Ind. Eng. Chem. Res. 1995,34, 49-58
49
KINETICS, CATALYSIS, AND REACTION ENGINEERING A n Experimental Study of the Kinetics of the Selective Oxidation of Ethene over a Silver on a-Alumina Catalyst Peter C. Bormant and K. Roe1 Westerterp' Chemical Reaction Engineering Laboratories, Department of Chemical Engineering, University of Twente, P.O. Box 21 7, 7500 AE Enschede, The Netherlands
The oxidation of ethene to ethene oxide, carbon dioxide, and water over a n industrial silver on a-alumina catalyst has been studied experimentally in a n internal recycle reactor. Several sets of rate expressions were tested, and three of them were found to describe the experiments with almost the same accuracy. Of these the expressions based on a Langmuir-Hinselwood mechanism in which adsorbed ethene reacts with dissociatively adsorbed oxygen is preferred:
K'i &
+ K'i +
i+
+ Pio
ri = (ki PE @&l PE K"8, K' Pc + K'k Pw These relations are able to describe our experimental ata with an average error of 20% for the epoxidation reaction and 15% for the combustion. Carbon dioxide, ethene oxide, and water were found to inhibit the rates of reaction and affect the selectivity of the reactions. The apparent activation energy of the combustion reaction is larger than that for the epoxidation reaction; they are 86 and 70 kJ/mol, respectively. Thus the selectivity toward ethene oxide decreases with increasing temperature. Deactivation of the catalyst used in the kinetic experiments was encountered. This deactivation was corrected for when fitting rate expressions. In a separate set of experiments fluctuations of catalyst activity were found during the first 100 h of operation under reacting conditions. The final activities for different batches of catalyst varied considerably. Introduction In our laboratories the modeling of cooled tubular reactors is being investigated. As a model reaction for the experimental work the oxidation of ethene to ethene oxide, carbon dioxide, and water catalyzed by silver supported on a ring-shaped a-alumina carrier is chosen. The reactions involved are the epoxidation
+ io2
C2H4
--+
C2H40
AH = -105
kJ/mol ethene
and the complete combustion C2H4
+ 302
-C
2C02
+ 2H2O AH = -1323 kJ/mol ethene
Generally the reaction scheme is considered to be parallel; however, oxidation of ethene oxide can also occur
+
1 C2H40 250,
-.-. 2C02 + 2H20 AH = -1218
kJ/mol ethene oxide
The reactions are strongly exothermic, and we desire t o use them for investigating heat effects in packed bed reactors. The occurrence of parallel and consecutive reactions enables us to study selectivity problems. In the industrial production of ethene oxide the reactions are carried out with oxygen and an excess of ethene,
* Author to whom correspondence should be addressed.
Present address: DSM Research, P.O. Box 18, 6160 MD Geleen, The Netherlands. t
above the upper explosion limit. For safety reasons, and because of the high mass flows required for experiments in the cooled tubular reactor, we chose to operate with air under the lower explosion limit. This limit is 3% ethene in the range of our operating conditions, see Craven and Forster .(1966). No chlorine modifier is added to the feed gas in our experiments. The oxidation of ethene over supported silver catalysts has been studied extensively. Reviews have been presented by Verykios et al. (1980), Sachtler et al. (19811, Srivastava (19881, and van Santen and Kuipers (1987). There is no agreement on the mechanism of the reactions. As a consequence kinetic relations presented by different authors vary in form and in parameter values. As we need accurate rate expressions to describe packed bed reactor experiments, we decided to investigate the kinetics of the reactions ourselves. The catalyst used in our study is a modern commercial silver on a-alumina catalyst. The particles are Raschig rings with an outer diameter of 8.4 0.2 mm, an inner diameter of 3.0 f 0.3, mm and a height of 8.6 k 0.4 mm. Because of confidentiality reasons we are not able t o provide detailed information on the catalyst formulation.
*
Literature
In the literature the partial pressures of ethene, oxygen, carbon dioxide, ethene oxide, and water have all been reported to influence the rates of reaction. In this section the adsorption behavior of the different components on silver and the influence of the partial pressures of these components on the reaction rates as reported by different authors will be briefly summarized.
0888-5885/95/2634-0049$o9.oo/0 0 1995 American Chemical Society
50 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995
Table 1. Survey of Different Rate Expressions for the Oxidation of Ethene As Presented by Different Investigators authors
reaction rate expressions
Klugherz and Harriot (1971)
Metcalf and Harriot (1972)
Petrov et al. (1985) Ghazali et al. (1983);Park and Gau (1987)
r -
+
KlPEpO K,PE
-1 Kg,
r.=
' (1 +
+
V E P O
r -1 Kg,
+
+ K4PE
K&EiKO,PEpO
+ KO$,'
+KEo,iP~~)2
Stoukides and Pavlou (1986)
Al-Saleh et al. (1987)
Three types of oxygen have been observed on silver surfaces, they being molecular, atomic, and subsurface oxygen, see van Santen and Kuipers (1987). Atomic oxygen species are believed t o be the reactive species for both reactions, see e.g., Gleaves et al. (1990) and van Santen and Kuipers (1987). Atomic oxygen weakly bound to the surface is thought to be responsible for epoxidation whereas strongly bound oxygen is responsible for the complete combustion. The presence of oxygen dissolved in the silver matrix, subsurface oxygen, is found to be a prerequisite for epoxidation activity. Ethene and carbon dioxide are reported not to adsorb on a reduced silver surface but do adsorb on an oxygencovered surface. Carbon dioxide forms surface carbonates, see Wachs and Keleman (1981). Water adsorbs on both silver and silver oxide. Benndorfet al. (1986) report ethene oxide t o adsorb on both an oxygen-free and an oxygen-covered silver surface. Ethene oxide decomposes over an oxygen-free silver surface, see van Santen and Kuipers (1987). Reaction rates as a function of ethene partial pressures go through a maximum, which depends on the partial pressure of oxygen, see Klugherz and Harriot (1971) and Park and Gau (1987). Reaction rates as a function of oxygen partial pressures also go through a maximum depending on ethene partial pressure, see Metcalf and Harriot (1972). A survey of the orders in ethene and oxygen partial pressures, as obtained by different investigators, can be found in the review by Sachtler et al. (1981). The orders vary between -0.3 and 1.5 for oxygen and -0.2 and 1 for ethene. Carbon dioxide strongly inhibits both reactions; ambiguous results have been presented with regard to which of the two reactions is more strongly inhibited, see Wachs and Keleman (1981). In recent studies carbon dioxide was shown to more strongly inhibit the complete combustion which leads t o an increase of the selectivity toward ethene oxide with increasing partial pressures of carbon dioxide, see Eliyas and Petrov (1990) and Grant et al. (1987). Metcalf and Harriot (1972) report a decrease of the epoxidation rate upon addition of ethene oxide, while the complete combustion remains unaffected during an initial period, followed by a slow decrease of both rates until almost no catalyst activity is left.
Stoukides and Pavlou (1986) report for unsupported silver a decrease of the epoxidation reaction and a slight increase of the complete combustion with increasing ethene oxide partial pressure. They explain this as a result of both the inhibition of the reactions by ethene oxide and the increased rate of the oxidation of ethene oxide at higher ethene oxide concentrations. Water is reported by Metcalf and Harriot (1972) to inhibit both reactions equally strong. Recently Liu et al. (1990) reported that water inhibits epoxidation and promotes the complete combustion. From the results of the different investigations it can be concluded that all components can influence the reaction rates and that reported results are sometimes contradictory. In Table 1 a brief survey of different reaction rate expressions as proposed by different investigators is presented. Klugherz and Harriot (1971)interpret their results based on a model in which ethene and oxygen compete for adsorption on an oxygen layer adsorbed on the silver surface. A bimolecular reaction between ethene and oxygen is the rate-limiting step. The influence of all products is lumped in one term. Metcalf and Harriot (1972)using the results of Klugherz and Harriot (1971) present expressions accounting for inhibition by reaction products. Petrov et al. (1985) use relations in which both reactions are assumed to proceed on the same catalytic site. Ghazali et al. (1983) and Park and Gau (1987) use dual site Langmuir-Hinselwood relations to represent their data. In both studies it is shown that under reacting conditions part of the catalytic surface is covered by deposits. Stoukides and Pavlou (1986) applied expressions in which epoxidation and complete combustion are considered to occur on the same site. They also account for the consecutive reaction of ethene oxide to carbon dioxide and water. AlSaleh et aZ. (1987) in their correlations account for inhibition by carbon dioxide. The brief survey shows that different rate expressions are used by different authors. Some are based on mechanistic assumptions, others are empirical. To our knowledge no rate expressions have been presented in
Ind. Eng. Chem. Res., Vol. 34, No. 1,1995 5 1
Figure 1. Schematic drawing of the experimental setup.
literature which take into account the dependence of the reaction rates on the partial pressure of all components.
Experimental Section The kinetic experiments were performed in an internal recycle reactor with a design similar to that of Berty (1974). The reactor contains a basket, in which a variable amount of catalyst can be placed, and a magnetically driven blower for the internal recirculation of the gas in the reactor. For a detailed discussion of the reactor design and a schematic drawing of the reactor, see Bos et al. (1989). The reactor allows kinetic investigations a t isothermal conditions while the influence of mass and heat transfer resistances on the reaction rates are largely avoided. To avoid falsification of the kinetic data by concentration and temperature gradients in the catalyst bed the experimental conversion of ethene is limited to 50%,see Borman (1992). In the catalyst bed the temperatures of two individual catalyst particles and that of the gas were measured. It was ensured that the difference between the temperatures of the gas and the particles never exceeded 2 K. The catalyst temperature was taken as the reaction temperature. Inter- and intraparticle mass transfer resistances are negligible in the experiments as was concluded on the basis of the criteria given by Mears (1971). The flow scheme of the experimental setup is shown in Figure 1. Premixed gases containing ethene, oxygen, carbon dioxide, and nitrogen were used to minimize experimental error in the flow rate and the gas composition. The composition of the different feed gases are given in Table 2. To investigate the influence of the ethene oxide partial pressure on the reaction rates in a number of experiments ethene oxide was added to the feed gas by feeding nitrogen with 1.5%ethene oxide and an ethene/air gas mixture simultaneously to the reactor. The influence of the partial pressure of water on the reaction rates was investigated by performing experiments with feed gases presaturated with water at a temperature of 46 "C. The reaction temperature was controlled by an electrical oven surrounding the reactor. The effluent gas was vented through a back-pressure controller. The mole fractions in the feed and the
Table 2. Compositions of Feed Gases Used in the Experiments To Investigate the Influence of the Ethene, the Carbon Dioxide, and the Oxygen Partial Pressures on Reaction Rates composition in vol % gas mixture
ethene
oxygen
carbon dioxide
1 2 3 4 5 6 7
1.98 2.49 2.38 1.00 1.00 1.00 1.00
7.7 13.6 20.3 7.0 12.0 12.0 7.0
0.01 0.02 0.03 0.17 0.17 1.00 1.00
Table 3. Partial Pressure Ranges Covered in the Experiments partial pressure in bar component ethene oxygen carbon dioxide ethene oxide water
lowest 0.006 0.110 0.002 0.002 0.001
highest 0.18 2.00 0.15 0.12 0.14
effluent were measured using a Varian 3400 gas chromatograph fitted with a Chrompak Poraplot Q fused silica column with a length of 12.5 m and an inner diameter of 0.53 mm. The carbon dioxide concentration in the effluent gas was continuously monitored using a Maihak UNOR 6 infrared spectrometer. All kinetic experiments were performed with one batch of 47 g of catalyst, 69 particles, a t 454, 476, 500, and 527 K and total pressures varying between 0.2 and 1.0 MPa. To stabilize the catalyst activity the catalyst used in the kinetic experiments was pre-exposed to reaction for 100 h in a wall cooled packed bed reactor. In Table 3 the ranges of partial pressures covered in the experiments are summarized. Between experiments and during periods in which the reactor was idle, the equipment was kept under nitrogen at the temperature required for the next experiment. The activity of silver catalysts used in the oxidation of ethene is known to vary, see e.g., Nault et al. (1962) or Klugherz and Haniot (1971). Therefore in a separate series of experiments the activity of different samples of catalyst was studied under standard operating conditions. These experiments were performed as follows.
52 Ind. Eng. Chem. Res., Vol. 34,No. 1, 1995 '
W
1
18 ~ " " " ' " ' ~ " " ' " " "
" 1 ' '
' 1 "
" " ' " ' ' " ,
04
O0 20
L -
0
1
2
3
4
/
,
"
24
"
'
25
'
'
26
27
20
29
Experimental time (hours]
Figure 2. Change of reaction rates with time at 0.5 MPa and 500 K after charging reactor with 32 g of fresh catalyst. Feed gas, 1.8% ethene in air; flow rate, 0.74 g/s. From t = 3.3 to 24 h and from t = 28.4 to 45 h the equipment was flushed with nitrogen. A, epoxidation reaction; 0, combustion reaction.
The reactor was charged with 32 g of fresh catalyst. Under a flow of nitrogen the reactor was heated to 500 K. After reaching this temperature a mixture of 1.8% ethene in air was fed to the reactor a t a flow rate of 0.74 g/s at 0.5 MPa reactor pressure. The change of the reaction rates with time was measured for a period of 150 h.
q
Interpretation of the Experimental Data In the experiments the mole fractions of ethene and carbon dioxide were measured in the effluent gas. From the known feed gas composition and the measured mole fractions of ethene and carbon dioxide in the effluent the conversion of ethene, the selectivity toward ethene oxide, and the mole fractions of the other components are calculated using the relations given in the Appendix. The production rates of ethene oxide and carbon dioxide are calculated from
where Tad, = m ] R and = H/(RTref). If the reference temperature, Tref,is chosen as the average experimental temperature and the experimental temperature range is relatively small, 8 will be around 1 for all experiments and hence, equal absolute changes in In(,%;) and yz have approximately the same effect on the reaction rates. This can be seen from the following relation:
Thus fitting ln(k,), ln($,-), yz, and
q instead
of kb,
I$ -, Tidand Tid+facilitates parameter estimation. The estimate of the kinetic parameters was performed with the SIMUSOLV program which determines optimum parameter values using the maximum likelihood principle, see Steiner et al. (1990). It enables fitting either all parameters from a model simultaneously or fitting subsets of parameters keeping others at fixed values. To facilitate parameter estimation the Arrhenius terms in the kinetic expressions are rearranged:
where Tid = Ei,/R,yi = E:l(RTref), and 9 = TlTref. Analogously the adsorption constants are rewritten as
it was not possible to fit the activation energy and the heats of adsorption simultaneously because of the strong cross correlations between the values of In (I$,-)and r": the results obtained were not statistically meaningfui. Thus, we first fitted relations in which the adsorption constants were assumed to be temperature independent. After that we tried to improve the goodness of fit by varying the different $ values with temperature. Results and Discussion Experiments on Initial Activity of Catalyst. In Figure 2 reaction rates are shown in the initial period for a fresh catalyst; they were measured a t standard conditions. The reactor was charged with a sample of 32 g of fresh catalyst and heated to 500 K under a nitrogen flow after which the reaction was started. The catalyst activity showed a decline, and after 3 h the conversion of ethene was too low for accurate measurement of the reaction rates. The reactor was flushed with nitrogen for 20 h, and then the reaction was started again. The activity had been restored, but again a
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 63 Table 4. Stabilized Reaction Rates As Found in the Catalyst Initial Activity Experimentsa
experiment 1 2 3
stabilized reaction rates after 100 hb rl r2 56 28 160 131 148 136
1. ,,,:,,,I. //I :. .I
.:. . . : . .:.. ... . : .:.:.: . . . . . . .I. . . .;, .... . . . . .(. ,
,
. . . . . . . .. . .:.
,
. . . . . . . .
W 31.6 32.5 32.4
a Experimental conditions were reactor pressure 0.5 MPa, reaction temperature 500 K, feed gas 1.8%ethene in air, flow rate 0.74 g/s. In lo6 moV(kg s). In g.
._
s
2 Y r CD v) 2 Y r N v CD
I I
, . . .. .. ~. ....,. . I I
@
.I
L L
1 .
.
.
.
.
.
. . . . . . . . . . .. . .. . . ., .. . . . . . . . . . . . . . . . .. . . . .. . ..................... . . .. .. .. . . . . .. . .. . . . ... . ... . . .. .. .. .. . . . . .. . . .. . . . . . . . .. .. ..
z
I
. .:... , ,
al
c
C
, .
. .
... .. . .. .
.-+-0
. . .
0
m
a:
. .
lo,-+j lod
)
!!
decline was observed after about 5 h. The reactor was flushed with nitrogen for 20 h, after which the reaction was resumed and continued for 75 h. The reaction rates became constant after about 115 h; during these 115 h the catalyst was exposed t o reaction for about 75 h. It was then tested whether changing the reactor temperature or the pressure or flushing the reactor with nitrogen for some hours affected the observed reaction rates at the chosen standard conditions. This was not the case: after restoring the old operating conditions the system returned rapidly to the old steady state. We conclude that the observed changes in reaction rates are due t o changes in the catalyst itself and not, e.g., due to slowly establishing an adsorption equilibrium of a component; in that case again a long stabilizing time would be expected after changing the operating conditions. A total of five of these experiments were performed. The experimental conversion a t the standard conditions in two of the experiments was too small for accurate measurement of the reaction rates. In the other three, fluctuations were observed for an initial period after which activity became constant. The final activities for these three experiments are given in Table 4. Of the five experiments only experiments 2 and 3 showed a final activity equal to each other within experimental error. The varying activity of silver catalysts used in the oxidation of ethene has also been reported by other investigators, see, e.g., Nault et al. (1962) or Klugherz and Harriot (1971). The catalyst is known to be sensitive to chlorine-containingcontaminants and sulfur poisoning. Contamination of feed gases is unlikely to be the cause of the fluctuations observed here. Though we have no definite proof, we contribute the changing activity to changes of the silver surface by, e.g., sintering of silver crystallites, changes in the oxidation state of the silver, and/or the formation of deposits on the surface. All these factors are known to influence the activity of silver catalysts, see Lee et al. (1989) and van Santen and Kuipers (1987). As the observed deactivation in the initial period is partly reversible the second and third factors are more likely than the first, as these are reversible processes. Removal of deposits of chemicals used in catalyst preparation may also affect activity in the initial period. To ensure compatibility between the kinetic study and the packed bed reactor study, a large amount of catalyst was exposed to reaction conditions in a wall cooled packed bed reactor until changes in catalyst activity were no longer observed. A sample of this catalyst was used in the kinetic experiments. All kinetic experiments were performed with the same batch of catalyst. During the course of the experiments the activity of this catalyst sample was regularly checked by performing an experiment a t standard conditions.
1.
. , , . . , .. . . . . . .. . . . . . . . .. . .: ...... . . . r J . .;. , ; . . , . . , , . . . . . . . . . . . . . .
catalyst massc
10'
. . . . . . . .
,
.
.
,
.
.
. . . . .
,:,I,: . . .
:I
.:'I
. . .. . .. . . . . . .. . . .. . .. . . .. . .. . . .. . . . . . . . . . . . .. . . . . . . . . . . . . . ., . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . .
. . . .. .. .. . . . . . .. . .. . ... . .. ... . .. .. .. .. . . . . . ... . . .. . . .
io5
10'
Reaction rate [mol/kg s] 7 % 0 2
Figure 3. Reaction rates measured with feed gases containing 12%oxygen versus those measured with feed gases containing 7% oxygen. Corresponding experiments are performed at the same temperature, pressure, and flow rate. 0 , rl gases 4 and 5; 0,r2 gases 4 and 5; A, r1 gases 6 and 7; 0, rl gases 6 and 7. For gas compositions see Table 2.
Correction Procedure for Long Term Deactivation of Catalyst. The kinetic experiments were performed in three series. Each series was performed with the same catalyst batch, and during such a series no variations of the catalyst activity were found. However, activity differences were found between the three series. Catalyst deactivation occurred while the reactor was idle. This deactivation has to be accounted for when determining rate expressions. In a differential reactor changes in activity do not lead to changes in concentrations in the catalyst bed as these are equal to those of the feed gas. The deactivation of the catalyst can therefore be quantified directly by comparing experiments performed at standard conditions, see, e.g., Klugherz and Harriot (1971). Correcting for deactivation when using a perfectly mixed reactor is more difficult. A change in catalyst activity results in a different gas composition at standard operating conditions. Thus the reaction rates are influenced by the changes of catalyst activity and concentrations simultaneously: therefore it is not possible to determine the deactivation from standard experiments without knowing the kinetics. We accounted for the deactivation by fitting correction factors, relating the activity of the catalyst in periods 2 and 3 to that in period 1, along with the kinetic parameters: (6)
Thereby we assumed that no significant deactivation occurred during an experimental series. We also assumed that the changes in the catalyst affect only the magnitude of the reaction rates and not the form of the expressions or the dependence of the rates on partial pressures or temperature. The same was presumed by, e.g., Klugherz and Harriot (1971) in their correction procedure. This assumption is not necessarily correct as can be seen from the work by Montrasi et al. (19831, where the activity of spent catalyst after 6 years of use
54 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 Table 5. Kinetic Rate Expressions for the Oxidation of Ethene. The Reaction Rate and Adsorption Constant Depend on Tempratve According to exp(T,JT) k: = k:" exp(-T,oJT) and =
*.-
model
rate expression
in an industrial plant is compared to that of fresh catalyst. They report a change in apparent activation energies. Kinetic Experiments on the Ethene Oxidation. A number of different rate expressions for both reactions was tested for their adequacy to fit the experimental data. Some qualitative considerations can be used to evaluate a priori whether rate expressions are adequate in describing the experimental data. For example, they have to account for inhibition by reaction products. The influence of the partial pressure of oxygen at our operating conditions can be examined by comparing the reaction rates as measured for feed gases which only differ in oxygen concentration. In Figure 3 data are compared for gases containing 7% and 12% oxygen, respectively. The corresponding experiments are performed a t the same temperature, pressure, and flow rate. We observe that the reaction rates measured with the gases with a high oxygen concentration are only a few percent higher. The influence of oxygen partial pressure on the reaction rate for our operating conditions is small. Thus the rate expressions must be able to predict near zero order behavior in oxygen partial pressure. Note that, in a well-mixed reactor, drawing conclusions from data obtained with different feed gas
compositions is only possible for a component that does not have a significant influence on the reaction rates, see the discussion on the quantification of the catalyst deactivation. Some authors have proposed expressions in which both reactions proceed over the same catalytic site, see Petrov et al. (1985) and Stoukides and Pavlou (1986). This means that the selectivity toward ethene oxide is not influenced by the partial pressures of reaction products. These types of expressions were rejected as this is in contradiction with our experimental observations. The models most adequate to fit our data are presented in Table 5. Model I is a dual site LangmuirHinselwood mechanism in which ethene and oxygen adsorb on different sites and react. A bimolecular reaction is assumed to be the rate-limiting step. Reaction products compete with ethene for adsorption. The coverage of the second site with oxygen was fitted with a power-law expression. Models I1 and I11 are Langmuir-Hinselwood expressions in which all reactants and products compete for adsorption on the same catalytic sites. Also here the rate-limiting step is a bimolecular reaction between adsorbed oxygen and ethene. In model I1 molecular adsorption of oxygen is assumed, in model I11 dissociative adsorption. Both reactions proceed over different catalytic sites. The parameter estimates for the different models are given in Table 6. Also the lumped reaction rate constants and the adsorption constants a t the reference are given. KJ are the adtemperature of 476 K, sorption constants at the reference temperature of 476 K the value of KJshould be used throughout the whole temperature interval in case no values for K;" and TadsJ are given; (kk)lwp is defined for model I as ky , for model I1 as kc$&E, and for model 111as ki(ICo)OFICE.
Kf,
In Table 7 the value of the log likelihood optimization function as used by the SIMUSOLV program is given. Though the value as such does not provide much
Table 6. Estimated Parameter Values for the Different Rate Expressions in Table 5 model I parameter
model I1
r1
r2
r1
r2
rl
8.7 104 8070 2.9 103 8070 30.0
7.02 107 11380 1.42 x lo6 11380 49.4
9.1 x 106 8550 3.43 1013 18070 12.9 2.67x 9520 83.9 91.8
3.77x 108 10470 8.1 109 14250 14.9 5.30 10-3 3780 107 40.0 1.49 1570 43.4 7.45 10-3 4130 8.76
8.9 x lo6 8520 4.72 x 10l2 17070 12.9 2.05 10-7 8550 83.9 91.8
87.4 90.0
114.4 48.8
53.0 0.368 2370
54.6 4.04 x 3430
0.127 0.52 0.37
0.140 0.49 0.32
47.9 1.99 1510 9.97 0.53 0.40
0.55 0.36
Table 7. Goodness of Fit for the Three Rate Expressions model I statistical parameters
LLF
model I11
average error (a) standard deviation ((5)
rl
1404.6 19.0 16.8
r2
1437.0 15.0 14.8
47.9 8.25 840 84.8 0.56 0.44
rz 3.53 x 106 10470 1.08x lo8 14650 26.0 4.0 x 10-3 4180 98.5 41.3 1.21 1680 48.9 0.109 2910 66.7
0.59 0.39
model I1
model I11
rl
rz
rl
1390.7 20.8 19.8
1422.8 18.0 13.9
1396.4 19.6 16.9
rz 1434.1 14.7 12.9
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 55 information, it may serve to compare the goodness of fit of the different models. The higher the value the better the model. Also the average error and the standard deviation are given in Table 7. The average error is defined as
io3
IO'
1
average error
IGalc,i
C
N i=l
- %xp,iI
rexp,i
(7)
where N is the total number of experiments. From the values of the optimization function we observe that the models fit the data with almost the same accuracy. This can also be seen from the values of the average relative error, so no best model can be chosen based on the value of the log likelihood function. In the literature, maxima have been reported in the reaction rates as function of the ethene and oxygen partial pressures. The rate expressions of models I1 and I11 are capable of describing such maxima, whereas those of model I are not. This fact combined with the slightly better fit of the data by model I11 when compared to model 11, and with recent studies on the mechanism of the reactions saying that atomic oxygen is the species active in both reactions, see Gleaves et al. (1990) and van Santen and Kuipers (19871, leads t o our preference for model 111. Only in a few cases did introducing a temperature dependence of an adsorption constant result in an improved fit of the expressions to the data. The values correlate strongly with the corresponding value of Tidsj $.-, as can be readily seen from eq 5 . of Parity plots for model I11 are presented in Figure 4. The parity plots for models I and I1 are similar and therefore not presented in this paper. For the different models the distribution of the relative errors as a function of various independent variables, such as the reaction temperature, the reactor pressure, the flow rate, and the partial pressure of any of the components, was inspected because significant correlations between relative errors and independent variables indicate inadequacies in the model. No such correlations were found. The relative error of the epoxidation reaction, however, does have a positive correlation with that of the complete combustion reaction as is shown in Figure 5 . This indicates that effects influencing the two reaction rates in the same way are, at least partly, responsible for the remaining deviations. Examples of such effects are experimental errors in the reaction temperatures or in the feed flow rates. In Table 6 also the correction factors for the catalyst deactivation are given as these were fitted along with the kinetic parameters. Because the epoxidation and the combustion reaction are assumed to proceed over different catalytic sites the rate expressions for both reactions are independent of each other. Therefore also the deactivation factors for both reactions can be determined independently. The determined factors are equal within experimental error. This means that the change in activity of the catalyst did not affect the catalyst selectivity significantly. In the last experimental series the catalyst activity was only about 40% of that in the first series. Influence of Reaction Products on the Selectivity of the Reactions. From Table 6 it can be seen that for the two reactions the adsorption constants for the different reaction products are not equal, which means one of the reactions is more strongly inhibited than the other. As a consequence the selectivity toward ethene
lo5
lo6 IO6
10.~
I0 . 4
10.'
R, m e a s u r e d [mol/kg s]
1
I0'c IO'
I
IOd 10)
io5
IO'
io3
R, m e a s u r e d [mol/kg s]
Figure 4. Reaction rates as calculated according to model I11 versus measured reaction rates. (a, top) epoxidation, and (b, bottom) complete combustion.
oxide is affected by changes of the product partial pressures. This is illustrated in Figure 6 as an example. As the adsorption constant of ethene oxide for the complete combustion reaction is smaller than that for the epoxidation reaction, an increase of the ethene oxide partial pressure leads to a decrease of the selectivity. An increase of the carbon dioxide partial pressure leads to a selectivity increase, while changes in the water partial pressure, in view of approximately equal adsorption constants, hardly affect the selectivity. It is important t o notice that these conclusions only apply to the investigated range of operating conditions. One should be cautious in extrapolating to conditions outside the investigated range because of the empirical character of the rate expressions. Ethene Oxide Oxidation. In the treatment of the data the oxidation of ethene oxide to carbon dioxide and water was neglected. To investigate the influence of this reaction, a limited number of experiments was performed in which ethene oxide was oxidized without ethene present in the gas phase. From these experiments the following power law relation was derived
A parity plot is given in Figure 7. Equation 8 was used
66 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 100
I
I
.............................. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . ,. .
.
, .... . :
.
...
.............. . . . . . . . . . . ./. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .., . . . .. .i 1; .
50
,,
,
0
-50
io5
-100 -100
.so
50
0
100
Oh deviation R ,
Figure 5. Relative deviation between calculated and measured reaction rates for model I11 for the epoxidation reaction against those for the complete combustion reaction. I
-s
778
,
'
,
,
,
,
1
I
65' 0 00
0 04
0 08
0 12
0 16
Partial pressure varying component [bar]
Figure 6. Selectivity calculated according to model 111, as a function of the partial pressure of carbon dioxide, -; ethene oxide, - -; and water, - * -. T = 476 K. Partial pressures of components if not varied are PE = 0.09 bar, PO = 1.06 bar, Pc = 0.07 bar, PEO= 0.06 bar, and PW = 0.07 bar. The range of partial pressures is equal to that covered in the experiments.
t o calculate r3 for the experiments on ethene oxidation. The ratio rlh-3 has a value between 0 and 0.3. However under ethene oxidation conditions, 7-3 will be much smaller due to the competitive adsorption of other components on the active surface. This is supported by Stoukides and Pavlou (19851,who found that ethene and ethene oxide compete for adsorption on the same sites. Also in our kinetic experiments on ethene oxidation no systematic deviation of the reaction rates was found at higher ethene oxide partial pressures; it therefore appears that ethene oxide oxidation is negligible at our operating conditions. Conclusions Rate expressions for the oxidation of ethene over an industrial silver on a-alumina catalyst for gas mixtures containing excess oxygen have been determined. It was found that all reactants and reaction products influence the reaction rates. The oxidation of the product ethene oxide to carbon dioxide and water was found to be negligible at our operating conditions. The fitted rate expressions describe our experimental data with an
10
R, measured (mol/kg s]
Figure 7. Reaction rates calculated from eq 8 versus measured rates for experiments on the ethene oxide oxidation; 0 , 4 7 6 K; A, 500 K.
average error of 20%for the epoxidation reaction and 15% for the complete combustion. The preferred rate expressions for the two reactions are based on a Langmuir-Hinselwood mechanism in which adsorbed ethene and dissociatively adsorbed oxygen react to yield ethene oxide and carbon dioxide and water. A bimolecular surface reaction is assumed to be the rate-limiting step. The two reactions are assumed to proceed over different catalytic sites. The determined parameter values indicate that higher partial pressures of carbon dioxide will lead us to an increase of the selectivity toward ethene oxide, higher partial pressures of ethene oxide will lead to a decrease of the selectivity, and higher partial pressures of water will not affect selectivity. The apparent activation energy, the combined temperature influence on the reaction rate constant, and the chemisorption of the total combustion reaction is larger than that for the epoxidation reaction, 86 and 70 kJ/mol, respectively. This leads to a decreasing selectivity toward ethene oxide with increasing temperature. Deactivation of the catalyst was found between different series of experiments performed with the same catalyst batch. This deactivation was accounted for when fitting the data by determining activity factors for the different series along with the kinetic parameters. The activity of different samples of identical catalyst was found t o vary, in spite of the fact that we tried t o accurately reproduce the catalyst activation procedure. The activity of a particular batch of catalyst will have to be corrected for when applying the kinetic expressions in modeling. Though the activity is likely to be different, it is not expected that the actual kinetic expressions vary between different batches. This expectation is based on the observation that deactivation in our experiments with one batch of catalyst can be corrected for using a multiplication factor: changes in neither the kinetic parameters nor the kinetic expressions are necessary.
Acknowledgment These investigations were supported by the Netherlands Foundation for Chemical Research SON with financial aid from the Netherlands Technology Founda-
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 57 Table 8. Formulas To Determine Gas Composition. Conversions (E and (C Are Calculated from Eq A 4 and A-5. From the Known Initial Gas Concentrations, the Composition after Conversion (E and (C Are Calculated. The Mole Fractions Are Obtained by Dividing This by the Total component
initial composition
composition &er conversions CE and t c
N = inert 0 = oxygen ref = reference U = outlet W = water 1 = epoxidation reaction 2 = complete combustion reaction 3 = ethene oxide oxidation reaction
Appendix oxygen
4 + 2.k-c
carbon dioxide ethene oxide water inert
4 XN
4
total
1
1 1 = -&2({E
+E(&
4 0 I XW
I
b.
- tC)
+ 2.E5,
Relations between Mole Fractions, Conversion, and Selectivity for Ethene Oxidation. Conversion parameters are defined for ethene and carbon dioxide as follows:
- &)
tion STW. The authors wish to thank K. van Bree, W. Leppink, A. H. Pleiter, and H. Vunderink for technical assistance, J. G . Wassenaar, C. N. Rooker, and J. G. B. Kottink for assisting in the experimental work, and the Royal Dutch Shell group for providing the catalyst material.
S;cis defined as the fraction of the ethene feed converted into carbon dioxide. The selectivity toward ethene oxide can be calculated from the conversions
Nomenclature E , = activation energy, kJImol f i , = deactivation factor for reaction i and experimental series j AH = heat of reaction, kJImol AHj = heat of adsorption for componentj , kJImol k: = reaction rate constant, see Table 5 k& = pre-exponential factor, see Table 5 $.= adsorption constant for component j in reaction i, lhar $,,-= pre-exponential adsorption factor for component j in reaction i, l h a r N = number of experiments Pi = partial pressure of component i, bar r = production rates of reaction, mol/(kg s) R = gas constant, J/(mol K) 9Z = recycle ratio T = temperature, K TBct = E J R for reaction i, K Tadsj = AHjlR for componentj in reaction i, K W = catalyst mass in reactor, kg x = mole fraction Greek Letters yi = EiIRTref dimensionless activation temperature for reaction i r$= q , I R T r e for f componentj in reaction i [ = conversion 6 = T/T,,f dimensionless temperature 4 = molar flow rate 0 = selectivity toward ethene oxide, see eq A-3 o = weight fraction of component i Subscripts and Superscripts b = catalyst bed C = carbon dioxide calc = calculated E = ethene EO = ethene oxide exp = experimental F = feed I = inlet
The conversion parameters can be calculated from the measured feed and effluent mole fractions of ethene, x:, and carbon dioxide, xg, according to
q 1-2c) The formulas for calculating the mole fractions of oxygen, ethene oxide, and water in the effluent gas from the initial composition of the feed gas and the conversion parameters are given in Table 8.
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