Kinetic Study of n-Butane Isomerization over Pt−H-Mordenite

Ind. Eng. Chem. Res. 2005, 44, 471-484

471

Kinetic Study of n-Butane Isomerization over Pt-H-Mordenite Ville Nieminen, Matias Kangas, Tapio Salmi, and Dmitry Yu. Murzin* Laboratory of Industrial Chemistry, Process Chemistry Centre, A° bo Akademi University, FIN-20500, Turku/A° bo, Finland

The kinetics of n-butane isomerization over bifunctional Pt-H-mordenite was studied by varying reactant partial pressure and temperature. The main products were isobutane, propane, and pentanes. Yields of other products, especially methane, ethane, ethene, and propene, were very low, which suggests that protolytic cracking and hydrogenolysis were present only to a minor extent. Especially the protolytic cracking was inhibited, since after introduction of Pt into H-mordenite all strong Brønsted acid sites disappeared and the total density of acid sites decreased. The reaction rate showed complex dependence on the reactant partial pressure, suggesting that two reaction mechanisms on the acid sites, i.e., monomolecular or bimolecular, for isobutane formation are present and the prevailing mechanism depends on the reaction conditions. Three kinetic models were developed based on the current understanding of the reaction mechanisms including hydrogenation and dehydrogenation steps on the metal sites, skeletal isomerization on the acid sites, and deactivation due to coke formation. Model A enabled the monomolecular isobutane formation path, model B the bimolecular, and model C both reaction paths. At high temperatures and low reactant dilutions, model B described the isomerization efficiency accurately but was not able to predict the increase in the selectivity to isobutane with increasing reactant dilutions at low temperature, opposite to models A and C. The kinetic modeling supported the conclusion that the prevailing mechanism depends on the reaction conditions. Introduction Skeletal isomerization of linear alkanes to branched counterparts has attracted attention to a large extent, since increasing the degree of branching of alkanes can boost the octane quality of a gasoline fraction. The application of branched hydrocarbons is an environmentally more acceptable alternative compared with other techniques, such as blending with aromatics or oxygenates. In general, alkane isomerization is thought to proceed as follows:1 A protonated alkene, CnH2n+1+ (most probably bonded to the catalyst framework as an alkoxide) is formed from the corresponding alkane. This can happen for instance by dehydrogenation of the alkane to alkene and consequent protonation or by protonation of the alkane followed by hydrogen abstraction. The next step is a rearrangement to branched hydrocarbon via protonated cyclopropyl intermediate. Branched alkane is formed from the iso-CnH2n+1+ intermediate for example by hydride (H-) abstraction or desorbed isoalkene is hydrogenated to isoalkane. However, isomerization of n-butane via this mechanism has been questioned, since the opening of the ring intermediate would virtually lead to a highly energetic primary carbenium ion species. Thus, isobutane is thought to be formed via a bimolecular reaction mechanism, which involves dimerization of two butyl isomers forming a C8 species as an intermediate, which can undergo isomerization (without the formation of primary carbenium ion species) followed by cracking. Indeed several factors are in favor of this proposal; for example, n-butane isomerization seems to run in an optimal mode when reaction conditions are chosen in a way that enables the bimolecular reaction mechanism.2 * To whom correspondence should be addressed. Fax: +358 2 215 4479. E-mail: [email protected].

The main byproducts, propane and pentanes, are also obtained by disproportionation of the dimerization products, i.e., C8 intermediates. However, some evidence exists that a monomolecular reaction mechanism is possible also for n-butane.3-9 This is understandable, since the key steps in the isomerization reaction of n-butane are similar to those for isomerization of linear butenes to isobutene, which is thought to form mainly monomolecularly.2,10 Several catalysts, such as zeolites, heteropoly compounds, and sulfated zirconia, have been reported to be active in the isomerization of n-butane.11-13 Typically a metal is introduced into the catalyst to obtain bifunctional properties in order to improve the dehydrogenation/hydrogenation function.12,14 Application of hydrogen as a carrier gas combined with Pt introduction has also been observed to be beneficial for catalyst stability. Brønsted acidic mordenite zeolite, especially promoted with Pt, has received a lot of attention in n-butane isomerization applications.3-5,11,14-30 The conclusions concerning the reaction mechanisms have been obtained mainly from the product distribution analysis, kinetic regularities, and carbon labeling studies. The main byproducts are propane and pentane isomers, indicating that dimerization-cracking has a major contribution to the reaction, also for the production of isobutane. However, it seems that reaction conditions influence whether isobutane is formed via a mono- or bimolecular pathway. The factors that favor bimolecular reaction pathways are low temperature, high density of (strongly) acidic sites, absence of hydrogen in the reaction feed, long reactant contact times, and low reactant dilution.2,3 A peculiar phenomenon in the reaction is that an excess of propane is typically formed; i.e., the rate of propane formation is higher than the rate of pentane formation. This has been explained by dimerization of pentyl and

10.1021/ie049544q CCC: $30.25 © 2005 American Chemical Society Published on Web 12/31/2004

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butyl intermediates followed by cracking of formed nonyl intermediates to three C3 products.3,14 This explanation somewhat contradicts the assumption that formation of bulky dimers, nonyl intermediates in this case, is virtually suppressed in the pores of mordenite.18 Pt introduction increases the amount of dehydrogenation/hydrogenation reactions producing olefins, i.e., butenes in this case, which are important intermediates for the n-butane isomerization reaction.31 However, the drawback of olefins is that they are known to be precursors for coke formation and therefore catalyst deactivation. For example, the stability of H-mordenite was increased in the presence of hydrogen due to the lower concentration of olefins.14 Thus, higher olefin concentrations can be inhibited using hydrogen as a diluent. However, H2 typically has a negative effect on the reaction rate. Furthermore, at high hydrogen partial pressures the presence of Pt also increases hydrogenolysis, i.e., the cleavage of the carbon-carbon bonds with the uptake of hydrogen, which decreases the selectivity to the desired product. Thus, tradeoff should be done with the reaction parameters to find the optimal conditions to produce isobutane. Some kinetic modeling of n-butane isomerization based on the single-event theory have been published.32 Surprisingly, there are very few studies, if any, on kinetic modeling of n-butane isomerization based on advanced reaction mechanisms, which would include also deactivation phenomena. Absence of quantification of reaction mechanism and deactivation models via numerical modeling and data fitting for experimental data obtained over a broad range of parameters resulted in discussion in the literature supporting one or another reaction mechanism. In our opinion, kinetic modeling is a powerful tool, which should be used in combination with other methods to elucidate reaction mechanisms, and this translates the chemical knowledge of a particular reaction to rate expressions, which could be also used for practical purposes. In this report, we present a kinetic study of the n-butane isomerization over Pt-H-mordenite zeolite. The reaction was carried out at three temperatures, 573, 623, and 673 K, with wide variation of the reactant partial pressure from 0.1 to 0.6 bar and with rather long reactant contact times. Hydrogen was used as a carrier gas. At least in principle, these conditions would enable both bimolecular and monomolecular reaction paths for isobutane formation. Furthermore, deactivation is clearly caused by coke formation due to low dilution. A kinetic model including deactivation due to the coke formation was developed based on the experiments. Such a model assisted in getting an insight into the prevailing reaction mechanism(s) at different conditions and also predicts the deactivation behavior, which is important in industrial applications. Experimental Section Catalyst Preparation and Characterization. Mordenite zeolite catalyst obtained from Zeolyst International with a SiO2/Al2O3 molar ratio of 20 was used in the experiments. Pt-H-mordenite was prepared by first modifying NH4-mordenite by impregnation with an aqueous solution of hexachloroplatinic acid hydrate for 24 h to obtain a loading equal to 0.5 mass % content of Pt, if all Pt is assumed to incorporate on the zeolite. The catalyst was dried after impregnation and calcined in a muffle oven at 623 K for 3 h.

Table 1. Concentration of the Strong (Desorption at 723 K), Moderate + Strong (Desorption at 623 K), and All (i.e., Weak + Moderate + Strong; Desorption at 523 K) Brønsted and Lewis Acid Sites by FTIR Spectra of Pyridine Adsorption for Pt-H-Mordenitea Brønsted acid sites, µmol/g catalyst H-mordenite Pt-H-mordenite

Lewis acid sites, µmol/g

523 K 623 K 723 K 523 K 623 K 723 K 331 270

284 147

212 0

71 6

50 1

39 0

a The corresponding acid sites for H-mordenite from ref 33 are given for comparison.

Characterization of the proton form of the catalyst is provided in ref 33. The acidity of the Pt-H-mordenite was measured by infrared spectroscopy (ATI Mattson FTIR) by using pyridine (g99.5 a.r.) as a probe molecule for qualitative and quantitative determination of Brønsted and Lewis acid sites. The sample was pressed into a self-supporting disk (12.5 mg/cm2). Pyridine was first adsorbed for 25 min at 373 K and then desorbed by evacuation at different temperatures (523, 623, and 723 K) to obtain a distribution of acid strengths. All spectra were recorded at 373 K with a spectral resolution equal to 2 cm-1. Spectral bands at 1545 and 1450 cm-1 were used to identify Brønsted acid sites (BAS) and Lewis acid sites (LAS), respectively. The amounts of BAS and LAS were calculated from the intensities of corresponding spectral bands by using the molar extinction coefficients reported by Emeis.34 The conversion of n-butane (99.9% AGA) over the catalysts was carried out in a fixed-bed reactor at atmospheric pressure. Catalytic experiments were conducted using hydrogen as a carrier gas with the nbutane partial pressure varying from 0.1 to 0.6 bar at temperatures of 573, 623, and 673 K using weight hourly space velocity (WHSV) values of 5, 10, and 15 h-1, respectively. The catalyst (pelletized and sieved to particle sizes of 125-250 µm) was pretreated with hydrogen at 723 K for 2 h before the experiments. The product analysis was carried out on-line by a gas chromatograph (Varian 3700) equipped with a flameionization detector (FID) and a capillary column (50 m × 0.32 mm i.d. fused silica PLOT Al2O3-KCl). Results and Discussion Characterization. The concentrations of the acid sites of Pt-H-mordenite are given in Table 1. The acidity of H-mordenite changed dramatically after introduction of Pt. Almost all LAS disappeared. However, the initial concentration of LAS is rather small for the studied mordenite. Accordingly, all strong BAS were lost as well and the total number of BAS (desorption at 523 K including strong, moderate, and weak BAS) decreased by 20%. On the other hand, the number of moderate and weak BAS doubled. The amount of acid sites determined by pyridine adsorption might be lower than obtained by other methods, since the acid sites in the side pockets of mordenite may not be accessible to pyridine.35,36 Kubicˇka et al. have studied the same mordenite structure with a very similar Pt impregnation method,37 and they obtained exactly the same results in the acidity measurements. It was concluded by Kubicˇka et al. that the changes in the acid site strength distributions could be expected due to interactions between platinum crystallites and acid sites. Furthermore, if all platinum particles are located at the outer

Ind. Eng. Chem. Res., Vol. 44, No. 3, 2005 473

Figure 1. Conversion as a function of TOS over Pt-H-mordenite with different reactant partial pressures at 573, 623, and 673 K.

surface of the zeolite crystallite, they would be far from the acid sites and therefore no interactions between Pt crystallites and the acid sites would exist. As a result, at least part of the Pt crystallites are in the vicinity of the acid sites and thus inside the pores. Therefore it can be inferred that at least part of the Pt particles are located inside the pores in Pt-H-mordenite as applied here. Catalyst Evaluation. The representative results of n-butane isomerization over Pt-H-mordenite are given in Figures 1-3. The main products in the n-butane isomerization were isobutane, propane, isopentane, and n-pentane. The fractions of methane, ethane, ethene, propene, butenes, and pentenes were obtained as well, but the selectivity to them was rather minor being mainly below 2.6 mol % at 573 K, below 5 mol % at 623 K, and 5-10 mol % at 673 K with the exception of 673 K and the 60:40 n-butane-to-hydrogen ratio, when the selectivity was 13 mol %. (a) Deactivation. The WHSV was chosen in a way to detect the changes in the catalyst performance due

Figure 2. Selectivities to propane, isobutane, and pentanes as a function of reactant partial pressures at 573, 623, and 673 K.

to coke formation at high reactant partial pressures. The conversion as a function of time on stream (TOS) is given in Figure 1. At 673 K with low reactant flow dilutions, the deactivation was very fast at the beginning of the run. In the case of the reactant-to-hydrogen ratio of 60:40, the conversion was 30 mol % at TOS ) 10 min but was decreased to ∼5 mol % at TOS ) 43 min. The initial conversion as well as the deactivation rate decreased with higher reactant flow dilutions. Negligible deactivation was observed with the n-butaneto-hydrogen ratio of 10:90 at the conversion level of ∼6 mol %. At 623 K the deactivation rate was less pronounced. For example, the conversion decreased from an initial value of 13 only to 8 mol % in 241 min with the reactant-to-hydrogen ratio of 40:60. The rate of deactivation was much slower at 573 K compared to higher temperatures tested. However, the initial activity was lower as well. For instance, with the reactant-to-

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Ind. Eng. Chem. Res., Vol. 44, No. 3, 2005 Table 2. Apparent Activation Energies (in kJ/mol) for Product Formation n-butane-to-hydrogen ratio propane isobutane pentane overall

60:40

50:50

40:60

20:80

10:90

84 50 59 69

68 44 46 56

86 51 58 67

122 71 92 91

116 71 168 89

Scheme 1. Brønsted Acid Site Catalyzed Reactions Used in the Kinetic Models

Figure 3. An example of the selectivities to propane, isobutane, and pentanes as a function of TOS.

hydrogen ratio of 60:40 at TOS ) 10 min initially the conversion was 19 mol % and it decreased to ∼9 mol % in 210 min. With a reactant-to-hydrogen ratio equal to or below 25:75, no deactivation was observed. (b) Selectivity. The selectivities to propane, isobutane, and pentanes as a function of reactant partial pressures at 573, 623, and 673 K are shown in Figure 2. It is apparent from Figure 2 that the reactant partial pressure influences the selectivity to isobutane and propane but has very little effect on the selectivity to pentanes. An example of the selectivities to propane, isobutane, and pentanes as a function of TOS is given in Figure 3. Deactivation has practically no influence on the selectivities to different products. This gives a possibility to compare the selectivities to different products at approximately the same level of conversion (around 8 mol %, a complete table is given in the Supporting Information). At all temperatures, the selectivity to pentanes varies mostly only between 10 and 12 mol %, regardless of reactant dilution or TOS. Furthermore, an excess of propane was always obtained compared to the yield of pentanes. At 673 K, the selectivity to isobutane increases with increasing hydrogen partial pressure. For instance, at 673 K the selectivity to isobutane at 0.6 partial pressure of nbutane is 23 mol % but the value increases to 50 mol % at 0.1 n-butane partial pressure. The selectivity to propane varies between 33 and 47 mol % and, in general, is lower at lower reactant partial pressures. At 623 K the selectivity to isobutane is around 50 mol % and the selectivity to propane is 30 mol % except at 0.6 reactant partial pressure, when the selectivities to isobutane and propane are 32 and 47 mol %, respectively. At 623 K the deactivation is not pronounced and the level of conversion is never exactly 8 mol %; therefore a straightforward comparison is difficult. In general, the selectivity to isobutane increases and the selectivity to propane decreases with decreasing reactant pressure. The selectivities to isobutane and propane varied between 52-87 and 31-13 mol %, respectively. The observation that the selectivity is not affected by the deactivation is in accordance with the earlier reports for H-mordenite showing that deactivation does not affect the product distribution.3 The deactivation is probably caused by coke formation, which blocks the pores of mordenite and consequently decreases the active surface area, since access to the active sites is hindered by the coke molecules. Obviously the reactant access to both active center types, Pt particles and

Brønsted acid sites inside the pores, is evenly blocked. Therefore it is reasonable to assume that the relative importance of coexisting reaction mechanisms does not depend on the extent of deactivation. (c) Activation Energies. The apparent activation energies based on Arrhenius plots are given in Table 2. The initial rates at TOS ) 0 min were extrapolated by taking into account the deactivation by fitting the results with the exponential decay function y ) y0 + Ae-(x-x0)/t. However, since only three temperature points were used, the values should be taken with care in mechanistic considerations. As can be seen in Table 2, the values are rather low at low reactant dilutions (reactant-to-hydrogen ratios of 60:40, 50:50, and 40:60), varying from 44 to 69 kJ/mol for isobutane, pentanes, and overall but slightly higher for propane (up to 86 kJ/ mol). At higher dilutions (reactant-to-hydrogen ratios of 20:80 and 10:90), the apparent activation energies are much higher for propane (122 and 116 kJ/mol, respectively) and pentanes (92 and 168 kJ/mol, respectively) but still rather low for isobutane (71 kJ/mol). Activation energies around 60 kJ/mol have been reported for propene, isobutene, and pentenes for 1-butene isomerization over ferrierite;38 however, higher activation energies for isobutene formation over ferrierite, up to ca. 130 kJ/mol, could be found in the literature.39 An Arrhenius plot for n-pentane isomerization over Pt-Hmordenite over a wide range of reaction temperatures was found to significantly deviate from linearity.18 Such deviations and dependence of the apparent activation energy on partial pressures point to the complex nature of the reaction mechanism, which is determined not by a single elementary step but rather by a sequence of steps. A similar trend is observed here, since the R2 value with 10:90 dilution is as low as 0.8446 for isobutane. Kinetic Modeling. A kinetic model based on the experimental results was developed. Only the reactions proposed in the literature to produce the main products, propane, isobutane, and pentanes, were taken into account while other reaction paths, such as hydrogenolysis and monomolecular butane cracking, were omitted. The reason for this is that the amount of byproducts is minor and neglecting them keeps the model reasonably simple, containing fewer estimated parameters while still being able to capture the main kinetic features of the reaction. Similarly, no inhibiting or promoting effects of Brønsted acid sites and Pt interaction, such as hydrogen spillover or surface dif-

Ind. Eng. Chem. Res., Vol. 44, No. 3, 2005 475 Scheme 2. Reactions Taking Place in the Kinetic Models on Pt and Brønsted Acid Sites

fusion, between the active sites were included in the model. The pentanes, isopentane and n-pentane, were lumped together, because both of them are (hydroged d nated) cracking products of Cd 8 f C3 + C5 . The modeled reaction network taking place over the zeolite active sites is shown in Scheme 1, and the overall network is depicted in Scheme 2. The reactions of olefins (subscript o), depicted in Scheme 1, taking place on the Brønsted acid sites (*H+) are as follows:

1 2 3 4 5 6 A B C D

k2θC2 4d,H+ ) k3θVθC8d,H+ + k5θVθC8d,H+ + k6θVθC8d,H+ (11) where θCd4 ,H+ is the coverage of n-butenes (subscript + Cd 4 ) on Brønsted acid sites (subscript H ) and θV is the coverage of the vacant sites. This becomes after rearrangement

θCd8 ,H+ )

1

0

0

0

0

(1)

0

1

1

1

1

(2)

n-C4 ) iso-C4 n-C4 ) iso-C4 n-C4 ) iso-C4 2n-C4 ) C3 + C5 3n-C4 ) 4C3

(12)

0

0

0

1

1

(3)

0

0

0

0

1

(4)

0

1

0

0

0

(5)

0

0

1

0

0

(6)

0

0

0

-1

-1

(7)

k2 2 K p 2 d θV k3 Cd4 ,H+ C4n

(13a)

k2 K2 p2 θ k3 + k6 Cd4 ,H+ Cd4 V

(13b)

θCd8 ,H+ ) and for models B and C

1

2

1

2

3

(8)

-1

-2

-1

0

0

(9)

0

0

0

-1

0

(10)

θCd8 ,H+ )

The rate equations of Langmuir-Hinshelwood type were derived using the assumption that rate-limiting steps are the surface reactions over Brønsted acid sites.

r1 )

where N(1) N(2) N(3) N(4) N(5)

k2 K2 p2 θ k3 + k5 + k6 Cd4 ,H+ Cd4 V

Neglecting k5, we get for model A

N(1) N(2) N(3) N(4) N(5) + *H+ n-C*H 4,o T iso-C4,o *H+ *H+ 2n-C4,o f C8,o + *H+ + *H+ f C*H 8,o + + *H+ C5,o + C*H 3,o *H+ *H+ C5,o + n-C4,o f 3C3,o + 2*H+ + *H+ C8,o + *H+ f 2iso-C*H 4,o *H+ + C8,o + *H f + *H+ iso-C*H 4,o + n-C4,o + *H + C3,o + *H Ξ C3,o + n-C4,o + *H+ Ξ n-C*H 4,o + + iso-C4,o + *H Ξ iso-C*H 4,o + *H + C5,o + *H Ξ C5,o

Model C includes routes N(1) and N(3)-N(5). Thus, in model C isobutane can be formed either monomolecularly or bimolecularly. Since no C6-C9 hydrocarbons were observed as products, a pseudo-steady-state approximation was applied for the coverage of Cd +. From the 8 , i.e., θCd 8 ,H steady-state approximation r2 ) r3 + r5 + r6, it holds that

k1(KCd4 ,H+pCd4 - Ki-Cd4 ,H+pi-Cd4 K1-1)

∑

reaction 1 in Scheme 1 reactions 2 and 5 in Scheme 1 reactions 2 and 6 in Scheme 1 reactions 2 and 3 in Scheme 1 reactions 2-4 in Scheme 1

On the right-hand side of eqs 1-10 above, the stoichiometric numbers of steps along independent routes are presented. Steps A-D are considered to be quasiequilibrated and correspond to adsorption of olefins on the acid sites. In fact, such an adsorption proceeds via protonation by olefins. Three different models were tested, representing the most commonly proposed models in the literature for n-butane skeletal isomerization. In all models, cracking of dimerized Cd 8 intermediates produces the byproducts, i.e., propane and pentanes (route N(4)). The excess formation of propane is exd plained by step 4, i.e., Cd 5 codimerization with C4 d d followed by consequent cracking to three C3 via C6 (route N(5)). Reaction 5 in Scheme 1 was neglected in all models, because including it did not noticeably improve the model fit but increased the estimated error of the parameters. For the same reason, reaction 6 in Scheme 1 was considered irreversible. Model A corresponds to monomolecular isobutane formation and included route N(1) as the sole path to isobutane. Routes N(4) and N(5) describe byproduct formation. In model B, isobutane is formed bimolecularly (N(3)) and the monomolecular path for isobutane formation is neglected. The valid routes are N(3)-N(5).

r2 )

k2KC2 d4 ,H+pC2 d4

r3 )

r4 )

(15)

∑2

k3θ′Cd8 ,H+

(16)

∑2

k4KCd5 ,H+pCd5 KCd4 ,H+pCd4

(17)

∑2

r6 )

(14)

k6θ′Cd8 ,H+

(18)

∑2

where

∑ ) 1 + i,olefin ∑ Ki,H pi + θ′C ,H +

d 8

+

(19)

i*Cd 8

and

θ′C8d,H+ )

θCd8 ,H+ θV

(20)

with θCd8 ,H+ defined in the most general form according to eq 12. The rate constants and their temperature dependence are modeled with the Arrhenius equation,

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slightly modified in order to improve simultaneous estimation of the pre-exponential factor and activation energy. The decoupling used to improve the parametrization of the model is described below.

pi-Cd4 )

ki ) Ai exp(-Ea,iq)

pCd5 )

(21)

where q is calculated according to

q)

(

1 1 1 Rg Tr Tmean

)

(22)

The temperature dependence of the adsorption coefficients is modeled similarly, but it includes a term for the carbon number, nC, which is comparable to the correlation between adsorption constants, Kj, and the carbon number described in refs 40 and 41:

Kj ) Aj exp(∆Hr,j nCq)

(23)

In this way the number of estimated parameters is decreased. The same adsorption constants for linear and branched hydrocarbons with the same nC were used, although they could be somewhat different.40 Equation 23 is also used for modeling the adsorption-desorption equilibria on platinum, although separate pre-exponential factors and heats of adsorption need to be used for olefins, alkanes, and hydrogen. (a) Pt-Catalyzed Reactions. All species, olefins (subscript o) and alkanes (subscript a), in the reaction network are assumed to adsorb and react on the surface of platinum particles (*Pt):

7 8 9 10 E F G H I J K L

*Pt T C*Pt C*Pt 3,o + 2H 3,a *Pt T n-C*Pt n-C*Pt + 2H 4,o 4,a *Pt iso-C*Pt 4,o + 2H *Pt T iso-C4,a *Pt T C*Pt C*Pt 5,o + 2H 5,a C3,a + *Pt Ξ C*Pt 3,a n-C4,a + *Pt Ξ n-C*Pt 4,a iso-C4,a + *Pt Ξ iso-C*Pt 4,a C5,a + *Pt Ξ C*Pt 5,a *Pt *Pt Ξ C3,o C3,o + n-C4,o + *Pt Ξ n-C*Pt 4,o iso-C4,o + *Pt Ξ iso-C*Pt 4,o C5,o + *Pt Ξ C*Pt 5,o

N(1)

N(2)

N(3)

N(4)

N(5)

0 -1 1

0 -1 1

0 -1 1

1 -2 0

4 -3 0

(24) (25) (26)

0 0 1 -1 0 0 -1 1 0

0 0 1 -1 0 0 -1 1 0

0 0 1 -1 0 0 -1 1 0

1 -1 2 0 -1 1 -2 0 1

0 -4 3 0 0 4 -3 0 0

(27) (28) (29) (30) (31) (32) (33) (34) (35)

The platinum-catalyzed reactions are dehydrogenation of alkanes and hydrogenation of olefins. Hydrogen disassociates on the surface and is added to the olefins in two steps. Because these steps are assumed to be fast compared to the reactions occurring on the acid sites and low yields of olefins were obtained, quasi-equilibria were applied for them. Therefore, the partial pressures for the olefins can be written as functions of the corresponding alkane:

pC3d ) pCd4 )

K7KC3,PtpC3 KH2,PtpH2KCd3 ,Pt K8KC4,PtpC4 KH2,PtpH2KC4d,Pt

(36)

(37)

K9Ki-C4,Ptpi-C4 KH2,PtpH2Ki-Cd4 ,Pt K10KC5,PtpC5 KH2,PtpH2KCd5 ,Pt

(38)

(39)

Migration of olefins formed on the metal sites to acid sites is considered to be fast. Thus, the expressions for the olefin coverages on Brønsted acid can be easily obtained using the following equation:

θo,H+ )

Ko,H+Ka,Pt Ki pθ KH2,PtKo,Pt pH2 a V

(40)

where o and a represent olefin and alkane, respectively, and i denotes the reaction number (7-10). Since all adsorption-desorption equilibria are modeled similarly, eq 40 can be simplified to

Ko,H+po )

θo,H+ Ki ) K′ pa θV pH2

(41)

where K′ is calculated in the following manner:

K′ )

Ao,H+Aa,Pt exp{q[nC(Ho,H+ + Ha,Pt - Ho,Pt) Ao,PtAH2,Pt HH2,Pt]} ) A′ exp[q(nCH′′ - HH2,Pt)] (42)

A value of 110 kJ/mol was used for hydrogen heat of adsorption on acid zeolite supported Pt.42 Thus, only two parameters, A′ and H′′, needed to be estimated for all adsorption equilibria over both types of sites. Because only very minor amounts of olefins were detected in the gas phase, eq 41 was used in the rate expressions for acid site catalyzed reactions (eqs 12-20) and the rates for the olefins and hydrogen were set equal to zero. The ratio between the gas-phase hydrogenation equilibrium constant and hydrogen partial pressure was calculated for each reaction using the HSC43 software package. For each equilibrium and reaction temperature, a polynomial for the value of Ki/pH2 as a function of hydrogen partial pressure was regressed and used in eq 41. An example of an equilibrium plot between isobutene and isobutane is given in Figure 4. However, using the gas-phase equilibrium in eq 41 means that K′ will no longer represent the true ratios between the adsorption equilibria. The HSC program was also used to calculate the thermodynamic equilibrium between n-butene and isobutene, K1. This equilibrium was approximated using an Arrhenius type equation and used in eq 14, since the adsorption constants for isobutene and n-butene are the same as they depend only on carbon number and not on the degree of branching (eq 23). (b) Deactivation Rate Equations. The deactivation rate equations are derived according to ref 44. The rates of the reactions are given by eq 43, where r0,i is the initial reaction rate for reaction i, and a denotes the relative activity. Since the hydrogenation and dehydrogenation steps over Pt are fast compared to the reactions of olefins over Brønsted acid sites and coke is assumed to be formed parallelly with n-butene as a precursor, even the rate-determining steps involving multiple sites

Ind. Eng. Chem. Res., Vol. 44, No. 3, 2005 477

exponential and hyperbolic relationships between the fraction of coke and time:44

[

1 R-1 1 + (R - 1)k′cP,0 t

f)

]

1/(R-1)

R-1 t) f ) exp(-k′cP,0

R*1

R)1

(49)

where k′ ) k φ(p, T, WHSV). Observe that k′ is only an apparent constant, as it depends on temperature, WHSV, and reactant pressure p. The deactivation rate is governed by the relationship between a and f. This relationship often takes the form44

a ) fβ

(50)

which, when combined with eq 42, can be expressed as Figure 4. The fraction K9/pH2 as a function of hydrogen partial pressure among the reacting species.

will not lead to a loss of separability between activity and the fraction of nondeactivated sites.

ri ) r0,ia

(43)

As discussed above, approximately constant selectivities with time on stream suggest similar deactivation of Pt and Brønsted acid sites. Equal rates of deactivation can be explained for example by coke plugging entire pores and thus decreasing the number of accessible Pt and Brønsted acid sites. The fraction of noncoked or nonpoisoned catalyst (f) can be expressed in terms of concentration of poison or coke on the catalyst surface (cP) and the catalyst capacity for coke or poison (cP,0).

f)

cP,0 - cP cP,0

(44)

Accumulation of coke on the catalyst is given by

dcP ) rP(cP, p, T, WHSV) dt

(45)

(46)

Assuming a power law for the dependence of rP on coke concentration, eq 46 takes the following form

dcP ) k(cP,0 - cP)R φ(p, T, WHSV) dt

(47)

which means that the rate of coke formation is proportional to some power (R) of unused capacity for adsorbing coke. Combining eqs 44 and 46, the time derivative of f is obtained.

df R-1 R f φ(p, T, WHSV) ) -kcP,0 dt

[

]

1 R-1 1 + (R - 1)k′cP,0 t

β/(R-1)

R-1 t) a ) exp(-βk′cP,0

R*1

R)1

(48)

Integrating for constant values of cP,0 and f gives linear

(51)

To obtain simpler deactivation functions more suitable for regression analysis, we introduce a new parameter γ:

γ)

β R-1

(52)

which combined with eq 51 gives the final forms for the activity functions:

a1 )

(

1 1 + k1t

)

a2 ) (1 - k2t)-γ

γ

R > 1, β > 0 0 < R < 1, β > 0

(53)

The exponential form of the deactivation function is merely a limit of eq 53 as R goes toward unity and is as such not necessary to include numerically. The constants in eq 53 are local to each run and are calculated based on the independent parameters, such as weight hourly space velocity, feed makeup, and temperature, according to

p exp(-Eaq) ki ) δ′iWHSV (1 - p)

which can be rewritten as

dcP ) rP(cP) φ(p, T, WHSV) dt

a)

(54)

where δ′i ) (R - 1)kcR-1 P,0 (R * 1), and p is the partial pressure of n-butane in the feed. As can be seen from eq 54, the inhibiting factor of hydrogen on coke formation14 has also been included in the model as pH2 ) 1 p. The effect of temperature on the deactivation is included in the term q as described by eq 22. The constant  has a physical meaning reflecting the number of butene species in deactivation steps; in the experiments it is typically >2, since the deactivation/coke formation is due to oligomerization of several ( > 2) species. Several expressions for the dependence of ki on the WHSV were tested (including the reciprocal one), and the best description was obtained assuming linear proportionality as in eq 54. (c) Reactor Model and Generation Rates. An ideal plug flow fixed bed reactor model was used. External and internal heat transport limitations were evaluated to be negligible by Mears45 and Anderson criteria,46 respectively, and similarly for the external mass transfer limitations (film diffusion) by the Mears47

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criterion. The calculated Weisz48,49 criterion confirms that internal heat and mass transport does not play an important role, since its value, 0.7, is below one required for the reaction order of 1. However, as the criteria are based on approximations rather than exact solutions, no decisive conclusions can be drawn for the case of pore diffusion, although it was also neglected in the kinetic models. Reaction and deactivation were assumed to be uniform throughout the reactor bed and the catalyst particles. For an isothermal reactor with constant p (1 atm), we get

dpj ) mcatrja dτ

j ) C3, C4, i-C4, C5

(55)

where the residence time τ is calculated as follows:

τ)

( )( )

mcatbed Tin pr FbedV˙ tot Tr pin

(56)

where bed is the bed porosity. A catalyst bed density Fbed of 513 kg/m3 was used. Overall isomerization rates of alkanes are determined by the isomerization of olefins on acid sites giving the following generation rates:

Table 3. Results from the Parameter Estimationa model A std error

parameter

value

A1bed E1 A2bed E2 A3bed E3 A4bed E4 A6bed E6 A′ H′′ δ γ Ea 

5.8 39.9 22.2 20.8 5.6 174.0 97.0 68.4

0.7 5.9 5.2 11.7 0.7 5.4 22.5 13.1

239 46.4 0.0033 1.6 92.2 2.9

30 1.5 0.0002 0.03 1.1 0.04

model B value

10.3 24.3 8.6 177.0 15.2 91.0 17.4 157.0 847 47.4 0.0019 2.1 74.7 2.5

model C

std error

value

std error

0.8 4.4 1.2 5.5 1.2 5.0 2.4 5.5 41 0.7 0.0001 0.05 1.0 0.05

2.5 97.7 4.1 124.0 27.2 207.0 18.2 187.0 1.1 173.0 684 62.6 0.0026 1.7 92.7 2.6

0.1 2.2 0.3 4.7 9.2 15.4 1.5 5.0 1.2 41.5 38 0.7 0.0001 0.03 1.0 0.03

a Activation energies and H′′ are given in (kJ mol-1), preexponential factors in (atm s-1gcat-1) and other are dimensionless. Tmean ) 623 K.

rC3 ) r3 + 3r4 (propane) ri-C4 ) r1 + r6 (isobutane) rC4 ) -r1 - 2r3 - r4 - r6 (n-butane) rC5 ) r3 - r4 (pentane) rH2 ) rCLH ) rC3d ) rC4d ) ... ) 0 Parameter Estimation. The following objective function (Q) was minimized in the parameter estimation:

Q)

∑j ∑t (pj,t - pˆ j,t)2wj,t

(57)

where j is the component index, t is the time on stream value, pˆ is the estimated partial pressure, and w is the weight matrix for the experimental data set. A weight factor of 10 was used for propane, isobutane, butane, and pentanes, and 1 was used for all other components. All parameters were estimated simultaneously by fitting against all experiments. A stiff ODE solver was used in the parameter estimation. The objective function was minimized with a Levenberg-Marquardt algorithm implemented in the software Modest.50 As expected, using a gradient-based optimizer for a complex reaction network with a large number of estimated parameters proved difficult. Initially, only the parameters describing deactivation and adsorption were well defined when all parameters were estimated simultaneously. The kinetic parameters were heavily correlated due to the consecutive-parallel nature of the system, and simultaneous estimation of frequency factors and activation energy found a number of different local minima. Therefore a sequential strategy was applied. Initially, rate constants were estimated separately at different temperatures, using fixed and reliable values for deactivation and adsorption. Surprisingly, Arrhenius plots of the separately estimated rate con-

Figure 5. A parity diagram for all experiments indicating the calculated molar fractions obtained by model C versus experimental molar fractions for all components.

stants showed only minor deviation from linearity. The regressed values of frequency factors and activation energy were then used as initial values for a final estimation of all the parameters to all the experiments, the results of which are presented in Table 3. (a) Results of the Kinetic Modeling. The degree of explanation (R2) and residual sum of squares are used for describing the adequacy of the kinetic models to fit the experimental data:

R2 ) 1 -

∑(yi - yˆ i)2 ∑(yi - yj)2

(58)

where yi is the experimental value, yˆ is the estimated value, and yj is the mean value of the all data points. The results of the parameter estimation are given in Table 3. All models fit the experimental results well, having an explanation factor of at least 99.89. A parity diagram for all experiments, given in Figure 5, indicates a good correlation between the calculated molar fraction by model C versus experimental molar fraction. In Figures 6-12, the kinetic models are compared to the experimental data. In Figure 6, the conversion of n-butane at TOS ) 10 min is plotted as a function of reactant partial pressure. As can be seen, all models can predict the initial conversion reasonably well and

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Figure 6. Conversion at TOS ) 10 min as a function of n-butane partial pressure at 573, 623, and 673 K by the kinetic models compared to the experimental values.

no large differences are observed between the models. All models underestimate the conversion at high nbutane partial pressures as well as at high reactant dilutions at 673 and 623 K. The fits of the models are particularly good at 573 K. The deactivation model can be compared in Figure 7, where the conversion is plotted as a function of time on stream. The models differ from each other very little, and when the deactivation rates are high, they can predict the deactivation adequately. However, minor divergence between models and the experimental data is observed when the deactivation rate is low. When no deactivation was present at high dilutions, the models underestimate the conversion level at higher temperatures. The following conclusions can be drawn from the selectivities to isobutane, propane, and pentanes as a function of n-butane partial pressure plotted in Figures 8-10. The selectivity to isobutane is almost constant for model B, regardless of temperature or reactant partial pressure. At higher temperatures,

Figure 7. Examples of conversion as a function of time on stream at 573, 623, and 673 K by the kinetic models compared to the experimental values.

it can predict the selectivity to isobutane sufficiently well. Models A and C can predict the increasing selectivity to isobutane with decreasing n-butane pressures. This tendency is overestimated at higher temperatures but very accurate at 573 K. All models can predict the decreased selectivity to propane at decreased reactant pressures (Figure 9). Particularly at 623 and 573 K, models A and C can predict the selectivity to pentanes sufficiently well, while in model B the selectivity to pentanes increases with decreasing reactant partial pressure. Since the formation of products other than propane, isobutane, and pentanes was neglected, there must be minor overestimations of the selectivities. Therefore, the relative selectivities are more illustrative for comparison of the models. The isomerization efficiency, defined as the ratio isoC4/(C3 + C5), is plotted as a function of n-butane partial

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Figure 8. Selectivity to isobutane at TOS ) 10 min as a function of n-butane partial pressure at 573, 623, and 673 K by the kinetic models compared to the experimental values.

pressure in Figure 11. All models have good predictions of isomerization efficiency at high n-butane partial pressures. However, model B cannot predict the increase in the isomerization efficiency at low reactant pressures. At 573 K, model C and especially model A are able to predict the increase in the isomerization efficiency with decreased reactant pressures at 573 K very well. The C3/C5 ratio as a function of n-butane partial pressure is given in Figure 12. All models give very similar results, predicting the ratio reasonably well, although the models underestimate the ratio at 673 and 623 K. The deviations from the experimental points are related to the fluctuation of the experimental data rather than to inaccuracy of the models themselves. At 573 K the models are very close to the experimental points. The estimated values of activation energies and other results of kinetic modeling are given in Table 3. The

Figure 9. Selectivity to propane at TOS ) 10 min as a function of n-butane partial pressure at 573, 623, and 673 K by the kinetic models compared to the experimental values.

activation energy of monomolecular n-butane isomerization E1 was 40 and 98 kJ/mol for models A and C, respectively, being below and above the values observed experimentally. The activation energy of the bimolecular isomerization E6 for models B and C was much higher, 157 and 173 kJ/mol, respectively. The dimerization activation energy E2 was rather low, just above 20 kJ/ mol for models A and B but higher, 124 kJ/mol, for model C. The activation energies for cracking E3 were very high, 174, 177, and 207 kJ/mol for models A, B, and C, respectively. However, an activation energy as high as 187 kJ/mol has been reported for n-octane cracking over sillimanite.51 There was a large variance in the activation energy E4 for propane production; the values for E4 were 68, 91, and 187 kJ/mol for models A, B, and C.

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Figure 10. Selectivity to pentanes at TOS ) 10 min as a function of n-butane partial pressure at 573, 623, and 673 K by the kinetic models compared to the experimental values.

(b) Product Formation. The main products in n-butane skeletal isomerization were isobutane, propane, and pentanes. The amount of other products including heavy hydrocarbons from hexanes to nonanes was negligible, in any case beyond the detection limit of the applied GC apparatus. The yields of methane, ethane, ethene, and propene were also very low. This is a clear indication that protolytic cracking of butane as well as hydrogenolysis occurred only to a minor extent. The lack of protolytic cracking can be rationalized, since the concentration of strong Brønsted acid sites vanished after Pt introduction into H-mordenite. This is consistent with the literature, since it has been reported that cracking of alkanes, such as hexane, can be considered a difficult reaction requiring strongly acidic sites.52 (c) Excess of Propane Formation. At all conditions, an excess of propane compared to pentanes was

Figure 11. Isomerization efficiency, defined as iso-C4/(C3 + C5) ratios, as a function of n-butane partial pressure at 573, 623, and 673 K by the kinetic models compared to the experimental values.

obtained. Therefore, only direct cracking of Cd 8 interd mediates to Cd 3 and C5 is not a plausible explanation for propane formation. One possibility for extra propane formation advanced in the literature is cracking of pentanes to propane and ethane. An excess of propane in conditions when there was no deactivation cannot be rationalized even assuming that the ethene intermediate is completely transformed to coke. This proposal can be ruled out, as no excess of ethane was observed. As can be seen in the kinetic models, the proposed reaction route for propane formation from consecutive reactions d d of Cd 5 dimerization with C4 to form C9 , which further d is cracked to three C3 intermediates via Cd 6 , is a plausible explanation of the excess of propane formation. The models were able to predict the selectivity to propane and the C3/C5 ratio reasonably well, especially at 573 K.

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mordenite predominantly olefins react on the Brønsted acid sites, and therefore, alkane reactions on the Brønsted acid sites were omitted in the models. This conclusion is also supported by the product distribution, since the yields of methane, ethane, ethene, and propene, which are products of monomolecular cracking of nbutane, are very low. Hydrogenolysis was not considered in the models either, also because of low yields of CLH and Cd 3 . Neglecting these two reaction paths in the models could explain some deviations between the predictions of the models and experiments. By comparing Figures 8-12 relating to the product distribution, one can infer that model A or model B alone cannot explain the selectivity to isobutane adequately. This is clearly visible in Figure 11, where the isomerization efficiency is plotted. At high reactant pressures, the bimolecular model B does give values very close to the observed ones, but at 573 K it fails miserably at low reactant partial pressures whereas the prediction at the same conditions is much better for models A and C, which enable monomolecular formation of isobutane. This suggests that both reaction mechanisms can contribute in the isobutane formation, depending on the reaction conditions. The bimolecular model can explain the isomerization efficiency very well at high reactant partial pressure, but at the same time, it does not predict the tendency that relatively more isobutane is formed at low reactant partial pressures. At the same time, this tendency is greatly overestimated for models A and C at higher temperatures but predicted sufficiently at 573 K. It is reasonable that at high reactant dilutions encounters of two molecules are hindered and thus, the possibility to have the dimerization-cracking route to produce isobutane as well as pentanes and propane is hindered. Consequently, the monomolecular reaction path can be more relevant for isobutane formation and the selectivity to isobutane is increased. Indeed, the isomerization efficiency at 573 K with the n-butane partial pressure of 0.1 was as high as 6.7, supporting this conclusion. Conclusions

Figure 12. C3/C5 ratio as a function of n-butane partial pressure by the kinetic models compared to the experimental values.

(d) Kinetic Models vs Reaction Mechanism. In the advanced kinetic models above, only olefins are supposed to be reacting on the Brønsted acid sites and dehydrogenation of alkanes to alkenes and hydrogenation of alkenes to alkanes occur on Pt. Over H-mordenite without platinum, n-butane is certainly protonated on the Brønsted acid site to form a pentacoordinated carbonium ion, which is the initial step of the isomerization reaction. This protonation requires strong acid sites, much stronger than those for protonation of olefin. Not surprisingly, skeletal isomerization of n-butane is almost nonexistent over materials that do not have such strong acid sites, like H-MCM-41,31 but isomerization of linear butenes over them is still possible.31,53 After introduction of platinum into Pt-H-mordenite, a total absence of the strong Brønsted acid sites was observed. Thus, it is reasonable to assume that over Pt-H-

The kinetics of n-butane isomerization over bifunctional Pt-H-mordenite was studied by varying the reactant partial pressure and temperature. The main products were isobutane, propane, and pentanes. Yields of other products, especially methane, ethane, ethene, and propene, were very low, suggesting that protolytic cracking and hydrogenolysis were present only to a minor extent. Especially the protolytic cracking was inhibited, since after introducing Pt into H-mordenite all strong Brønsted acid sites disappeared and the total density of acid sites decreased. The reaction rate did not depend linearly on the reactant partial pressure, suggesting that in kinetic modeling and mechanistic considerations it is important to take into account contribution of both mechanisms, i.e., monomolecular and bimolecular. The discrepancy in the literature can be thus attributed to the possibility that reported prevailing reaction mechanisms in fact depend on the reaction conditions. Three kinetic models were developed based on the current understanding of the reaction mechanism. The models included hydrogenation and dehydrogenation steps on the metal sites, skeletal isomerization on the Brønsted acid sites following both monomolecular and bimolecular mechanisms, and deactivation due to coke formation. In the present study,

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the conclusion of involvement of two pathways is further supported by the selectivity analysis of the kinetic models. The model that enabled the bimolecular reaction path for isobutane formation had a good fit on the selectivity to isobutane at high reactant pressures but was incapable of predicting the increase in selectivity to isobutane with decreasing n-butane pressures. At the same time, the above-mentioned tendency was very well predicted by the models enabling the monomolecular mechanism for isobutane formation. The kinetic modeling also supported the proposal that an excess of propane compared to pentanes is due to consecutive d d codimerization of formed Cd 5 with C4 to C9 followed by d cracking to three C3 species. Acknowledgment This work is part of the activities at the Åbo Akademi Process Chemistry Centre within the Finnish Centre of Excellence Programme (2000-2005) by the Academy of Finland. Financial support from the Graduate School of Materials Research to Ville Nieminen and the Graduate School in Chemical Engineering for Matias Kangas is gratefully acknowledged. Supporting Information Available: Comparison of the selectivities to propane, isobutane, and pentanes at approximately the same conversion level. This material is available free of charge via the Internet at http:// pubs.acs.org. Nomenclature A E ∆H K Q Rg T Tmean TOS V˙ tot WHSV R β γ δ  a cP cP,0 f k mcat bed Fbed nC p r t θ τ

pre-exponential factor activation energy heat of adsorption equilibrium constant objective function gas constant temperature mean temperature time on stream total inlet flow weight hour space velocity/h-1 power in the rate equation of coke concentration power in the rate equation of uncoked catalyst fraction power in the activity function lumped parameter in the deactivation function number of butene species in the deactivation step activity concentration catalyst capacity for coke fraction of coke rate constant catalyst mass catalyst bed porosity catalyst bed density carbon number pressure generation/formation/reaction rate time coverage residence time

CLH C3 Cd 3 i-C4 C4 Cd 4 i-Cd 4 C5 Cd 5 Cd 8 H2 P V 0 H+ Pt a h o i in j r

light hydrocarbons (methane, ethane, ethene) propane propene isobutane n-butane n-butene isobutene pentane(s) pentenes octenes hydrogen coke or poison vacant site initial (value) Brønsted active site platinum active site alkane hydrogenation olefin reaction index inlet feed component index reaction

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Received for review May 26, 2004 Revised manuscript received October 11, 2004 Accepted November 8, 2004 IE049544Q