Single-Event Kinetic Model for Cracking and Isomerization of 1

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Single-Event Kinetic Model for Cracking and Isomerization of 1-Hexene on ZSM-5 Tassilo von Aretin, and Olaf Hinrichsen Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie503628p • Publication Date (Web): 19 Nov 2014 Downloaded from http://pubs.acs.org on November 24, 2014

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Industrial & Engineering Chemistry Research

Single-Event Kinetic Model for Cracking and Isomerization of 1-Hexene on ZSM-5 Tassilo von Aretin and Olaf Hinrichsen* Technische Universität München, Department of Chemistry, Lichtenbergstraße 4, 85748 Garching b. München, Germany Technische Universität München, Catalysis Research Center, Ernst-Otto-Fischer-Straße 1, 85748 Garching b. München, Germany Single events, kinetic model, olefins cracking, ZSM-5

The single-event kinetic modeling approach is applied to olefins cracking. Experimental data from literature is used for the model development and the identification of reaction pathways in olefins cracking. A detailed product spectrum from a 1-hexene feed on ZSM-5 gives insight into the reactivity through the fractions of 20 different product olefins and the combined C7= - C12= olefins. The reaction network comprising all possible elementary reactions on ZSM-5 is generated using a matrix notation. Single-event rate constants for cracking and isomerization of 1-hexene are determined from parameter estimation. The results show the capability of the modeling approach to reproduce the complex product distribution observed on ZSM-5.

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Introduction: Both ethene and propene offer a wide range of applications for the production of synthetic materials. These hydrocarbons are mainly produced by steam cracking of naphtha or catalytic cracking of crude oil into petroleum fractions1. Since the demand for propene is growing faster than for ethene, the production of low olefins on demand offers economic advantages2. In this context the catalytic cracking of higher olefins on acid zeolites allows a process design with high propene yield. To obtain further mechanistic insight into the reactions occurring during catalytic cracking of olefins, a kinetic model is developed. Due to the large number of reaction possibilities, the single-event kinetic modeling approach is used to link catalyst design and product distribution in catalytic cracking. The aim of this work is to reproduce the product distribution of olefins cracking with consideration of the complex elementary reactions on ZSM5.

Experimental Data: Since only few kinetic models for olefins cracking are found in literature3,4, experimental data sets suited for the development of a kinetic model are rare. Vahteristo et al.3 study skeletal isomerization of 1-pentene on ZSM-22. Here, however, only the pentene isomers are given in detail with dimerization and fragmentation products regarded as two combined responses3. Borges et al.4 determine rates of consumption for light olefins on ZSM-5, but product distributions are only given at certain temperatures with carbon numbers being lumped. Experimental data for cracking of n-butene solely shows the fractions of main products on ZSM5 with fractions of pentenes or hexenes being combined5,6. Thus, detailed information about the occurring pathways leading to the corresponding isomers is not included in the data set. Also not


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suited for kinetic modeling are data points which are given over time on stream instead of conversion or residence time7,8. Abbot and Wojciechowski9 investigate catalyst deactivation on ZSM-5 with the experiments being conducted in an integral plug flow reactor9,10. Here, a detailed product spectrum obtained from a 1-hexene feed at 350°C is given depending on conversion in the absence of catalyst deactivation9,11,12. It contains the weight fractions of 20 olefin isomers in the range of C2= to C6= and the combined weight fraction of C7= - C12= olefins9. Thus, this product spectrum allows mechanistic insight into the reaction pathways on ZSM-5 and the extent of occurring dimerization reactions. Three catalyst to reactant mass ratios are used9. The integral conversion is determined from the conversion at the reactor outlet 13. =

(1)

Here is the total duration for which a certain mass of feed is passed through a certain mass of catalyst11. Hence, the residence time in the reactor is dependent on and the catalyst to reactant mass ratio 14. =

(2)

Abbot and Wojciechowski9,15 give the integral conversion of the feed 1-hexene depending on . Thus, every data point for one catalyst to reactant mass ratio corresponds to a different residence time in the reactor9,11. Hereby, the catalyst is fully deactivated for large values of since a further increase in residence time does not result in a higher integral conversion9,14. Consequently, a dependence between residence time and conversion, which can be used for the steady state modeling of a plug flow reactor, is not available. The detailed product spectrum, however, can be used for the determination of kinetic parameters for cracking and isomerization of 1-hexene. Absolute values of the rate constants are consequently not covered by the


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experimental data. The ratios of the rate constants, however, represent the reaction pathways occurring on ZSM-5 and correspond to the experimentally obtained product distribution. A silicium to aluminum ratio of 80 is used by Abbot and Wojciechowski9. From this value the number of acid sites is calculated using the stoichiometric formula NanAlnSi96-nO192 ∙ 16 H2O for ZSM-516 and a stoichiometric coefficient n of 1.2 for Al. Assuming that all aluminum atoms are accessible, the number of acid sites is calculated to be 0.1976

. Since the product

spectrum is only given at one temperature, it is not possible to determine activation energies9. Instead rate constants for cracking and isomerization are determined by kinetic modeling to show the applicability of the single-event kinetic approach to olefins cracking. According to the experimental data by Abbot and Wojciechowski9, doublebond-isomerization is reported to be a comparatively fast reaction. Thus, conversion of the 1-hexene feed is calculated from any component other than linear hexenes and the weight fractions of the doublebond-isomers of 1-hexene are not listed9,15. For linear pentenes, 3-methylpentenes and partly for 2-methylbutenes as well as for 2-methylpentenes the mole fractions of the doublebondisomers can be plotted over conversion of n-hexene. As shown in figure 1, the mole fractions of the doublebond-isomers are independent of the conversion, indicating equilibrium among these. For the 3-methylpentenes, however, the assumption of equilibrium among the doublebond-isomers is only valid at conversions larger than approximately 20 %. This might be due to 2-ethylbut-1-ene being an impurity in the feed as described by Abbot and Wojciechowski9. Despite of this, equilibrium among doublebondisomers is assumed in the model, which is valid for most olefins over a wide range of conversions. Herby, the olefins shown in figure 1 are regarded to be representative of the product


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spectrum in olefins cracking. Moreover, an equilibration between doublebond-isomers also indicates a protonation equilibrium.

Figure 1: Mole fractions of various doublebond-isomers of C5= and C6= olefins depending on the conversion of n-hexene9

Reaction pathways for hexene cracking: Abbot and Wojciechowski9,15 identify the unimolecular cracking of C6= to propene and the dimerization of C6= to a C12= intermediate as reaction pathways at the given temperature of


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350°C. This C12= intermediate subsequently cracks into either C9= and C3=, or C8= and C4=, or C7= and C5=. The olefins produced by cracking can thereby undergo consecutive reactions, like the cracking of C9= to C6= and C3= olefins9,15. By analysis of the liquid residue of all conducted experiments on ZSM-5, Abbot and Wojciechowski9,17 conclude that no olefins larger than C12= are obtained with a hexene feed. Using a pentene feed, C10= is the largest detected hydrocarbon15. Thus, in the reaction network oligomerisation of the feed is regarded to be limited to the formation of dimers. In the liquid residue of the experiments of Abbot and Wojciechowski9 mostly linear and monobranched olefins were detected, with dibranched olefins having the methyl side groups at different carbon atoms. Tabak et al.18 also report a low degree of branching for product olefins in the range of C11= to C20= on ZSM-5, with most branches being methyl side groups. Weitkamp19 investigates the cracking of paraffins on ZSM-5 and concludes that tribranched carbenium ions are not formed due to steric constraints. Abbot and Wojciechowski9 do not list olefins with quaternary carbon atoms in their product spectrum on ZSM-5. Hereby, even the dibranched olefins 2,3-dimethlybut-1-ene and 2,3-dimethlybut-2-ene are observed only in small amounts, which is regarded to be due to pore size restrictions9. Thus, species with quaternary carbon atoms are excluded from the reaction network generation due to steric constraints on ZSM-5. Branching is limited to a maximum of two methyl side groups and the maximum carbon number considered in the elementary reactions is twelve. Furthermore a low weight fraction of C7= - C12= olefins is detected in the experimental product spectrum9. The thermodynamic data at 350°C, however, allows the formation of large olefins in considerable amounts. Thus, in the model a free gas-phase equilibrium is not assumed. Instead dimerization pathways via secondary educt and tertiary product carbenium ions are excluded


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from the reaction network due to steric constraints in the pores of ZSM-5. Only dimerization pathways via secondary carbenium ions are included in the model and cracking via tertiary to secondary carbenium ions is regarded as an irreversible reaction. Further dimerization reactions of product olefins like e.g. propene, butenes and pentenes with each other and the feed are also considered thus accounting for the complex reaction possibilities between olefins and carbenium ions on the acid zeolite. According to Abbot and Wojciechowski9 ethene is only formed as a secondary product at high conversions of hexene. Buchanan20 studies the cracking of hexene at 538°C on ZSM-5 and identifies propene and butene as the main products. Ethene is regarded to be formed from pentene at long residence times20. Buchanan et al.21 investigate hexene cracking on ZSM-5 at 510°C and determine reaction rates for the different cracking modes. Hereby, the rate of ethene formation is determined to be low compared to propene formation due to the low stability of the primary carbenium ions involved21. When considering cracking of an octene feed on ZSM-521, faster cracking modes via the more stable tertiary and secondary carbenium ions are available. Thus, the slower cracking pathways to ethene become insignificant21. In the model ethene is regarded to be only formed from the cracking of linear pentenes. It is considered to be a slow reaction compared to cracking via secondary or tertiary carbenium ions. For linear pentenes, however, cracking to ethene and propene is the only available cracking pathway. Assuming cracking to ethene being a slow reaction corresponds to the experimental observation that ethene is only formed in low amounts at high conversion9.

Reaction network generation:


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To incorporate the reactivity of olefins into a kinetic model, a reaction network including all possible elementary reactions occurring on the acid catalyst is generated. A matrix notation assigning a unique Boolean relation matrix to every olefin and carbenium ion considered is applied22,23,24,25. Three-dimensional matrices are used, with the first plane describing the carbon skeletal structure, the second the doublebond structure and the third the charge structure of the molecule. This is depicted in table 1 for the but-2-yl carbenium ion and isobutene.

Table 1: Matrix notation for but-2-yl carbenium ion and isobutene

Carbon skeletal

Doublebond

structure

structure

C1 C2 C3 C4

Charge structure

C1 C2 C3 C4

C1 C2 C3 C4

But-2-yl

C1

0

1

0

0

C1

0

0

0

0

C1

0

0

0

0

carbenium

C2

1

0

1

0

C2

0

0

0

0

C2

0

1

0

0

ion

C3

0

1

0

1

C3

0

0

0

0

C3

0

0

0

0

C4

0

0

1

0

C4

0

0

0

0

C4

0

0

0

0

C1 C2 C3 C4

Isobutene

C1 C2 C3 C4

C1 C2 C3 C4

C1

0

1

0

0

C1

0

1

0

0

C1

0

0

0

0

C2

1

0

1

1

C2

1

0

0

0

C2

0

0

0

0

C3

0

1

0

0

C3

0

0

0

0

C3

0

0

0

0

C4

0

1

0

0

C4

0

0

0

0

C4

0

0

0

0


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The first row of the carbon skeletal structure of the but-2-yl carbenium ion in table 1 indicates a bond between carbon atom C1 and carbon atom C2. Since no further C-C bonds are present on carbon atom C1, the rest of this row contains zeroes. The second row shows a bond between carbon atom C2 and C1 as well as C3. Doublebonds are defined analogously in the doublebond structure. Positive charges only correspond to one carbon atom, as indicated for carbon atom C2 in the charge structure of the but-2-yl carbenium ion. Forming the sum over the second row in the carbon skeletal structure of isobutene in table 1 gives three, thus indicating the tertiary carbon atom in isobutene. Elementary reactions are interpreted as matrix operations by deleting or creating bonds in the matrices. In the reaction network every product has also been considered as a reactant, thus ensuring that all reaction possibilities are taken into account. The matrix notation allows the computer aided generation of the reaction network independent of the considered olefin. The reactivity of olefins on ZSM-5, on which the reaction network generation is based, is shown in figure 2 for exemplary olefins26,27,28. Due to the equilibrium between doublebond isomers observed in figure 1, the hydride shift reactions in figure 2 (b) are also equilibrated. For PCP-branching reactions shown in figure 2 (c) both alpha and beta PCP-branching are considered27.


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Figure 2: Elementary reactions with transition states considered in the reaction network generation for olefins on ZSM-5: (a) protonation/deprotonation, (b) hydride shift, (c) methyl shift, (d) PCP-branching with protonated cyclopropane (PCP) ring as transition state and (e) cracking and dimerization

To handle the large number of parameters necessary for the kinetic description of the reaction network, the single-event kinetic model is applied23,25,28,29. Using the single-event approach the rate constant for every elementary reaction is divided into two parts30,31,32. The first part accounts for the different types of carbenium ions involved, e.g. secondary or tertiary ions. This procedure subdivides the elementary reactions into different reaction families, which are described by only one rate constant depending on the reactant and product carbenium ion25,33,34. Hereby, this part of


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the rate constant consists of an enthalpic as well as an intrinsic entropic contribution and is called the single-event rate constant35. The second part of the rate constant considers the entropy difference between reactant and transition state by accounting for the structure of molecules via global symmetry numbers23,30,32. Structural differences between elementary reactions, like e.g. the position of methyl side groups in a molecule, are comprehended by this second part of the rate constant called the number of single events35. Global symmetry numbers are calculated from the matrix notation described above by determining external and internal rotational axes in the molecule as well as the number of chiral centers23,36,37. With the conformations of transition states taken from literature, which are shown in figure 2, the number of single events is obtained from these global symmetry numbers for every elementary reaction in the network27,28,38. Thus, multiple elementary reactions are comprehended by a limited amount of kinetic parameters, since only the single-event rate constants have to be determined from an experimental data set.

Rate Equations: The concept of rate determining steps is used to describe the reaction pathways in the acidcatalyzed cracking of olefins. Cracking, dimerization, methyl shift and PCP-branching reactions are considered as rate determining steps due to equilibria observed in the experimental data. The reaction rate of a carbenium ion of the type m, i.e. tertiary, secondary or primary, into a product carbenium ion of type n is given below for the considered rate determining steps. ; ! =

$

" # ;

! &

(3)

%

$

'(/** ; ! =

" #'(/** ;

+,' ; ! =

$

" #+,' ;

! & %

! & -./ %

(4) (5)


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For isomerization and cracking the rate equations are implemented as first-order reactions in the concentration of carbenium ions on the surface34,39. Dimerization is considered to be the reaction between a carbenium ion adsorbed on the zeolite and a gas-phase olefin. Thus, the rate of this rate determining step depends on the concentration of the carbenium ion and the partial pressure of the educt olefin. From a protonation equilibrium the concentration of the carbenium ion & is determined depending on the concentration of the physisorbed olefin .% . %

01%

& = 0 %

2& %

456 76 ; ! 3 489 78 ; 76 ! . 3 %

(6)

According to the single-event kinetic approach a reference olefin is applied for the protonation equilibrium23,25. As shown by Vynckier and Froment25 this procedure is necessary to avoid thermodynamic inconsistencies in the description of equilibria between doublebond-isomers. For pentenes and larger olefins the 2-methylalkenes are the reference olefins, whereas for smaller olefins the 1-alkenes are used28,34. The physisorption of gas-phase olefins is implemented via a Langmuir approach39. :;,1% 51%

.% = @ ∑

(7)

B :;,1B 51B

Thus, the reaction rate of every olefin can be calculated depending on the gas-phase partial pressures. Hereby, a reaction pathway proceeds via equilibrated physisorption and protonation steps to the rate determining step. Desorption reactions following the rate determining step, leading to the product olefins are also equilibrated34. The rate of formation of an olefin C.% is obtained by summing up the reaction rates of the different reaction pathways. E+,' C.% = ∑E DF D ; G , 78 ! − ∑DF D , 78 ; G ! + C & %

(8)

By the sum over the number of cracking reactions C the formation of olefin 78 from the arbitrary carbenium ions and G is considered. The consumption of 78 is taken into account


12

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via the sum over all dimerization reactions JKL. Reaction rates of carbenium ions stemming from olefin 78 are comprehended by C& , which is explained below: %

C& = ∑ '(/** ; 8 ! − ∑ '(/** 8 ; ! + ∑ ; 8 , 7M ! − %

∑ 8 ; , 7M ! + ∑ +,' , 7M ; 8 ! − ∑ +,' 8 , 7M ; !

(9)

Hereby, all carbenium ions in the reaction network are considered by the summation over the index k. Rate determining steps forming the carbenium ion i are added to the rate of formation of carbenium ion C8@ , others consuming it are subtracted. The olefin 7M is arbitrary and does not affect the rate of the rate determining step for cracking reactions34. To obtain the flow rates of every olefin in the reaction network, the design equation for an isothermal plug flow reactor is solved34. NO1% NP

= C.%

(10)

This ordinary differential equation is solved by integrating the molar flow Q.% of the olefin 78 over the mass of catalyst R with the ode15s solver in MATLAB.

Equilibria in the derivation of the reaction rate: Cracking and dimerization can be considered as forward and reverse reactions. Thus, the rate constants for cracking and dimerization are not independent from each other. Instead the rate constants for two pathways involving the same olefins have to follow the constraint that after long residence times the gas-phase equilibrium is established.


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Figure 3: Reaction pathways for cracking and dimerization splitted into forward and reverse reactions to determine an equilibrium constant for the rate determining step

Figure 3 shows one dimerization pathway starting from the gas-phase olefins 78 and 7M over the rate determining step, leading to olefin 7S . The reaction pathway for the backward reaction starts from olefin 7S . To express the rate constant for dimerization via the rate constant for cracking, an equilibrium constant for the rate determining step is used. 3+( =

TUV E;!

(11)

W2 ;E!

In figure 3 the equilibrium constant for the rate determining step is obtained by multiplication of the equilibrium constants for physisorption, protonation and between the gas-phase olefins. Thus, the educts of the rate determining step are linked with the product carbenium ion via the gas-phase equilibrium constant. 3+( F :

;XY .% ;E!

:

;,1%

3"G 35Z[9,.\ 356 7S ; !

(12)


14

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Here, the protonation equilibrium also has to be described with the corresponding reference olefins. To calculate the single-event rate constant for dimerization from the single-event rate constant for cracking, all equilibrium constants have to be single-event equilibrium constants. This can be derived by equating the reaction rates for cracking and dimerization, thus yielding the equilibrium condition. Hence the following equation results: 4

4

4+( F :]^ :;,1\% :;XY 3 4 4 `. ,Ea : : ;XY

X

4%>Y_ .\ ;.X\ ! .X\ ,! :

% %>Y_ `.% ;.X a :;,1%

(13)

Here, all symmetry numbers cancel out when converting equilibrium constants to single-event equilibrium constants23. The different reference olefins are labeled, being 768 the reference olefin corresponding to olefin 78 . Since no change in the symmetry numbers is assumed for physisorption, the equilibrium constant for physisorption is assumed to be equal to the corresponding single-event equilibrium constant. The advantage of this procedure is a reduction in the number of kinetic constants to be determined from parameter estimation. The same equilibrium considerations which describe cracking and dimerization as forward and backward reaction have to be applied for PCP-branching32. Here, elementary reactions via the single-event rate constants #$** ; b! and #$** b; ! are also forward and backward reactions32. Thus, these two single-event rate constants are linked by a thermodynamic constraint32. Derived from a scheme similar to figure 3, the single-event rate constant for #$** ; b! is expressed via #$** b; !, the equilibrium constants in both reaction pathways and the gas phase equilibrium constant between the educt and product olefins of the isomerization pathway. 4

$

>

4

>

4

. . ! > :;XY X ;9! :%>Y_ > ;.X 4+( = cWc ;9! = :]^ :;,1 3 $ 4 4 `. ;a : `. ;. a : 9;! : cWc

;XY

X

%>Y_

X

;,1

(14)

Hereby, symbols from the forward reaction pathway proceeding from olefin 7 via a tertiary educt carbenium ion are labeled with , whereas symbols of the backward reaction pathway with


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olefin 79 as educt over a secondary carbenium ion are labeled with b. Equating the reaction rates of both pathways for PCP-branching with #$** ; b! and #$** b; ! yields the correct equilibrium condition between the olefins. The number of differential equations is reduced by considering equilibrium among doublebond-isomers. Therefore, the molar flows of all doublebond-isomers corresponding to one carbon skeletal structure are combined. At one experimental condition the mole fractions of these doublebond-isomers are determined. To obtain the molar flow of one specific olefin for calculating the reaction rate, the molar flow of its carbon skeletal structure is multiplied with its mole fraction in doublebond-isomerization equilibrium. Thus, e.g. the molar flow of 1-pentene is obtained from the molar flow of linear pentenes multiplied with the mole fraction of 1-pentene in equilibrium among 1-pentene, cis-2-pentene and trans-2-pentene. Consequently, the number of differential equations necessary to calculate the rate of all linear pentenes is reduced to one. When considering larger olefins, like dodecenes, this reduction becomes more advantageous. This procedure is comparable to the a posteriori lumping applied by Cochegrue et al.40 or by Guillaume et al.41, who also consider equilibria between isomerization reactions. In the calculation of equilibria, cis- and trans-isomers have to be distinguished. As e.g. for doublebond-isomers like 1-alkenes and 2-alkenes, the enthalpy of cis- and trans-isomers also differs42,43. Thus, an isomer group of cis- and trans-isomers is formed to consider the difference in thermodynamic data44. Δe,f = − Cg h ijk- l

mnf%> o

p + jk- l

mnfXq> o

pr

(15)

This Gibbs' energy of an isomer group Δe,f is taken to determine equilibrium constants in the model when cis- and trans-isomers are involved.


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Thermodynamic data: For the calculation of equilibrium constants, Gibbs' energies are used. Experimental data from Alberty and Gehrig42 are available for olefins up to hexenes. For larger olefins estimates of the Gibbs' energy are obtained with Benson's group contribution method43,45. To be used together, Gibbs' energies from both sources are referred to the elements hydrogen in the gas-phase and crystalline graphite42,46,47. Thermodynamic data for physisorption and protonation are taken from theoretical calculations by Nguyen et al.48, who consider linear olefins with carbon numbers ranging from two to eight. Linear correlations are given to determine the thermodynamic data for physisorption and chemisorption on ZSM-548. A Si/Al ratio of 95 is investigated by Nguyen et al.48 and thus the data is comparable to the Si/Al ratio of 80 used by Abbot and Wojciechowski9. Differences in the Si/Al ratio are regarded to influence the activity, but for hexene cracking similar product distributions are obtained from different Si/Al ratios on ZSM-5 as shown by Buchanan20. Hereby, Nguyen et al.48 distinguish between 1-alkenes as well as 2/3/4-alkenes and state different linear correlations for these. For protonation this discrimination is applied in the model, but to describe physisorption only the data for 1-alkenes is used. The physisorption data from Nguyen et al.48 corresponds to the one for linear olefins, whereas in the reaction network linear and branched olefins are considered. Here, using the discrimination between 1-alkenes and 2/3/4alkenes for physisorption as proposed by Nguyen et al.48 results in an inferior description of the experimental product spectrum by the kinetic model. Thus, the physisorption parameters determined by Nguyen et al.48 for 1-alkenes seem to be better suited for the description of linear and branched olefins. Nguyen et al.48 consider the protonation of a physisorbed olefin to an alkoxide. Whether the intermediate on zeolites is an alkoxide or a carbenium ion is not finally


17


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clarified in literature49,50,51. Regarding the reactivity, however, the same conclusions are obtained for carbenium ions and alkoxides by the single-event approach39. Reaction pathways via activation of tertiary carbon atoms are faster than pathways via secondary ones19,34,39. Since according to Nguyen et al.48 the protonation of a physisorbed alkene leads to an alkoxide, alkoxides are also considered as the reaction intermediates in the presented model. Kazansky et al.52 conclude that alkoxides are the stable intermediates on zeolites, but carbenium ions are regarded as the high energy transition states. Hereby, the stability of primary, secondary and tertiary alkoxides is found to be comparable53 and consequently no stability difference between these has to be considered in the presented model39.

Parameter estimation: The assumptions described above reduce the number of kinetic parameters to be determined from experimental data. With quaternary carbon atoms being excluded from the reaction network, cracking reactions with tertiary product carbenium ions become impossible. The same holds for methyl shift reactions involving tertiary carbenium ions as well as for PCP-branching reactions between tertiary educt and product carbenium ions. A Levenberg-Marquardt algorithm is applied to minimize the difference between molar flows predicted by the model and the experimental data54. Therefore, the solver lsqnonlin is used in MATLAB with ode15s being applied to determine the molar flows of olefins in the reactor model. Boundary conditions on the reactor inlet are set according to the feed composition given by Abbot and Wojciechowski9. Thus, the feed consists of 98.39 % 1-hexene and 1.61 % 2-ethylbut-1-ene9. In total the kinetic model is based on 144 methyl shift, 784 PCP-branching, 141 cracking and 119 dimerization reactions with 593 different olefins being considered. Due to the assumption of equilibrium in


18

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doublebond-isomerization, 86 ordinary differential equations have to be solved for the carbon skeletal structures of the olefins in the reaction network. The mass balance of the model and the correct implementation of the equilibrium condition between reaction pathways have been checked. The single-event rate constants are determined from the experimental data of Abbot and Wojciechowski9. The ratios of the estimated single-event rate coefficients, which are normalized with #$ b; -!, are given in table 2.

Table 2: Ratios of single-event rate constants estimated from the experimental data according to Abbot and Wojciechowski9 #$ b; -! #$ b; -!

#$ b; b! #$ b; -!

#$ ; b! #$ b; -!

#$'( b; b! #$ b; -!

#$** b; b! #$ b; -!

#$** ; b! #$ b; -!

1.0

2.5 ∙ 10m

1.2 ∙ 10x

8.5 ∙ 10x

1.7 ∙ 10m

5.0


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With the estimated single-event rate constants from table 2 the product distribution depending on the conversion of n-hexene is calculated and compared to the experimental data from Abbot and Wojciechowski9. This is shown in figure 4 for the C2= to C5= olefins and in figure 5 for the C6= as well as the C7= - C12= olefins

Figure 4: Comparison between experimental product distribution according to Abbot and Wojciechowski9 and the single-event kinetic model with the rate constants from table 2 for the C2= to C5= olefins


20

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Figure 5: Comparison between experimental product distribution according to Abbot and Wojciechowski9 and the single-event kinetic model with the rate constants from table 2 for the C6= and the C7= - C12= olefins

The experimental mass fractions of the C2= to C5= olefins in figure 4 are in good agreement with the model predictions. Propene shows a systematic deviation of approximately 0.5 wt% and a slight underprediction is observed for the linear pentenes. Hereby, the equilibrium mole fractions in doublebond-isomerization lead to a slight overprediction of cis-pent-2-en in


21


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combination with an underprediction of trans-pent-2-ene. Similar observations are obtained in figure 5 for some isomers of the methylpentenes. According to the experimental data the predicted weight fractions of 2,3-dimethylbutenes show the behavior of a stable secondary product9, but at high conversions the model overpredicts the weight fractions by roughly 0.5 wt%. At medium conversions, an overprediction is also observed for the weight fraction of the C7= - C12= olefins in figure 5.

Discussion of the results: Cracking and isomerization of 1-hexene on ZSM-5 are described according to the single-event kinetic approach. The influence of the catalyst on the reactivity is included into the model via steric constraints. Thus, compared to the free gas-phase chemistry reaction pathways are excluded from the reaction network based on experimental observations. Molecules with a high degree of branching or quaternary carbon atoms are excluded from the reaction network since these are not experimentally detected by Abbot and Wojciechowski9,15. This affects the parameter estimates as having more reaction pathways with the same rate constants would result in different formation rates for the separate olefins. On the contrary it is also possible that these molecules are formed as intermediates in the zeolite pores, but react before they diffuse out of the catalyst. Haag et al.55 determine the diffusion coefficients for linear hexenes, 3methylpentenes

and

2,2-dimethylbutenes

to

3 ∙ 10m| }~ b m,

4 ∙ 10mx }~ b m,

7∙

10m }~ b m, respectively. Consequently, it might also be possible that sterically demanding olefins with e.g. a quaternary carbon atom or more than two methyl side groups are present as reaction intermediates, but have a higher residence time in the zeolite pores due to the lower diffusion coefficient. This might cause sterically demanding olefins to react before leaving the


22

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zeolite pore system. Internal diffusion limitations in the pores of ZSM-5 have been investigated by Vandegehuchte et al.56 for n-hexane conversion with a model accounting for intracrystalline diffusion limitations and thus the diffusion coefficients of different hydrocarbons. Here, it is concluded that intracrystalline diffusion limitations but not transition-state shape selectivity or physisorption selectivity are the reason for the observed selectivity effects56. From the experimental data on olefins cracking available it does not seem possible to conclude whether highly branched olefins or olefins containing quaternary carbon atoms exist as intermediates or not. Thus, these are excluded from the reaction network in order to only consider reaction pathways leading to experimentally detected olefins. Only dimerization pathways via secondary carbenium ions are included in the reaction network. Consequently, cracking of tertiary educt to secondary product carbenium ions is an irreversible reaction. This results from the conducted parameter estimations. Otherwise a significantly larger amount of C7= - C12= olefins compared to the experimental data is obtained by the kinetic model. At 350°C, the gas-phase equilibrium favors the formation of large olefins. Abbot and Wojciechowski9, however, detect only a small amount of C7= - C12= olefins in their product spectrum. This supports the assumption that an equilibrium composition of olefins as in the free gas-phase is not obtained. Instead, it is assumed that these reaction pathways are blocked due to steric constraints and thus excluded from the reaction network. Hereby, a maximum is observed for the modeled C7= - C12= olefins in figure 5, which is not clearly identifiable from the data of Abbot and Wojciechowski9. Since the C7= - C12= olefins are regarded as reaction intermediates which undergo subsequent cracking, a maximum in their weight fraction is reasonable. Judged from the weight fraction of C7= - C12= olefins, the single-event kinetic model comprehends the extent of dimerization reactions on ZSM-5.


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Considering the ratios of the single-event rate constants in table 2, increasing values for the single-event rate constants are expected with more stable carbenium ions taking part in the reaction28,34,57. This is the case for PCP-branching and also observed for the two single-event rate constants #$ b; b! and #$ ; b!. The single-event rate constant #$ b; b!, however, is smaller than #$ b; -!. Moreover, the systematic deviation in the weight fraction of propene (cf. figure 4) also indicates that #$ b; b! is too small. Propene is found to be the only olefin in the reaction network which can be formed via #$ b; b! from hexenes without a dimerization step and subsequent cracking21. Thus, a value for #$ b; b!, which is too small, has to result in a lower predicted weight fraction of propene compared to the experimental data in figure 4. Taking into account the relatively small systematic deviation observed for propene of 0.5 wt%, the estimated value for #$ b; b! does not seem to be significantly too low. Thereby, #$ b; b! is linked to the gas-phase equilibrium constant. A higher value for this rate constant directly leads to faster dimerization and a larger weight fraction of C7= - C12= olefins in the product spectrum. This might indicate that too many reaction pathways for dimerization are considered in the reaction network. A further reduction of these pathways, however, can hardly be justified from the experimental data available. Another explanation for the apparently illogical ordering of the estimated single-event rate constants #$ b; -! and #$ b; b! in table 2 might be intracrystalline diffusion limitations in ZSM-5 as investigated by Vandegehuchte et al.56. Taking this into account, it cannot be excluded that the estimated kinetic parameters might also be influenced by diffusion effects in the zeolite pores. Further experimental data seems, however, necessary to conclude on whether intracrystalline diffusion limitations, steric constraints imposed on certain reaction pathways as


24

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presented in this paper or combinations of these effects lead to the observed product distribution of 1-hexene on ZSM-5. Dimerization is assumed to proceed via an Eley-Rideal mechanism over a carbenium ion being chemisorbed on the zeolite reacting with a gas-phase olefin. This allows the description of dimerization as the reverse reaction of cracking. A Langmuir-Hinshelwood mechanism with both educts of dimerization adsorbed on the zeolite might also be possible. Data for adsorption are, however, only available for physisorption of an olefin on an empty acid site, which are determined by Nguyen et al.48. In a Langmuir-Hinshelwood mechanism the physisorption of the olefin 7M has to be considered on an acid site on which a hydrocarbon is already adsorbed. Thermodynamic data for this process is not available, since data taken from Nguyen et al.48 is assumed to be different from physisorption data on an acid site covered with an adsorbed hydrocarbon. Hence, the assumption of an Eley-Rideal mechanism allows the use of the data provided by Nguyen et al.48 to describe all sorption processes. As an assumption the physisorption parameters determined by Nguyen et al.48 for 1-alkenes are used to describe the physisorption of all linear and branched olefins in the reaction network. Hereby, the discrimination between 1-alkenes and 2/3/4-alkenes proposed by Nguyen et al.48 is not applied. Using this discrimination, it is observed from the parameter estimation results that the ratios of 2-methylpentenes and 3-methylpentenes would be predicted contrary to the experimental data. Thus, the correlation given by Nguyen et al.48 for 1-alkenes seems to be better suited to describe the physisorption of linear and branched olefins on ZSM-5. The experimental data from Abbot and Wojciechowski9 allows no evaluation of the dependency between residence time and conversion of n-hexene. Consequently, absolute values of the single-event rate constants are not covered by the experimental data from Abbot and


25


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Page 26 of 39

Wojciechowski9. The ratios of these rate constants, however, allow to draw conclusions on the overall rate of the different reaction mechanisms. These ratios reflect the reactivity of olefins on ZSM-5, leading to the product spectrum depending on the conversion. Minor deviations in the equilibrium mole fractions in the figures 4 and 5 result from the thermodynamic data used. This leads e.g. to different ratios of cis- and trans-2-pentene in figure 4, but despite of that the total amount of linear pentenes is reproduced by the kinetic model. Given the predicted fractions of linear butenes and methylbutenes in figure 4, the assumption of equilibrium in doublebond-isomerization can be regarded as valid. This also holds for the 2methylpentenes in figure 5. Here, deviations in the weight fractions of cis- and trans-4methylpent-2-ene are also due to the thermodynamic data used since the single-event approach does not discriminate between cis- and trans-isomers23. A comparably large deviation between model and experiment is observed for trans-4-methylpent-2-ene. This, however, is due to the large fraction of the total 2-methylpentenes in the product spectrum. The weight fraction of trans-4-methylpent-2-ene is calculated from the total molar flow of 2-methylpentenes and the mole fraction of trans-4-methylpent-2-ene in doublebond-isomerization equilibrium. Thus, small discrepancies in this equilibrium mole fraction result in comparably large absolute deviations for trans-4-methylpent-2-ene (cf. figure 5). As shown in figure 1, the assumption of equilibrium between doublebond-isomers is not valid for the 3-methylpentenes at conversions below 20 %. This explains the deviations in figure 5 for 2-ethylbut-1-ene, which is an impurity in the feed9. For conversions larger than 20 % the model reproduces the experimentally obtained weight fractions of 3-methylpentenes, showing the suitability of this assumption. Assuming equilibrium in doublebond-isomerization allows the use of the concept of the rate determining step in the


26

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derivation of the rate equations as presented. The alternative of estimating kinetic parameters for protonation is not regarded to be possible from the experimental dataset available. Based on experimental observations, the formation of ethene is considered to occur from pentenes20,21. Other reaction pathways leading to ethene are excluded from the reaction network and ethene is also not regarded as an educt for dimerization reactions. This assumption is based on the low reactivity of ethene compared to larger olefins58. Considering the small weight fraction of ethene being formed even at high conversions in figure 4, this assumption seems to be justified under the experimental conditions.

Conclusion: The single-event kinetic modeling approach is capable of describing the complexity of the reactions occurring during cracking and isomerization of 1-hexene on ZSM-5. Hereby, 1188 reaction pathways with 593 different olefins are considered in the reaction network according to which the rate equations are set up. In the model formulation, steric constraints are used to represent the influence of the catalyst on the reactivity of olefins. Based on experimental observations on ZSM-5, reaction pathways are excluded from the reaction network as a result from these steric constraints. The advantage of applying the single-event kinetic approach is the small number of parameters necessary to describe the complex reactivity. This results in an increased stability of the parameter estimation routine used for determining single-event rate constants from the experimental data. Insight into the ratios of reaction rates for different reaction pathways leading to the detailed experimental product distribution on ZSM-5 is obtained from the estimated single-event rate constants. To describe the reaction rates of olefins on the zeolite, the concept of


27


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Page 28 of 39

rate determining steps and equilibrated elementary reactions in the different reaction pathways can be used. Hereby, the complex product spectrum of hexene cracking on ZSM-5 with 20 different olefin isomers and the combined C7= - C12= olefins is reproduced by the proposed kinetic model.

Corresponding Author [email protected]

Acknowledgments: The authors acknowledge the financial support from Clariant Produkte (Deutschland) GmbH.

Supporting Information The single-event methodology is applied to a reference case from literature34 to show that the chosen modeling approach is used correctly. This information is available free of charge via the Internet at http://pubs.acs.org/.

Abbreviations CR, cracking; DIM, dimerization; MS, methyl shift; PCP, protonated cyclopropane ring; RDS, rate determining step; List of Symbols:


28

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


&

Concentration of carbenium ion C8@ on the zeolite surface

h #

.%

Concentration of physisorbed olefin 78 on the zeolite surface

h #

Total concentration of acid sites on the zeolite

Q.%

Molar flow of olefin 78 in the reactor

%

Δe89

Gibbs energy of cis-isomer

Δe,f

Gibbs energy of an isomer group consisting of cis- and trans isomer

Δe6E9 # ; !

Gibbs energy of trans-isomer

Rate constant for cracking reaction between educt carbenium ion of type to product carbenium ion of type

#$ ; !

Single-event rate constant for cracking reaction between educt carbenium ion of type to product carbenium ion of

h # h b h h h 1 b 1 b

type #$+,' ; !

Single-event rate constant for dimerization reaction between educt carbenium ion of type to product carbenium ion of

1 b

type


29


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489 78 ; 76 ! 3

Single-event equilibrium constant for isomerization of olefin

Page 30 of 39

[-]

78 to reference olefin 76 35Z[9,.% 456 76 ; ! 3

Equilibrium constant for physisorption of olefin 78

Single-event equilibrium constant for protonation of reference

1 [-]

olefin 76 to carbenium ion of type 456 `768 , ma 3

Single-event equilibrium constant for protonation of the

[-]

reference olefin 76 corresponding to olefin 78 to carbenium ion of type 3+(

Equilibrium constant of the rate determining step of a reaction pathway

4+( 3

Single-event equilibrium constant of the rate determining step of a reaction pathway

"

C JKL

-./

1 1

Number of single events

[-]

Number of all cracking reactions in the reaction network

[-]

Number of all dimerization reactions in the reaction network

[-]

Catalyst to reactant mass ratio

Partial pressure of olefin

# # ""N


30

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+( ; !

Rate of rate determining step from educt carbenium ion of type to product carbenium ion of type

C

Universal gas constant

h # b h 3

C.%

Rate of formation of olefin 78

h # b

C &

Rate of formation of carbenium ion C8@

h # b

Secondary carbenium ion

[-]

.%

Symmetry number of olefin 78

[-]

.%,B

Symmetry number of olefin stemming from paraffin

[-]

&

Symmetry number of carbenium ion C8@

[-]

&

Symmetry number of carbenium ion # stemming from

[-]

%

b

%

%,

paraffin g

Temperature

3

Tertiary carbenium ion

Duration of an experiment

b

Residence time in the reactor

b

[-]


31


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R

Mass of catalyst in the reactor

#

Conversion of component A at the reactor outlet

[-]

Integral conversion of component A

[-]


32

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