Ind. Eng. Chem. Res. 2009, 48, 10439–10447
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The Development of a Macro Kinetic Model for a Commercial Co/Pt/Al2O3 Fischer-Tropsch Catalyst F. Gideon Botes,* Braam van Dyk, and Craig McGregor Sasol Technology, R&D DiVision, 1 Klasie HaVenga Road, Sasolburg, 1947, South Africa
An experimental study was performed with an aged Co/Pt/Al2O3 catalyst in a laboratory slurry reactor to develop a macrokinetic expression for the Fischer-Tropsch (FT) synthesis. A semiempirical model was found to be the preferred two-parameter rate equation of the reaction. However, it was shown that this model is virtually indistinguishable from a mechanistically derived three-parameter rate model that assumes the following kinetically relevant steps in the cobalt-FT synthesis: CO dissociation occurs without hydrogen interaction and is not a rate-limiting step; the first hydrogen addition to surface carbon and the second hydrogen addition to surface oxygen are the rate-determining steps. 1. Introduction The Fischer-Tropsch (FT) synthesis involves the conversion of syngas (CO and hydrogen) to hydrocarbons (mainly linear paraffins and olefins). Two types of catalyst platforms are of commercial interest, namely iron- and cobalt-based catalysts. As pointed out by Davis,1 the mechanisms over these two types of catalysts may well differ. However, there is mechanistic evidence that over cobalt-FT catalysts an oxygen-free C1 surface intermediate (probably a CHx species) is formed first, which is then either hydrogenated to methane or grows to form longer chain hydrocarbons.2 This means that the FT reaction is actually composed of two separate mechanisms, namely a CO hydrogenation reaction followed by a polymerization reaction. It has further been found that the formation of the monomer is a very slow step compared to chain growth and product desorption, implying that the rate of CO conversion is essentially determined by the CO hydrogenation reaction.2 This is an important aspect, since it suggests that the FT reaction kinetics can be described with a fairly simple explicit rate equation, unlike the more detailed approaches followed by others3,4 that yielded highly implicit models to calculate the overall rate of CO conversion simultaneously with the product distribution. Review articles on FT kinetics are available in literature,5,6 while Zennaro et al.7 and Das et al.8 have presented in tabulated format the explicit rate equations that have been proposed for the cobalt-FT synthesis. Consequently, only a brief discussion on cobalt-FT kinetic models will be included here. The early power law rate equations were based on hydrogen and CO only, since it was believed that water had no influence on the chemical reaction kinetics in the cobalt-FT synthesis.5,8 It was generally found that the reaction order of hydrogen was positive, whereas that of CO was negative, the latter being ascribed to an extensive coverage of the catalyst surface by adsorbed carbon monoxide. Subsequently, more detailed kinetic studies have been performed which yielded LangmuirHinshelwood-Hougen-Watson type models accounting for the negative influence of CO in a mechanistically justifiable way. In one of the earlier systematic cobalt-FT kinetic studies, Rautavuoma and Van der Baan9 performed experiments with a Co/Al2O3 catalyst in a fixed bed reactor operated at atmospheric pressure and a temperature of 250 °C. By keeping the conversion below 2%, differential conditions were * To whom correspondence should be addressed. Tel: 0027 16 960 2914. Fax: 0027 11 522 3306. E-mail:
[email protected].
ensured. This allowed for one reagent’s partial pressure to be varied while that of the other was kept constant. It was concluded that the reaction rate was directly proportional to the hydrogen partial pressure, suggesting a reaction order of unity for this reagent. The following kinetic model was proposed from the study: rFT ) A
PH2PCO0.5 (1 + kCOPCO0.5)3
(1)
Sarup and Wojciechowski10 derived six rate expressions for the FT synthesis, which can all be represented by the following general form: rFT ) A
b PHa 2PCO
(1 +
∑kP i
d 2 c i H2PCO)
(2)
The exponents in eq 2 (a, b, c, and d) could assume various values, including fractions such as 0.25 and 0.75. After testing the models against their data, four rate expressions were rejected, leaving the following two which described the data more or less equally well: rFT ) A
rFT ) A
PH20.5PCO (1 + kCOPCO + kH2PH20.5)2 PH20.5PCO0.5
(1 + kCOPCO0.5 + kH2PH20.5)2
(3)
(4)
Yates and Satterfield11 correctly pointed out that there is often a high degree of covariance between the parameters of a kinetic model, so that several terms in the denominator can rarely be justified from a statistical perspective. Therefore, they only considered models with one adsorption parameter (usually assuming that CO is the only abundant species on the catalyst surface). The following emerged as their preferred reaction rate model: rFT ) A
PH2PCO (1 + kCOPCO)2
10.1021/ie900119z CCC: $40.75 2009 American Chemical Society Published on Web 10/13/2009
(5)
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However, from the results reported, there was clearly no basis for concluding that eq 5 is more accurate than the rate equation proposed by Rautavuoma and Van der Baan,9 since the two models describe the data equally well. In fact, because of a very high degree of parity between eq 1 and eq 5 (as shown in the Supporting Information), it is virtually impossible to distinguish between these two models when only macrokinetic data are available. The influence of water on the cobalt-FT reaction kinetics has become quite topical in the literature in recent years and some have started to include water in the kinetic models.12-14 However, the results of water cofeeding studies have not been very consistent, as some reported a positive15-17 and some a negative14,18 influence of water on the reaction rate, while others have found no significant effect at all.19,20 We have recently found that water has no notable influence on the overall rate of CO conversion over the commercial alumina-supported cobaltFT catalyst used for the current kinetic study.21 Consequently, the rate equations considered here will only include the partial pressures of hydrogen and CO. 2. Experimental Section The catalyst was prepared by means of aqueous slurry impregnation of a Puralox 5/150 gamma alumina support with a solution containing cobalt nitrate and the platinum promoter. After impregnation and drying, the catalyst precursor was calcined in air at 250 °C and then reduced in pure hydrogen at 425 °C. The fresh (reduced) Co/Pt/Al2O3 catalyst contained 20 wt % cobalt and 0.05 wt % platinum. Many cobalt-FT kinetic studies reported in literature have been performed with relatively young (fresh) catalysts. Since the industrial lifetime of a cobaltbased FT catalyst is expected to be quite long, it is arguably more representative to use a well-aged catalyst for kinetic studies. Therefore, the catalyst selected for the current study was obtained from a 100 barrel/day slurry bubble column reactor after five months of testing at commercially relevant FT synthesis conditions. More details about the catalysts have been presented elsewhere.22-25 The reactor setup was exactly the same as during the preceding study that was published previously.21 To summarize briefly, the experiments were performed in a mechanically stirred laboratory slurry reactor with an internal volume of 600 mL. The following gases, with minimum purities indicated, were fed from cylinders: hydrogen (99.999%), CO (99.9%), and Ar (99.999%). The flow rate of each gas was controlled with a Brooks mass flow controller. The combined feed entered the reactor via a dip tube that extends to just above the lower of two impellers. The reactor effluent passed through two knockout pots (a hot pot at 200 °C and a cold pot at ambient temperature) and then into a vent line. The reactor pressure was controlled with a back-pressure regulator situated after the cold knockout pot. The tail gas sample point was located between the cold knockout pot and the back-pressure regulator. The total feed and the tail gas were analyzed with an online gas chromatograph (Gow-Mac series 600) equipped with a thermal conductivity detector (TCD). All experiments were performed at 230 °C and typically runs lasted for 2-3 weeks. More details about the reactor system, as well as a schematic diagram, are presented elsewhere.26 By variation of the stirring speed, gas-liquid mass transfer limitations could be eliminated, as discussed previously.21 All flow rates were related to that of the internal standard (argon). Since water was not analyzed on the GC-TCD, its production rate was calculated from an oxygen balance under
the assumption that the contribution from oxygenates in the product spectrum was negligible. The FT reaction rate is defined as the amount of CO converted to hydrocarbons per unit time per unit amount of catalyst. Even though the water-gas-shift rate was very low (almost negligible), the CO2 production rate was subtracted from the total CO conversion rate to obtain the FT reaction rate. 3. Kinetic Models and Methodology As is evident from the discussion in the Supporting Information, it can sometimes be very difficult to distinguish between models that appear significantly different from each other. In general, one would expect the degree of parity between rival models to be even greater when the number of model parameters is larger. Furthermore, the extreme process conditions typically covered during a kinetic study can result in catalyst deactivation, making it even more difficult to discriminate clearly between similar models. Therefore, the following methodology was followed during the kinetic study: (i) Only models with two parameters (one activity parameter and one adsorption parameter) were initially considered to limit the covariance between parameter values and to facilitate model discrimination. (ii) All measurements were performed at the same temperature to identify the functional form of the kinetic model. Once this is known, the temperature can be varied during a subsequent study to estimate activation energies. Again this is to avoid the covariance between estimated values for the activation energy and other model parameters. (iii) The approach followed here was to effect systematic variations in the process conditions over short time periods, which would keep any catalyst deactivation effect to a minimum. Models that failed to predict the measured trend in the FT reaction rate were then assumed to contain systematic errors and could be eliminated. Finally, the models were tested against the complete data set to verify the findings. The models considered during this study have been organized into three classes and are presented in Tables 1-3. However, in the interest of conciseness, only certain selected models will be discussed in detail to illustrate the approach followed in the study. The overall range of conditions that was ultimately covered during the study is reported in Table 7. 4. Systematic Variations in Process Conditions 4.1. Run 1: Variation of Reactor Pressure at Different Inlet H2/CO Ratios. The denominators of most of the rate equations in Tables 1-3 have the following functional form: a PHb 2)c (1 + kadsPCO
(6)
To obtain an accurate value for the adsorption constant in the above expression, it is clear that the measured data must contain conditions where the term with reactant partial pressures varies extensively relative to the constant term. This can be achieved by varying the operating pressure over a wide range. To this end, a series of measurements were performed over a range of reactor pressures (ca. 5, 15, 30, and 40 bar). At every condition, sufficient time was allowed for the reactor to attain steady state (this time varied from about 20 min to four hours, depending on the flow rate and pressure). Three different inlet H2/CO ratios, namely 1.6, 2.1, and 3.2, were investigated to cover conditions above, at, and below the usage ratio of the cobalt-FT synthesis. During a given pressure series, the inlet H2/CO ratio was kept constant and each pressure series was performed in duplicate.
Ind. Eng. Chem. Res., Vol. 48, No. 23, 2009 Table 1. Class I Models (Based on One Site Occupation by CO or Surface Carbon) Considered during the Kinetic Study on a Commercial Alumina-Supported Cobalt-FT Catalyst model
I.1
I.2
I.3
I.4
I.5
rate equation
rFT ) A
rFT ) A
rFT ) A
rFT ) A
rFT ) A
comments
PH2PCO (1 + kCOPCO)2
PH20.5PCO (1 + kCOPCO)2
PH2PCO0.5 (1 + kCOPCO0.5)2
PH20.5PCO0.5 (1 + kCOPCO0.5)2
PH2PCO (PH2
0.5
+ kCOPCO)
2
Model I.1 was fitted to the data from each pressure series individually by optimizing the activity and adsorption coefficients to obtain the lowest relative variance between the predicted and measured rates, defined as Srel ) 100
1 n-m
n
∑ i)1
(
robserved - rpredicted i i robserved i
)
Table 2. Class II Models (Based on Two-Site Occupation by CO or a Reaction Intermediate) Considered during the Kinetic Study on a Commercial Alumina-Supported Cobalt-FT Catalyst model
CO dissociates via interaction with H. The first hydrogenation step is reversible and fast, while the second is slow and rate determining. CO dissociates via interaction with H. All hydrogenation steps are irreversible OR the first hydrogenation step is slow and rate determining. CO dissociation is reversible and does not involve hydrogen. The first hydrogen addition to surface carbon is reversible and fast, while the second is slow and rate determining. CO dissociation is reversible and does not involve hydrogen. All hydrogenation steps are irreversible OR the first hydrogenation step is slow and rate determining. CO dissociation is unassisted by hydrogen and irreversible OR CO dissociation is unassisted by hydrogen and rate determining.
2
(7)
The optimized values obtained for the CO adsorption coefficient are presented in Table 4. At each of the inlet H2/CO ratios, there is good agreement between the adsorption constant values obtained for the initial measurements and for the repeat measurements (i.e., the values are reproducible). However, it is clear that the CO adsorption coefficient is in fact not constant, but increases strongly with H2/CO ratio. This suggests a systematic error in the kinetic model. Model I.1 was also fitted to the data by only allowing one value of kCO for all the different pressure series, which yielded an optimized value of 1.0 bar-1 for the adsorption constant (see Table 6). The ratio of the measured to the predicted rates (Figure 1a) indicates serious systematic deviations in the kinetic model when it is attempted to keep the adsorption coefficient constant for all conditions. For the highest inlet H2/CO ratio, there is a shift from a severe under prediction in the rate at low syngas pressures to an overestimation at high pressures. For the low inlet H2/CO ratio, the opposite trend is noted. At the usage ratio, the model prediction is reasonable with only a slight systematic error. Model I.2 was evaluated in a similar way. First, the CO adsorption coefficient was optimized for every series individually, and the results are reported in Table 5. Again there is good agreement between the values obtained for the initial series and
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II.1
II.2
rate equation
rFT ) A
PH2PCO0.5 (1 + kCOPCO0.5)3
rFT ) A
PH2PCO (1 + kCOPCO)3
II.3a
rFT ) APH2PCO[s]3
II.4a
rFT ) APH20.5PCO[s]3
II.5a
rFT ) APH2PCO0.5[s]2
II.6a
rFT ) APH20.5PCO0.5[s]2
comments Surface carbon reacts simultaneously with two H atoms OR the partially hydrogenated carbon species occupies two sites. Undissociated CO reacts with H and form intermediate that occupies two sites. Hydrogenation of this species is rate determining. Undissociated CO occupies two sites. Undissociated CO interacts with H. The second hydrogenation step is rate determining. Undissociated CO occupies two sites. Undissociated CO interacts with H. The first hydrogenation step is rate determining. Molecular CO occupies two sites and is most abundant. CO dissociation is unassisted by hydrogen. Second hydrogenation step is rate determining. Molecular CO occupies two sites and is most abundant. CO dissociation is unassisted by hydrogen. First hydrogenation step is rate determining.
a
[s] )
√(4kCOPCO + 1) - 1 2kCOPCO
the repeat series for a given H2/CO ratio, but there is clearly a strong trend in the value of kCO with H2/CO ratio. When using the same kCO value for all data, an optimized value of 0.31 bar-1 was obtained (Table 6). The accuracy of the model is presented in Figure 1b as a function of the syngas partial pressure, also indicating severe systematic errors in model I.2. At each of the inlet H2/CO ratios tested, the accuracy of the rate equation forms a parabolic shape with increasing syngas partial pressure. This is especially evident for the data measured at the high H2/CO ratio, but is also visible for the other two conditions. Three models were found that could describe the pressure variation data much better, namely models I.4, III.3, and III.5. The optimized adsorption coefficient for each model is presented in Table 6, while the ratio of the measured to predicted reaction rate is presented in Figure 1c-e. Of these three rate expressions, model III.3 arguably has the most significant systematic deviations (Figure 1d), but generally the models are accurate to within about 10% of the measured rates. Clearly all three models are a big improvement over models I.1 and I.2. The common feature of the three best fit models is that they all have a reaction order of 0.5 for CO in the numerator. This is consistent with a mechanism where CO first dissociates before interaction with hydrogen, contrary to models I.1 and I.2 that imply hydrogen-assisted dissociation of CO. 4.2. Run 2: Variation of Inlet Flow Rate of One Reagent. It is clear that there are very strong similarities between models I.4, III.3, and III.5, which will make it difficult
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Table 3. Class III Models (Having Nontraditional Hydrogen Reaction Orders) Considered during the Kinetic Study on a Commercial Alumina-Supported Cobalt-FT Catalyst model
rate equation
rFT ) A
III.1
rFT ) A
III.2
III.3
rFT ) A
III.4 rFT ) A
PH2PCO (1 + kCOPCOPH20.5)2
PH2PCO0.5 (1 + kCOPCO0.5PH20.5)2
PH20.75PCO0.5 (1 + kCOPCO0.5PH20.25)2
PH20.75PCO0.5 (1 + kCOPCO0.5PH2-0.25)2
rFT ) A
III.5
comments
PH20.75PCO0.5 (1 + kCOPCO0.5)2
Same as model I.1, but it is assumed that [COHs] is the only abundant surface species. Same as model I.3, but it is assumed that [CHs] is the only abundant surface species. First hydrogenation of carbon and second hydrogenation of oxygen are rate determining steps, with [Cs] the only abundant surface species OR second hydrogenation of carbon and first hydrogenation of oxygen are rate determining steps, with [CHs] the only abundant surface species. First hydrogenation of carbon and second hydrogenation of oxygen are rate determining steps, with [Os] the only abundant surface species OR second hydrogenation of carbon and first hydrogenation of oxygen are rate determining steps, with [Cs] the only abundant surface species. Semiempirical model. Reaction term consistent with mechanisms of models III.3 and III.4.
Table 4. Values Obtained for the CO Adsorption Coefficient of Model I.1 When Fitted to Data Measured by Varying the Reactor Pressure over a Range of ca. 5 to 40 bar at Various H2/CO Ratiosa optimized kCO [bar-1] inlet H2/CO ratio
outlet H2/CO ratio
initial pressure series
repeat pressure series
1.6 2.1 3.2
1.2-1.5 2.1 4.0-6.0
0.61 0.97 2.41
0.77 0.93 2.25
a
The value of the adsorption coefficient was optimized for each pressure series individually. Experimental conditions: well-mixed slurry reactor; aged Co/Pt/Al2O3 catalyst; reaction temperature of 230 °C.
to discriminate between these three rate expressions. Therefore, in a subsequent experimental run, it was attempted to vary the reactor partial pressure of one reactant (hydrogen or CO), while keeping that of the other constant. This was only moderately successful, since the first two attempts yielded data where the hydrogen partial pressure varied between 9.3 and 10.7 bar (considered to be constant), while the CO partial pressure varied between 0.6 and 4.5 bar. For the remainder of the run, it was decided rather to vary the inlet flow rate of either of the two components over a wide range while keeping that of the other reactant constant. The rate equations were tested against the data without reoptimization of the adsorption parameters, that is, the CO adsorption coefficient values from Table 6 were used. The accuracy of each kinetic expression was evaluated by plotting the ratio of the measured to the predicted rate as a
function of the CO partial pressure inside the reactor (Figure 2). Model I.1 has serious systematic deviations for the data where either the hydrogen or CO feed rate was varied (Figure 2a), while model I.2 fails comprehensively for data where the CO partial pressure varied at fairly constant hydrogen partial pressure (Figure 2b). This confirms that these two models have been rightfully discarded previously. Models I.4 and III.3 also have clear systematic errors which are especially evident for data measured at constant hydrogen but varying CO partial pressure (Figure 2 panels c and d, respectively). To the contrary, as is evident from Figure 2e, model III.5 has remarkable accuracy for all data from the run and no significant trends in the accuracy are visible. 4.3. Run 3: Diagonal Relationship between Inlet H2/CO Ratio and Reactor Pressure. Even though the foregoing results indicated certain systematic deviations in models I.4 and III.3, one would ideally want more evidence before these rate equations are finally discarded. Therefore, process conditions were systematically varied during a further experimental run in an attempt to identify any other inconsistencies in these models. Considering the experimental space depicted by Figure 3, it is clear that the experiments of run 1 (pressure series data) only covered variation in the direction of the horizontal (dotted) lines. Therefore, in run 3, it was decided to also cover variation in the diagonal direction (solid lines in Figure 3), that is, to vary conditions from a high inlet H2/CO ratio at high pressure to a low inlet H2/CO ratio at low pressure, as well as from a high inlet H2/CO ratio at low pressure to a low inlet H2/CO ratio at high pressure. As previously, the rate equations were tested against the data without reoptimization of the adsorption parameters, that is, the values from Table 6 were used. The accuracies of the three main rival rate equations are presented in Figure 4 as a function of the H2/CO ratio inside the reactor. These graphs show clear systematic trends in the accuracy of models I.4 and III.3 which are especially evident at high H2/CO ratios (Figures 4a,b, respectively). The deviations in model III.5 are notably smaller and, more importantly, no systematic trends with variation in the H2/CO ratio are evident (Figure 4c). 5. Evaluation of Rate Equations with the Lumped Data Set The rival rate expressions of Tables 1-3 were also fitted to the combined set of data from runs 1 to 3 by minimizing the relative variance. The lumped data set contained 70 measurements which covered broad ranges of component partial pressures, as shown in Table 7. The jackknife method,27 a commonly used method for resampling mathematical data, was used to calculate confidence intervals for the model parameters. Values for the model parameters were regressed on each of the resampled data sets. The confidence interval was estimated using the percentile method, that is, the lower bound was taken as the 2.5 percentile value and the upper bound as the 97.5 percentile value to give a 95% confidence interval. This method assumes no underlying distribution in the parameter values. The 95% confidence intervals, included with the results in Table 8, are generally fairly narrow. This presumably indicates that the variations in the reaction rate due to changes in operating conditions were much larger than the measurement errors in the data, which allowed for reasonably accurate parameter estimates as well as clear discrimination between rival kinetic models. The results of Table 8 indicate that model III.5 has a significantly lower relative variance than any of the other models considered during the study. Furthermore, the optimized adsorp-
Ind. Eng. Chem. Res., Vol. 48, No. 23, 2009 Table 5. Values Obtained for the CO Adsorption Coefficient of Model I.2 When Fitted to Data Measured by Varying the Reactor Pressure over a Range of ca. 5 to 40 bar at Various H2/CO Ratiosa optimized kCO [bar-1] inlet H2/CO ratio
outlet H2/CO ratio
initial pressure series
repeat pressure series
1.6 2.1 3.2
1.2-1.5 2.1 4.0-6.0
0.24 0.31 0.47
0.27 0.30 0.50
a
The value of the adsorption coefficient was optimized for each pressure series individually. Experimental conditions: well-mixed slurry reactor; aged Co/Pt/Al2O3 catalyst; reaction temperature of 230 °C.
tion constant values of the main two rival rate equations (models I.4 and III.3) are much higher than previous estimates, whereas that of model III.5 is essentially exactly the same as the original
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Table 6. Optimized Adsorption Coefficient Values for Selected Kinetic Models As Obtained by Fitting the Rate Equations to the Lumped Pressure Series Dataa model
optimized value of adsorption constant
I.1 I.2 I.4 III.3 III.5
1.0 bar-1 0.31 bar-1 0.52 bar-0.5 0.34 bar-0.75 1.58 bar-0.5
a Experimental conditions: well-mixed slurry reactor; aged Co/Pt/ Al2O3 catalyst; reaction temperature of 230 °C.
estimate (compare Tables 6 and 8). As a last test, the hydrogen reaction order in model III.5 was optimized with the lumped data set rather than being specified. The optimal value obtained was 0.73, which is almost exactly the same as the original value
Figure 1. Accuracy of selected kinetic models, with absorption parameter values as per Table 6, as a function of syngas partial pressure for the data from run 1 (pressure series data). Experimental conditions: well-mixed slurry reactor; aged Co/Pt/Al2O3 catalyst; reaction temperature of 230 °C: (a) model I.1, (b) model I.2, (c) model I.4, (d) model III.3, (e) model III.5.
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Figure 2. Accuracy of selected kinetic models, with absorption parameter values as per Table 6, as a function of CO partial pressure for the data from run 2 (variation of the inlet flow rate of one reactant). Experimental conditions: well mixed slurry reactor; aged Co/Pt/Al2O3 catalyst; reaction temperature of 230 °C: (a) model I.1, (b) model I.2, (c) model I.4, (d) model III.3, (e) model III.5.
of 0.75, suggesting that the reaction order of hydrogen in model III.5 is correct. The parity plot of model III.5 for the lumped data set, provided in Figure 5, confirms the accuracy of the model over a wide range of reagent partial pressures. 6. Mechanistic Basis of the Preferred Kinetic Model In the interest of achieving clear and unambiguous model discrimination during this study, it was decided to initially only consider rate equations with two parameters, namely one activity and one adsorption parameter. This only allows for one species to be abundant on the catalyst surface (i.e., to be included in the denominator of the equation). The foregoing analyses and evaluations suggested that model III.5 is the preferred twoparameter rate equation for the cobalt-FT synthesis. Unfortunately though, it does not appear as if this kinetic expression can be derived from an assumed reaction mechanism and therefore must be regarded as a semiempirical model for the
time being. Nevertheless, the numerator of model III.5 seems to be consistent with the following sequence of elementary reaction steps: • CO dissociates before interaction with hydrogen (consistent with the 0.5 reaction order for CO as found during the current experimental macrokinetic study). • There are mechanistic pathways that allow for the fast dissociation of CO, so that this step should not be rate determining for the overall synthesis. • The first addition of hydrogen to surface carbon is much slower than the second and third additions, implying that this first hydrogenation step may be the rate limiting step of monomer formation. • The first hydrogen addition to surface oxygen is much faster than the second addition, implying that the hydrogenation of surface OH species is also a rate limiting step for monomer formation.
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Figure 3. Experimental space (variation in process conditions) of runs 1 and 3.
Applying the above principles, the following three parameter rate equation can be derived (see Supporting Information for detailed derivation): Model IV.1: rFT ) A
PCO0.5 PH0.75 2 (1 + kC/OHPCO0.5PH20.25 + kOPCO0.5PH2-0.25)2 (8)
This equation contains three terms in the denominator. The first term (a constant of one) represents vacant sites, the second term represents site coverage by surface carbon and/ or OH groups, and the third site occupation by surface oxygen. By omitting either the second or the third term in the denominator, model III.3 or III.4 is obtained. Since both of these rate expressions have previously been eliminated, it appears as if all the terms in the denominator of model IV.1 are important. Model IV.1 was also evaluated with the lumped data set from runs 1 to 3 and the results are included in Table 8. Judging by the similar Srel values, it is clear that model IV.1 is as accurate as the preferred two-parameter model. Because of the apparent similarities between these two expressions, their predictions for all conditions in the lumped data set of runs 1 to 3 are compared in Figure 6. Clearly the correlation between the two models is so strong that they are virtually indistinguishable. For 95% of the data, the rates predicted by the two models differ by less than 3%, which is around the experimental accuracy of the measured rates. This means that the available data are simply not adequate to confidently distinguish between models III.5 and IV.1. In fact, it is anticipated that it will be extremely difficult to empirically discriminate between these two models on the basis of macrokinetic data only. The reason for the strong similarity between the two models becomes apparent when model IV is rearranged slightly: Model IV.1: rFT ) A
PH20.75PCO0.5 (1 + [kC/OHPH20.25 + kOPH2-0.25]PCO0.5)2
(9)
In other words, what has been denoted in model III.5 as a CO adsorption coefficient is in fact not a constant, but a
Figure 4. Accuracy of selected kinetic models, with absorption parameter values as per Table 6, as a function of the reactor H2/CO ratio for the data from run 3 (diagonal relationship between inlet H2/CO ratio and reactor pressure). Experimental conditions: well-mixed slurry reactor; aged Co/Pt/ Al2O3 catalyst; reaction temperature of 230 °C: (a) model I.4, (b) model III.3, (c) model III.5. Table 7. Range of Component Partial Pressures and Other Conditions Covered by the Lumped Data Set of Runs 1 to 3a conditions inside CSTR
minimum
maximum
reactor pressure (bar abs.) H2 partial pressure (bar) CO partial pressure (bar) H2O partial pressure (bar) (H2 + CO) partial pressure (bar) H2/CO ratio
5.9 1.9 0.5 0.4 3.1 1.0
40.9 21.7 9.3 14.5 26.1 15.5
a Experimental conditions: well-mixed slurry reactor; aged Co/Pt/ Al2O3 catalyst; reaction temperature kept constant at 230 °C during entire study.
pseudocoefficient dependent on the hydrogen partial pressure according to the function
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kCO,pseudo ) kC/OHPH20.25 + kOPH2-0.25
(10)
The coefficient value calculated according to eq 10 is presented in Figure 7 as a function of the hydrogen partial pressure. The value of the pseudocoefficient is essentially constant over the whole hydrogen partial pressure range covered during the experimental study. Moreover, the estimated values Table 8. Results Obtained When Fitting the Kinetic Models of Tables 1-3 to the Lumped Data Set from Experimental Runs 1 to 3a model I.1 I.2 I.3 I.4 I.5 II.1 II.2 II.3 II.4 II.5 II.6 III.1 III.2 III.3 III.4 III.5 IV.1
optimized adsorption parameter value (95% confidence interval in brackets) -1
0.78 bar 0.47 bar-1 2.23 bar-0.5 0.95 bar-0.5 1.59 bar-0.5 0.67 bar-0.5 0.27 bar-1 5.02 bar-1 1.45 bar-1 2.13 bar-1 0.55 bar-1 0.17 bar-1.5 0.28 bar-1 0.48 bar-0.75 2.29 bar-0.25 1.55 bar-0.5 kC/OH ) 0.51 bar-0.75 kO ) 1.18 bar-0.25
(0.74-0.80) (0.45-0.49) (2.12-2.34) (0.92-1.00) (1.50-1.65) (0.65-0.69) (0.26-0.28) (4.76-5.21) (1.37-1.54) (1.95-2.29) (0.52-0.59) (0.16-0.17) (0.27-0.28) (0.46-0.50) (2.17-2.41) (1.50-1.61) (0.50-0.53) (1.11-1.22)
Srel 20.3 18.5 17.0 15.6 17.4 17.6 24.1 17.0 15.9 17.0 15.8 19.3 16.3 16.0 20.7 11.9 11.6
a Experimental conditions: well mixed slurry reactor; aged Co/Pt/ Al2O3 catalyst; reaction temperature of 230°C.
Figure 7. Pseudo-CO-adsorption coefficient (eq 10) as a function of hydrogen partial pressure.
are around 1.6, almost precisely what has been estimated for the adsorption coefficient of model III.5 (see Tables 6 and 8). Clearly a rise in the hydrogen partial pressure increases the first term of eq 10 to more or less the same extent that the second term is decreased, with the result that the net influence on the adsorption constant is negligible. It is thus evident that, even though model III.5 is at face value an empirical model, it is for practical purposes a truthful representation of the mechanistically derived model IV.1. The implications are quite favorable. The mechanistically derived kinetic model, containing three parameter values, can be accurately represented by a semiempirical, twoparameter model of which the parameter values can presumably be determined with a smaller set of data. This will be advantageous in subsequent phases of the study when the influence of temperature on the parameter values must still be determined or for applying the model to a different cobalt-FT catalyst. 7. Independent Verification of the Preferred Kinetic Model
Figure 5. Parity plot of preferred kinetic model (model III.5) for the lumped data set from runs 1 to 3.
In separate work from the chemical reaction kinetic study, a generic form of the rate expression was combined with detailed deactivation and selectivity models and regressed on a more comprehensive database (ca. 70 microreactor runs at various conditions) in order to fit values for the reaction orders and rate constants of the kinetic equation. Since it was anticipated that there would be a significant amount of cross-correlation between parameters in the overall model, the values allowed for the various parameters were bounded and initial estimates were based on previous experience with other kinetic expressions, such as the model by Yates and Satterfield.11 The various parameters were then regressed on the large database. In this manner, values for the rate constant, reaction orders, and the CO adsorption constant were obtained that were in very close proximity to the values determined in the dedicated kinetic study, albeit from a different, more empirical starting point. 8. Conclusions
Figure 6. High degree of agreement between the predictions of models III.5 and IV.1 for the lumped data set of runs 1 to 3.
A kinetic investigation was performed on an aluminasupported cobalt-FT catalyst in a laboratory slurry reactor. The catalyst selected for the study was obtained from a 100 barrel/ day slurry bubble column reactor after five months of testing at commercially relevant conditions. It is believed that the relevance of the study was broadened by using a catalyst that is more representative of the lifetime average age of a commercial FT catalyst than a fresh catalyst.
Ind. Eng. Chem. Res., Vol. 48, No. 23, 2009
A variety of two parameter rate equations were derived from assumed sets of elementary reaction steps. The approach followed here was to vary the process conditions systematically and to test which of the models could describe the influence of these variations on the reaction rate. Rate expressions that failed were assumed to contain systematic errors and consequently discarded. The only equation that could reasonably account for all the variations in the reaction rate was the semiempirical model III.5. Testing all the kinetic expressions against the lumped set of data from three different runs confirmed that this is indeed the preferred model. Further analysis revealed that model III.5 is in fact a very accurate representation of a mechanistically derived three parameter rate equation, named here model IV.1. This model is consistent with the following sequence of kinetically relevant reaction steps in the cobalt-FT synthesis: CO dissociation is fast and occurs without involvement of hydrogen; the first hydrogenation step of surface carbon and the second hydrogenation step of surface oxygen are slow and determines the overall rate of CO conversion to hydrocarbons. Acknowledgment The authors would like to thank Gerhard van Tonder for his meticulous execution of the experimental work during the kinetic study. Supporting Information Available: High degree of parity between kinetic models proposed by Rautavuoma-Van der Baan and Yates-Satterfield; derivation of model IV.1. This material is available free of charge via the Internet at http:// pubs.acs.org. Literature Cited (1) Davis, B. H. Fischer-Tropsch synthesis: Current mechanism and futuristic needs. Prepr. Symp.sAm. Chem. Soc., DiV. Fuel Chem. 2000, 45 (1), 129. (2) Van Dijk, H. A. J. The Fischer-Tropsch Synthesis: A Mechanistic Study Using Transient Isotopic Tracing. Ph.D. Thesis. Technische Universiteit Eindhoven, Eindhoven, The Netherlands, 2001. (3) Wang, Y.; Ma, W.; Lu, Y.; Yang, J.; Xu, Y.; Xiang, H.; Li, Y.; Zhao, Y.; Zhang, B. Kinetics modelling of Fischer-Tropsch synthesis over an industrial Fe-Cu-K catalyst. Fuel 2003, 82, 195. (4) Yang, J.; Liu, Y.; Chang, J.; Wang, Y.; Bai, L.; Xu, L.; Xiang, H.; Li, Y.; Zhong, B. Detailed kinetics of Fischer-Tropsch synthesis on an industrial Fe-Mn catalyst. Ind. Eng. Chem. Res. 2003, 42, 5066. (5) Van der Laan, G. P.; Beenackers, A. A. C. M. Kinetics and selectivity of the Fischer-Tropsch synthesis: A literature review. Catal. ReV. Sci. Eng. 1999, 41 (3, 4)), 255. (6) Wojciechowski, B. W. The kinetics of the Fischer-Tropsch synthesis. Cat. ReV. Sci. Eng. 1988, 30 (4), 629. (7) Zennaro, R.; Tagliabue, M.; Bartholomew, C. H. Kinetics of FischerTropsch synthesis on titania-supported cobalt. Catal. Today 2000, 58, 309. (8) Das, T. K.; Conner, W. A.; Li, J.; Jacobs, G.; Dry, M. E.; Davis, B. H. Fischer-Tropsch synthesis: kinetics and effect of water for a Co/ SiO2 catalyst. Energy Fuels 2005, 19, 1430.
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ReceiVed for reView January 23, 2009 ReVised manuscript receiVed September 7, 2009 Accepted September 17, 2009 IE900119Z
