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Estimation of reversible and irreversible coke by transient experiments
9 Elsevier Science B.V. All rights reserved Catalyst Deactivation 1997 C.H. Bartholomew and G.A. Fuentes, editors
673
E s t i m a t i o n o f R e v e r s i b l e a n d Irreversible C o k e b y T r a n s i e n t E x p e r i m e n t s Mikael Larsson, Niklas Henriksson and Bengt Andersson Department of Chemical Reaction Engineering, Chalmers University of Technology, S-412 96 G6teborg, Sweden, mikael @cre.chalmers.se, http://www.cre.chalmers.se
Catalyst deactivation by coke formation can occur through a more or less reversible mechanism. We have applied a transient approach to model the reversible behavior of the deactivation, and to separate the deactivation from the main reaction kinetics. The deactivation of a Pt-Sn/A1203 catalyst was studied during propane dehydrogenation. The gas composition and temperature were varied during the experiments, which allowed us to model the deactivation by assuming one reversible and one irreversible type of coke. It was found that the deactivation increased with the propene concentration but was independent of the partial pressure of propane. Hydrogen decreased the deactivation rate and could even activate the catalyst by removing reversible coke.
1. INTRODUCTION Although many phenomenological models that include steps with reversible coke have been proposed, only a few attempts have been made to model this mechanism quantitatively [1,2]. Our goal in this study has been to model the reversible behavior observed during propane dehydrogenation by changing the inlet gas composition during runs. We wanted to find a method to separate the deactivation from the kinetics. Unfortunately there is no obvious way to do the latter. Many processes, such as adsorption, desorption, reaction and deactivation, occur simultaneously. For a hydrocarbon reaction deactivated due to coke formation, we can divide these processes into four types: (1) Processes much faster than the reaction rate (milliseconds), i.e. processes in equilibrium. (2) Processes in the same range as the reaction rate (seconds), i.e. processes at steady-state. (3) Relatively fast deactivation processes (minutes - hours). (4) Slower deactivation processes (hours - years). The system chosen here is the dehydrogenation of propane on Pt-Sn/A1203. This catalyst is used commercially because of its relatively high stability against coke formation and high selectivity during dehydrogenation reactions and naphtha reforming [3-7]. We have earlier measured the effect of altered reaction conditions on the amount of coke and activity [8] on this reaction system. We found that only a minor part of the coke caused the deactivation of the catalyst. This deactivating coke is formed in parallel with the non-deactivating coke. In the present work we will focus on the deactivating coke and model it by a transient method, in which the reaction conditions are changed a number of times during a run.
674
2. EXPERIMENTS About 30 mg of a Pt-Sn/A1203 catalyst were used in each run. The particle size were chosen small enough to avoid internal mass transfer limitations. The catalyst was prepared by sequential impregnation of a commercial "t-alumina support with aqueous solutions of SnC12 and H2PtC16 [9]. Characterization data are summarized in Table 1. The experiments were conducted in a fully automated flow reactor. The gas compositions were analyzed by a GC (see [8] for details). The reactor was fed with a mixture of propane, propene, hydrogen and nitrogen to achieve differential conditions. This was desired to avoid changes in the gas compositions along the bed leading to a non-uniform coke profile, and also to reduce the computational effort. The gas flow rates were controlled by mass flow controllers. The temperatures were 780, 800 and 820 K, and the total pressure was 1.5 bar. The inlet gas composition was changed in accordance with an extended 23 factorialdesigned experiment [ 10]. For each temperature, the experiment was divided into two parts to avoid very long experiments with severe deactivation. Reference conditions were repeated three times during each run. The total experimental plan contained six runs, each with 10 experimental points. The order of the points and the length between the steps (143 - 176 min) were randomized. The experiments conducted at 780 K will be named A1 and A2, while those performed at 800 and 820 K will be called B 1, B2, C1 and C2. In one experiment, the temperature experiment, the temperature was changed at constant gas composition, the same gas composition as the reference conditions in the main runs. This experiment was done in order to correlate the runs at different temperatures with each other. The catalyst was reduced in a flow of 5 ml/min of HE and 10 ml/min of N2 (flows at 273 K and 1.0 atm) at 1.5 bar for 180 min at 850 K. After that, the temperature was adjusted to the reaction temperature and allowed to stabilize for 30 min before the flow of hydrocarbons was introduced. The inlet gas composition was changed in the following range: 30 - 46 kPa C3H8, 4.5 - 7.5 kPa C3H6, and 6.8 - 11.2 kPa HE. The total flow trough the reactor was always 60 ml/min. The first GC analysis was taken after 5 minutes on stream, and the following ones every eleventh minute. Table 1. Catalyst Properties Catalyst
Particle size
Pt loading I Sn loading I
Dispersion 2 BET surface
Pt-Sn]A1203
0.05-0.14 mm
0.74 wt %
29%
1.53 wt %
172 m2/g
~By atomic absorption spectrometry. 2By hydrogen chemisorption in a volumetric system assuming H:Pt=l:l.
3. R E S U L T S Figure l a shows the gas compositions and the turnover frequency (TOF) in an experiment performed at 780 K (A1). From the TOF curve, one can see that the deactivation rate, i.e. the derivative of the TOF, changes with altered reaction conditions. The activity may even increase with time in some experimental points (not shown here). This demonstrates that it is
675 necessary to include a reversible part in a coke model. The results from the experiments will, in the following analysis, be evaluated as outlined in Figure 2. 3.1. Estimation of the deactivation function
In order to use the transient experiments to calculate the surface coverage of coke, we first introduce the continuous deactivation function. We define the deactivation function as the activity related to the first analysis after 5 minutes and compensated for the changes in reaction conditions. The compensation is carried out by assuming that the degree of deactivation immediately before and after a change in reaction conditions is the same. To be able to do so, a few assumptions have to be made (see Discussion): 1. The coke coverage varies only slowly when the reaction conditions are changed. 2. A specific coke coverage causes the same degree of deactivation independent of gas composition and reaction temperature. If these assumptions are valid, the degree of deactivation will be the same immediately before and after a change in gas composition. We have seen earlier that this is true for a change in temperature at constant gas composition for the present reaction [8]. Using these assumptions, the deactivation function for each experiment was calculated by extrapolating the reaction rates to the time for a gas change and equating the degrees of deactivation before and after the change. Figure lb shows the deactivation functions for the curve in Figure 1a. To examine the quality of the deactivation function, the relative activities in the repeated experiments were compared with the deactivation function. If the deactivation function would describe the degree of deactivation entirely, the deactivation function and the repeated experiments would agree. The agreement shown in Figure lb is good. However, slightly larger deviations occur in some of the experiments. This deviation was incorporated by adjusting the deactivation function linearly in order to achieve total correlation between the deactivation function and the repeated experiments. 1.4
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Figure 1. (a) The turnover frequencies (TOF) and gas compositions for one of the experiments performed at 780 K (A1). TOF is based on hydrogen chemisorption on a fresh catalyst [9]. The numbers in the figure indicate: (1) the first analysis after 5 minutes, (2) from where the modeling began (3) the last analysis during the second repeated experimental point with reference conditions. (b) The deactivation function and calculated total surface coverage for the same experiment (A1). The plus signs in the figure are repeated experiments with the same reaction conditions. The point-dotted section of the surface coverage curve was not used in the modeling.
676
I Malnexperiments~ A1,A2,I]I,B2,CI andC2
Determination H ofTOF
Estimation ofthe L deactivationfuncfloni ~ Temperature ~Wl experiment |
Estimationof the ~,~ coverage
surface
Modeling
]
Figure 2. Schematic picture of how the experimental data was treated.
3.2. Estimation of the surface coverage In the this paragraph we will relate the activity to changes in coke coverage. We assume that the deactivation function is proportional to the free metal surface area, i.e. the metal surface not covered by either reversible or irreversible coke. To relate the activity to the surface coverage by coke is however problematic. It is not possible to extrapolate to time zero and assume zero surface coverage, because the surface to a large extent is covered almost immediately [9,11]. Neither can we say that the initial surface coverage is the same in all experiments, since it may change with reaction conditions. Instead, the activity has to be correlated with the surface coverage by independent methods. Lin et al. [ 11 ] pulsed n-hexane on a Pt-Sn/A1203 catalyst and found by hydrogen chemisorption that about 70% of the metal surface rapidly became covered by coke, and that additional hydrocarbon pulses only slightly reduced the free metal surface. Larsson et al. [9] ran propane dehydrogenation on a PtSn/A1203 catalyst and found that the activity for the reaction between H2 and D2 was only about 15% of the activity for a fresh catalyst after 10 h on stream. In the present study, we will, in accordance with these findings, assume that the surface coverage of coke is 80% after 16 h on stream in the temperature experiment, and will then relate the other runs by comparing the activities. We assume that when the same reaction condition is applied, i.e. the same gas composition and temperature, differences in activity are only due to the degree of deactivation. Therefore, we can estimate the surface coverage for points with the same gas composition but from different runs given that the surface coverage is known in one run. Data from the temperature experiment was used to estimate the effect of changed temperature at constant coke coverage on the reaction rate. The relative activities were 0.584, 1 and 1.47 for 780, 800 and 820 K respectively. As described above, we assumed that the total coke coverage was 0.8 in the temperature experiment after 16 h, and estimated the surface coverage for all the experiments by using the activities at the end of the sixth experimental point (see number 3 in Figure l a). In this point the gas composition was the same in all the experiments. Figure 1b shows the estimated surface coverage for experiment A1. 3.3. Modeling of the surface coverage The following model of the deactivation has been made as simple as possible. A few fundamental assumptions have been used: 1. Only the coke covering the active sites is involved in the modeling. 2. Two types of coke that cause the deactivation exist, one reversible and one irreversible. 3. The reversible type of coke can be removed, be converted into a harmless type of coke, or form irreversible coke on a time-scale slow enough to be detected by the GC analysis. The amount of reversible coke is changed by modifications in the reaction conditions. 4. The irreversible coke cannot be removed in the time-scale concerned in the experiments.
677
5. The reversible and irreversible types of coke occupy the same number of active sites per carbon atom. The irreversible coke is formed only from the reversible coke. 6. A pseudo steady-state for the reversible coke is reached at the end of the first point in the experiments (after about 5 hours). The last assumption leads to the following equation:
d( Orev,O 1--Oirr,O )
dt
=0
(1)
where E)rev,0 and Oirr,0 are the surface coverages of reversible and irreversible coke, respectively, .when the modeling begins. We did not involve the first five hours of the experiments in the modeling because the deactivation process in the beginning of a run is different from the following region in the experiment [8,12]. The modeling was done by minimizing the sums of squares from the residuals between the model and the estimated surface coverage functions. This non-linear regression was solved with a Levenberg-Marquardt routine in the MATLAB software package. A number of different models that fulfilled the six assumptions above were fitted to the experimental data. Equation (2) describes the model that gave the most satisfying fit. The same equations have been used by Wolf and Petersen [1] to describe the reversible deactivation behavior during methylcyclohexane dehydrogenation on Pt/)'-A1203.
dOrev
dt -k,. PC3H6.~ Pn2 --Orev-- Oirr )-k2 . PH. 20rev . .
dOirr dt
l('3, ~)rev
(2)
- k3 "Orev
However, problems in identifying physically acceptable solutions occurred. We found for the two series at 800 K (B 1 and B2) that, after 5 h, the initial deactivation was not finished and subsequently, the pseudo steady-state assumption was probably not fulfilled. Hence, in experiment B1 and B2, the next point was omitted and the modeling began from there. Difficulties with convergence still existed and, after comparing the runs, it was found that the deactivation behavior differed in run B2. Thus the latter was omitted from the analysis, and it was now possible to find an acceptable solution. Results from the modeling are shown in Figure 3 and the parameter estimation, with linearized 95% confidence intervals, is given in Table 2. The highest correlation between the parameters was 0.87. One can see that the activation energies have relatively large confidence intervals. This can be explained by both the correlation between the parameters and the relatively small temperature interval in which the experiments were conducted. The validity of the model was checked by studying the residuals. No patterns indicating effects that had been neglected were found.
678
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Figure 3. The results from the modeling: reversible, irreversible and total coverage of coke. The experimental results are indicated with dashed lines and the model with solid lines. The ratios between the coverage of reversible coke and the surface not covered with irreversible coke are also shown. The predicted versus the experimental surface coverages are shown in the last graph. Table 2. The parameter values and linearized 95% confidence intervals Parameter Value 1.199" 10 -4 -i- 1.748" 10-5 Al (s -l) Pre-exponential factor l A2 (s-lPa -l) Pre-exponential factor 1 1.372" 108 + 4.794" 10.9 A3 (s l ) Pre-exponential factor 1 6.178.10 -5 + 8.968.10 -4 Ehl (kJ mol l ) Activation energy 119.5 + 43.8 EA2 (kJ mo1-1) Activation energy 68.5 + 103.3 EA3 (kJ mol -~) Activation energy 41.9 + 42.0 IEstimated from the centered Arrhenius expression ki=Ai'exp(Ehi/R'(1/T-I/T0)), T0=800 K.
4. DISCUSSION Equation (2) explains the transient deactivation with a model describing reversible and irreversible coke. We can see that the partial pressure of propane in the reactor does not influence the deactivation. This has also been demonstrated in an earlier study of the same system [8]. This observation is consistent with kinetic models for propane dehydrogenation proposed by Loc et al. [ 13]. They suggested that the rate-determining step is the dissociative adsorption of propane. From this mechanism it follows that the deactivation will be
679 independent of the propane partial pressure if the deactivation is caused by coke formed from intermediates in the reaction. The formation of reversible coke in Equation (2) can be explained by a model where a coke precursor first is formed from adsorbed propene by dehydrogenation. This precursor is in equilibrium with the propene and hydrogen in the gas phase, and it will form coke through a reversible mechanism. Finally irreversible coke is formed from the reversible coke. Figure 4 shows a mechanism for the formation of deactivating coke during propane dehydrogenation. The mechanism is derived from Equation (2) and from the propane dehydrogenation mechanism proposed by Loc et al. [13]. The coke formation part is in every sense consistent with a model proposed by Wolf and Petersen [ 1]. The definition of reversible coke is not clear in the literature, but is usually said to be the portion of coke that can be removed relatively easily by hydrogen treatment. The definition in this study has been, in effect, the portion of the coke that can be altered by changing the reaction conditions. This portion will vary according to how the experiments are carded out. More extreme changes in reaction conditions would allow a larger part of the coke to be modified. Two transient processes are superimposed when performing transient experiments on a deactivating reaction system. The difficulty in separating the two processes was overcome by running the reaction at differential conditions and using the deactivation function. In order to convert the turnover frequency curves to deactivation functions, it was assumed that the degree of deactivation did not change when the gas composition or the temperature was changed. This assumption is essential for the whole modeling. The basic idea is that what we define as coke coverage is changed only slowly and does not change during the short time it takes to change the reaction conditions. Repeated experiments were performed to verify the assumption and the small differences detected were corrected for. It is also necessary that the reaction mechanism does not change when the reaction conditions are altered. Our preliminary kinetic model of the main reaction kinetics indicates that this assumption is valid [ 14]. It was difficult to fulfill the objective of achieving differential conditions and producing accurate measurements when the activity was decreased by sometimes more than 90%. We had to admit non-differential conditions in the beginning of some runs (the first few hours). Because of the objective above, the variation in the variables had to be relatively limited. Therefore the parameter values are only valid in this limited range. The problems can be solved by changing the space velocity during the run and/or using a reactor that can be described as a stirred tank reactor. Hofmann and Kolb [15] and Beirnaert et al. [ 16] discuss the benefits of using a recycle reactor in deactivation studies. The surface coverage was assumed to be 80% after 16 h in the temperature experiment. This choice is not important for the qualitative analysis of the experiments, but will of course affect the parameter values. The method could be improved if the deactivation were correlated with the surface coverage by some independent method. Rivera-Latas et al. [17] have compared several methods to estimate the active surface on a deactivated catalyst and recommended using titration of preadsorbed 02 by H2.
C3H8
C3H7.+ H* /
Coke Precursor + H2 r2 l~rl +H 2
C3H6 -~ ~ C3H6-+ H* Reversible Coke
r3
Irreversible Coke
Figure 4. A model for the formation of deactivating coke during propane dehydrogenation.
680 5. CONCLUSIONS The experiments clearly indicated the existence of reversible deactivation on the catalyst. It was possible to explain this behavior by a simple model including reversible and irreversible types of coke, and a mechanistic model based on the results was proposed in Figure 4. The transient approach, in which the reaction conditions were changed a number of times during each run, was powerful and yielded abundant information in a limited number of runs. Transient experiments were necessary in order to distinguish between the two types of deactivation. However, interpretation was difficult and it requires extensive numerical evaluations.
ACKNOWLEDGMENT This work was supported by the Swedish Research Council for Engineering Sciences (TFR).
REFERENCES 1. E.E. Wolf and E. E. Petersen, J. Catal., 46 (1977) 190. 2. J. Corella, J. Adanez and A. Monz6n, Ind. Eng. Chem. Res., 27 (1988) 375. 3 . L. C. Loc, N. A. Gaidai, S. L. Kiperman, in M. J. Phillips and M. Ternan (Editors), Proc. 9th Int. Congr. on Catalysis, Calgary 1988, Vol. 3, Chem. Inst. Canada, Ottawa, 1988, p. 1261. 4. P. Praserthdam, U. Panchareon and J. Tscheikuna, Kenkyu Hokoku - Asahi Garasu Zaidan, 61 (1992) 313. 5. R. Srinivasan and B. H. Davis, Platinum Metals Rev., 36 (1992) 151. 6. F.M. Dautzenberg, J. N. Helle, P. Biloen and W. M. H. Sachtler, J. Catal., 63 (1980) 119. 7. R. Burch and L. C. Garla, J. Catal., 71 (1981) 360. 8. M. Larsson, M. Hult6n, E. A. Blekkan and B. Andersson, J. Catal., 164 (1996) 44. 9. M. Larsson, B. Andersson, O. A. Bari~s and A. Holmen, Stud. Surf. Sci. Catal., 88 (1994) 233. 10. D. C. Montgomery, "Design and Analysis of Experiments", 2nd ed., John Wiley & Sons, New York, 1984. 11. L. Lin, T. Zhang, J. Zang and Z. Xu, Appl. Catal., 67 (1990) 11. 12. L. K. Loc, N. A. Gaidai, S. L. Kiperman, N. M. Podkletnova and S. B. Kogan, Kinetics Catal., 29 (1988) 989. 13. L. K. Loc, N. A. Gaidai, S. L. Kiperman, H. S. T'huoang, N. M. Podkletnova and S. B. Kogan, Kinetics Catal., 32 (1991) 61. 14. M. Larsson, N. Henriksson and B. Andersson, in preparation. 15. H. Hofmann and G. Kolb, Stud. Surf. Sci. Catal., 88 (1994) 257. 16. H. C. Beirnaert, R. Vermeulen and G. F. Froment, Stud. Surf. Sci. Catal., 88 (1994) 97. 17. F. J. Rivera-Latas, R. Dalla Betta and M. Boudart, AIChE J., 38 (1992) 771.
673
E s t i m a t i o n o f R e v e r s i b l e a n d Irreversible C o k e b y T r a n s i e n t E x p e r i m e n t s Mikael Larsson, Niklas Henriksson and Bengt Andersson Department of Chemical Reaction Engineering, Chalmers University of Technology, S-412 96 G6teborg, Sweden, mikael @cre.chalmers.se, http://www.cre.chalmers.se
Catalyst deactivation by coke formation can occur through a more or less reversible mechanism. We have applied a transient approach to model the reversible behavior of the deactivation, and to separate the deactivation from the main reaction kinetics. The deactivation of a Pt-Sn/A1203 catalyst was studied during propane dehydrogenation. The gas composition and temperature were varied during the experiments, which allowed us to model the deactivation by assuming one reversible and one irreversible type of coke. It was found that the deactivation increased with the propene concentration but was independent of the partial pressure of propane. Hydrogen decreased the deactivation rate and could even activate the catalyst by removing reversible coke.
1. INTRODUCTION Although many phenomenological models that include steps with reversible coke have been proposed, only a few attempts have been made to model this mechanism quantitatively [1,2]. Our goal in this study has been to model the reversible behavior observed during propane dehydrogenation by changing the inlet gas composition during runs. We wanted to find a method to separate the deactivation from the kinetics. Unfortunately there is no obvious way to do the latter. Many processes, such as adsorption, desorption, reaction and deactivation, occur simultaneously. For a hydrocarbon reaction deactivated due to coke formation, we can divide these processes into four types: (1) Processes much faster than the reaction rate (milliseconds), i.e. processes in equilibrium. (2) Processes in the same range as the reaction rate (seconds), i.e. processes at steady-state. (3) Relatively fast deactivation processes (minutes - hours). (4) Slower deactivation processes (hours - years). The system chosen here is the dehydrogenation of propane on Pt-Sn/A1203. This catalyst is used commercially because of its relatively high stability against coke formation and high selectivity during dehydrogenation reactions and naphtha reforming [3-7]. We have earlier measured the effect of altered reaction conditions on the amount of coke and activity [8] on this reaction system. We found that only a minor part of the coke caused the deactivation of the catalyst. This deactivating coke is formed in parallel with the non-deactivating coke. In the present work we will focus on the deactivating coke and model it by a transient method, in which the reaction conditions are changed a number of times during a run.
674
2. EXPERIMENTS About 30 mg of a Pt-Sn/A1203 catalyst were used in each run. The particle size were chosen small enough to avoid internal mass transfer limitations. The catalyst was prepared by sequential impregnation of a commercial "t-alumina support with aqueous solutions of SnC12 and H2PtC16 [9]. Characterization data are summarized in Table 1. The experiments were conducted in a fully automated flow reactor. The gas compositions were analyzed by a GC (see [8] for details). The reactor was fed with a mixture of propane, propene, hydrogen and nitrogen to achieve differential conditions. This was desired to avoid changes in the gas compositions along the bed leading to a non-uniform coke profile, and also to reduce the computational effort. The gas flow rates were controlled by mass flow controllers. The temperatures were 780, 800 and 820 K, and the total pressure was 1.5 bar. The inlet gas composition was changed in accordance with an extended 23 factorialdesigned experiment [ 10]. For each temperature, the experiment was divided into two parts to avoid very long experiments with severe deactivation. Reference conditions were repeated three times during each run. The total experimental plan contained six runs, each with 10 experimental points. The order of the points and the length between the steps (143 - 176 min) were randomized. The experiments conducted at 780 K will be named A1 and A2, while those performed at 800 and 820 K will be called B 1, B2, C1 and C2. In one experiment, the temperature experiment, the temperature was changed at constant gas composition, the same gas composition as the reference conditions in the main runs. This experiment was done in order to correlate the runs at different temperatures with each other. The catalyst was reduced in a flow of 5 ml/min of HE and 10 ml/min of N2 (flows at 273 K and 1.0 atm) at 1.5 bar for 180 min at 850 K. After that, the temperature was adjusted to the reaction temperature and allowed to stabilize for 30 min before the flow of hydrocarbons was introduced. The inlet gas composition was changed in the following range: 30 - 46 kPa C3H8, 4.5 - 7.5 kPa C3H6, and 6.8 - 11.2 kPa HE. The total flow trough the reactor was always 60 ml/min. The first GC analysis was taken after 5 minutes on stream, and the following ones every eleventh minute. Table 1. Catalyst Properties Catalyst
Particle size
Pt loading I Sn loading I
Dispersion 2 BET surface
Pt-Sn]A1203
0.05-0.14 mm
0.74 wt %
29%
1.53 wt %
172 m2/g
~By atomic absorption spectrometry. 2By hydrogen chemisorption in a volumetric system assuming H:Pt=l:l.
3. R E S U L T S Figure l a shows the gas compositions and the turnover frequency (TOF) in an experiment performed at 780 K (A1). From the TOF curve, one can see that the deactivation rate, i.e. the derivative of the TOF, changes with altered reaction conditions. The activity may even increase with time in some experimental points (not shown here). This demonstrates that it is
675 necessary to include a reversible part in a coke model. The results from the experiments will, in the following analysis, be evaluated as outlined in Figure 2. 3.1. Estimation of the deactivation function
In order to use the transient experiments to calculate the surface coverage of coke, we first introduce the continuous deactivation function. We define the deactivation function as the activity related to the first analysis after 5 minutes and compensated for the changes in reaction conditions. The compensation is carried out by assuming that the degree of deactivation immediately before and after a change in reaction conditions is the same. To be able to do so, a few assumptions have to be made (see Discussion): 1. The coke coverage varies only slowly when the reaction conditions are changed. 2. A specific coke coverage causes the same degree of deactivation independent of gas composition and reaction temperature. If these assumptions are valid, the degree of deactivation will be the same immediately before and after a change in gas composition. We have seen earlier that this is true for a change in temperature at constant gas composition for the present reaction [8]. Using these assumptions, the deactivation function for each experiment was calculated by extrapolating the reaction rates to the time for a gas change and equating the degrees of deactivation before and after the change. Figure lb shows the deactivation functions for the curve in Figure 1a. To examine the quality of the deactivation function, the relative activities in the repeated experiments were compared with the deactivation function. If the deactivation function would describe the degree of deactivation entirely, the deactivation function and the repeated experiments would agree. The agreement shown in Figure lb is good. However, slightly larger deviations occur in some of the experiments. This deviation was incorporated by adjusting the deactivation function linearly in order to achieve total correlation between the deactivation function and the repeated experiments. 1.4
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Figure 1. (a) The turnover frequencies (TOF) and gas compositions for one of the experiments performed at 780 K (A1). TOF is based on hydrogen chemisorption on a fresh catalyst [9]. The numbers in the figure indicate: (1) the first analysis after 5 minutes, (2) from where the modeling began (3) the last analysis during the second repeated experimental point with reference conditions. (b) The deactivation function and calculated total surface coverage for the same experiment (A1). The plus signs in the figure are repeated experiments with the same reaction conditions. The point-dotted section of the surface coverage curve was not used in the modeling.
676
I Malnexperiments~ A1,A2,I]I,B2,CI andC2
Determination H ofTOF
Estimation ofthe L deactivationfuncfloni ~ Temperature ~Wl experiment |
Estimationof the ~,~ coverage
surface
Modeling
]
Figure 2. Schematic picture of how the experimental data was treated.
3.2. Estimation of the surface coverage In the this paragraph we will relate the activity to changes in coke coverage. We assume that the deactivation function is proportional to the free metal surface area, i.e. the metal surface not covered by either reversible or irreversible coke. To relate the activity to the surface coverage by coke is however problematic. It is not possible to extrapolate to time zero and assume zero surface coverage, because the surface to a large extent is covered almost immediately [9,11]. Neither can we say that the initial surface coverage is the same in all experiments, since it may change with reaction conditions. Instead, the activity has to be correlated with the surface coverage by independent methods. Lin et al. [ 11 ] pulsed n-hexane on a Pt-Sn/A1203 catalyst and found by hydrogen chemisorption that about 70% of the metal surface rapidly became covered by coke, and that additional hydrocarbon pulses only slightly reduced the free metal surface. Larsson et al. [9] ran propane dehydrogenation on a PtSn/A1203 catalyst and found that the activity for the reaction between H2 and D2 was only about 15% of the activity for a fresh catalyst after 10 h on stream. In the present study, we will, in accordance with these findings, assume that the surface coverage of coke is 80% after 16 h on stream in the temperature experiment, and will then relate the other runs by comparing the activities. We assume that when the same reaction condition is applied, i.e. the same gas composition and temperature, differences in activity are only due to the degree of deactivation. Therefore, we can estimate the surface coverage for points with the same gas composition but from different runs given that the surface coverage is known in one run. Data from the temperature experiment was used to estimate the effect of changed temperature at constant coke coverage on the reaction rate. The relative activities were 0.584, 1 and 1.47 for 780, 800 and 820 K respectively. As described above, we assumed that the total coke coverage was 0.8 in the temperature experiment after 16 h, and estimated the surface coverage for all the experiments by using the activities at the end of the sixth experimental point (see number 3 in Figure l a). In this point the gas composition was the same in all the experiments. Figure 1b shows the estimated surface coverage for experiment A1. 3.3. Modeling of the surface coverage The following model of the deactivation has been made as simple as possible. A few fundamental assumptions have been used: 1. Only the coke covering the active sites is involved in the modeling. 2. Two types of coke that cause the deactivation exist, one reversible and one irreversible. 3. The reversible type of coke can be removed, be converted into a harmless type of coke, or form irreversible coke on a time-scale slow enough to be detected by the GC analysis. The amount of reversible coke is changed by modifications in the reaction conditions. 4. The irreversible coke cannot be removed in the time-scale concerned in the experiments.
677
5. The reversible and irreversible types of coke occupy the same number of active sites per carbon atom. The irreversible coke is formed only from the reversible coke. 6. A pseudo steady-state for the reversible coke is reached at the end of the first point in the experiments (after about 5 hours). The last assumption leads to the following equation:
d( Orev,O 1--Oirr,O )
dt
=0
(1)
where E)rev,0 and Oirr,0 are the surface coverages of reversible and irreversible coke, respectively, .when the modeling begins. We did not involve the first five hours of the experiments in the modeling because the deactivation process in the beginning of a run is different from the following region in the experiment [8,12]. The modeling was done by minimizing the sums of squares from the residuals between the model and the estimated surface coverage functions. This non-linear regression was solved with a Levenberg-Marquardt routine in the MATLAB software package. A number of different models that fulfilled the six assumptions above were fitted to the experimental data. Equation (2) describes the model that gave the most satisfying fit. The same equations have been used by Wolf and Petersen [1] to describe the reversible deactivation behavior during methylcyclohexane dehydrogenation on Pt/)'-A1203.
dOrev
dt -k,. PC3H6.~ Pn2 --Orev-- Oirr )-k2 . PH. 20rev . .
dOirr dt
l('3, ~)rev
(2)
- k3 "Orev
However, problems in identifying physically acceptable solutions occurred. We found for the two series at 800 K (B 1 and B2) that, after 5 h, the initial deactivation was not finished and subsequently, the pseudo steady-state assumption was probably not fulfilled. Hence, in experiment B1 and B2, the next point was omitted and the modeling began from there. Difficulties with convergence still existed and, after comparing the runs, it was found that the deactivation behavior differed in run B2. Thus the latter was omitted from the analysis, and it was now possible to find an acceptable solution. Results from the modeling are shown in Figure 3 and the parameter estimation, with linearized 95% confidence intervals, is given in Table 2. The highest correlation between the parameters was 0.87. One can see that the activation energies have relatively large confidence intervals. This can be explained by both the correlation between the parameters and the relatively small temperature interval in which the experiments were conducted. The validity of the model was checked by studying the residuals. No patterns indicating effects that had been neglected were found.
678
(9
1
•r 0.8
(9 1 A2
A1
/"-
~ 0.8
~0.6
(9 O 0.4 't~'0. 2
(9 ~ 0.4
0.4
5
1'0 l's 2'0 2s 30
o;
~...
9
,5
/
,,ao~/(]-o~,)
~ ~
~
O~ 1.o
0to~~~
~~:
..-
~ 0.7
= ~5 o.
Orev r~ 0"2 0
1'0 1'5 2'0 ;~5 3'0 Time, hours
0to
~ 0.4
1'0 1'5 2'0 ~5 3'0 Time, hours
1'0 1'5 ;~0 25 30 Time, hours
1 C2
r~o.6
r~J
B1
'0.2
1 C1
~176
~ 0.8 0.8
Time, hours
8
"
0.6
r.)
00
(9 1
5
1'0 1'5 2'0 2'5 3'0 0.5o.s o'.B 0'.7 ola 0'.9 Ii0 Time, hours Experimental 0total
Figure 3. The results from the modeling: reversible, irreversible and total coverage of coke. The experimental results are indicated with dashed lines and the model with solid lines. The ratios between the coverage of reversible coke and the surface not covered with irreversible coke are also shown. The predicted versus the experimental surface coverages are shown in the last graph. Table 2. The parameter values and linearized 95% confidence intervals Parameter Value 1.199" 10 -4 -i- 1.748" 10-5 Al (s -l) Pre-exponential factor l A2 (s-lPa -l) Pre-exponential factor 1 1.372" 108 + 4.794" 10.9 A3 (s l ) Pre-exponential factor 1 6.178.10 -5 + 8.968.10 -4 Ehl (kJ mol l ) Activation energy 119.5 + 43.8 EA2 (kJ mo1-1) Activation energy 68.5 + 103.3 EA3 (kJ mol -~) Activation energy 41.9 + 42.0 IEstimated from the centered Arrhenius expression ki=Ai'exp(Ehi/R'(1/T-I/T0)), T0=800 K.
4. DISCUSSION Equation (2) explains the transient deactivation with a model describing reversible and irreversible coke. We can see that the partial pressure of propane in the reactor does not influence the deactivation. This has also been demonstrated in an earlier study of the same system [8]. This observation is consistent with kinetic models for propane dehydrogenation proposed by Loc et al. [ 13]. They suggested that the rate-determining step is the dissociative adsorption of propane. From this mechanism it follows that the deactivation will be
679 independent of the propane partial pressure if the deactivation is caused by coke formed from intermediates in the reaction. The formation of reversible coke in Equation (2) can be explained by a model where a coke precursor first is formed from adsorbed propene by dehydrogenation. This precursor is in equilibrium with the propene and hydrogen in the gas phase, and it will form coke through a reversible mechanism. Finally irreversible coke is formed from the reversible coke. Figure 4 shows a mechanism for the formation of deactivating coke during propane dehydrogenation. The mechanism is derived from Equation (2) and from the propane dehydrogenation mechanism proposed by Loc et al. [13]. The coke formation part is in every sense consistent with a model proposed by Wolf and Petersen [ 1]. The definition of reversible coke is not clear in the literature, but is usually said to be the portion of coke that can be removed relatively easily by hydrogen treatment. The definition in this study has been, in effect, the portion of the coke that can be altered by changing the reaction conditions. This portion will vary according to how the experiments are carded out. More extreme changes in reaction conditions would allow a larger part of the coke to be modified. Two transient processes are superimposed when performing transient experiments on a deactivating reaction system. The difficulty in separating the two processes was overcome by running the reaction at differential conditions and using the deactivation function. In order to convert the turnover frequency curves to deactivation functions, it was assumed that the degree of deactivation did not change when the gas composition or the temperature was changed. This assumption is essential for the whole modeling. The basic idea is that what we define as coke coverage is changed only slowly and does not change during the short time it takes to change the reaction conditions. Repeated experiments were performed to verify the assumption and the small differences detected were corrected for. It is also necessary that the reaction mechanism does not change when the reaction conditions are altered. Our preliminary kinetic model of the main reaction kinetics indicates that this assumption is valid [ 14]. It was difficult to fulfill the objective of achieving differential conditions and producing accurate measurements when the activity was decreased by sometimes more than 90%. We had to admit non-differential conditions in the beginning of some runs (the first few hours). Because of the objective above, the variation in the variables had to be relatively limited. Therefore the parameter values are only valid in this limited range. The problems can be solved by changing the space velocity during the run and/or using a reactor that can be described as a stirred tank reactor. Hofmann and Kolb [15] and Beirnaert et al. [ 16] discuss the benefits of using a recycle reactor in deactivation studies. The surface coverage was assumed to be 80% after 16 h in the temperature experiment. This choice is not important for the qualitative analysis of the experiments, but will of course affect the parameter values. The method could be improved if the deactivation were correlated with the surface coverage by some independent method. Rivera-Latas et al. [17] have compared several methods to estimate the active surface on a deactivated catalyst and recommended using titration of preadsorbed 02 by H2.
C3H8
C3H7.+ H* /
Coke Precursor + H2 r2 l~rl +H 2
C3H6 -~ ~ C3H6-+ H* Reversible Coke
r3
Irreversible Coke
Figure 4. A model for the formation of deactivating coke during propane dehydrogenation.
680 5. CONCLUSIONS The experiments clearly indicated the existence of reversible deactivation on the catalyst. It was possible to explain this behavior by a simple model including reversible and irreversible types of coke, and a mechanistic model based on the results was proposed in Figure 4. The transient approach, in which the reaction conditions were changed a number of times during each run, was powerful and yielded abundant information in a limited number of runs. Transient experiments were necessary in order to distinguish between the two types of deactivation. However, interpretation was difficult and it requires extensive numerical evaluations.
ACKNOWLEDGMENT This work was supported by the Swedish Research Council for Engineering Sciences (TFR).
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