Ind. Eng. Chem. Res. 1987,26, 400-401
400
Comments on “Synthesis of Alcohols from Carbon Oxides and Hydrogen. 1. Kinetics of the Low-Pressure Methanol Synthesis” Sir: Villa et al. (1985) investigated the kinetics of the low-pressure methanol and reverse-shift (RSR) reactions over a commercial Cu/ZnO/A1203 catalyst, using a Berty reactor. Their rate equation parameters were estimated by regression analysis on the component outlet mole fractions rather than the more common procedure using reaction rates calculated from measured flow rates and component mole fractions. The present correspondence discusses their rate equation formulation and points out discrepencies between the predictions reported by the authors and calculated from their parameter estimates. It is shown that the CO heat of adsorption and CH30H apparent activation energy estimated from their parameter values are negative, a result of the data reported at 235 “C. Analysis of their data as three isothermal sets gives more consistent pararr eter values. The authors data were analyzed according to the following two equations for the methanol and RSR, respectively, rl =
fCOfHz2 - f C H ~ 0 H / ~ e l
(cl + cZfCO
+
c3fC02
+
c4fH2
+ C5fCH30H)3
and f C O i H 2 - fCOfH20/Ke2
r2 = c6(1
+
c7fC0
+ cE!fC02 + c9fH,)2
which are reparameterized forms of - fCH30H/Kel)
klKC&H~(fCOfH22
rl =
+ KCOfCO + K C O i C 0 2 + K H i H , + KCHs0HfCH30H)3 r2 =
k2KC02KH2(fCOiH2
- fCOfH20/Ke2)
(1 + Kcofco + Kco.jco2 + KH~H,)’
where
cj = exp[ Bi, + Biz(
+ k)]
R(7
-
k , = kio exp[ -Ei 1 -
$) ]
Table I. Parameter Values as a Function of Temperature, from Villa et al. (1985) temp, K 488 46.8 0.73 129.4 8.5 0.016 2.76 0.18
c 1
c* c3 c4
c7
CB c9
506 32.8 12.6 40.4 4.7 0.38 1.23 0.14
519 25.7 86.8 18.4 3.1 3.38 0.72 0.12
Table 11. Parameter Values Estimated from CH,OH Rate Data Compared to the Values of Villa et al. (1985) 4 2
6 1
C, C, C3
C,
rate data“ 4.61 1.26 1.76 0.716
Villa et al. 3.49 2.53 3.70 1.54
rate datan 4 334 -41 230 9 178 7 235
Villa et al. 4 883 -39 060 15 948 8 229
“Residual variance was 3.53 with rates in Fmol/(g.s).
Hence, the parameters of the two equations are related and should be estimated simultaneously. According to the authors, “In the course of the analysis, constants C5, C y , C8, and Cg turned out to be negligible.” Calculating C7, C8, and Cg from the above relationships shows that they are not negligible (Table I) relative to other terms in the denominator and must be included in their equation (17). The reported parameter values also give predictions of the CH30H reaction rate almost an order of magnitude lower than the observed values. For run 25, assuming CO, H P ,and COz fugacity coefficients of unity while &H OH = 0.645 and @ H 2 0 = 0.695 with K,, = 3.27 x and ke2 = the predicted CH30H rate is 0.70 X 8.61 X mol/(min.g) and the RSR is -4.2 mol/(min.g). Villa et al. (1985) report values of 13.4 X and 2.35 X lo-* mol/ (min-g), respectively. Finally, if the authors had estimated the activation energies and heats of adsorption from their Bizvalues, they would have obtained -AHco2 = 22 kcal/mol -AH2 = 7 kcal/mol -AHco = -87 kcal/mol EcH,OH
ERsR
= -45 kcal/mol
= 47 kcal/mol
The negative heat of CO adsorption and negative CH30H apparent activation energy suggest a problem with either their experimental data, the parameter estimation procedure, or the form of the kinetic expressions. To resolve some of the above discrepancies, C1-C, were reestimated by regression analysis of their CH30H rate data. Similar values to those reported by Villa et al. (1985) were obtained for B,, as shown in Table 11. If, however, the methanol rate data are analyzed as three sets of isothermal data at 215,235, and 246 “C, the values of Table I11 are obtained. The adsorption and rate constants calculated from C1-CI are also given in Table 111. It is concluded that the data at 235 “C are responsible for the negative CO heat of adsorption and apparent activation energy calculated from Villa’s parameters above. The two sets of data at 215 and 246 “C yield the adsorption constants and apparent activation energy summarized in
It follows that
0888-5885/87/2626-0400$01.50/0
0 1987 American Chemical Society
Ind. Eng. Chem. Res. 1987,26, 401-402 Table 111. Parameter Values Estimated from Isothermal Rate Data temp, OC c1
CZ C3
C,
215
235
246
79.0 17.7 23.8 2.52
103.4 0 5.68 2.31
94.6 29.4 0.917 1.12
residual variance” 0.50
kl
0.008 90 0.224 0.031 9 0.301
Kco KHz
KC02
2.74
3.43
0 0.0224 0.0554
0.0271 0.311 0.0119 0.0097
ORates in Hmol/(g.s).
Table IV. Adsorption Constants and Activation Energy from Methanol Rate Data this work
Klier et al., 1982
16 56 18 -40 -116
12 31 17 -23 -56
-AH*a -AHco;
E’, ASo aSoH2 co2b (I
40 1
(1982), the adsorption values all satisfy the general guidelines (except for ASocoJ given by Vannice (1979) and Boudart (1960), while the CHBOH apparent activation energy is positive and in good agreement with the data of Klier et al. (1982). Considering the standard error associated with the Kco estimate, it could be taken approximately constant ovei the catalyst and temperature ranges of Villa’s work. Finally, if the data reported at 235 “C are accepted as correct, the inconsistent parameter values obtained at this temperature suggest that their assumed form of the kinetic expression is invalid. The authors have not discussed the choice of their kinetic equation, and it is not clear if other equations were considered.
Literature Cited Boudart, M. T h e Surface Chemistry of Metals and Semi-Conductors; Gatos, H. G., Ed.; Wiley: New York, 1960; p 409. Klier, K.; Chatikavanij, V.; Herman, R. G.; Simmons, G. W. J . Catal. 1982, 74, 340. Vannice, M. A.; Hyun, S. H.; Kalpakci, B.; Liauh, W. C. J . Catal. 1979, 56, 358. Villa, P.; Forzatti, P.; Buzzi-Ferraris, G.; Garone, G.; Pasquon, I. Ind. Eng. Chem. Process Des. Deu. 1985, 24, 12. Current address: Department of Chemistry, Lehigh University, Bethlehem, PA 18015.
In kcal/mol. *In cal/(mol.deg).
Table IV. Values reported by Klier et al. (1982) for a Cu/ZnO catalyst are included for comparison. Although the values are higher than those reported by Klier et al.
Kevin J. Smith’ Research Department Sasol Technology P t y . Ltd. Sasolburg 9570, Republic of S o u t h Africa
Response to Comments on “Synthesis of Alcohols from Carbon Oxides and Hydrogen. 1. Kinetics of the Low-Pressure Methanol Synthesis” Sir: The first comment of Smith (1986) concerns the rate equation formulation. He writes eq 11and 12 of Villa et al. (19851, which give the rate of methanol synthesis and of the reverse shift reaction (RSR), respectively, in the forms klKC&H,2(fCOfH,2
r1 =
( l + KCOfCO + KCO$C02
r2 =
k2KC02KH2(fCO$H2
- fCH30H/Keq -k KH$H2
1)
+ KCH30HfCH30H)3
- fCOfH20/Keq
2)
(1 + Kcofco + Kco$co, + KHJH,)’ which implies the following relations between the Ci, K1, and K , parameters KCo = C = C 2 / C 1 KCO,
=
Klier e t al. (1982) in discussing the kinetics of methanol synthesis over a Cu-ZnO catalyst provided evidence that the reaction proceeds via a (bicentric) redox mechanism. We also notice that CO is reduced in methanol synthesis, whereas it is oxidized in the shift reaction. For these reasons, eq 11and 12 were considered in Villa et al. (1985) as empirical expression to be used for design purposes only, and the constants of the equations were treated as independent adaptive parameters. In a second remark Smith observes that “the reported values give predictions of the CH,OH reaction rate almost an order of magnitude lower than the observed values”. On this point we have to acknowledge a typing error in the regression program. The parameters were calculated by using for rl and r2 expressions 1and 2. The denominator
c*= C d C , fCO$Hz
r2 = It2
=
cl2/(c3C4c6)
Accordingly the parameters of the two equations would be related and should be estimated simultaneously. Indeed, the derivations of eq 11and 12 in Villa et al. (1985) lead to the above relations between the parameters assuming L-H-H-W models and the additional hypothesis that the active centers for the two reactions are the same. However, the L-H-H-W models are derived from a number of simplifying hypotheses which hardly apply to real systems and in particular imply a monocentric mechanism. 0888-5885/87/2626-0401$01.50/0
- fCOfHpO/Keq
2
c6
(2)
of eq 1is squared, and this contradicts eq 16 in Villa et al. (1985) where the same denominator is raised to the third power. Furthermore the value C6 so found must be corrected in exp(5.18 + 938[(1/T) When eq 1 and 2 and the correct parameter values are used, the agreement between the estimated and experimental outlet mole fractions of the different components is satisfactory, as reported in Figures 2-5 of Villa et al. (1985). A similar agreement exists between estimated rate values and values derived from experimental data. 0 1987 American Chemical Society
(1/n].
