Ind. Eng. Chem. Res. 1992,31, 1621-1625 Katz, S.; Croat, J. J.; Laukonis, J. V. Lanthanum Lead Manganite Catalyst for Carbon Monoxide and Propylene Oxidation. Ind. Eng. Chem. Prod. Res. Dev. 1975,14,274-279. Lauder, A. Metal Oxide Catalytic Compositions. U.S. Patent 3897367, 1975. Libby, W. F. Promising Catalyst for Auto Exhaust. Science 1971, 171,499-500. Mai, G.; Siepmann, R. Catalyst for Purifying Exhaust Gases. U.S. Patent 3905918, 1975. Mai, G.; Siepmann, R.; Kummer, F. Catalyst for the Reduction of Nitric Oxides. U.S.Patent 3900428,1975a. Mai, G.; Siepmann, R.; Kummer, F. Oxidation Catalyst for Combustibles in Gas Mixtures. U.S.Patent 3901828,1975b. McCann, E. L., III. Catalytic Perovskites on Perovskite Supports and Process for Preparing Them. U S . Patent 4151123,1976. Meadowcroft, D.B. Low-cost Oxygen Electrode Material. Nature (London) 1970,226,847-848. Nakamoto, K. Infrared and Raman Spectra of Inorganic and Coordination Compounds, 4th ed.; John Wiley & Sons: New York, 1986;pp 139,245. Seiyama, T.; Yamazoe, N.; Eguchi, K. Characterization and Activity of Some Mixed Oxide Catalysts. Ind. Eng. Chern.Prod. Res. Dev. 1985,24,19-27. Subba Rao, G. V.; Rao, C. N. R. Infrared and Electronic Spectra of Rare Earth Perovskites: Ortho-Chromites, -Manganites and -Ferrites. Appl. Spectrosc. 1970,24 (4),436-445. Tasch, J. M. D.; Mendioroz, S.; Tejuca, G. L. Preparation, Characterization and Catalytic Properties of LaMeO, Oxides. 2.Phys.
1621
Chern. (Munich) 1981,124,109-127. Voorhoeve, R. J. H. In Advanced Materials in Catalysis; Burton, J. J., Garten, R. L., Eds.; Academic Press: New York, 1977; pp 129-180. Voorhoeve, R. J. H.; Remeika, J. P.; Freeland, P. E.; Matthias, B. T. Rare-Earth Oxides of Manganese and Cobalt Rival Platinum for the Treatment of Carbon Monoxide in Auto Exhaust. Science 1972,177,353-354. Voorhoeve, R. J. H.; Remeika, J. P.; Johnson, D. W., Jr. Rare-Earth Manganites: Catalysta with Low Ammonia Yield in the Reduction of Nitrogen Oxides. Science 1973,180,62-64. Voorhoeve, R. J. H.; Johnson, D. W., Jr.; Remeika, J. P.; Gallagher, P. K. Perovskite Oxides: Materials Science in Catalysis. Science 1977,195,827-833. Yamamura, H.; Watanabe, A,; Shirasaki, S.; Moriyoahi, Y.; Tanada, M. Preparation of Barium Titanate by Oxalate Method in Ethanol Solution. Cerarn. Znt. 1985,11 (l),17-22. Yu-Yao, Y. F. The Oxidation of Hydrocarbons and CO Over Metal Oxides IV. Perovskite-Type Oxides. J. Catal. 1975a,36,266-275. Yu-Yao, Y. F. The Oxidation of Hydrocarbons and CO Over Metal Oxides V. SOz Effects. J. Catal. 1975b,39,104-114. Zhang, H. M.; Teraoka, Y.; Yamazoe, N. Preparation of PerovskiteType Oxides with Large Surface Area by Citrate Process. Chem. Lett. 1987,665-668. Received for review September 3, 1991 Revised manuscript received February 18, 1992 Accepted March 19,1992
Oxidative Coupling of Methane over Li/MgO: Kinetics and Mechanisms Wen-Yuan Tung and Lance L. Lobban* School of Chemical Engineering and Materials Science, University of Oklahoma, Norman, Oklahoma 73019
Methane coupling over a Li/MgO catalyst was studied under differential conversion conditions in a flow reactor. Ethane selectivities greater than 90% were observed, but under the experimental conditions employed, no CO or C2H4was observed, indicating that these are secondary reaction products. The source of COz is methane or methyl radicals, and both gas-phase and surface oxygen are involved in the complete oxidation process. Among those tested, a single site mechanism best describes the experimental results.
Introduction A high yield process for conversion of methane to higher hydrocarbons would enjoy several advantages for the production of petrochemical feedstocks. The most promising route currently appears to be oxidative coupling of methane, which has been the subject of a number of investigations in recent years, as reviewed recently by Lee and Oyama (1988) and by Amenomiya et al. (1990). Despite many studies related to the mechanism of the coup l i i reaction over various catalysts, however, uncertainty exists concerning important features of the reaction. For example, the source of the undesired carbon oxides remains in question. Ito and Lunsford (1985) and Ito et al. (1985), using a Li/MgO catalyst, concluded that oxidation of methyl radicals was the source of COX,as did Iwamatsu and Aika (1989) using a Na/MgO catalyst. DeBoy and Hicks (1988) using a Sr/La203catalyst and Peil et al. (1989) using Li/MgO concluded that CO was a primary reaction product and that a significant fraction of C02 came from CO oxidation. In contrast to these conclusions, Roos et al. (1989) suggested that oxidation of ethylene and/or ethane is the primary source of COX,as did Sofrank0 et al. (1987) and Ekstrom and Lapszewicz (1989). Researchers disagree on other features of the reaction mechanism as well. Both single site (Iwamatsu and Aika, 1989) and dual site (Hutchings et al., 1989) mechanisms
* To whom correspondence should be addressed.
have been proposed to explain the observed selectivities to C2hydrocarbons and CO,, depending on the assumed importance of adsorbed methane or adsorbed methyl radicals. The contribution of surface oxygen to the undesired complete oxidation proceases is also debated in the literature. We studied the kinetics of methane coupling over Li/ MgO under differential conversion conditions in a flow reactor in order to determine possible simple mechanisms which adequately describe the observed phenomena and to address the disagreements noted above. From proposed mechanisms, reaction rate expressions predicting the dependence of conversion and selectivity on reactant partial pressures and temperature were obtained. Besides aiding in model discrimination, the rate expressions are important for defining optimal reactor configurations and operating conditions. Li/MgO was selected for this initial study for several reasons. Li/MgO was shown by Ito and Lunsford (1985) and Ito et al. (1985) to be active and selective for methane coupling, and results using this catalyst remain among the best reported to date. Moreover, Korf et al. (1989) have shown that this catalyst can be improved with small amounts of additives, making more likely the eventual commercial use of the catalyst.
Experimental Description The Li/MgO catalysts were prepared by adding 48 g of MgO and 19.23 g of Li2C03to approximately 500 cm3 of
0888-588519212631-1621$03.00/0 0 1992 American Chemical Society
1622 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
deionized water and evaporating the water, while stirring, until only a thick paste remained. The paste was dried at 140 "C in a vacuum oven for 12 h and then calcined at 800 O C for 6 h. The sample was ground to powder and then pressed at 6000 psi. The resulting pellet was crushed and sieved, and the 20-40 mesh size was used in all experiments. The specific surface area measured by the BET method was 2.6 m2/g before reaction. Prior to reaction, the catalyst was pretreated in the reactor under oxygen flow (10 cm3(STP)&-I) at 500 "C for 3 h, following which the temperature was raised to the desired level. The reactor was a 7-mm4.d. quartz tube tapered onto a 2-mm4.d. quartz tube of the same outer diameter. This design served to rapidly remove the effluent gases from the heated zone, minimizing gas-phase reactions. The catalyst was held in place by a plug of quartz wool. The reactor was placed in a furnace with approximately 15 cm of the tube serving as a preheat zone. A K-type thermocouple placed against the outside of the tube was used to measure the reactor temperature. The temperature in the catalyst bed was calibrated against the outside thermocouple under conditions of He and CHI flow only. Reactant flow rates were controlled using electronic mass flow controllers, and the effluent gas was analyzed using a Carle GC with a thermal conductivity detector. Experiments were carried out at 600,650,700, and 750 "C at a total pressure of 1atm. The usual catalyst charge was 0.5 g, but, at 600 "C, 1.5 g of catalyst was used in order to obtain measurable conversion. Reaction rates reported at 600 "C have been divided by 3 to be on the same basis as rates reported at other temperatures. Methane partial pressure in the reactor was varied from 0.025 to 0.35 atm., and the oxygen partial pressure was varied from 0.0012 to 0.032 atm. Helium was used as a carrier gas to maintain the total pressure at 1 atm. The total flow rate was approximately lo00 cm3(STP)mi&. At this flow rate, the contact time between the gas mixture and the catalyst is on the order of a few milliseconds, depending on the amount of catalyst and the temperature. Methane and oxygen conversions were less than 10% except for several runs at very low oxygen partial pressure for which the oxygen conversion was as high as 30%. Several researchers have noted lithium loss from this catalyst under reaction conditions. In our experiments, the catalyst was periodically replaced, and no deactivation was observed. Blank runs (Le., typical flow rates and temperatures but in the absence of catalyst) showed negligible reaction.
Results In all experiments, measurements were taken after waiting until no change in the conversion or selectivity was detectable. All reported values are an average of at least three measurements at the indicated conditions. In the following, R, indicates the rate of formation of carbon oxides CO and COz. In our experiments, no CO was detected; thus, R1is the rate of formation of COP Rzis the rate of formation of Cz hydrocarbons. In these experiments, no ethylene was detected; thus, Rz is the rate of formation of ethane only. Results for the conversion of methane to ethane and carbon dioxide at 600 and 700 "C are shown in Figures 1-3. Reaction rates versus oxygen partial pressure at a fixed methane partial pressure are shown in Figure 1,while rates versus methane partial pressure at fixed oxygen partial pressure are shown in Figure 2. Figure 3 shows the variation of ethane selectivity (defined as 2Rz/(2Rz + R,)) versus oxygen and methane partial pressures at 700 "C. Results at other temperatures were qualitatively similar to those shown in Figures 1-3.
-5 h
.-
E :
P
E
v 0)
. . I
d
T = 600°C. P,,, = 0.0929am 0 40
-5 .-
[
1
3
2
I
T = 700eC,P, = 0.1043am
30
h
E
E
20
E E v 0) *
2 0
I
I
I
I
1
2
3
4
P, (atm) XIO' Figure 1. Experimental and predicted (using mechanism 1) reaction rates versus oxygen partial pressure at 600 (bottom).
O C
(top) and 700
81
O C
i
T = 6Oo0C, Po = 0.0085 am
'
0.0
I
I
I
0.1
0.2
0.3
0.4
--
.-
h
0
601
R, (exp.)
--- R, R2 (model) R~(ex/
T = 700°C,Po = 0.0106 am
2E 4 0 E E
0
________------
0
0.0
0.1
0.2
0.3
0.4
P, (atm) Figure 2. Experimental and predicted (using mechanism 1) reaction rates versus methane partial pressure at 600 O C (top) and 700 O C (bottom).
Several simple reaction mechanisms were considered for modeling the experimental results; three of these mechanisms are presented here. The first mechanism was suggested by Iwamatsu and Aika (1989) for modeling methane coupling over a Na/MgO catalyst. They made the following assumptions: (i) Active centers (designated by Oz*s in the following model) are formed by adsorption of oxygen from the gas phase. Lunsford and co-workers (It0 and Lunsford, 1985; Ito et al., 1985) have suggested that the active site is an [Li+O-]center on the catalyst surface. (ii) Methyl radicals, formed by reaction of gas-phase methane with the active centers, either release quickly to the gas phase for further reaction or are oxidized quickly on the
Ind. Eng. Chem. Res., Vol. 31, No. 7,1992 1623 100 on
Table I. Kinetic Parameters Estimated for Mechanism 1 Using Experimental Data at Each Temperature
T m O ,P,,,=0.0929 am -exp., model, T&CO0. Pm=0.0929 am I
',
I
\" L 40' 0
I
I
1
2
P, (atm)
Ea, kcal/ 600 "C 650 OC 700OC 75OOC g-mol kl,mmol/(min.atm) 2.01 14.3 23.4 74.0 36.5 k2,mmol/(min.atm) 0.124 0.509 0.784 1.66 28.3 K34, 0.546 0.706 0.330 0.176 -10.6 (min.atmx)/mmol 1: 1.46 1.22 1.30 1.37 x,, = 1.34
I
3
4
XIO'
Table 11. Kinetic Parameters Estimated for Mechanism 1 Using the Levenberg-Marquardt Method and Data at All Temperatures
loB
8?l
I
I
I
I
0.1
0.2 P,,, (atm)
0.3
0.4
Figure 3. Experimental and predicted (using mechanism 1)selectivity at two different reaction temperatures versus oxygen partial pressure (top) and versus methane partial pressure (bottom).
surface. (iii) Reaction intermediates 02*s and CH3' are assumed to be at pseudo-steady state. The four-step mechanism is given below. CH4 + 02.5 CH3'
k2 +
+ XO
CH3'
k,
+ O2H.S
(2)
COX,H20
(3)
+
2CH3' A C2He (4) Following the derivation by Iwamatsu and Aika (1989),the rate expressions can be obtained
"[
R1 = 4K34 (1 +
8klk&34Pm
)"'
Pox-l(kJ'o + k2Pm)
- 1] ( 5 )
where K34 = k4/k32 It is not possible to determine separately the parameters k3 and kq. Thus, at each temperature, there are four parameters, k,, k2,KU, and x , to be estimated based on the reaction rates R1and RP. We used the modified Levenberg-Marquardt (L-M) method contained in MathCAD to minimize the sum of squares of the deviation between model and experiment, i.e., to minimize the functions (7) SO% = Z(Rl,mod,- R1,exJ2 SoS2 = Z(R2,rnod, - R2,exp,I2 i
1.80 X 28.3
lo6
1.20 X -10.4
In kcal/g-mol.
I exp., T m 0 , P,=O.0085 am
-model.T=600°, P,=00.0085 a m exp.. T=7Oo0.P,=O.OlOa am - -.model,T=700'. P,=O.OlOa a m 4
K,
k,
ki
preexponential factor 4.59 X activation e n e r w 36.5
(8)
The four parameters obtained from data at each temperature are presented in Table I. It is noteworthy that the parameter x is relatively constant over the range of temperatures. kland k2 increase with temperature, and from these values an activation energy and preexponential factor for Arrhenius-type rate constants can be obtained
from a plot of In k versus 1/T. The parameter KU does not show as clear a trend, but an activation energy was obtained in the same fashion. The activation energies calculated by this method are presented in the last column of Table I. The temperature-dependent form of the rate constants, together with an average value of the parameter x , was used to quantify how well the model matched the experimental results over the entire temperature range. Using these values to calculate the reaction rates R l 4 and R-d, the total sum of squares (SoSbt = SoSl+ S0S2)for all data is 1.29 X We also calculated for both R1mod and R2,modthe correlation coefficient 1.2 (Holman, 1984) to evaluate the fit of the model to experimental data, A value of 0.94 was obtained for the correlation coefficient for both R l 4 and Rad A slightly better (asindicated by the sum of squares of the errors and the correlation coefficients) estimate of the parameters is obtained using the L-M method with experimental data at all temperatures to simultaneously estimate the kinetic parameters k ,k,, and Ka0 (the preexponential factors), El,Ea, and EU (the activation energies), and x . The parameters thus obtained are presented in Table 11, and the estimated value for x is 1.35. Using this set of parameters, the calculated SoSbt is 1.18 X a small improvement, and the correlation coefficients for Rl,,d and.Rq,,d are 0.96 and 0.95, respectively. The model predictions for R1 and R2 versus Po and P, are shown by the solid and dashed lines in Figures 1 and 2. The selectivity predicted by the temperaturedependent model compares quite well with the experimental selectivity over the entire range of temperatures and partial pressures. Predicted selectivities versus Poand P, at 600 and 700 OC are shown in Figure 3. The second mechanism assumes reversible adsorption of both methane and oxygen on independent sites, followed by reaction between the adsorbates to form the active methyl radical, as shown below.
-
+ S 02.5 Krn CH4 + s CH4.s KO
0 2
*-c
CH4.s
+ 02.9
CH,'
k*
CH3'
+
+ O2H.S + s
+ x 0 2COX,H20
(9) (10) (11)
(12)
2CH3' % -! C2H6 (13) Gas-phase oxygen and methane are assumed to be in equilibrium with their adsorbed species, and the reaction intermediates' concentrations are assumed to be at pseu-
1624 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 Table 111. Kinetic Parameters Estimated for Mechanism 2 Using the Levenberg-Marquardt Method and Data at All Temperatures
Km
KO
5.29 X lo3 2.53
preexponential factor activation energ)+' a
3.75
k* K34 4.42 X lo7 9.42 X lo4
X
-14.5
36.9
-10.7 a
In kcal/g-mol.
do-steady state. The following rate expressions are then derived (Iwamatsu and Aika, 1989):
R1 =
c[ + Poz-1(K20 8k*KoKrnK34Pm + l)(KmP, + 4K34 (1
1))
2 -
11
In Table I11 are the preexponential factors and activation energies for the parameters k*, KO,K,, and KN obtained using the L-M method with data at all temperatures. The estimated value for x is 1.37. On the basis of the sum of squares of errors, model 2 is a slightly better fit to the data than model 1, with a SoS, of 5.33 X and a correlation coefficient for both R1 and R2,1pdof 0.97. The plots of R1 and R2 predicted %; mechanism 2 are very similar to those of mechanism 1. The third model includes reversible adsorption of oxygen and reaction between gas-phase methane and adsorbed oxygen, as shown below: 0 2
+8
CH4 + 0 2 0 s CH3'
KO
k2 +
+ XO
CH3'
k8 +
(16)
020s
+ 02H.s
(17)
COX,H2O
(18)
2CH3' -% C2H6 (19) Using the assumptionsof reversible oxygen adsorption and intermediates at steady state, the rate expressionsbecome
R1 - 4K34 R2 -
Table IV. Kinetic Parameters Estimated for Mechanism 3 Using the Levenberg-Marquardt Method and Data at All Temperatures KO k, KQA preexponential factor 6.50 X 108 1.97 X lo6 5.72 X activation energyo 26.5 29.0 0
[( [
(1
+
+
8Kok2K34pm
)2-1]
8Kok2K34Pm
) 2 -
Pox-l(KOpo+ 1)
(20)
112 (21)
16K34 Pox-l(K,,Po+ 1) In Table IV are the preexponential factors and activation energies for the parameters k2, KO,and Ka obtained using the L-M method with all experimentaldata. A value of 1.59 was estimated for r. This model fits the data poorly because neither Rlmd or Rw show inhibition by methane at high methane partial pressures. The sum of squares of errors in this case is 4.30 X the worst of the three mechanisms, and the correlation coefficients for RIFd and R2,,d are 0.87 and 0.86, respectively.
Discussion and Conclusions No measurable ethylene was formed at the low catalyst contact times used in this study. This agrees with other works showing ethylene to be produced by dehydrogenation of ethane rather than by a direct oxidative route. It is also notable that no CO was observed in our experiments, for which there are two possible explanations. CO
In kcal/g-mol.
may form only on the catalyst surface, and then be very efficiently oxidized to COPbefore being released to the gas phase. However, measurements by Cant et al. (1990) of CO oxidation over a Li/MgO catalyst indicate this is unlikely. The second, and more likely, explanation is that CO is also a secondary reaction product, i.e., produced by the oxidation of ethylene and/or ethane. We conclude, then, that both ethylene and CO are secondary reaction products which were not observed because of the low residence times. This suggests that only primary reaction products were observed in our experiments, and it is very unlikely that a significant fraction of C02is derived from subsequent oxidation of ethane. Rather, at low residence times, the carbon source of the C02is only methane and/or methyl radicals. Both one site (mechanisms 1 and 3) and two site (mechanism 2) models were used to describe our experimental results. Mechanism 3 was rejected because of poor fit to the experimental data and because of unreasonable parameters. While both mechanisms 1 and 2 fit the experimental data well, the dual site model (mechanism 2) estimates a positive activation energy for KO,implying that the equilibrium adsorbed oxygen coverage increased with temperature, an unlikely result. All parameters in the single site model (mechanism 1)are reasonable, and under the conditions of our experiments, we conclude that a single catalytic site is important and adsorbed methane does not play a significant role in the reactions. A second type of active site may become important for secondary reactions such as ethane dehydrogenation, CO oxidation, and ethanelethylene oxidation. For mechanism 1,the parameter x is estimated to be 1.35. As noted by Iwamatsu and Aika (1989),x less than 2 Suggests that not just gaseous oxygen but surface oxygen of some form is involved in the complete combustion of methane to COP Thus, both gas-phase oxygen and surface oxygen of some form (adsorbed or lattice) are involved in the complete oxidation of methane and methyl radicals over the Li/MgO catalyst. It will be important to determine which form of oxygen is relevant, since this has implications for reactor operation and catalyst design. Work is underway in our laboratory to determine the importance of each form of oxygen. The mechanisms presented here account for several important primary processes. Absent are important coneiderations such as the effects of reaction products' (C02, C2&, C2H4, HzO)partial pressures on the reaction rates. Studies of these effects are currently underway.
Acknowledgment This research was supported by the Oklahoma Center for the Advancement of Science and Technology and by the Sarkeys Energy Center of the University of Oklahoma. Literature Cited Amenomiya, Y.; Bires, V. I.; Goledzinowski, M.; G d w k a , J.; Sanger, A. R. Conversion of Methane by Oxidative Coupling. &tal. Rev.-Sci. Eng. 1990, 32, 163. Cant, N. W.; Lukey, C. A.; Nelson, P. F. Oxygen Isotope Transfer Rates during the Oxidative Coupling of Methane over a Li/MgO Catalyst. J. Catal. 1990, 124, 336.
I n d . Eng. Chern. Res. 1992, 31, 1625-1637 DeBoy, J. M.; Hicks, R. F. Kinetics of the Oxidative Coupling of Methane over 1 w t ISr/La20B. J. Catal. 1988,113,517. Eketrom, A,; Lapszewicz, J. A. A Study of the Mechanism of the Partial Oxidation of Methane over Rare Earth Oxide Catalysts Using Isotope Transient Techniques. J. Phys. Chem. 1989,93, 5230.
Holman, J. P. Experimental Methods for Engineers; McGraw-Hill: New York, 1984, p 87. Hutchings, G. J.; Scurrell, M. 5.; Woodhouse, J. R. Selective Oxidation of Methane in the Preeence of N O New Evidence on the Reaction Mechanism. J. Chem. Soc., Chem. Commun. 1989,765. Ito, T.; Luneford, J. H. Synthesis of ethylene and ethane by partial oxidation of methane over lithium-doped magnesium oxide. Nature 1985,314,721. Ito, T.; Wang, J.-X.; Lin, C.-H.; Lunsford, J. H. Oxidative Dimerization of Methane over a Lithium-Promoted Magnesium Oxide Catalyst. J. Am. Chem. Soc. 1985,107,5062. Iwamatsu, E.; Aika,K.-I. Kinetic Analysis of the Oxidative Coupling of Methane over Na+-Doped MgO. J. Catal. 1989,117, 416. Korf, S. J.; Roos, J. A.; Veltman, L. J.; van Ommen, J. G.; Ross, J.
1625
R. H. Effect of Additives on Lithium Doped Magnesium Oxide Catalysts Used in the Oxidative Coupling of Methane. Appl. Catal. 1989,56, 119. Lee, J. S.; Oyama, S. T. Oxidative Coupling of Methane to Higher Hydrocarbons. Catal. Rev.-Sei. Eng. 1988,30,249. Peil, K. P.; Goodwin, J. G., Jr.; Marcelii, G. A n Examination of the Oxygen Pathway during Methane Oxidation over a Li/MgO Catalyst. J. Phys. Chem. 1989,93, 5977. Roos, J. A.; Korf, S. J.; Veehof, R.H. J.; van Ommen, J. G.; ROSS,J. R.H. Reaction Path of the Oxidative Coupling of Methane over a Lithium-Doped Magnesium Oxide Catalyst-Factors Affecting the Rate of Total Oxidation of Ethane and Ethylene. Appl. Catal. 1989, 52, 147.
Sofranko, J. A.; Leonard, J. J.; Jones, C. A. The Oxidative Conversion of Methane to Higher Hydrocarbons. J. Catal. 1987, 103, 302.
Received for review August 12, 1991 Revised manuscript received March 23, 1992 Accepted April 13, 1992
Synthesis of Reaction Mechanisms Consisting of Reversible and Irreversible Steps. 1. A Synthesis Approach in the Context of Simple Examples Michael L. Mavrovouniotis* Department of Chemical Engineering and S y s t e m Research Center, A . V. Williams Building, University of Maryland, College Park, Maryland 20742
George Stephanopoulos Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
The analysis of pseudo-steady states of a chemical system can be aided by the identification of mechanisms responsible for overall reactions, from a known set of elementary steps that involve overall reactants and products as well as reaction intermediates. In the context of examples of catalytic synthesis of ammonia and methanol, an alternative approach for the construction of mechanisms from steps is presented. The approach is based on successive processing and elimination of reaction intermediates which should not appear in the net stoichiometry of the overall reactions accomplished.
Introduction Consider a given set of elementary reaction steps which are feasible in a system, and the species involved in these steps. Following Happel and Sellers (1982,1983,1989), Happel (1986), Sellers (1984, 19891, and Happel et al. (1990)-this set of references is hereafter referred to as H&S-species can be classified as either intermediates, which occur in very small amounts, or terminal species which can occur in significant amounta and constitute the raw materials and products of the process. An overall reaction mechanism (Horiuti and Nakamura, 1967; Horiuti, 1973; Temkin, 1973,1979) consists of steps combined in specific proportions, such that the net transformation involves only terminal species. Over the course of a reaction, there is significant net production of some terminal species, and signifhnt net consumption of others. Within the pseudo-steady-state assumption, concentrations of intermediates are sufficiently low and, for each intermediate, the rate of production by some steps is balanced by ita rate of consumption by other steps, with the net rate being very small. The pseudo-steadystate assumption seta
* T o whom correspondence should be addressed.
the accumulation term in the mass balance for an intermediate to zero. Overall reactions can thus be defined as the set of net transformations permissible under the pseudo-steady-state assumption, while overall mechanisms are the combinations of steps that accomplish this. This article focuses on the synthesis of reaction mechanisms, the systematic identification of seta of mechanism steps that accomplish net reactions involving only terminal species. One is particularly interested in direct mechanisms (Milner, 1964), which are the smallest possible physically distinct mechanisms; direct mechanisms cannot be shortened through elimination of a step or reduced to a combination of smaller submechanisms. Once direct mechanisms are identified, all other possible mechanisms can be viewed as combinations of direct ones. Another way to define direct mechanisms is to state that they are cycle-free; i.e., the steps participating in a direct mechanism cannot be combined into a “loop” or cycle accomplishing no net transformation. What is usually referred to simply as a reaction mechanism in the literature is often implicitly required to be a direct mechanism, because physical intuition compels avoidance of cycles or excess steps. The concept of direct mechanisms has been well established
0888-588519212631-1625$03.00/00 1992 American Chemical Society
