Znd. Eng. Chem. Res. 1991,30, 2114-2123
2114
Microkinetic Analysis of Methane Dimerization Reaction Luis M. Aparicio,' Stefan0 A. Rossini,' Domenico G. Sanfilippo,* James E. Rekoske,i And& A. Treviiio,f and James A. Dumesic**i Shanahan Valley Associates, Madison, Wisconsin 53719, Snamprogetti, S.p. A., 20097 San Donato Milanese, Italy, and Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706
Microkinetic analysis of experimental kinetic data on methane dimerization at low conversions over alkali-metal-promoted alkaline earth oxide cataly~tareinforces mechanistic ideas proposed previously in the literature and suggests new conclusions. Active sites for this reaction appear to be produced via two elementary steps. In the first step, surface peroxide species are formed by adsorption of gaseous dioxygen, and in the second step methane-activating sites are produced via 0-0 bond cleavage. Gas-phase C2 combustion alone cannot account for the observed C2yield limit, and surface-catalyzed C2combustion is suggested to play an important role in determining selectivity.
Introduction In view of diminishing liquid petroleum resources and extensive natural gas reserves worldwide, the functionalization of methane is a problem of current industrial interest. One potential route to methane activation that eliminates the costly formation of synthesis gas is oxidative dimerization to produce dicarbon species over metal oxide catalysts at elevated temperatures. In recent years, this reaction has been studied extensively at a basic research level, providing valuable spectroscopic and reaction kinetics data. In this paper, we demonstrate that quantitative microkinetic analysis of existing data reinforces mechanistic ideas proposed previously in the literature and provides important new information about the essential surface chemistry involved. Microkinetic analysis of catalytic processes has been shown in a variety of cases to be an effective approach for the interpretation and generalization of kinetic data (e.g., Dumesic et al., 1987;Dumesic and Trevifio, 1989;Goddard et al., 1989;Amiridis et al., 1991;Stoltze and Norskov, 1988;Oh et al., 1986;Fisher et al., 1987). The strategy of this method is to analyze the existing knowledge about the reaction in terms of fundamental chemical steps and their individual rates. In the course of the analysis, those characteristicsof the reaction mechanism that are essential to the explanation of the existing data are identified. The result is a working microkinetic model that can provide new information about the reaction and be used as a guide for further experiments. An important role of the microkinetic model for this purpose is to quantify the surface chemistry and to predict how changes in surface chemistry may be reflected in changes in catalyst performance (Rudd and Dumesic, 1991). In the present paper, the above approach is applied to experimental kinetic data obtained at low conversions for methane dimerization over alkali-metal-promotedalkaline earth oxides. Particular emphasis is placed on the studies by Lunsford et al. of methane dimerization over Li-promoted MgO catalysts (Ito et al., 1985). Initial analysis involves identifying those chemical steps that are necessary to explain in a quantitative fashion the observed macroscopic behavior of these catalysts. We then develop a simple model that describes the overall consumption of methane. Next, we next extend the analysis to formulate a more complete microkinetic model that describes the observed selectivitiesof the various productrr. Finally, this
* Author to whom correspondence should be addressed. Shanahan Valley Associates.
* University Snamprogetti, S.p. A. of Wisconsin.
more complete microkinetic model is used to address the factors that control selectivities. Analysis Interaction of Gaseous Methane with the Surface. There is strong evidence in the literature that the cleavage of the methane C-H bond proceeds irreversibly under typical methane dimerization conditions, i.e., temperatures of 800-1050 K and CH4/02 ratios in the feed of 2-10. This evidence comes from various isotopic labeling experiments, in which no substantial CH4-CD4scrambling was detected over Li/MgO and Li/NiO catalysts under dimerization conditions (Otsuka et al., 1989; Mims et al., 1989;Nelson et al., 1988). Since the cleavage of the methane C-H bond presumably occurs during the interaction of methane with the surface, it is instructive to apply microkinetic analysis to this process. If one assumes that the only consumption route for methane is through its interaction with the surface, then the rate of this process in the forward direction, RMa, must be greater than or equal to the overall rate of methane consumption, Rov (RMa would be equal to Roy if the initial methane-surface interaction were irreversible and higher if it were reversible). First, let us consider a one-step, non-precursor-state mechanism for the interaction of methane with the surface. In this m e , the rate of the proceas in the forward direction can be expressed as the product of three quantities: the rate RCoLat which methane molecules collide with the surface, a steric factor Ps that accounts for portions of the surface not being active for dissociation,and an activation energy term for the step. The resulting expression is
where EA is the activation energy of the elementary step, R is the gas constant, and Tis the absolute temperature. Since the steric factor must be less than or equal to 1, the above expression can be rearranged as follows:
Lunsford and ceworkera have reported that a 7% Li/MgO catalyst could achieve an overall methane consumption rate, Rev, of ca. lo-' mol m-2 s-l at 894 K with 40 kPa of CH,and 8 kPa of O2in the feed (It0 et al., 1985). Collision theory provides an estimate of 1 X 109 mol m-2 s-l for RCOL at these conditions. Substitution of these values into eq 2 indicates that the activation energy of the methanesurface interaction step must be less than or equal to 171 k J mol-'. In contrast, the apparent activation energy of
0888-5885/91/2630-2114$02.50/00 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 9, 1991 2116 the overall reaction was measured to be 218 kJ mol-’ from 830 to 930 K (Ito et al., 1985). Similar calculations can be made for related catalysts with essentially identical results. Since the above analysis assumed a one-step surface interaction not involving a precursor adsorption state, it is instructive to discuse the importance of this assumption. The interaction can also be assumed to consist of an equilibrated molecular precursor adsorption step for methane followed by a C-H bond cleavage step: CHI + * CH4(adsorbed) CH4(adsorbed) products If we further assume Langmuirian adsorption kinetics, we can obtain an expression for the forward rate of the methane-surface interaction, RM-s: RM-S = kdsa*CHle* (3) where kdb is the rate constant of the C-H bond dissociation, Kadris the equilibrium constant of the precursor adsorption, PCH4is the pressure of methane, and 8, is the fractional coverage of methane adsorption sites. From a kinetic point of view, the process occurs as if it consisted of one step with a rate constant equal to the product of kdis and KadaThe equilibrium constant for adsorption of the precuIsor state, Kab, can be expressed as
- -
(4)
where A,& and Ad- are the preexponential factors for adsorption and desorption, respectively, and AHab is the heat of adsorption of the precursor state. The rate constant for the C-H bond cleavage step, k&, can be expressed as (5)
where A& is the preexponential fador for the step and E& is its activation energy. Adis and Ad-, both being preexponential factors for unimolecular surface reactions involving the same species (adsorbed methane), would be expected to be roughly equal. Thus,eq 3 can be rearranged as follows:
The activation energy for the methane-surface interaction in this case would therefore be E& + AH* Because Aab is the preexponential factor of a step involving a collision between methane and the surface, RM-s can also be expressed as
This expression is equivalent to eq 1. If the elementary step (or steps) in which methane dissociates by reaction with the surface proceeds irreversibly but has a lower activation energy than the overall reaction, it follows from this analysis that the surface concentration of sites active for methane activation increases with temperature. This result is independent of the choice of either a one-step dissociation or a precursor adsorption model for the initial interaction of methane with the surface. Thus,microkinetic analysis suggests that the temperature dependence of the concentration of sites active for methane dissociation makes a substantial con-
tribution to the activation energy of the overall reaction. In summary, microkinetic analysis shows the methane C-H bond cleavage has an activation energy lower than the overall reaction. The corollary is that the concentration of methane-activating sites increases with temperature. Interaction of Gaseous Oxygen with the Surface. The maximum activation energy for the chemical step in which gaseous dioxygen interacts with the surface can be estimated by the method outlined above to be ca. 152 kJ/mol, again significantly lower than the activation energy of the overall reaction. This result is essentially identical whether obtained by a direct dissociation model or a precursor, molecular adsorption state model. Because it is difficult to imagine how the sites with which gaseous dioxygen interacts can be significantly temperature dependent, the microkinetic analysis implies that this elementary step is reversible and cannot act as a rate-determining step under typical dimerization conditions. In this case, microkinetic analysis reinforces a conclusion reported previously in the literature. Isotopic labeling studies have shown that ‘602-1802scrambling over Li/MgO occurs at a faster rate than the methane dimerization reaction (Cant et al., 1990),and dioxygen adsorption must, therefore, be reversible during reaction. The same conclusion can also be reached from the results of transient kinetics experiments. For example, Labinger and Ott carried out experiments of the reaction of methane with a NaMn04/Mg0 catalyst that had been pretreated with oxygen from air (Labinger and Ott, 1987). Although in this case the chemical step in which gaseous dioxygen interads with the surface was absent during the measurement of reaction rates, the measured activation energy, 243 kJ/mol, was still close to the value measured under steady-state co-feed conditions over Li/MgO. If the adsorption of gaseous dioxygen were rate-determining under the steady-state conditions, different activation energies would be expected for the two experiments. Microkinetic analysis of the interaction of oxygen with the catalyst surface reinforces previously reached conclusions. Specifically, microkinetic analysis and previous experiments agree that the adsorption of oxygen proceeds reversibly and is, therefore, not the rate-limiting step in the dimerization of methane. Methane-Activating Surface Species. Several research groups have observed that the methane reaction order approaches zero and the oxygen reaction order remains relatively high as the CH4/02ratio is increased to values greater than ca. 6 (e.g., Ito et al., 1985; Wada et al., 1989;Kooh et al., 1989). It was concluded in the previous section that the individual chemical step through which gaseous dioxygen adsorbs on the surface is reversible under reaction conditions. However, these steady-state kinetics results suggest the process through which gaseous dioxygen interacts with the catalyst to generate methane-activating sites controls the overall rate of reaction at high CH4/O2 ratios. Thus, the adsorption of oxygen must remain reversible while the formation of methane-activating sites must become rate determining at these conditions. Microkinetic analysis can interpret the high experimental reaction order for oxygen and the near zero kinetic order of methane at high CH4/02ratios by a model in which the adsorption of gaseous dioxygen on the catalyst surface and the formation of the methane-activating site are two separate elementary steps. The adsorption of oxygen remains reversible over the entire range of experimental conditions. A subsequent step in which adsorbed dioxygen is transformed into a species that is responsible for the dissociation of the C-H bond in methane becomes
2116 Ind. Eng. Chem. Res., Vol. 30, No. 9, 1991
-16.5 I 0
I
I
1
1
1
2
3
4
5
In (Po?/ 1 kPa)
Figure 1. Log-log plot of overall methane conversion rate versus oxygen pressure. Catalyst: Li/MgO. Catalyst weight 1 g. Total flow rate at STP: 0.83 cm3 Temperature: 893 K. Methane pressure: 40 kPa Total reactor pressure including inert: 101.3 kPa. Data from It0 et al. (1985).
irreversible and rate limiting at high CH4/02 ratios, making the overall reaction close to zero order in methane. By analyzing experimental oxygen reaction orders, one can obtain insight regarding the nature of the methaneactivating surface species and its precursor, presumably the species formed when gaseous dioxygen first adsorbs on the surface. For example, a logarithmic plot of the overall methane consumption rate over Li/MgO versus the O2pressure, at constant CHI pressure, is shown in Figure 1. This plot was generated from literature data collected over Li/MgO (Ito et al., 1985). It can be seen that the overall rate is proportional to the O2 pressure to the power at low CH,/02 ratios, while at high ratios the overall rate is proportional to the O2 pressure to the 1/2 power. If one assumes that the chemical steps that convert the active site precursor into the active site involve one precursor species, and that the methane activation step involves one active site, then this result implies the following: (a) The concentration of the active site precursor is proportional to the O2 pressure to the power. (b) The concentration of active sites, when at equilibrium, is proportional to the O2 pressure to the 1/4 power. This behavior can be explained by assuming that the active site precursor is a surface peroxide produced by the adsorption of gaseous dioxygen: 02 + 2M-0-M 2M-0-0-M step 1: Furthermore, the methane-activating site is generated by the cleavage of the 0-0 bond in the surface peroxide: step 2: M-0-0-M 2M-0' The final necessary assumption is that the concentration of M U M on the surface exceeds those of M W M and M-O' (i.e., M U M is the most abundant surface species). At low CH4/02ratios, steps 1and 2 are both in equilibrium while at high CH4/02 ratios step 1 is in equilibrium and step 2 is rate-determining. Again we see that microkinetic analysis reinforces previous literature suggestions linking surface dioxygen species to catalytic activity. For example, Otsuka and Jinno have, on the basis of kinetic results, suggested that dioxygen species are involved in the activation of methane over samarium oxide catalysts (Otsuka and Jinno, 1986; Otsuka et al., 1987). Lunsford and co-workershave detected 02centers on La203 catalysts and shown these centers to be active for the production of methyl radicals (Lin et al., 1986;Wang and Lunsford, 1986). Also, catalytic activity has been observed over BaPb03, a material shown to possess 022species as determined by XPS (Kharas and Lunsford, 1989; Lunsford, 1990). The analysis also reinforces previous proposals linking the methane-activating
-
.+
site to 0-speciesobserved in EPR spectra (Ito et al., 1985). The species formed when a surface peroxide undergoes an 0-0bond cleavage would have an unpaired electron on an oxygen atom and could, therefore, correspond to the 0-species. Most importantly, microkinetic analysis has suggested two specific elementary steps involving previously proposed species that describe the steady-state and transient kinetics results as well as the isotopic labeling experiments. In this manner, microkinetic analysis provides important information about the surface chemistry involved in the catalytic reaction mechanism and links experimental results from different typea of measurements. It is instructive to examine the possibility that step 2 is responsible for the observed overall activation energy. We may expect that the cleavage of an 0-0bond contributes to the overall activation energy since this is expected to be an endothermic process. However, since the bond clgvage produces two active sites, the activation energy of this reaction would be twice the activation energy of the overall reaction (ca. 435 kJ mol-') for this reaction to be solely responsible for the observed activation energy. This hi& activation energy requires an unreasonable high preexponential factor for this reaction to explain the observed rate of methane consumption. Thus, we conclude that the activation energy of reaction is shared between two or more elementary steps. Since the dissociation of the C-H bond in methane proceeds irreversibly under reaction conditions, this reaction is likely to contribute to the apparent activation for methane consumption as well. In this section, microkinetic analysis has consolidated the requirement for a temperature-dependent active-site concentration for the dissociation of methane with observed steady-state and transient kinetic information as well as isotopic studies of oxygen adsorption and reaction under dimerization conditions. Methane-activating sites are suggested to be produced from gaseous dioxygen through a two-step process. In the first step, gaseous dioxygen is adsorbed on the surface as a peroxide, and in a subsequent step the surface peroxide undergoes an 0-0 cleavage to produce 0-species which can activate methane. The high endothermicity of the second step is suggested by the microkinetic analysis to contribute to the high apparent activation energy for methane consumption. Simple Model for Overall Methane Consumption The microkinetic analysis outlined above permits the construction of a simple model that explains in a satisfactory manner the overall experimental methane consumption as a function of temperature, oxygen pressure, and methane pressure. The model consists of the two elementary steps stated above, plus a step in which methane is activated irreversibly: step 3: CH4 + M-0' products We note that our assumption of the dissociation of the C-H bond of methane in one step (step 3) is not critical, as any precursor adsorption state of methane would be nearly equilibratedwith the gas phase. Thus,the precursor adsorption state would not be kinetically significant. If it is assumed that step 1 is in equilibrium, step 2 is reversible, step 3 is irreversible, and the coverage of M0-M is essentially 1.0, then it can be shown that the rate of overall methane consumption is given by Rov = ( a / 4 ) [ ( a 2+ 16b)'l2 - a] (8) where Rov = overall methane consumption rate, a = k3PcH4/(k2')1/2, 6 = k2(KJ'02)1/2, K1 = equilibrium Constant for step 1, k 2 = forward rate constant for step 2, k i = reverse rate constant for step 2, k3 = rate constant for step
-
Ind. Eng. Chem. Res., Vol. 30, No. 9, 1991 2117 1.2,
1
8-1)
0.9
8 0.3
K
825
0.4
850
900
875
925
,
0
950
1
I
I
I
I
I
14
28
42
56
70
Po, (kPa)
0
15
I
1
I
I
I
30
45
60
75
90
P,,
Figure 2. Experimental versus theoretical overall methane conversion rate ae a function of temperature (A), oxygen pressure (B),
and methane pressure (C).Catalyst: Li/MgO. Catalyst weight: 1 g. Total flow rate at STP: 0.83 cma 8-l. Temperature in B and C: 893 K. Methane pressure in A and B: 40 kPa. Oxygen pressure in A and C: 8 P a . Total reactor pressure including inert: 101.3 P a . Solid lines are results from eq 8. Experimental data from It0 et al. (1985).
3, PFH,= methane pressure, and Po2 = oxygen pressure. m e 2 show experimentalmethane consumption rates for Li/MgO (1)compared with model results obtained with eq 8 and the following parameters (the rate constants are expressed per gram of catalyst): K1= 1.0 X lo4 kPa-'
k2 = (3.4 x 101' mol s-l g-l) exp
k3
magnitude of the value of 3.5 X 108 mol s-' g-l (1013site-'
= (75 mol P a - ' s-l g-') exp
286 kJ mol-'
63 kJ mol-'
Only two independent parameters, a and b, determine the overall rate at each temperature. These parameters were adjusted using a least-squares fit to generate the result shown in Figure 2. Since different seta of individual equilibrium and rate constants can yield the same a and 6 parameters, the choice of equilibrium and rate constants is somewhat arbitrary. The constants listed above were selected in view of the following constraints: (a) K1would be within several orders of magnitude of the value of 1.5 X 10-' kPa-l, expected if oxygen adsorption occurred at the rate predicted from collision theory and the rate constant for oxygen desorption were 3.5 X 108mol s-' g-' (10'3 site-' 8-1). (b)The preexponential factors for step 2 in the forward and reverse directions would be within several orders of
*
(c) The preexponential factor for step 3 would be equal to the value predicted by collision theory. The agreement between the model and experiment is satisfactory considering the small number of independent parameters. The remaining disagreement between eq 8 and experimental results can be reduced significantly if a small amount of reversibility is allowed for step 3. Otsuka and Jinno (Otsuka and Jinno, 1986) have proposed a model that describes the consumption of methane during dimerization of methane over a samarium oxide catalyst. However, the kinetic behavior observed for samarium oxide is substantially different than the observed kinetics over alkali-metal-promoted alkaline earth oxides. These differences are clearly illustrated by comparing the apparent activation energy for methane consumption for a samarium oxide catalyst obtained by Otsuka and Jinno of 149 kJ mol-' with the value reported by Ito et al. for Li/MgO of 218 kJ mol-'. Thus, it appears development of a general kinetic model for the dimerization reaction is not possible. For example, the model presented by Otsuka and Jinno is probably limited to unpromoted rare earth metal oxides, and our analysis appears to be limited to alkali-metal-promoted alkaline earth metal oxides. In conclusion, microkinetic analysis permits the construction of a simple kinetic model that describes in a satisfactory manner the overall experimental methane consumption observed for an alkali-metal-promoted alkaline earth metal oxide catalyst. The model was obtained through microkinetic analysis of the experimental evidence accumulated for the methane and oxygen surface interaction steps. We note, however, that a more quantitative agreement between model and experiment can be obtained by allowing a small amount of reversibility for the methane activation step.
Extension of the Simple Model The above simple model appears to capture the essential chemistry of methane consumption during the dimerization of methane over alkali-metal-promotedalkaline earth metal oxides. We now extended the microkinetic analysis to investigate the importance of various processes that control the selectivity of the dimerization reaction. Pathway of Direct C1 Oxidation. An important question in oxidative methane dimerization is whether surface or gaseous oxygen species are primarily responsible for direct C1 oxidation (Le., without passing through a C2 intermediate). Microkinetic analysis can be used to address this question by considering not only the conversion of methane expressed in Figure 2 but also the selectivities of the various products. Since these experiments were conducted at low conversions, one can assume that the production of COXthrough the combustion of C2 species is negligible since the concentration of C2 species in low. In addition, the activation energy observed for the production of COXspecies is approximatelyone-half the value observed for the production of C2 species. Since COX produced through C2 species should have an apparent activation energy at least equal to the activation energy of C2production, we conclude this is not a likely pathway for the data presented in Figures 2. We shall show later that C2 oxidation does play an important role at high conversions. In general, step 5 below represents the coupling process, in which the C1species capable of undergoing coupling is step 5: 2CHx Czspecies denoted CHx. This species may be either a gaseous CH3'
-
2118 Ind. Eng. Chem. Res., Vol. 30, No. 9, 1991
radical or a surface methoxy species at this point. We define rs as the forward rate of this elementary step, kS as the forward rate constant, and Ccm as the concentration of species CH= The rate of step 5 can then be expressed as follows: rg
ks(CCHX)2
0.55
s-'ln
(9)
Given the low concentration of C2 species present in the data of Figure 2, step 5 is assumed to be irreversible. Thus, when the rate of C2 combustion is negligible, F~ should equal the experimentally determined rate of C2production. We may rewrite the above equation as follows: R c 2 = ks(CCHX)2 (10) where Rc2 is defined as the net rate of C2 production. c , should Equation 10 can be rearranged to show that C be proportional to the square root of Rc2: CCHX= ( R c z / ~ s ) ' / ~ (11) In the development of the above simple model for methane consumption, we assumed step 3 to be irreversible, in accord with the isotopic labeling evidence. Applying this assumption again, we write ROV k3PCH4eM0 (12) where k3 is the forward rate constant of step 3 and BM0 is the fractional coverage of M-O' species. Since step 3 may become reversible at higher conversions, eq 12 should be valid only at low conversions. Thus, eq 12 indicates that 6Mo should be proportional to Rov divided by PCHl at constant temperature and low conversion: h 0 R0V/k8CH4 (13) The direct combustion of C1would be expected to be proportional to the product of CCm, the concentration of the C1species being oxidized, and the concentration of the oxidizing species. We define Rcox as the net rate of production of COX species. Assuming gas-phase oxygen and the surface species M-0' and M-O-O-M are responsible for oxidation of oxidation of C1 species, we can write the following: (14) RCOX = kaCCHXeMO + k b C C H X e M o o M + k c C C H X P O 2 where k,, k b , and kc are rate constants and 6MmM is the concentration of surface peroxide species. Since step 1is most likely at equilibrium, 6MmM is proportional to the square root of the oxygen pressure and we may change eq 14 to RCOX = kaCCHXeMO + kd(11/2CCHXP02'/2 + kcCCHXP02 (15) Combining eqs 11,13, and 15 to eliminate Ccm and BMo, we obtain
Rcox
In the experiments of Figure 2C,the temperature and the oxygen pressure were kept constant. Thus, the two final terms in eq 16 remain constant and the experimental quantity ( R C ~ ~ / R C should ~ ' / ~ ) vary linearly with the experimental quantity ( R o V / P c H 4 ) . This is confirmed in Figure 3. The fact that the line has a measurable slope shows that oxidation involving the M-0' species in not negligible. However, the fact that its y intercept is large shows that the dominating oxidation route involves either
0
4
8
12
16
20
R ~ J (pnoi P ~ s" ~ 9.' Pa.')
Figure 3. Rcox/(RC2)1/2 versus Rov/PcH,. Catalyst: Li/MgO. Catalyst weight: 1g. Total flow rate at STI? 0.83 cma 8-l. Temperature: 893 K. Oxygen pressure: 8 kPa. Total reactor pressure including inert 101.3 kPa. Data from Ito et al. (1985). 1
31
0
14
28
42
56
70
,P W a )
Figure 4. [RC&(RC~)'/~ - (so00 kPa g'lz s1I2 ~ O ~ - ' ~ ~ ) R O V / P C H ~ I versus oxygen pressure. Catalyst: Li/MgO. Catalyst weight: 1 g. Total flow rate at STP: 0.83 cm38-l. Temperature: 893 K. Methane premure: 40 kPa Total reactor pressure including inert 101.3 kPa Data from Ito et al. (1985).
surface peroxide or gaseous oxygen. From the slope of the line in Figure 3, the quantity (k,/k kS1l2) at 893 K is estimated to be ca. 8000 kPa g1/2s1f2 mol-'/2. With this estimate, one can write eq 16 as
To determine which of the two terms on the right-hand side of eq 17 predominates, one can test how the left-hand side of this equation varies with oxygen pressure for the experiments of Figure 2B (these studies also conducted at 893 K). Figure 4 shows a linear variation with oxygen pressure, suggesting that the second term on the left-hand side of eq 17 predominates and that the oxidizing species primarily responsible for C1oxidation is gaseous oxygen. From the slope of Figure 4, one can estimate the quantity (k,/k61/2)to be ca. 4.5 X 10" moW2 g-1/2 sm1I2kPa-'. It must be noted that although C2 combustion is not a major source of COXunder the low conversion conditions examined here, it is undoubtedly a contributing factor at higher temperatures and conversions. Geerta et al. have shown that ethane and ethylene react with gaseous oxygen, particularly at high temperatures (Geerta et al., 1989). Also, these species may be oxidized by surface-catalyzed routes at high conversion conditions. The above microkinetic analysis suggests that the rate of carbon oxide formation can be described by oxidation
Ind. Eng. Chem. Res., Vol. 30,No. 9,1991 2119 of C1 species with gas-phase oxygen and, to a leaser extent, with surface M-O' species. While the combustion of C2 species was shown to be negligible at conditions of the analysis, these pathways are likely to become important at higher conversions and temperatures. Surface versus Gas-Phase Coupling. A critical aspect of the methane dimerization reaction is identifying whether C1 coupling to C2species occurs primarily on the catalyst surface or through the reaction of a pair of CH; radicals in the gas phase. Most of the recent literature suggests the dimerization reaction occurs in the gas phase after surface initiation of methyl radicals. Li/MgO and rare earth oxide dimerization catalysts have been shown to be effective in generating gaseous CH,' radicals (e.g., Driscoll et al., 1985;Campbell et al., 1988;Lin et al., 1986; Tong et al., 1989). Also, the observed CH,' radical concentration produced by several catalysts has been correlated with the catalytic performance for dimerization (Driscoll et al., 1985;Lunsford, 1990). In addition, most previously proposed models describing the performance of dimerization catalysts have involved coupling and/or combustion of gaseous methyl radicals (e.g., Otsuka and Jinno, 1986;It0 et al., 1985). While microkinetic analysis alone cannot determine whether coupling occurs in the gas phase or on the surface, we can use microkinetic analysis to examine the feasibility of such processes. It is consistent with the evidence previously proposed in the literature to initially assume coupling occurs in the gas phase. To analyze this possibility, we develop further our model by adding certain proceases. First, we must make an arbitrary choice of the CHx species involved in the coupling and oxidation reactions. The natural choice, based on the literature results, is a gaseous methyl radical, CH3*. Thus, we can rewrite steps 3 and 5 as follows: CH4 + M-0' CH3' + M-OH step 3:
-
+
step 5:
2CH3'
C2H6
In accordance with the previous section, we describe the main route for C1 oxidation via the following steps which have been studied in the gas phase (Khachtryan et al., 1982;Plumb and Ryan, 1981;Baldwin et al., 1970;Kegeyan et al., 1977;Ewig et al., 1987): step 6: CH3' + 02 CH3O2' CH2O + OH'
-
step 7: CH20 + OH'
+
+ oxidizing agents
-
C02 and H20
A secondary route for C1 oxidation involving M-O', as discussed in the previous section, can be visualized as occurring via the following steps: CH3* + M-0' -w M-OCHS step 8:
-
step 9: M-OCH3 + oxidizing agents C 0 2 and H20 With this picture, the concentration Cc, discussed in the previous section is replaced by PCH3, the constant k , corresponds to k8, and the constant k , corresponds to k6, where k6 and kl, are rate constants for steps 6 and 8. Although coupling probably occurs in the gas phase, the gaseous CH3' pressure under reaction conditions must be lower than that given by the following overall equilibrium: CHI + y402 CH3' + '/zH2O
-
Specifically, if a catalyst performed well enough to each this equilibrium, then addition of water to the feed would inhibit the overall rate of methane consumption. It has been reported in the literature that the addition of water
enhances the rate of reaction over Li/MgO (Kimble and Kolts, 1986). Because that experiment was conducted only at high CH4/02 ratio, we repeated it in our laboratories at both low and high CH4/02ratios, obtaining the same result. From the estimated thermodynamics for the above reaction, the following relationship can, therefore, be derived if the enthalpy change of the reaction is assumed to be temperature-independent: 92 kJ mol-' PcH~Po~'/~ PCH3 < (124 kPa1I4)exp (18)
(
RT
pH20112
where PCH3, PCH4, PO2, and p H 2 0 are pressures of gaseous species. At 893 K, with an inlet flow rate of 0.83 cm3 (STP)/scontaining 50 kPa of He, 40 kPa of CH4, and 8 kPa of 02,1 g of the Li/MgO catalyst produces 4.5 X 10-8 mol of C2H&8.4 x lo4 mol of C02, 6.5 x 10-g mol of C2H4, and 1.3 X mol of CO per second (Ito et al., 1985). From these values, it can be estimated that the H20 pressure should have been close to 0.74kPa under these conditions. From eq 18,we can estimate that the maximum CH3*pressure allowed by thermodynamics is equal to 40 Pa. It is now important to calculate the CH3' pressure required to explain the amount of COXproduced through step 8,if k8 is estimated from collision theory. Collision theory should provide a good estimate for step 8 because it is a reaction between a surface radical and a gas-phase radical and a low activation energy is expected. This estimate for kE is 75 mol kPa-l s-l g-l, The M-O' coverage can be estimated by using eq 13 and the value of k3 used to construct Figure 2. At 893 K, with an inlet flow rate of 0.83cm3/s containing 50 kPa of He, 40 kPa of CH,, and 8 kPa of O2over 1 g of catalyst, this estimate is for BMO is 3 X lo-'. According to Figure 4,Step 8 was responsible for ca. 9% of the overall COXproduction rate, or ca. 1 X mol s-l g-l. Therefore, the estimated CH3' pressure under these conditions is 0.4 Pa, 2 orders of magnitude lower than if the production of CH3' were in equilibrium. From the estimate of the quantity [k8/(k3ks1I2)] from Figure 3 and the collision theory estimate for kE,we can estimate k6,the rate constant for the coupling step. Using the value of k3 used to construct Figure 2, one can estimate k6 to be ca. 0.36 mol kPa-2 s-l 8'. The rate constant of step 5 on a per volume basis is known from experimental gas-phase kinetics (Tsang and Hampson, 1986; Khachtryan et al., 1982;Parkes et al., 1976). Thus, the calculated value for k6 can be used to estimate the gas-phase volume in which CH; radicals exist. The value of k6 on a per volume basis is 0.4 mol kPa-2 s-l ~ m - Therefore, ~. the volume in which CH; radicals exist is estimated to be ca. 0.9 cm3/g, of the same order of magnitude as the pore volume of the catalyst (It0 et al., 1985). The microkinetic analysis presented has shown coupling in the gas phase to be capable of quantitatively describing the observed experimental results for Li/MgO. While microkinetic analysis is incapable of proving the existence of this pathway, the literature evidence and the analysis suggest the coupling reaction can occur in the gas phase at rates that approximate the observed reaction rates. Ethane Hydrogenation. If one assumes that ethane is activated by the same site that activates methane, microkinetic analysis can be used to estimate the rate constant for the elementary step that determines the rate of ethane dehydrogenation. By analogy with step 3, this step can be written as step 10 C2He + M-0' C2H6*+ M-OH
-
2120 Ind. Eng. Chem. Res., Vol. 30, No. 9, 1991 Table I. ComDlete Methane Dimerization Mechanism reaction Methyl Radical Production 02 + 2M-0-M 2M-0-0-M M-0-0-M 2M-O' CHI + M-O' * CHS' + M-OH 2M-OH HZO + M U M
--
5
Coup1ing 2CH3' * CzHB
C1 Oxidation CHS' + 02 .-+ CHZO + OH' CHZO + OH' + * / 4 0 2 COZ + s/zHZO CH< + M-O' M-OCHS M-OCH, + * / 2 0 2 .-+ CO2 + HzO + M-OH 10 11 12
- - ++
Ethane Dehydrogenation + M-O' C2H5' M-OH C2HI' + '/do2 .-+ CZH, '/zHzO
(22%
Cz Oxidation C2H4 + 202 .-+ 2CO + H20
The CzH6'species produced could quickly lose hydrogen through elementary steps such as step lla: CzHS' O2 C2H4 + HOB'
+
--
step Ilb: CzHb' + M-0' C2H4 +M-OH To estimate klo, one needs estimates for OMO at two temperatures for which rates of ethane dehydrogenation have been measured. With the use of eq 13 and the value of k3 used to construct Figure 2, OMo on a Li/MgO catalyst is estimated to be 3.2 X lW7 at 893 K and 8.1 X lW7 at 935 K for a CHI pressure of 40 kPa and an O2 pressure of 8 kPa. At 893 K under these conditions, the rate of dehydrogenation is 5.8 X 1O-g mol 8-l g1and the ethane pressure is 0.13 kPa; thus, klo is estimated to be 0.14 mol kPa-ls-l g-l. At 935 K under these conditions, the rate of dehydrogenation is 7.5 X 1O-emol s-' g-l and the ethane preasure is 0.52 P a ; thus, kl0 is estimated to be 0.18 mol kPa-' g-l. With these two values, klo can expressed as (52 mol Pa-ls-lg-') exp(-44 kJ moF/RT). The preexponential factor of 52 mol Wa-' 8-l g-l is in excellent agreement with the value predicted by collision theory. Microkinetic analysis has provided an estimate for the rate constant for ethane activation by surface M-0' species. The obtained value is consistent with the obse~ed rates of ethylene production and collision theory estimates.
Microkinetic Model A microkinetic model based on the above analysis was constructed in an attempt to explain quantitatively the behavior of a Li/MgO catalyst for oxidative methane dimerization. This model consisted of the 12 steps listed in Table I. Seven of these steps are meant to be elementary steps. In contrast, steps 6,7,9,11, and 12 represent parta of the process consisting of more than one elementary step but whose elementary breakdown is not significant in the reaction kinetics under the reaction conditions being discussed. Step 6 consists of the elementary steps CH3' + O2 CH3O2' and CH30; CHzO + OH'. Steps 7,9, and 11 are the consumption of the intermediates CH20, OH', M-OCH3,and C2H6'. Since these steps are expected to be fast, it is not important how they are written provided that the intermediates are quickly consumed. Step 12 was included to describe gas-phase Czoxidation and to account for a source of CO. Ethylene is much more reactive toward oxygen than ethane, and ita main COX product is known to be CO (Geerta et al., 1989). For steps 7-12, first-order kinetics were assumed regardless of the stoichiometry. In addition, these steps were assumed to
-
-
Table 11. Rate Constants Uwd with Complete Methane Dimerization Mechanism forward forward reverse reverse preexponential activation preexponential activation step factor" energyb facto? energyb 1 49.8 0 2.28 X 10' 18.5 2 3.18 X 10" 299.5 6.57 X 10" 8.2 3 74.7 52.3 14.7 101.8 4 505 0 14.7 0.9 5 0.28 0 3.98 X lo' 360.8 6 0.014 46.9 7 1 x 108 0 8 74.7 0 1.45 X 1@ 382.5 9 1 x 106 0 10 49.8 32.3 0.59 105.4 11 1 x 106 0 12 0.19 130.2 'Units: mol 8-l g-l, mol 8-l g-l kPa-l, or mol 8-l g-l kPa-*. *Unite: kJ/mol.
be irreversible. The model did not take into account carbonate formation through the reaction of COz with the surface. The model was calibrated using low conversion kinetics, and in the limit of zero conversion such a reaction should be insignificant in the reaction kinetics. The rate constants for important elementary steps were adjusted to minimize differences between model and experimental activities and selectivities. A set of rate constants that is consistent with known thermodynamics and known gas-phase kinetics and that leads to effective description of the experimental data is summarized in Table 11. The number of parameters that was adjusted to generate Table I1 was 12. They were the forward preexponential factors of steps 2,4, and 5, the forward activation energies of steps 2,3,6,10, and 12, the reverse preexponential factor of step 2, and the reverse activation energies of steps 2, 3, and 4. The forward preexponential factors of steps 1, 3,8, and 10 and the reverse preexponential factors of steps 3 and 4 were estimated from collision theory. The reverse preexponential factor and activation energy of step 1were calculated so the rate constants of steps 1-4 would reproduce the enthalpy and Gibbs free energy changes of the overall reaction: CH4 + 7 4 0 2 *-, CH3' + f/zH20 The reverse preexponential factor and activation energy of step 5 were calculated so they would reproduce the enthalpy and Gibbs free energy changes of the step. The reverse preexponentialfactor and activation energy of step 10 were calculated so the rate constants of steps 1-5 combined with those of step 10 would reproduce the enthalpy and Gibbs free energy changes of the following overall reaction: 2CH4 + Y402 CzHC + YzH20
-
The forward preexponential factors of steps 6 and 12 were calculated from the forward preexponential factor of step 5 such that all three values would correspond to the same volume in which homogeneous reactions were taking place. The reverse preexponential factor and activation energy of step 8 were calculated from the rate constants of steps 3 and 4 assuming the same enthalpy and Gibbs free energy of formation of M-OH and M-OCH3 bonds. The preexponential factors of steps 7,9, and 11were simply set to a high value (1 X lo6 mol s-l g-I kPa-2). Zanthoff and Baerns have recently published a kinetic simulation of the gas-phase dimerization of methane (Zanthoff and Baerns, 1990). Two steps considered in our microkinetic model have analogues in the model proposed by Zanthoff and Baerns, steps 5 and 6. While the kinetic
Ind. Eng. Chem. Res., Vol. 30, No. 9, 1991 2121 1500 1
: 3
1200
8
1200
I
1
I
A
I
600
W
z
2
300 I
0 0
0.8
1.6
2.4
0
3.2
14
28 42 Po2W a )
CONTACT TIME (g s ~ m ' ~ )
Figure 5. Experimental and theoretical methane converted to various products versus pseudocontact time, W/F. Catalyst: Li/ MgO. Catalyst weight: 1g. Temperature: 893 K. Methane inlet pressure: 40 kPa. Oxygen inlet pressure: 8 kPa. Total reactor pressure including inert: 101.3kPa. Solid lines: model summarized in Table I. 0,overall. 0, to C&. A, to COB. 0 ,to C2Hk A, to CO. Experimental data from Ito et al. (1985). 1500
n I
I
: h
1200
825
850
875
900
925
T (K)
parameters for step 5 in both models are in good agreement, differences exist in the kinetic parameters for step 6. Our parameters for this step are based on the intermediate formation of the methylperoxy radical (CH30z'), while the parameters of Zanthoff and Baems are not based on this species as an intermediate. Since the methylperoxy radical is believed to play an important role in the oxidation of methane at low temperature (
