Catalytic Cracking of Isobutane and 2-Methylhexane over USY Zeolite

control for both isobutane and 2-methylhexane at low conversions and high ... and β-scission steps for the larger molecule 2-methylhexane as compared...
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Ind. Eng. Chem. Res. 2002, 41, 4016-4027

Catalytic Cracking of Isobutane and 2-Methylhexane over USY Zeolite: Identification of Kinetically Significant Reaction Steps Nitin Agarwal,† Marco A. Sanchez-Castillo,† Randy D. Cortright,† Rostam J. Madon,‡ and James A. Dumesic*,† Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706, and Engelhard Corporation, 101 Wood Avenue, Iselin, New Jersey 08830

Reaction kinetics analyses were conducted for isobutane and 2-methylhexane conversion over USY zeolite (both calcined and steam-treated) at 773 K, where reaction is initiated by activation of the reactant paraffin. These analyses indicate that increasing the severity of catalyst steam treatment leads to an increase in the composite activation barriers of kinetically significant steps (initiation and hydride transfer), except for the reaction step involving dehydrogenation of the reactant paraffin, which may be enhanced by extraframework aluminum species introduced via steam treatment. We use sensitivity analyses to probe the degrees of rate control for all reaction steps as a function of the extent of conversion, reaction temperature, and size of the reactant molecule. Initiation steps (i.e., monomolecular reactions) have a high degree of rate control for both isobutane and 2-methylhexane at low conversions and high temperature, whereas the degree of rate control for hydride transfer steps becomes more significant at higher conversions and at lower temperatures. The β-scission steps have relatively lower degrees of rate control. The initiation steps have greater kinetic significance than the hydride transfer and β-scission steps for the larger molecule 2-methylhexane as compared to isobutane. Extrapolation of the kinetic model to higher temperatures, 848 K, suggests that initiation steps dominate over the whole conversion range, especially for the larger 2-methylhexane molecule. Introduction Catalytic cracking of heavy hydrocarbon feeds over Y zeolite based catalysts is a complex process consisting of a very large number of reactions. To obtain a basic understanding of this reaction chemistry, researchers have studied reactions of model hydrocarbons on zeolites.1-13 For example, we have conducted reaction kinetics studies of small hydrocarbons on various USY zeolite catalysts and analyzed kinetic data in terms of reaction schemes involving well-established acid-catalyzed processes (e.g., monomolecular initiation or cracking, isomerization, oligomerization/β-scission, and hydride transfer).14-18 Recently,19 we developed a comprehensive model to describe the reactions of isobutane over a wide temperature range (i.e., 523-773 K) to obtain reliable kinetic parameters under conditions where catalyst deactivation is negligible. Isobutane, besides being a tractable molecule for study, has an important characteristic in that only hydrogen and methane are produced via monomolecular cracking. All other products are made via different pathways. Indeed, Corma et al.20 noted that it is not reliable to conduct kinetic analyses for the reactions of large hydrocarbon molecules, where it is difficult to distinguish whether products such as propane, nbutane, etc., are formed via monomolecular initiation or via hydride transfer reactions. We have circumvented this problem by first conducting kinetic analyses for isobutane reactions,19 obtaining reliable kinetic parameters, and then, as we show in this paper, extending these analyses to 2-methylhexane conversion. Addition* To whom correspondence should be addressed. E-mail: [email protected]. † University of Wisconsin. ‡ Engelhard Corp.

ally, we investigate the effects of steaming on the performance of USY catalysts by comparing kinetic parameters obtained via the model. Steam treatment of catalysts as shown in this study generally leads to a destabilization of the transition states of kinetically significant steps with respect to gas-phase reactants. In our earlier study of isobutane cracking,19 we used sensitivity analysis21 and Campbell’s degree of rate control22 to identify kinetically significant steps, and we obtained 31 such steps out of the 367 steps considered. In the present paper, we use our model to extend sensitivity analyses for both isobutane and 2-methylhexane cracking to obtain an understanding of the most kinetically relevant steps in catalytic cracking and show how their significance changes with conversion and temperature. Experimental Section For this study, we used reaction kinetics data previously reported by Yaluris et al.,15,17,23 who carried out experiments over four USY zeolite catalysts. Isobutane conversion was studied using a calcined USY catalyst, USY-C, and its steam-treated analogue, USY-S. The conversion of 2-methylhexane was studied over two steam-treated USY catalysts with different steaming severities, USY-S1 and USY-S3. Table 1 lists the physical properties of these catalysts. Reaction kinetics measurements were carried out at 773 K in a fixed-bed reactor system, using a reactant mixture of 25 mol % isobutane in He (99.999% purity) or a mixture of 10 mol % 2-methylhexane in He. The space velocity was adjusted to achieve the desired conversion. The purity of the reactants was higher than 99.5%. The catalyst was purged between runs with flowing He for about 2 h and then regenerated in flowing air at 773 K for 8 h.

10.1021/ie020041z CCC: $22.00 © 2002 American Chemical Society Published on Web 07/09/2002

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For 2-methylhexane, there are nine initiation steps, as shown below. All steps except the last one are elementary steps. Step 9, which we assume to be irreversible, accounts for the formation of ethylene and involves the splitting of a C-C bond involving secondary carbon atoms.

Table 1. Properties of the Catalysts Used in the Kinetic Studiesa catalyst zeolite surface area (m2 g-1) total surface area (m2 g-1) zeolite contentb (%) unit cell size (nm) Alfc Si/Al Brønsted sites (µmol g-1) Lewis sites (µmol g-1)

USY-C USY-S USY-S1 USY-S3 274 418 38 2.443 20.56 8.3 532 304

221 349 31 2.430 6.64 27.9 52 81

233 371 32 2.433 9.85 18.5 129 164

178 297 25 2.427 3.00 63 6.3 27.5

a USY-C and USY-S catalysts were used for kinetic studies involving isobutane conversion, whereas USY-S1 and USY-S3 catalysts were used for kinetic studies involving 2-methylhexane conversion. b From BET measurements, assuming that surface area of pores 5) and seven activation energies for 2-methylhexane conversion (EC3, EC4, EiC4, EC5, EC6, EiC6, and EC>6); here, for example, EiC4 represents the hydride transfer step that leads to the formation of isobutane from the reaction of 2-methylhexane with the isobutylalkoxy species. In summary, the current study employs six kinetic parameters for isobutane conversion, namely, Einit,H2, Einit,CH4, EC3, EC4, EC5, and EC>5, and 16 kinetic parameters for 2-methylhexane conversion, namely, Einit,H2, Einit,CH4i, Einit,CH4, Einit,C2H6, Einit,C3H8i, Einit,C3H8, Einit,iC4, Einit,nC4, Einit,C2H4, EC3, EC4, EiC4, EC5, EC6, EiC6, and EC>6. Later we will show that not all of these values are kinetically significant, thus reducing the number of kinetic parameters. We have assumed that the reactor operates as a plug-flow reactor. Accordingly, we solve 100 differential equations for isobutane conversion and 105 differential equations for 2-methylhexane conversion, corresponding to the gaseous molecular flow rates versus reactor length. These equations are combined with 89 steady-state equations for the fractional surface coverages by adsorbed species and one site-balance equation. Sensitivity Analysis. The change in the overall rate of reaction caused by small equal changes in the values of the forward and reverse rate constants for a particular reaction step, keeping all other rate constants in the reaction sequence unchanged, provides information about the kinetic significance of the reaction step in controlling the reaction kinetics of the overall reaction. The reaction steps with the highest degree of rate control are the kinetically significant steps of the overall reaction scheme and become particularly informative for a complex multicyclical process like catalytic cracking. These analyses also allow us to show how the kinetic significance of one step with respect to another changes with reaction conditions. The dimensionless sensitivity, φi, of the overall rate r with respect to ki is defined21 as

φi,for )

( )

(5)

( )

(6)

ki,for ∂r ∂ki,for kj r

and for the reverse step

φi,rev )

ki,rev ∂r ∂ki,rev kj r

where each partial derivative represents the change in the overall rate r with respect to a change in the forward or the reverse rate constant for step i, keeping all other rate constants kj constant. Campbell’s degree of rate control22 XRC,i for step i is defined as

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XRC,i )

( ) ∂r ∂ki,for

( )

ki,for ∂r ) r ∂k Keq,i,kj i,rev

ki,rev r Keq,i,kj

(7)

where each partial derivative represents the change in the overall r with respect to a change in the forward or reverse rate constant for step i, keeping the equilibrium constant for step i, Keq,i, and all other rate constants kj constant. In general, XRC,i is equal to the sum of the forward and reverse sensitivities for step i:

XRC,i ) φi,for + φi,rev

(8)

In the above expressions, the overall rate r is given by the consumption of the reactant isobutane or 2-methylhexane. The sum of the values of XRC,i for all of the steps is equal to unity for a reaction scheme that leads to a single overall reaction:21

∑i XRC,i ) 1

(9)

However, as the conversion approaches 100%, the rate of consumption of the reactant is controlled by the flow rate to the reactor rather than by the values of the rate constants. As a result, at these conditions the sum of values of XRC,i approaches zero at 100% conversion. Also, a sum of XRC,i greater than unity indicates the existence of multiple reaction pathways for consumption of the reactant.

Table 5. Values and Confidence Limits of the Kinetic Parameters for 2-Methylhexane Conversiona parameter

USY-S1

USY-S3

RH Floc Einit,H2 Einit,CH4i Einit,CH4 Einit,C2H6 Einit,C3H8i Einit,C3H8 Einit,iC4 Einit,nC4 Einit,C2H4 Eβ,tt + ∆H°3 Eβ,st ()Eβ,ss) + ∆H°3 EC3 + ∆H°3 EC4 + ∆H°3 EiC4 + ∆H°3 EC>4 + ∆H°3 ∆Sqhydride

-0.54b 1.17b 142.8 ( 0.7 c 144.4 ( 0.7 152.5d 139.7 ( 6.9 c 129.2 ( 2.4 142.1 ( 4.0 144.5 ( 0.6 12.2b 25.1b -38.1 ( 4.0 -15.2 ( 7.1 -45.0 ( 6.6 -27.8b -24.3b

-0.54b 1.17b 137.3 ( 2.9 c 144.4 ( 1.4 155d c c 137.3 ( 2.9 b 154.7 ( 2.1 12.2b 25.1b -29.6 ( 1.5 -10.4 ( 1.5 -38.3 ( 6.2 -27.8b -24.3b

a Activation energies and R are given in kJ mol-1 and entropy H changes in J mol-1 K-1, and Floc is dimensionless. The value of ∆H°3 for both catalysts was -90 kJ mol-1. The 95% confidence interval of the kinetic parameter is indicated next to the value. b Value constrained to that for USY-C. c Pathway not used by the kinetic model. d Value constrained to match the ethane concentration in the effluent.

Results Analyses of Reaction Kinetics. We use the kinetic models outlined above to analyze experimental data collected at 773 K for isobutane conversion over USY-C and USY-S and for 2-methylhexane conversion over USY-S1 and USY-S3. Values of the fitted parameters, along with the corresponding 95% confidence intervals, were obtained using Athena Visual Workbench.37 Tables 4 and 5 summarize the value of the parameters obtained for each case. The activation barriers for the hydride transfer and β-scission steps are given in terms of composite barriers (i.e., E + ∆H°3) because the value of ∆H°3 is kinetically insignificant. Figures 1-4 show the experimental data and the predictions of the kinetic models (i.e., the solid lines) for the sum of paraffins and olefins for all four catalysts. The kinetic models describe the trends correctly for all of the cases considered in

Figure 1. Experimental and simulated TOF values for the sum of paraffins and the sum of olefins as a function of isobutane conversion over USY-C at 773 K. Symbols represent experimental data, and solid lines represent predictions from the complete model and dashed lines those from the simplified model.

Table 4. Values and Confidence Limits of the Kinetic Parameters for Isobutane Conversiona parameter

USY-Cb

USY-S

RH Floc Einit,H2 Einit,CH4 Eβ,tt + ∆H°3 Eβ,st ()Eβ,ss) + ∆H°3 EC3 + ∆H°3 EC4 + ∆H°3 EC5 + ∆H°3 EC>5 + ∆H°3 ∆Sqhydride

-0.54 1.17 ( 0.01 156.5 ( 0.5 154.3 ( 0.5 12.2 ( 5.8 25.1 ( 5.7 -25.7 ( 1.4 -13.5 ( 1.4 -27.8 ( 1.7 -27.8 ( 1.4 -24.3 ( 2.2

-0.54c 1.17c 158.3 ( 1.5 159.5 ( 1.6 12.2c 25.1c -20.4 ( 1.7 -7.9 ( 1.8 -22.7 ( 2.2 -35.5 ( 5.3 -24.3c

a Activation energies and R are given in kJ mol-1 and entropy H changes in J mol-1 K-1, and Floc is dimensionless. The value of ∆H°3 for both catalysts was -90 kJ mol-1. The 95% confidence interval of the kinetic parameter is indicated next to the value. b Values from Sanchez-Castillo et al.19 c Value constrained to that for USY-C.

Figure 2. Experimental and simulated TOF values for the sum of paraffins and the sum of olefins as a function of isobutane conversion over USY-S at 773 K. Symbols represent experimental data, and solid lines represent predictions from the complete model and dashed lines those from the simplified model.

this work. The apparent discontinuity observed for some model predictions is caused by differences in the space velocities. The values of the parameters and their corresponding confidence intervals for USY-C in Table 4 are from our

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Figure 3. Experimental and simulated TOF values for the sum of paraffins and the sum of olefins as a function of 2-methylhexane conversion over USY-S1 at 773 K. Symbols represent experimental data, and solid lines represent predictions from the complete model and dashed lines those from the simplified model.

Figure 4. Experimental and simulated TOF values for the sum of paraffins and the sum of olefins as a function of 2-methylhexane conversion over USY-S3 at 773 K. Symbols represent experimental data, and solid lines represent predictions from the complete model and dashed lines those from the simplified model.

previous study.19 For the results on USY-S, we kept all parameters equal to those for USY-C, except for the activation energies for the initiation and hydride transfer steps. The composite activation energies for initiation and hydride transfer are higher on USY-S by ca. 5 kJ mol-1 compared to USY-C, in contrast to the value of Einit,H2, which increases by a smaller amount. Accordingly, the activated complexes for all of these steps appear to be destabilized by ca. 5 kJ mol-1 on USY-S compared to USY-C. Table 5 displays the values of kinetic parameters obtained from analyses of 2-methylhexane conversion over USY-S1 and USY-S3. Here again, we allowed only the activation energies for the initiation and hydride transfer steps to vary. For hydride transfer steps, we found only three activation energies to be kinetically significant: EC3, EC4, and EiC4. We fixed the energy for the remaining hydride transfer step (EC>4) at the value determined from the isobutane reaction over USY-C.19 The values for the composite activation energy barriers (EC3 + ∆H°3), (EC4 + ∆H°3), and (EiC4 + ∆H°3) are higher for USY-S3 compared to USY-S1. This trend is the same as that for isobutane conversion; i.e., increased steaming severity causes a destabilization of the activated complexes for hydride transfer. The activation energies of the initiation steps for 2-methylhexane conversion show slightly different trends over the two steam-treated catalysts. The composite activation energy for step 1, in which 2-methylhexane forms H2 and an adsorbed C7 species, decreases by about 6 kJ mol-1 from USY-S1 to USY-S3. This apparent

increase in the initiation rate constant may be caused by the larger amount of nonframework aluminum present in the more severely steamed catalyst which provides paraffin dehydrogenation sites.10,26,38,39 The composite activation energies for initiation steps 3 and 4 leading to the formation of methane and ethane remain essentially the same for both catalysts. In contrast, the composite activation energies for initiation steps 7 and 9, involving the formation of isobutane and isopentane, respectively, increase by about 9 kJ mol-1 from USY-S1 to USY-S3. Initiation steps involving the cleavage of internal C-C bonds leading to smaller surface species, steps 5 and 7, are favored over cleavage of terminal C-C bonds leading to larger surface species. This behavior is consistent with the results of Bamwenda et al.7 and Brait et al.,10 who report the preferential cleavage of internal C-C bonds compared to terminal C-C bonds during the initiation of 2-methylhexane and n-hexane. Values for composite activation energies (Table 5) obtained from our model are close to those reported by Bamwenda et al.,7 except for hydrogen formation. These authors report the following values for 2-methylhexane conversion: 184.7 kJ mol-1 (formation of H2), 154.6 kJ mol-1 (formation of methane), 159.6 kJ mol-1 (formation of ethane), 161.9 kJ mol-1 (formation of propane), 145.6 kJ mol-1 (formation of butane), and 148.9 kJ mol-1 (formation of pentane). According to the kinetic model, the coverage of surface acid sites by adsorbed hydrocarbon species is very low at 773 K for both isobutane and 2-methylhexane conversion over USY zeolite catalysts. Approximately 99.9% of the acid sites or greater are free at all reaction conditions, and increased steam treatment further decreases surface coverage. For all reaction conditions, the most abundant surface species are predicted to be n-butyl and isobutyl species, followed by the isopentyl and propyl species. Sensitivity Analyses. Using the approach outlined by eq 7, we calculated the degree of rate control for each step, XRC,i, to identify kinetically significant steps in the reaction scheme. This analysis allows us to build smaller kinetic models by combining these kinetically significant steps with a limited number of quasi-equilibrated processes such as desorption/adsorption of important olefins and isomerization steps. Though the latter steps do not appear as significant steps for rate control, they are essential to interconnect quasi-equilibrated reaction intermediates. We have given such a simplified scheme for isobutane conversion elsewhere,19 and we give the simplified scheme for 2-methylhexane in Figure 5. The dotted lines in Figures 1-4 show the predictions from such simplified reaction schemes. These predictions agree closely with those of the complete models, thus substantiating that we have correctly identified the kinetically significant steps. Using the parameter values for isobutane conversion over USY-C (Table 4), we are able to simulate the catalyst performance at various conversions and temperatures. Figure 6a shows plots of the absolute values of the degree of rate control for initiation, hydride transfer, and β-scission steps versus isobutane conversion at 673, 773, and 848 K. The solid lines are the sums of the absolute values of XRC,i for these three classes of reactions. We also calculated the steady-state net rates for initiation, hydride transfer, and β-scission steps at the same three temperatures versus isobutane conver-

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Figure 5. Simplified reaction scheme for 2-methylhexane conversion.

sion, and we show these results in Figure 6b. These rates were evaluated at the effluent of the plug-flow reactor considered in the model, which explains why the rates approach zero at 100% conversion. The feed in all cases is free of olefins and consists of 25 mol % isobutane. For comparison with the behavior of isobutane, we have used the parameter values in Table 5 to simulate the catalyst performance for 2-methylhexane conversion. We show in Figure 7a,b the degrees of rate control and net rates, respectively, for initiation, hydride transfer, and β-scission processes at 773 and 848 K for 2-methylhexane conversion over USY-S1. Discussion We found for the conversions of both isobutane and 2-methylhexane that, as the severity of catalyst steaming increases, the activation energies of certain kinetically significant steps increase (Tables 4 and 5). This behavior suggests that the cationic transition states for these kinetically sensitive steps are stabilized to a lesser

degree as steaming severity increases. Consider, for instance, a hydride transfer elementary step in which a paraffin AH2 reacts with a surface alkoxy species BH-Z via a carbenium ion-like transition state [AH2BH+-Z-]q to give a paraffin product BH2 and a surface alkoxy species AH-Z.

AH2,gas + BH-Z a [AH2BH+-Z-]q f AH-Z + BH2,gas The rate of this step may be written as

r)

( )

kBT q K PAH2,gasθBH-Z h

(10)

where the first term is a frequency factor, Kq is the equilibrium constant between the reactants and the transition state, PAH2,gas is the pressure of paraffin A, and θBH-Z is the fractional surface coverage of the alkoxy species BH-Z. The equilibrium constant Kq may be defined in terms of the standard entropy change, ∆S°q, and enthalpy change, ∆H°q, in going from the reactants

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Figure 6. (a) Sum of absolute values of Campbell’s degree of rate control as a function of isobutane conversion over USY-C at various temperatures. Bold solid lines represent the sum over all significant steps. Symbols: (O) initiation steps, (0) hydride transfer steps; (4) oligomerization/β-scission steps. (b) Sum of absolute values of the net rates as a function of isobutane conversion over USY-C at various temperatures. Bold solid lines represent the sum over all significant steps. Symbols: (O) initiation steps; (0) hydride transfer steps; (4) oligomerization/β-scission steps.

to the transition state:

Kq ) exp

( ) (

)

∆S°q -∆H°q exp R RT

(11)

The adsorption of the olefin B to form the adsorbed alkoxy species, BH-Z, is a quasi-equilibrated process. Accordingly, at the low surface coverages appropriate for our studies of USY zeolite, θBH-Z can be written in terms of the equilibrium constant for the adsorption of the olefin B onto the surface, Kads, and the pressure of olefin B, PBgas:

r)

( ) (

)

k BT ∆S°q -∆H°q exp PAH2,gasKadsPBgas (12) exp h R RT

Thus, the rate expression for the hydride transfer step is given by

r)

(

)

k BT ∆S°q + ∆S°ads × exp h R -(∆H°q + ∆H°ads) exp PAH2,gasPBgas (13) RT

(

)

Equation 13 shows that the reaction rate is controlled by the standard enthalpy change in going from the gasphase reactants to the transition state of a hydride transfer step. The second exponential term in eq 13 represents the composite activation barrier of the hydride transfer reaction, Ecomp, given as

Ecomp ) Eintr + ∆H°ads

(14)

where Eintr represents the intrinsic activation energy (for example, Eβ, EH, and Eiso defined in Table 3 with respect to surface species). The above result, that the rate of the hydride transfer reactions is controlled by the composite activation barriers, also holds for β-scission and isomerization steps. Therefore, any change in the properties of the zeolite that leads to changes in the heat of adsorption of gas-phase olefins will affect the composite activation energy barriers for the different reaction steps. As noted above, the value of the parameter ∆H°3 could not be accurately determined because of the low surface coverages for the reaction conditions of this study. Accordingly, we cannot distinguish whether a change in the value of a composite activation energy barrier is caused by a change in the intrinsic activation

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Figure 7. (a) Sum of absolute values of Campbell’s degree of rate control as a function of 2-methylhexane conversion over USY-S1 at various temperatures. Bold solid lines represent the sum over all significant steps. Symbols: (O) initiation steps; (0) hydride transfer steps; (4) oligomerization/β-scission steps. (b) Sum of absolute values of the net rates as a function of 2-methylhexane conversion over USY-S1 at various temperatures. Bold solid lines represent the sum over all significant steps. Symbols: (O) initiation steps, (0) hydride transfer steps; (4) oligomerization/β-scission steps.

barrier and/or a change in the value of ∆H°3. Figure 8 shows two limiting cases for the effect on the composite activation barrier; in Figure 8a, the change in the composite activation barrier is caused entirely by a change in the intrinsic activation energy, whereas in Figure 8b, it is caused entirely by a change in the heat of adsorption onto the surface. Interestingly, the results of this study indicate that the composite activation energy barriers for hydride transfer and oligomerization/ β-scission reactions are altered by similar extents as the activation barriers for monomolecular initiation reactions. Therefore, it appears that the interactions responsible for stabilizing the transition states for monomolecular cracking (e.g., van der Waals interactions with the walls of the zeolite) are also important for stabilizing the transition states for hydride transfer and oligomerization/β-scission reactions. It is probable that changes in the composite activation barriers caused by stream treatment are in certain cases at least partially caused by a change in the heat of adsorption on the catalytic site. In general, however, it is apparent that the relatively severe steam treatments given to the catalysts used in this study affect the Brønsted acid sites in a way that the cationic transition states are destabilized, leading to higher composite activation energies and lower rates of reaction. We can only speculate whether this result of steaming is due to a decrease in the intrinsic acid strength of the Brønsted acid site or whether the steam-distorted lattice structure and nonframework aluminum within the zeolite influences the properties of the acid site. Rate Control in Catalytic Cracking. For a complex multicyclical process like catalytic cracking, sensitivity analysis using the degree of rate control, XRC,i, enables one to determine the critical steps that influence the overall rate and product selectivity. It also indicates how

the kinetic relevance of a particular step may change with conversion of reactants and experimental conditions. In contrast, the actual rate of the step is influenced by other reactions, for example, via competition for surface sites or intermediates. Therefore, improvement of catalytic processes should be based on enhancing those steps which show the highest degree of rate control. For isobutane conversion at the low temperature of 673 K (Figure 6a), the sum of the degrees of rate control for initiation steps, which is highest at very low conversions, decreases monotonically until it becomes lower than that for hydride transfer and β-scission reactions. Importantly, even though the net rate of initiation steps is extremely low at 673 K (Figure 6b), after about 15% isobutane conversion, hydride transfer has a higher degree of rate control than initiation. The situation at 773 K is similar, but the crossover point for rate control from initiation to hydride transfer occurs at about 50% conversion. For both temperatures, β-scission steps have the highest total net rates, followed by hydride transfer steps, while the net rates of initiation steps are very low. The higher rates for β-scission steps, as compared to the other reactions, indicate the existence of multiple β-scission cycles per cycle of the other steps, hence leading to a sum of XRC,i values greater than unity. At 848 K, there is a significant shift in the degree of rate control. The sum of the degrees of rate control for initiation steps is significantly greater than that for hydride transfer. The sums of the net rates of the two processes are closer to each other at 848 K than at the lower temperature; e.g., at 40% conversion the sum of hydride transfer rates is ca. 60% higher than the sum of initiation rates. The results for 2-methylhexane cracking (Figure 7a,b) show a different pattern compared to isobutane. At 773

Ind. Eng. Chem. Res., Vol. 41, No. 16, 2002 4025 Table 6. Reaction Steps with the Highest Degree of Rate Control (XRC,i) for ca. 30% Conversion of Isobutane at 773 Ka

a

Figure 8. Energy diagrams illustrating changes in the composite activation barrier caused by (a) a change in the intrinsic activation barrier and constant heat of adsorption and (b) a change in the heat of adsorption of gaseous species onto the surface and constant intrinsic activation barrier.

K, the degrees of rate control for initiation and hydride transfer cross at about 70% conversion. In contrast, the degree of rate control at 848 K for initiation is much greater than that for the other steps. In this case, the combined sum of the degrees of rate control for all steps (solid line in Figure 7a) is less than the one at all conversions, indicating the absence of multiple pathways and showing that initiation truly controls the cracking of 2-methylhexane at 848 K. Importantly, the net rate of initiation at 848 K is higher than the rates of β-scission and hydride transfer at all conversions. For example, at 40% conversion, the sum of initiation rates is 6 times greater than the sum of hydride transfer rates. This represents a significant difference between 2-methylhexane cracking and isobutane cracking. These analyses on two relatively simple molecules show that, even though the overall chemistry of cracking is the same for isobutane and 2-methylhexane, the size of the molecule has an impact on the determination of the critical roles the reaction processes play. If we extrapolate this result to catalytic cracking of larger molecules at high temperatures, it is apparent that enhancing the initiation function of the catalyst would lead to higher overall activity. Enhancing the hydride transfer process could be important for determining product selectivity, which we have not discussed here,

The feed consists of 25 mol % isobutane and no olefins.

but it would not play as major a role in increasing the overall cracking activity as would enhancing the initiation reactions. Tables 6 and 7 compare individual steps with the highest degrees of rate control for 30% conversion of isobutane and 2-methylhexane at 773 K. For isobutane conversion, the methane formation step has the highest degree of rate control, followed by the initiation step leading to the production of hydrogen and the hydride transfer reactions leading to the formation of propane and n-butane. For 2-methylhexane conversion, the most kinetically relevant steps are initiation and hydride transfer steps that produce propane and isobutane. Thus, initiation via cleavage of the inner C-C bonds of 2-methylhexane is kinetically more significant than that via cleavage of terminal C-C bonds, in accordance with previous proposals.7,10 Conclusions Kinetic analyses conducted for isobutane and 2methylhexane conversion over USY zeolite at 773 K, where the reaction is initiated by activation of the reactant paraffin, helped to elucidate the effect of steam treatment on these catalysts. Increasing the steaming severity of USY leads to an increase in the composite activation barriers of kinetically significant initiation and hydride transfer steps, except for the reaction steps involving the dehydrogenation of reactant paraffins. Our analyses cannot distinguish whether the heat of adsorption of a reactant, olefin or paraffin, or the intrinsic activation of the step is affected by steaming. We propose that steaming leads to destabilization of the transition states for kinetically sensitive reaction steps, with respect to the gas phase, hence increasing the overall activation energy and lowering the reaction rate. Changes in the composite activation energy may also, at least partially, be caused by changes in the heat of

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Table 7. Reaction Steps with the Highest Degree of Rate Control (XRC,i) for ca. 30% Conversion of 2-Methylhexane at 773 Ka

a

The feed consists of 10 mol % 2-methylhexane and no olefins.

adsorption of the reactant on the Brønsted site. This result, derived from our model, is important because this approach may be used to compare acid sites in different zeolites or sites influenced by exchanged cations. Kinetic modeling and the attendant sensitivity analyses enabled us to identify kinetically significant steps in the complex multicyclical cracking process. Using the degree of rate control approach, not only are we able to differentiate between steps that are kinetically relevant and those that are not but also we can show how critical steps respond to changes in experimental conditions. Interestingly, we find that steps with the highest degree of rate control do not necessarily have the lowest reaction rate. At low temperatures, for both isobutane and 2-methylhexane conversion, initiation steps show the highest degree of rate control at low conversions, whereas hydride transfer steps have a higher degree of rate control at higher conversions. The conversion at which

the degrees of rate control for initiation and hydride transfer are equal sequentially increases with temperature and with the size of the reactant molecule. β-Scission steps have relatively low degrees of rate control and decrease further as the temperature increases. Compared to isobutane at the same temperature, initiation steps for the larger 2-methylhexane molecule have a much greater significance compared to hydride transfer and β-scission. In fact, at 848 K, initiation steps are predominant; they show the highest degree of rate control as well as the highest rate of reaction over the whole conversion range for 2-methylhexane cracking. The fact that our analyses indicate that the size of a molecule plays an important role in determining the relative importance of different reaction steps is quite important. It teaches us that initiation reactions play a critical and dominant role for the high-temperature cracking of large hydrocarbons. Catalytically enhancing

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Received for review January 16, 2002 Revised manuscript received May 14, 2002 Accepted May 29, 2002 IE020041Z