Ind. Eng. Chem. Res. 2001, 40, 101-107
101
The Kinetics of the Palladium-Catalyzed Vapor-Phase Thermal Decomposition of Ethanol J. Michael Davidson* and Caroline M. McGregor (ne´ e Shirridan) School of Chemical Engineering, University of Edinburgh, King's Buildings, Mayfield Road, Edinburgh EH9 3JL, United Kingdom
L. K. Doraiswamy Department of Chemical Engineering, Iowa State University, Ames, Iowa 50010
The rate of thermal decomposition (190-231 °C) of ethanol on Pd/Al2O3 to yield CH4, CO, and H2 has been studied in a tubular reactor at differential conversion and in a Berty reactor. Ethanal is a byproduct that is also present as an intermediate species formed in a dehydrogenation reaction. The presence of H2 is necessary in the decomposition of ethanal to suppress coking, and under these conditions, decarbonylation is faster than dehydrogenation of ethanol. The differential rate data (206 °C) were fitted to a large number of alternative LHHW kinetic models. These effectively describe the relative strength of adsorption (C2H5OH ≈ CH3CHO > CO > H2 > CH4), whereas discrimination between different kinetic pathways in the surface reaction is difficult. Nevertheless, models that describe the adsorption of ethanol or its surface dehydrogenation perform well. Desorption of H2 is not rate-limiting. In the modeling, the goodness of the fit is dependent on the number of kinetic constants, and they can be increased by elaboration of the mechanistic steps. Introduction Under conditions of oil shortage, fermentation broths have potential as a source of ethanol for a fuel or feedstock. The costs of recovery by distillation are well documented,1,2 and steam reforming has also been considered.3,4 The catalytic decomposition of ethanolwater vapor mixtures (reaction 1) to yield CO, H2, and CH4 also has economic potential compared to the production of fuel-grade ethanol by distillation. We find that alumina-supported palladium is a good catalyst for the decomposition reaction, free of deactivation effects. The present paper is concerned with steady-state kinetic studies and the approach to the steady state. LHHW kinetic models have been fitted to differential rate data, and although they are appropriate for design, they are not expected to be diagnostic of the detailed mechanism but rather to highlight some important characteristics such as the relative strengths of adsorption of reactants and products under reaction conditions. Ethanal, present as a byproduct, is a likely intermediate,5-7 in which case the overall gas-phase decomposition of ethanol ( reaction 1) can thus be represented as the sum of steps 2 and 3.
C2H5OH f CH4 + CO + H2
(1)
C2H5OH T CH3CHO + H2
(2)
CH3CHO f CH4 + CO
(3)
Reaction 2 is promoted by a variety of catalysts8 and is both endothermic and reversible, giving 16% equilibrium conversion at 200 °C and 1.0 atm. Reaction 3 is irreversible, and there are no known catalysts for the back reaction. Thus, reaction 1 is overall endothermic and irreversible; viewed as a decarbonylation, it has also * Author to whom correspondence should be addressed.
been the subject of previous reviews.5 The byproducts are ethanal and traces of ethane, propene, propane, and CO2, the last arising from the shift reaction when water vapor is present. Pulse reactions show that the reaction is more complex than is indicated by the steady-state behavior. These experiments and the LHHW models, which make a fruitful comparison with the previously reported surface science studies of Barteau and co-workers6,7 using Pd(111) and Pd(110) in UHV, are described in the following paper.9 Experimental Section Catalyst screening tests and the studies on the approach to steady state were carried out at integral conversion levels using a small tubular reactor with 5.0 g of catalyst. Evaluation of a range of noble metal catalysts was reported in a preliminary account,10 and palladium on alumina was chosen for further study [from Johnson Matthey, 0.5% palladium deposited (40% dispersion) in the 20-30 µm external layer of 3 × 3 mm cylinders of 100 m2/g chloride-free alumina with a void volume of 0.38 cm3/g). The dilute feed (ethanol mole fraction of up to 0.34) was obtained from a saturator, and the analysis was performed using fid (Porapak Q column; organic components) and tcd (5-Å molecular sieve column; CH4,CO, N2, and O2) chromatographs in parallel. For a molar feed rate of 2.40 × 10-4 mol of ethanol/min, which was small in relation to the surface area of the support, the steady state at saturation was attained after about 30 min. Quantitative rate data were obtained using a tubular differential reactor at 206 °C (Table 1, yC2H5OH ) 0.220.74; XC2H5OH < 3%) and a Berty internal recycle reactor at 196-231 °C. Gas chromatography using Porapak Q columns in temperature-programmed mode (90-160 °C
10.1021/ie000077w CCC: $20.00 © 2001 American Chemical Society Published on Web 12/02/2000
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Table 1. Differential Reaction Rate Dataa-c pEtOH
pAcH
pH2
pCO
pCH4
rAcH
rH2
rH2,calc
rCO
rCH4
rCH4,calc
0.224 0.229 0.233 0.312 0.329 0.421d 0.455 0.457 0.488 0.501 0.510 0.511f 0.513 0.519e 0.522 0.530 0.533 0.538 0.541 0.548 0.549 0.560 0.584 0.736 0.741 0.742
0.00121 0.00119 0.00169 0.00197 0.00221 0.00378 0.00244 0.00447 0.00337 0.00457 0.00314 0.00348 0.00799 0.00448 0.00343 0.00444 0.00575 0.00389 0.00448 0.00275 0.00471 0.00582 0.00487 0.00411 0.00439 0.00390
0.00315 0.00339 0.00401 0.00536 0.00571 0.00855 0.00597 0.00984 0.00728 0.0850 0.00728 0.00720 0.00464 0.00830 0.00728 0.0566 0.00624 0.00426 0.00568 0.00647 0.0110 0.0116 0.0108 0.00889 0.00944 0.00887
0.00230 0.00238 0.00267 0.00383 0.00375 0.00531 0.00369 0.00598 0.00467 0.00369 0.00455 0.00424 0.00508 0.00480 0.00434 0.00380 0.00456 0.00472 0.0217 0.00399 0.00644 0.00653 0.00634 0.00533 0.00569 0.00535
0.00237 0.00246 0.00276 0.00382 0.00388 0.00532 0.00374 0.00593 0.0855 0.00368 0.00452 0.00420 0.00520 0.00473 0.00431 0.00375 0.00459 0.00053 0.00138 0.00396 0.00635 0.00642 0.00632 0.00523 0.00561 0.00533
5.83 6.13 7.78 6.94 8.26 10.03 11.20 10.18 9.79 13.90 9.33 11.07 -1.35 11.50 10.54 13.98 5.94 12.32 14.55 9.26 7.26 10.30 9.48 9.324 9.71 8.69
15.26 17.36 18.45 18.84 21.37 22.65 27.38 22.44 21.16 20.32 21.68 22.89 14.08 21.33 22.42 19.99 19.80 13.02 17.76 21.79 16.91 20.41 21.07 20.16 20.86 19.77
15.69 13.99 14.59 17.50 17.78 17.13 23.83 16.78 20.92 16.22 23.27 22.54 14.00 19.81 23.06 18.65 17.97 22.31 13.68 27.04 19.35 17.56 20.30 28.84 27.78 29.79
11.15 12.22 12.38 13.48 14.03 14.09 16.91 13.63 13.57 11.23 13.54 13.50 15.41 12.34 13.36 11.98 14.47 1.919 4.29 13.44 9.92 11.55 12.33 12.74 12.57 11.92
11.48 12.60 12.72 13.44 14.52 14.10 17.15 13.53 11.73 11.21 13.45 13.35 15.77 12.16 13.27 11.79 14.56 1.668 4.48 13.33 9.78 11.36 12.29 11.85 12.40 11.88
12.02 14.34 13.34 12.56 13.11 12.79 13.56 12.31 12.58 11.18 13.23 13.7 12.11 13.29 13.58 12.11 13.29 13.53 5.80 13.53 11.95 11.77 12.02 12.81 12.54 12.76
a Partial pressures are average values over the reactor, in atmospheres, and reaction rates are in mmol (g of catalyst)-1 min-1. b Partial pressures in bold face are values for which the component was added to the gaseous feed. c Rates are experimental values, except for rH2,calc and rCH4,calc, which are calculated using model D2. d Partial pressure of water vapor in the feed ) 0.00099. e Partial pressure of water vapor in the feed ) 0.00167. f Partial pressure of water vapor in the feed ) 0.00059.
at 10 °C/min) was found to be suitable for complete analysis. Standard deviations for replicate analyses of the calibration gas mixtures and product mixtures were 3.49 (H2), 2.82 (CO), 2.20 (CH4), and 12.58 (CH3CHO) in terms of percent of the means. Components of the feed to the differential reactor were obtained by vaporization of liquid ethanal, ethanol, and water in small pressure vessels held in precision ovens. The vapors escaped through pinhole orifice plates, and the flows could be adjusted by changing the temperature of the oven. Argon (inert diluent), CH4, CO, and H2 were monitored by rotameters corrected for the downstream pressure. Numerous steady-state runs of a few hours duration were carried out with little sign of catalyst deactivation. In the Berty reactor, the feed was an ethanol-water mixture, used to simulate the reaction of a flash distillate with conversion of ethanol up to 25%. The decomposition and shift reactions occurred simultaneously. When conditions allowed a direct comparison between the two reactor systems, good agreement was obtained for the rate of production of methane, rCH4. Results General Characteristics of Ethanol Decomposition. Variation of the stirrer speed in the Berty reactor and calculation of the Weisz modulus11 were used to test for the possibility of external mass transfer control and pore diffusion control, respectively. It was concluded that the catalytic decomposition of ethanol proceeds under chemical control. Overall activation energies were obtained from the Berty reactor experiments on the basis of rates of production of H2 and CH4. The values obtained were 62 and 77 kJ/mol, respectively. Effect of Ethanol Partial Pressure on the Rate and Selectivity. At low mole fractions of ethanol (yC2H5OH ) 0.028 in N2 carrier), the yield of methane (moles per mole of ethanol reacted) at the initial rate is 95%, and
both propane and propene are present as byproducts. Saturation of the catalyst takes some time, and as it approaches steady state, the propene disappears. The interpretation is that aldol condensation of the initially formed ethanal yields 2-butenal, which is then decarbonylated to propene.12,13 It was confirmed independently that 2-butenal in mixtures with ethanol vapor loses CO at 170 °C over Pd/alumina. Propene is hydrogenated to propane by H2 from reaction 2. The aldol condensation is characteristic of Pd/alumina-catalyzed reaction at low surface coverage and does not take place on the alumina-free support. The rate of decomposition of ethanol, -rC2H5OH, increases to 27.4 µmol (g of catalyst)-1 min-1 as yC2H5OH is increased up to 0.46 at 200 °C and 1.0 atm and then decreases to 20.0 µmol (g of catalyst)-1 min-1 at yC2H5OH ) 0.74. Near the maximum rate, the reaction appears to be overall pseudozero-order. An additional principal feature of the reaction is the change in selectivity from production of CH4/ CO/H2 to production of ethanal/H2 as the partial pressure of ethanol is raised. At low partial pressures of ethanol (yC2H5OH ≈ 0.02 atm), the yield of CH4/CO/H2 is about 95%. As the partial pressure of ethanol is increased to about 0.5 atm., the yield drops to 55% and then remains constant up to pC2H5OH ) 0.77 atm. Ethanal, the only other significant product, makes up the balance. Effect of the Partial Pressure of Product Species on the Rate and Selectivity. Addition of CO to the feeds in otherwise similar steady-flow experiments showed inhibition of the overall rate, presumably because of chemisorption of the CO. (See Table 1.) There was also a very strong shift in the selectivity from production of CH4/CO/H2 to ethanal/H2, the rate of production of the latter being increased. Inhibition by H2 was slight, and again, there was a small change in selectivity toward ethanal. Tests of the effect of H2O on the rate of ethanol decomposition showed only a slight
Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001 103 Table 2. Comparison of Decomposition Rates for Ethanol and Ethanal at 206 °C and Yieldsa ethanal feed -rCH3CHO -rC2H5OH YCH4 YC2H5OH YCH3CHO YC3H8 YC3H6 YCO
186.5 -2.2 78.4 1.22 5.67 13.77 88.6
Table 3. Mechanism and Rate-Determining Steps of Series B and D Modelsa
ethanol feed -11.5 (approx.) 21.0 45 54.8 0 0 39.6
a Rates are in µmol (g of catalyst)-1 min-1, and yields, Y , are i percentages relative to the reactant.
reduction in -rC2H5OH. Using an ethanol-water feed (Berty reactor), CO2 was a product and represented about 25% conversion of the initially formed CO via a shift reaction. There was a corresponding increase in rH2. Added methane did not affect the rate, despite evidence of slight chemisorption from its exchange with D2 on the palladium catalyst at 200 °C. Addition of ethanal to the feed increased the rate of production of methane and resulted in a slight decrease in -rC2H5OH, possibly because of an effect on the reversible dehydrogenation of ethanol. Catalytic Decomposition of Ethanal. Palladium/ alumina catalyses the fast decomposition of ethanal, but with rapid catalyst deactivation. Addition of dihydrogen to the feed prevents deactivation, and steady decarbonylation takes place at 206 °C. Reaction rates are given in Table 2, on the basis of molar feed rates, conversions, and product yields to allow a direct comparison with the ethanol decomposition reaction in the presence of H2. It is likely that, at comparable concentrations, decarbonylation of ethanal would be much faster than ethanol dehydrogenation and, hence, that ethanol decomposition can be sustained by quite a low partial pressure of the intermediate. In an experiment in the differential reactor in which the reactor feed was switched from ethanal/H2 at steady state to ethanal alone, the rate dropped to 65.4 µmol (g of catalyst)-1 min-1 after 1 h. On a further switch to ethanol feed, the catalyst sustained only a very low rate, (-rC2H5OH) ) 2.0 µmol (g of catalyst)-1 min-1, and there was no recovery. The catalyst activity could be restored by decoking with 3% O2 in N2 using a slow temperature ramp to 206 °C. LHHW Kinetic Models. Initially we assumed that the CH4, CO, and H2 mixture is produced from ethanol via ethanal according to eqs 2 and 3. Attempts to model the complex kinetics by means of power-law rate equations (series A) were not successful, and therefore we turned to the LHHW method, which allows greater elaboration of the mechanism through adsorptiondesorption and surface reaction steps. Details of the data fitting for all of the models tested are given in the Supplementary Information, Table S1. The decomposition of ethanol, with ethanal as a byproduct, requires description by two independent reactions, and hence, two rate-determining steps (rds) must be used to generate the LHHW model equations from trial mechanisms.14-16 If those used were rH2 and rCH4, then the other rates satisfy the relationship rCO ) rCH4 ) rH2 - rCH3CHO. For each class of multistep mechanism (series B to series L), there are a number of possible combinations of rds that can be chosen (e.g., D1-D4, Table 3), the remaining steps constituting pseudo-equilibria of fast reactions. In many cases, one of the rds was the
mechanistic step 5 6B 6D 7B 7D 8 9 10 11 12 13 14 15
C2H5OH + S T [C2H5OH]S [C2H5OH]S T [CH2CHO]S + H2 S + [C2H5OH]S T [CH3CHO]S + [H2]S [CH3CHO]S f [CO]S + CH4 S + [CH3CHO]S f [CO]S + [CH4]S [CH3CHO]S T CH3CHO + S [CO]S T CO + S [H2]S T H2 + S [CH4]S T CH4 + S C2H5OH +2S T C2H5OS + HS C2H5OS + S T [CH3CO]S + HS C2H5OS f [CO]S + CH4 + HS 2HS T H2 + 2S
rate-determining steps B2, D2 B1 D1 B1, B2, B3 D1, D2, D3, D4 B3, D3, J3 D4 J2 J1 J1, J2, J3
a Series B models consist of eqs 5, 6B, 7, 8, and 9. Series D models consist of eqs 5, 6D, 7D, and 8-11. Series J models consist of eqs 12-15, 8, and 9.
irreversible formation of methane, either as a gas or adsorbed on the catalyst. The LHHW equations were fitted to the differential rate data set of Table 1 using the EO4CCF multivariable function minimization routine of the NAG library. The algorithms are given in Appendix 1. More than 50 isothermal (206 °C) models were tested, having from 5 to 9 constants. Extension to a nonisothermal treatment would require an enormously increased quantity of data. Reliable discrimination between the higher models having a larger number of constants would also require a very large data set. For reactor design, the goodness of fit is paramount, regardless of whether the mechanism is described in full detail. In practice, models giving a good fit are likely to incorporate significant features of the kinetics, such as strong chemisorption of CO. In the following paper,9 we examine the extent to which surface science methods assist us in confirming the mechanism. In the series B-D mechanisms, only gaseous and adsorbed molecular species are represented in the chemical equations. However, the surface reaction steps might themselves be multistep processes involving adsorbed radicals such as surface hydrogen, ethoxide, acetyl, and methyl (series E-K models, Table S1). Surface combination of hydrogen atoms affords dihydrogen, either physically adsorbed or as a free molecule. Certain surface reaction steps used in the models parallel those established in homogeneous reactions of complexes,17,18 where ethanol loses hydrogen atoms sequentially, forming first ethoxide and then adsorbed ethanal. Chemisorbed ethanal yields a surface acetyl species from which surface methyl and CO are derived by a methyl migration step. Models J and K describe dissociative chemisorption of ethanol, followed by decomposition of surface ethoxide in a single step without the intermediacy of surface ethanal; that is, CH4/CO/H2 and ethanal are formed by different routes. In series L models, dissociative chemisorption of ethanol onto two types of sites is followed by formation of molecular CH4 and CO from adsorbed ethanal. Of the LHHW models that were tested, the lowest value of the objective function, S(b)min, was given by model D2, which has seven constants, all of which are positive. The common mechanisms and the rds of models B1-B3, D1-D4, and J1-J3 are given in Table 3, and the results of the data fitting are given in LHHW form in eqs 16 and 17 of Table 4. In eqs 5-15 (Table 3),
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Table 4. LHHW Models for Catalytic Decomposition Models B2 and D2
r H 2 ) r5 ) rCH4 ) r7 )
model
k5
(
k5 pC2H5OH -
)
pCH3CHOpH2 Ke
(16)
(1 + K′6pCH3CHOpH2 + K8pCH3CHO + K9pCO + K10pH2 + K11pCH4) k7K8pCH3CHO
(17)
(1 + K′6pCH3CHOpH2 + K8pCH3CHO + K9pCO + K10pH2 + K11pCH4)n
K′6
k′7
K8
K9
K10
K11
S(b)min
S(β)95%
351.6 1632 29571 1601 357.9 2664 2975 114.3 408.1 26271 333.9 90.94 2.987 0.825 1759 2027 In model B2, K′6 ) K8/K6B, k′7 ) k7BK8 and n)1; in model D2, K′6 ) K8K10/K6D, k′7 ) k7DK8 and n ) 2. Ke ) pCH3CHOpH2/pC2H5OH ) 0.01067 atm-1 at 473K. The rate constants k5 and k7 have units µmol (g of catalyst)-1 atm-1 min-1 and µmol (g of catalyst)-1 min-1, respectively. K′6 has dimensions atm-2; other Ki are adsorption coefficients and have units atm-1.
B2 D2
Model J3 k14K12 (pC2H5OHxpH2) xK15 rCH4 ) r14 ) K12pC2H5OH K12K13pC2H5OH + 1+ + K9pCO + xK15pH2 K15pH2 x(K15pH2)
(
rCH3CHO ) r8 )
(
1+
( )(
K12pC2H5OH
xK15pH
)
K12K13 pC2H5OH pCH3CHO K15 pH 2 ke
k8
2
+
K12K13pC2H5OH K15pH2
)
(18)
2
)
2
+ K9pCO + xK15pH2
(19)
k14(K12/xK15) ) 13.43 µmol (g of K12/xK15 ) 0.1205 K12K13/K15 ) 0.007799, K9 ) 51.86 atm-1, -0.5 -1 -1 -xK15 ) 0.3822 atm , k8K12K13/K15 ) 0.2885 µmol (g of catalyst) min , S(b)min )1789 and S(β)95% ) 2029. catalyst)-1
atm-1.5
min-1,
atm-0.5,
Model BB rH2 ) (1147pC2H5OH - 551.5pCH3CHOpH2)/D
(20)
rH4 ) (569.8pC2H5OH + 15538pCH3CHO)/D
(21)
D ) (1 + 38.91pC2H5OH + 0.01763pH2 + 908.3pCO - 30.42pH2 + 11744pCH3CHOpH2 + 16.01pCOpH2)
S represents a free surface adsorption site; [CH3CHO]S, etc. represent adsorbed species; and HS is a chemisorbed hydrogen atom. Model D1 also had a low value of S(b)min, but the adsorption coefficient for CH4 was negative, although close to zero. Models D3 and D4 were rejected as physically unrealistic because of negative values of one or more of the kinetic constants. The related, and simpler, series B LHHW models (Table 4) have five kinetic constants, allowing for formation of gaseous H2 and CH4 without adsorption. Models B1 and B2 were statistically and physically acceptable, and indeed model B1 is only slightly inferior to D1, which has two more constants. The forms of the series B and series D rate equations differ with respect to the power of the adsorption term because of the involvement of more active sites in the latter mechanism. Model J3 expresses the independent formation of [CH3CHO]S and [CO]S/HS/[CH4]S from chemisorbed ethoxide. One further model of considerable significance is also based on the series B network without the rds assumptions. In model BB, the rate of formation of methane, rCH4, is predicted from the rate of irreversible decomposition of adsorbed ethanal (7B) with the assumption that the remaining steps (5, 6B, 8, and 9) are all at equilibrium. This procedure generates a nine-constant model that expresses the ultimately irreversible decomposition of ethanol to CH4/CO/H2 in a batch system. Ethanal is important only as a transient intermediate. In a batch system, rCH3CHO will be positive at first and later negative. In conjunction with the differential rate data set, model BB (Table 4, eqs 20 and 21) gives a
better fit than any of the rds models [S(b)min ) 1262, S(β)95% ) 1500]. Presumably, the performance arises from the larger number of kinetic constants, rather than from any mechanistic realism. Model BB can be considered a useful design equation that should accurately reflect adsorption effects, but physical insight is obscured by the profusion of nonlinear terms. Some nonisothermal rate data were collected from the Berty reactor (196-231.5 °C) and, by using runs having nearly constant outflow conditions, various estimates of the overall activation energy could be made. For example, using the rate of appearance of methane, a value of Ea ) 77 kJ/mol was obtained. This accords well with literature values of 77.8-96.2 kJ/mol for dehydrogenation of ethanol on copper catalysts and 64 kJ/mol for dehydrogenation on nickel/alumina.18,19 The value for an oxide catalyst, MgO, is much higher at 122.6 kJ/ mol.20 In the testing of kinetic models, this comparison provides limited evidence that dehydrogenation of ethanol is the overall rate-determining step, rather than decarbonylation of ethanal. Discussion In the presence of H2, which can be generated in situ, ethanol undergoes catalytic decomposition at 190-231 °C, yielding CH4/CO/H2 with ethanal as a byproduct. Under these conditions, steady-state reaction is free of the complexities of the start-up or of the coking seen in the case of ethanal, and so reproducible differential rate data were readily obtained. Using these data, LHHW models were derived and tested for statistical signifi-
Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001 105
cance,21-23 with the outcome being that, although discrimination between the best models is poor, important common features can be discerned. Where successful models contain linear adsorption terms of the form Kipi they decrease in the order C2H5OH ≈ CH3CHO > CO > H2 > CH4, which fits well with our qualitative observations. That is, the reactants ethanol and ethanal are strongly adsorbed, and of the products, only CO is strongly adsorbed, so that it is an inhibitor. From observations of start-up of a fresh catalyst sample, it is clear that much ethanol is adsorbed onto the support, which is reflected in the high values of the adsorption coefficient. The weak, nearly zero-order dependence of -rC2H3OH on the partial pressure of ethanol is consistent with its high surface coverage. It was found by direct measurement that the rate of decarbonylation of ethanal is fast compared with the rate of reaction of ethanol. This suggests that one of the steps in the dehydrogenation of ethanol is an rds and, in practice, models giving a good fit have either the adsorption of ethanol, the dehydrogenation of adsorbed ethanol, or the decomposition of surface bound ethoxide (J3) as an rds. The models for fast equilibrium dehydrogenation of ethanol followed by slow decomposition of ethanal and a further slow desorption step were physically unrealistic; ratedetermining competition between desorption and decomposition of adsorbed ethanal invariably gave negative adsorption coefficients for ethanol (B3 and D3). Similarly, models in which the formation of gaseous H2 is desorption limited had a poor fit to the data and were rejected on similar grounds. In the steady-state reaction, the rates of steps for production of CH4 and CO are equal, and one of these must be considered as the second rds. Assuming irreversible formation of CH4, either gaseous or adsorbed, the LHHW method cannot be applied to rate-determining desorption of CO because its surface concentration cannot be found from any of the pseudo-equilibria. However, the necessary high coverage does not seem likely in competition with strongly adsorbed ethanol, at least at the partial pressures of CO that occur in our study. Furthermore, in our pulse reaction studies of the decomposition of ethanal, carbon monoxide desorbed before methane.9 We return to this question in the following paper. The most satisfactory LHHW models combined rate-limiting irreversible formation of CH4 with either adsorption of ethanol (B2 and D2) or dehydrogenation of adsorbed ethanol (B1). In general, there does not appear to be any advantage in the further elaboration of the molecular processes within the models as the minimized values of the objective functions were larger, despite a larger number of kinetic constants. One exception is model J3 in which surface hydrogen and ethoxide are formed by dissociative adsorption. The latter undergoes dehydrogenation to yield adsorbed ethanal and simultaneously decomposes to gaseous methane and adsorbed CO and hydrogen (Table 3, eqs 12-15). Physical interpretation of the rate equations (Table 4) is difficult because of nonlinearities in the adsorption term, but the model is of interest because our transient reaction studies and surface science results support the possibility of independent decomposition pathways, of which only one should persist in steady-state operation. The nine-constant model BB, which gave the lowest value of the objective function, was derived assuming equilibrium relationships for all of the reaction steps,
other than the irreversible formation of methane. In practice it differs little from the five-constant model B1 because, under our conditions, terms of the form Cnpipj were small compared with the adsorption terms Cmpi and could be regarded as introducing polynomial corrections. An alternative approach is to derive the rate equations from values of the surface concentrations of ethanol, ethanal, CO and H2 using the pseudo-steadystate approximation. The result is another nine-constant model of even more complex form than model BB. Conclusions The thermal decomposition of ethanol vapor over a Pd/Al2O3 catalyst is a clean reaction, and the LHHW method has been used to derive a number of trial kinetic rate equations based on surface reaction rates of adsorbed species and the appropriate adsorption-desorption pseudo-equilibria. These have been fitted to steadystate isothermal differential rates of thermal decomposition of ethanol to CH4/CO/H2 via the intermediate ethanal. From the goodness of fit, the relative strengths of adsorption of the component species of the system are readily found. Successful modeling requires identification of two rate-determining steps, and many possibilities can be rejected on the grounds of poor fit or physically unacceptable kinetic constants. For example, it is clear that the mechanism does not involve the fast equilibrium dehydrogenation of ethanol to ethanal. Discrimination between the best models is partial in character and relates to adsorption effects and stoichiometric descriptions rather than identification of detailed mechanisms, which requires the use of additional physical methods. Potential side reactions are unimportant under the conditions of steady operation; the H2 product supresses coking, and aldol condensation of ethanal does not take place at high catalyst coverage by ethanol. Appendix Modeling Methods.21 Each differential rate experiment yielded values of v observed reaction rates. In this case, v ) 4, and these dependent variables, to be predicted by the LHHW rate equations, are rCH3CHO, rH2, rCO, and rCH4. The model equations, containing p parameters represented by β and expressed as a function of the independent composition variables (z), are to be fitted to the data set
y ) f(z,β) + where is the column vector of the v experimental errors associated with the observations, y. The target in the modeling is to choose the form of f(z,β) and the values of the parameters so that a suitable function of the errors is minimized. Various objective functions are based on the form of the probability distribution of the errors. The joint probability density function of the errors is p(,ψ), where ψ represents the means and variances of the independent variables. The residuals, γ - f(z,β), replace the errors, yielding the likelihood function L(β,ψ) ) p[z - f(x,β)]. For the case in which the experimental errors in each response are independent of the errors in the other responses, the likelihood function can be maximized by minimizing the objective function S(β)22
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Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001 v
S(β) )
Φ ) Weisz modulus σqr ) element of the covariance matrix ψ ) function of independent variables
n
∑ σqr s)1 ∑ (ysq - yˆ sq)2 q)1
where σqr are the elements of the covariance matrix to be determined from replicate experiments. The objective function was minimized as S(b)min, where b is the approximation to the parameter vector β, using the nonlinear least squares simplex routine EO4CCF in the NAG library. Initial guesses were obtained by linearization of the LHHW form for use in a linear least squares program. Tests are required for the statistical adequacy or lack of fit of the model. The F-test of Froment23 calculates the significance of the overall regression for the multiresponse objective function; the mean regression sum of squares is compared with the mean residual sum of squares to determine whether Fc exceeds the tabulated percentage point, in this case with R ) 0.05. v
∑
Fc )
q)1 v
∑
yˆ sq2/p
s)1
n
σ ∑ (ysq - yˆ sq)2/(nv - p) ∑ q)1 s)1 qr
For the case of a meaningful regression, an approximate confidence interval, S(β), was calculated.21
[
S(β) ) S(b) 1 +
One of us (C.M.M.) thanks the Birse Family Trust for the award of a studentship and is most grateful to Professor L. K. Doraiswamy and the staff of the National Chemical Laboratory for their most extraordinary hospitality during the year when much of this work was carried out at Pune. Supporting Information Available: Details of the data fitting for all of the models tested, Table S1. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited
n
σqr
Acknowledgment
]
p F(p, (nv-p), (1-R)) (nv - p)
Nomenclature Subscripts i relate to chemical species Co,i ) bulk gas concentration of species i, mol/cm3 D ) adsorption term in LHHW equations De ) effective diffusivity, cm2/s fid ) flame ionization detector Ea ) activation energy, kJ/mol Fc ) F-test function i ) subscript related to the chemical species kx ) reaction rate constants in eq x, mol/(g cat) atm s etc Ke ) partial pressure based equilibrium constant Kx ) adsorption coefficient for eq x, atm-1 L ) diffusion distance, cm LHHW ) Langmuir-Hinshelwood-Hougen-Watson n ) exponent of D in LHHW equations pi ) partial pressure of species i, atm p ) number of parameters in LHHW equations pi ) partial pressure of species i, atm q ) subscript of observed reaction rate rds ) rate-determining step -ri, +rj, etc. ) rates of reaction, mol (g of catalyst)-1 min-1 s ) subscript of the n replicate observations of a reaction rate S(b)min ) minimized value of the objective function S(β)95% ) 95% confidence limit of the objective function tcd ) thermal conductivity detector v ) number of observed reaction rates XC5H5OH ) Fractional conversion of ethanol yi ) mole fraction of species i ysq ) experimental value of sth observation of q yˆ sq ) predicted value of sth observation of q Greek Letters R ) tabulated percentage point β ) function of kinetic parameters ) experimental error associated with an observation of y
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Received for review January 18, 2000 Revised manuscript received August 3, 2000 Accepted October 4, 2000 IE000077W
