OH(s) + OH(s) 98 H2O + O(s) + s

(26a) (27a) (28a)

Several simplistic kinetic mechanisms were previously proposed in the literature.17,18 Xu et al.18 proposed a LangmuirHinshelwood mechanism, where O2 and CH4 were first adsorbed on the catalyst surface. This was followed by the surface reaction of the two reactants, which led to the formation of CH3· and HO2·. This mechanism may be valid at very low conversions, but it cannot account for observations made over a wide range of experimental parameters. De Groote et al.19 used a different approach to simulate the POM reaction. The kinetic modeling was composed of eight global equilibrium reactions, such as combustion or reforming reactions, and the corresponding rate expressions were derived from previous empirical works. This mechanism was combined to a one-dimensional plug flow reactor model. In our work, we focused on elementary reactions, which may happen in the gas phase or on the catalyst surface,

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Figure 2. Comparison between experiments (symbols) and simulations (solid lines) at 700 and 850 °C, as a function of the residence time with one catalyst pellet: (a) H2 molar fraction, (b) CO molar fraction, (c) CO2 molar fraction, (d) C2H4 molar fraction, (e) C2H6 molar fraction, and (f) XCH4-methane conversion. Table 3. Comparison between the Calculated Values of the Pre-exponential Factors from the Benson’s Techniques and the Fitted Values for Some of the Heterogeneous Reactions reaction number

heterogeneous reaction

A(fitted)

A(calc)

A(fitted)/A(calc)

1a 2a 3a 5a 7a 20a 26a 28a 30a

O2 + s f O2(s) O2(s) + s f 2O(s) CH4 + O(s) f CH3 + OH(s) C2H6 + O(s) f C2H5 + OH(s) C2H4 + O(s) f C2H3 + OH(s) CO + O(s) f CO2 + (s) H(s) + H(s) f H2 + 2s OH(s) + OH(s) f H2O + O(s) + s H2 + O(s) f OH(s) + H

3.00 × 106 5.30 × 1023 3.00 × 108 2.00 × 109 2.50 × 109 8.31 × 108 4.00 × 1023 3.00 × 1023 1.00 × 109

1.80 × 107 1.30 × 1023 7.50 × 108 9.50 × 109 5.5 × 108 4.70 × 109 1.30 × 1023 1.30 × 1023 1.00 × 1010

0.17 4.1 0.4 0.2 4.5 0.18 3.1 2.3 0.1

and we assumed that the reactor behavior was almost ideal. This approach is similar to that adopted by various authors.1,20-22 4. Results and Discussion 4.1. Comparison between Experiments and Simulations. In the following sections, the homogeneous and heterogeneous mechanism components were combined to perform the simulations. Figure 2 shows the outlet experimental and simulated concentrations of the main products and the methane conversion at 700 and 850 °C, as a function of residence time, using one catalyst pellet. The agreement between experimental data (symbols) and simulated compositions (solid lines) is satisfactory. Before validating the mechanism, we performed additional experiments using different amounts of catalyst. Figure 3 shows the results obtained at 750 °C and τ ) 3 s, as a function of the number of catalyst pellets (within the range of 1-8). Again,

the simulations based on the complete mechanism reproduce the experimental data satisfactorily. Hence, the mechanism is consistent with experimental observations made over a wide range of experimental parameters: that is, temperature, residence time, and catalyst amount. 4.2. Mechanistic Details about the Interactions between Homogeneous and Heterogeneous Reactions. As was done previously, a flow analysis was performed at 850 °C and τ ) 3 s, XCH4 ) 16%, and XO2 ) 45% with four catalyst pellets. The main reacting steps are given in Figure 4, and the importance of the corresponding steps is proportional to the arrow thickness. The numerical values in Figure 4 are given in percentages. The values should be read according to the following example: 30%

A 98 B

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phase with molecular oxygen, collision partners, or other radicals such as the HO2· radicals. As previously reported, lanthanum oxide favors the products of total oxidation; therefore, it is not surprising that both H2O and CO2 come from heterogeneous reactions. The formation of carbon monoxide follows the sequence

CH3· f HCHO f HCO f CO It is interesting to note that the formation of HCHO can be direct or can proceed by involving the CH3O· radical. In this case, the decomposition of CH3O· to HCHO is complete. The key point is that the formation of the CH3O· radicals requires the presence of the hydroperoxyl HO2· radicals. The HO2· radicals can be formed by reactions with compounds in the oxidative route or by reaction with the C2H5· radical and oxygen. Furthermore, it is clear that the oxidative route is autoaccelerated, because the formation of HCHO and CHO· compounds, and their degradation, are accompanied by the formation of HO2· radicals. Hence, C2 selectivity is expected to be better at low conversions, which is consistent with our simulations performed under these conditions. In addition, the fact that C2H3· and C2H2 can react with O2 to produce the oxidative compounds HCHO and CHO· is a second argument for the low C2 selectivity at higher conversions. It is also noteworthy that, in the absence of catalyst, our simulations predict that the following reaction occurs:

CH4 + H‚ f CH3‚ + H2 In this reaction, methane is consumed to produce a methyl radical and hydrogen in the gas phase. However, we observed, from our simulations, that, in the presence of a catalyst, the indirect pathway is favored: Figure 3. Comparison between experiments (symbols) and simulations (solid lines) at 750 °C and τ ) 3 s, as a function of catalyst loading: (a) molar fractions of H2, CO, and CO2; (b) molar fractions of C2H6 and C2H4; and (c) conversion of XCH4 and XO2.

means that 30% of species A is consumed to give species B. This figure clearly shows that homogeneous and heterogeneous reactions are interdependent, and that they occur simultaneously. Hutchings et al.11,12 suggested that C2H4 could be formed from C2H6 via two ways: an oxidative route and a non-oxidative route, depending on the operating conditions and the catalyst. This is consistent with our work, where the oxidative pathway becomes the main route in the presence of catalyst. Moreover, the catalyst has the ability to form radicals efficiently. Indeed, from Figure 4, >75% of the C2H6 degradation into C2H5· radicals is performed on the catalyst surface, and the C2H4 is totally converted to C2H3· radicals via heterogeneous steps that involve both sites (s) and O(s). It was reported that lanthanum oxide is able to generate methyl radicals efficiently.1-3 We also observed that methane activation, and its reaction into CH3· radicals, was performed mainly on the catalyst surface (∼80% under these conditions). To a larger extent, lanthanum oxide seems to be an excellent free radical generator, and the most important heterogeneous steps are as follows: Cat

CH4 98 CH3‚ Cat

C2H6 98 C2H5‚ Cat

C2H4 98 C2H3‚ The radicals produced via heterogeneous steps react in the gas

CH3‚ + H2 f CH4 + H‚ In this case, hydrogen, which is produced via heterogeneous steps, reacts with methyl radicals to give back methane (see Figure 4). This reaction becomes increasingly important at higher conversions, when XCH4 > 15%. This loop has two major effects. First, it limits methane conversion, and as was discussed in the first part,4 we observed that methane conversion is much lower than oxygen conversion in the presence of this catalyst. Second, the formation of H2 is necessarily limited, as well as its yield and selectivity, because the produced hydrogen becomes a reactant. This fact was also observed in the experimental section. The fact that the indirect pathway is favored in the presence of the catalyst is probably due to the high concentration of methyl radicals generated at the surface of the catalyst. As a consequence, it appears that the following reaction behaves as a buffer reaction:

CH4 + H‚ / CH3‚ + H2 This type of reaction was extensively investigated by Weissman et al.23 Hence, the proposed mechanism supports all the major experimental findings in qualitative and quantitative ways. Moreover, our main conclusions are consistent with the suggestions made by Nelson et al.24 related to the C2 oxidation over a Li/MgO catalyst. Using carbon,13 the authors suggested that ethylene is mainly produced by further reactions of ethane and that CO oxidation is the main source of the CO2. Hu et al.25 also suggested, by means of transient kinetic studies, that CO2 is subsequently generated from CO. Nelson et al.24 also

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Figure 4. Flux rate analysis of the main heterogeneous-homogeneous reaction paths at 850 °C, τ ) 3 s, XCH4 ) 16%, XO2 ) 45%, with four catalyst pellets.

suggested that the C2 oxidation is an important source of carbon oxides for temperatures of >740 °C. Shi et al.26 showed that the transformation of the C2 hydrocarbons into COx was important at higher temperatures and for specific catalysts such as Ba/MgO or Sr/La2O3. They estimated that the percentage of COx from the C2 product was ∼16% at 700 °C and reached ∼41% at 800 °C over a Sr/La2O3 catalyst. Our results agree with these findings. According to our mechanism, the transformation of the C2 product to COx proceeds via two main steps: the first step is the heterogeneous transformation of the C2 hydrocarbons into the corresponding C2 radicals, and the second step is the homogeneous oxidation of the C2 radicals leading to the formation of oxidized species. 4.3. Sensitivity Analysis. To determine the most-sensitive reactions involved in the heterogeneous-homogeneous mechanism, a sensitivity analysis was performed at 850 °C, τ ) 3 s, and a loading of catalyst pellets. The analysis was performed for the minor and major products, and the results are shown in Figure 5. The numbers indicated at the immediate proximity of the diagram boxes refer to the reaction numbers in Tables 1 and 2. The first-order sensitivity coefficient for species n and reaction i is defined according to

Si,n )

ki dxn dki xn

where ki is the kinetic constant of reaction i and xn is the molar fraction of species n. Hence, the larger the sensitivity coefficient, the more sensitive the reaction. Moreover, a positive sensitivity coefficient Si,n means that an increase of the kinetic constant ki leads to an increase of the concentration of species n. When the sensitivity coefficient is