Single-Event Kinetic Model for 1-Pentene Cracking ... - ACS Publications

Article pubs.acs.org/IECR

Single-Event Kinetic Model for 1‑Pentene Cracking on ZSM‑5 Tassilo von Aretin,†,‡ Stefan Schallmoser,†,‡ Sebastian Standl,†,‡ Markus Tonigold,§ Johannes A. Lercher,†,‡ and Olaf Hinrichsen*,†,‡ †

Technische Universität München, Department of Chemistry, Lichtenbergstraße 4, D-85748 Garching b. München, Germany Technische Universität München, Catalysis Research Center, Ernst-Otto-Fischer-Straße 1, D-85748 Garching b. München, Germany § Clariant Produkte (Deutschland) GmbH, Waldheimer Str. 13, D-83052 Bruckmühl, Germany ‡

S Supporting Information *

ABSTRACT: A single-event kinetic model for 1-pentene cracking on ZSM-5 is presented. In the kinetic model, the influence of the catalyst on the reactivity is comprehended via steric constraints in the zeolite pores. Compared to gas-phase chemistry, reaction pathways with sterically demanding olefins are excluded from the reaction network because of these constraints. The number of estimated kinetic parameters is reduced by choosing operating conditions for which double-bond isomerization and skeletal isomerization are in thermodynamic equilibrium. Thus, only cracking and dimerization remain as rate-determining steps. The data set comprises 23 different experimental conditions being varied at different residence times. From this data set, significant kinetic parameters with small confidence intervals are determined. A good parity between model and experiment was obtained, which supports the applicability of the single-event methodology to the complex reactivity of olefins cracking on ZSM5 and gives mechanistic insight into the reaction pathways leading to the product distribution. Furthermore, the possibility to use these kinetic parameters for extrapolation purposes beyond the experimentally covered range of reaction conditions is shown. ratio of the ZSM-5 catalyst11 was 90 and the number of acid sites was determined to 0.135 mol/kgcat. The catalyst had a crystallite size in the range between 10 and 50 nm. A gas chromatograph (Agilent 7890A) in combination with a flame ionization detector and a thermal conductivity detector was used for the analysis of the product composition.11 With this setup, olefins up to decene were detected. The fractions of all different pentene isomers in the product distribution were given, whereas for isobutene and 1-butene, only a combined fraction could be determined. Because of the large number of isomers, the C6−C12 olefins are considered as one combined response in the analytics. With this experimental insight into the product distribution of 1-pentene cracking on ZSM-5, a wide range of experimental parameters was investigated to separate the effects of the two main reaction pathways, i.e., the monomolecular cracking of pentenes to ethene and propene and the dimerization of two pentenes into decenes followed by their subsequent cracking.12 Therefore, eight temperatures from 633 to 733 K, two partial pressures of 1-pentene in the feed of 42.7 and 70.3 mbar, as well as two flow rates at the reactor inlet of 300 and 400 N mL/ min were chosen as experimental parameters to be varied. This amounts to 23 different experimental conditions in the kinetic data set. By using different amounts of catalyst at each of these conditions, the conversion was varied between 2.6 and 55%. 2.2. Analysis of Experimental Results. Both double-bond and skeletal isomerization reactions were regarded to be in thermodynamic equilibrium under all experimental conditions

1. INTRODUCTION Lower olefins, especially propene, are widely needed for the synthesis of different polymers. Currently, ethene and propene are mainly produced by steam cracking of naphtha or catalytic cracking of crude oil into petroleum fractions.1 Because the demand for propene grows faster than that for ethene, the selective synthesis of propene offers economic advantages2 with catalytic cracking of olefins being the most promising approach. Because the network of cracking reactions on a catalyst is very complex, kinetic modeling offers conceptually the opportunity of obtaining a faceted insight into the reactions. Despite this potential, only a few reports discussing kinetic models of catalytic cracking of olefins are available in literature; most of them address hydrocracking.3−9 Thus, we report here fundamental kinetic parameters of 1pentene cracking on ZSM-5 to gain insight into the effects of reaction conditions on the product distribution in olefins cracking. On the basis of elementary reactions, this kinetic model describes the complex reactions on the acid catalyst over a wide range of experimental conditions. The aims are on the one hand to obtain insight into reaction pathways of olefins on ZSM-5, which lead to the observed product distribution, and on the other hand to quantitatively describe the effect of reaction conditions on the yields of lower olefins. The single-event kinetic modeling approach is used because it is able to consider different reaction pathways with only a small number of kinetic parameters.3,10 2. EXPERIMENTAL PART 2.1. Experimental Setup. Kinetic measurements were conducted in an isothermal plug flow reactor. 11 The isothermicity of the reaction zone was achieved by diluting the catalyst with SiC and the feed with nitrogen. The Si/Al © 2015 American Chemical Society

Received: Revised: Accepted: Published: 11792

July 23, 2015 November 1, 2015 November 6, 2015 November 6, 2015 DOI: 10.1021/acs.iecr.5b02629 Ind. Eng. Chem. Res. 2015, 54, 11792−11803

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Industrial & Engineering Chemistry Research

Figure 1. Mole fractions of pentene isomers depending on conversion for reaction temperatures of 633 K (left) and of 733 K (right).

Figure 2. Mole fractions of butene isomers depending on conversion for reaction temperatures of 633 K (left) and of 733 K (right).

Figure 3. Product selectivities depending on conversion for reaction temperatures of 633 K (left) and of 733 K (right) at 42.7 mbar partial pressure of 1-pentene and a flow rate of 400 N mL/min.

investigated. This is shown in Figure 1 for the mole fractions of the pentene isomers at the lowest as well as the highest considered temperature. The mole fractions of the different pentene isomers in Figure 1 approach a constant value even at low conversions. Because of the fast isomerization, conversion was in this case defined from reactions of 1-pentene to any products except pentene isomers. At the lowest conversions shown in Figure 1, the isomerization equilibrium of pentene isomers is not fully attained. By comparison to the calculated equilibrium mole

fractions of pentene isomers (Table S1), deviations from the experimental mole fractions in Figure 1 are not regarded to be significant. Likewise, the butene isomers (Figure 2) were also equilibrated over the whole conversion range (Table S2). As shown by Buchanan et al.,13 the reactivity of olefins increases with carbon number; thus, isomers of hexenes or larger olefins are also deemed to be equilibrated. Under one selected condition, this is shown for detectable hexene isomers in Figure S1. Thus, kinetic parameters for isomerization reactions do not need to be determined from the experimental 11793

DOI: 10.1021/acs.iecr.5b02629 Ind. Eng. Chem. Res. 2015, 54, 11792−11803

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the fact that shape-selective constraints prevent formation of all possible isomers on ZSM-5.20,21 Figure 4 compares the data of Garwood19 to our own calculations, for which the global equilibrium fractions of the

data set, and isomerization reactions are described by equilibrium compositions. Figure 3 shows the selectivity to reaction products depending on conversion for the lowest and highest reaction temperature. Product selectivities over conversion at a third intermediate temperature are presented in Figure S2. Low selectivities to ethene and higher selectivities to C6− C12 olefins were obtained at 633 K (Figure 3, left) compared to the highest reaction temperature of 733 K (Figure 3, right). These exemplary product distributions illustrate the significant effect of reaction conditions on the selectivity.

3. ELEMENTARY REACTIONS AND REACTION PATHWAYS A reaction network including all possible elementary reactions of olefins and carbenium ions on the acid catalyst was generated in MATLAB.14 A Boolean relation matrix3,10,15,16 was assigned to every species considered in this reaction network allowing computer-aided reaction network generation.14 The influence of the catalyst on product distribution was implemented by excluding some reaction pathways if the olefins involved are sterically too demanding. These assumptions are based on either results reported earlier12,17 or our own experimental data. The main assumptions of the reaction network are shown in bulleted list form; further explanation can be found in the following two paragraphs: • Maximum of two methyl side groups per compound was considered. • Quaternary carbon atoms cannot react. • Maximum carbon number of 12 per molecule. • Exclusion of 2,3-dimethylbutenes. Branching was limited at the upper limit of two methyl side groups17 without considering quaternary carbon atoms17 in the olefins for the reaction network. This was derived from an analysis by Abbot and Wojciechowski,17 who found mostly linear or methyl-branched olefins in the product spectrum of ZSM-5. Highly branched olefins are not observed, and dibranched olefins have their methyl side groups on different carbon atoms.17 A low degree of branching for olefins in the range of C11−C20 on ZSM-5 is also reported by Tabak et al.18 Besides, 2,3-dimethylbut-1-ene and 2,3-dimethylbut-2-ene are excluded from the reaction network because 2,3dimethylbutenes were found only in minor amounts in the product spectrum17 as a result of pore size restrictions. Abbot and Wojciechowski12 observed that when converting pentenes decenes were the largest olefins detected with ZSM-5. In the present case, hexenes were formed in considerable amounts, especially at low temperatures. To account for secondary dimerization reactions of hexenes as well, the maximum carbon number in the reaction network was limited to 12. The global equilibrium distribution over all carbon numbers obtained with only the olefins described above present in the reaction mixture is compared to experimental data on olefin equilibration on ZSM-5 by Garwood.19 Using different feeds ranging from ethene to decene, identical products were obtained.19 This distribution was compared by Quann et al.20 to the calculated distribution with all possible isomers present or with reaction mixture of only n-1-alkenes. Neither the equilibrium among only n-1-alkenes nor that among all possible isomers was able to describe the experimentally observed compositions of Garwood.19 The difference was attributed to

Figure 4. Comparison of experimental equilibrium distribution measured by Garwood19 with our own calculations assuming steric constraints excluding olefins from the reaction network compared to the free gas phase.

different carbon numbers were calculated. Using only the olefins, which are present in the reaction network after application of the assumptions shown above, an equilibrium distribution that is close to the experimental results of Garwood19 is obtained. Thus, the use of steric constraints in the generation of the reaction network enables the kinetic model to describe the correct distribution of olefins on ZSM-5. The only irreversible elementary reactions in the reaction network are cracking reactions with a primary product carbenium ion. These carbenium ions were not considered as reactants,3 owing to their lower stability compared to secondary or tertiary carbenium ions. Primary product carbenium ions are concluded to be formed because ethene was observed experimentally, the formation of which must proceed via a primary carbenium ion. Hence, all possibilities for cracking via secondary educt and primary product carbenium ions are considered in the reaction network. Because cracking reactions from secondary to primary carbenium ions were included in the reaction network, reaction possibilities for cracking reactions from tertiary educt to primary product carbenium ions also have to be considered. Figure 5 shows a scheme of the considered reaction pathways in 1-pentene cracking. Reaction pathways described in literature12,13 involve the dimerization of two pentene molecules to a C10 intermediate, which can undergo subsequent cracking. At first, the 1-pentene feed in Figure 5 reacts to pentene isomers. These pentene isomers can undergo either monomolecular cracking to ethene and propene or dimerization to a decene isomer. Subsequent cracking of this C10 olefin leads to a broad spectrum of olefins. Further secondary dimerization and cracking reactions of these olefins are not displayed in Figure 5 for clarity, but they are considered in the reaction network and are relevant to describe the reactivity of olefins on ZSM-5. On the basis of these assumptions, a reaction network was generated involving 1292 cracking reactions and 293 dimerization reactions with 591 olefins in total. The number 11794


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Figure 5. Scheme of the reaction pathways for 1-pentene cracking on ZSM-5 considered in the reaction network.

Figure 6. Two different elementary reactions, which are described by the same single-event rate constant for cracking via tertiary educt to secondary product carbenium ions; the number of single events is two (forward direction) and four (backward direction) for the upper reaction and one (forward direction) and four (backward direction) for the lower reaction.

Differences between the two elementary reactions shown in Figure 6 resulting from the structures of the molecules are considered in the number of single events via the symmetry numbers of reactant and transition state. These symmetry numbers are calculated for every molecule with the conformations of the different transition states taken from literature.14,27,28 Because the single-event rate constants are defined depending on the types of carbenium ions involved in the elementary reaction, only a limited number of kinetic parameters has to be determined from the experimental data.3,4 The number of single events accounting for the different reaction rates of the two exemplary cracking reactions shown in Figure 6 is calculated only from the structure of the molecules. Thus, the application of the single-event kinetic modeling approach allows the description of multiple elementary reactions via a limited number of kinetic parameters without reducing the complexity of the considered reaction network.

of cracking reactions exceeded the number of dimerization reactions because of the irreversible cracking reactions with primary product carbenium ions. Primary propyl or butyl carbenium ions, for example, are also considered as products of cracking reactions. Secondary dimerization reactions of product olefins, e.g., propene or butenes, with each other and the feed are also included in the reaction network, thus accounting for the complex reaction possibilities between olefins and carbenium ions on the acid zeolite.14

4. SINGLE-EVENT KINETIC MODEL A large number of reaction possibilities exist in the catalytic cracking of 1-pentene on ZSM-5. To account for all possible reaction pathways leading to the formation of the decene intermediates, their isomerization, and further cracking, a large number of elementary reactions were considered. Hence, the single-event kinetic modeling approach is used to keep the number of kinetic parameters within acceptable limits. In the single-event approach, the rate constant for every elementary reaction is divided into two parts.14,22−25 The first part accounts for the different types of carbenium ions involved, e.g., primary, 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 ion.4,10,14,26 The second part of the rate constant accounts for the structure of the molecules by considering the entropy difference between reactant and transition state.3,14,22,24 This methodology is illustrated in Figure 6 for two different cracking reactions, which proceed via the same types of educt and product carbenium ions. Hence, both are described via the same kinetic parameter, which is in this case the single-event rate constant for cracking via a tertiary educt to a secondary product carbenium ion.

5. RATE EQUATIONS The concept of rate-determining steps was used to describe the reaction pathways in the acid-catalyzed cracking of olefins. Because skeletal isomerization reactions are considered to be equilibrated as steric constraints permit and side reactions such as cyclization or hydride transfer were negligible (deduced from product distribution), cracking and dimerization reactions are the only rate-determining steps in the reaction network.27,29 Overall, a catalytic cycle consists of hydrogen bonding of the olefin, its protonation, the rate-determining step, the deprotonation of carbenium ions, and the desorption. Apart from the rate-determining step, all elementary reactions were assumed to be quasi-equilibrated.4,14 Thus, the reaction scheme for pentene cracking on ZSM-5 is addressed by the single-event rate constants for cracking and 11795


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Table 1. Catalytic Cycle for the Derivation of the Reaction Rate for Cracking and Dimerization of 1-Pentene on ZSM-5 step 1

educt Oi(g)

product ⇌

equation

COi =

Oi

C tK phys, Oi pO

i

1 + ∑j K phys, Oj pO

j

σOi

K̃ prot(Or ; m) K̃ isom(Oi ; Or) COi

2

Oi

⇌

R+i

C R i+ =

3a

R+i

→

R+p + Ol(g)

̃ (m; n) C R + rCR (m; n) = nek CR i

3b

R+i + Ov(g)

→

R+q

̃ (m; n) C R +p rDIM(m; n) = ne kDIM i O

σ R i+

v

Figure 7. Scheme for the calculation of the single-event rate constant for dimerization from the single-event rate constant for cracking via forming an equilibrium constant for the rate-determining step. Two reaction pathways are shown starting from either the olefins Oi and Ov via dimerization as the rate-determing step or olefin Ow via cracking.

phase olefin Ov leading to the carbenium ion R+q in step 3b of Table 1 is the backward reaction of the corresponding cracking reaction. Consequently, the rate constant for dimerization can be expressed via the rate constant of the corresponding cracking reaction and the equilibrium constant of the rate-determining step.14 This procedure ensures the microscopic reversibility of the two elementary reactions, and consequently, a reaction pathway for cracking and the corresponding dimerization pathway can reach the gas-phase equilibrium composition between the educt and product olefins. Therefore, an equilibrium constant of the rate-determining step is calculated by multiplication of the equilibrium constants of the physisorption and protonation steps of both reaction pathways as well as the gas-phase equilibrium constant between the educt and product olefins of the pathways.14 This scheme for expressing the single-event rate constant for a dimerization reaction via the single-event rate constant for cracking is displayed in Figure 7. Figure 7 shows one reaction pathway for dimerization starting from the gas-phase olefins Oi and Ov, leading to the rate-determining step and another reaction pathway for cracking starting from the gas-phase olefin Ow. Both reaction pathways are connected via the gas-phase equilibrium constant

dimerization. All isomerization reactions of olefins with the same carbon number are expressed by the corresponding equilibrium constants. This reaction scheme is presented in Table 1 together with the equations to describe the elementary steps.14 Step 1 in Table 1 represents the physisorption of a gas phase olefin Oi on the zeolite, which is expressed as adsorbing following a Langmuir isotherm.5,14 The protonation of physisorbed olefins is described in step 2 of Table 1 and leads to the formation of the carbenium ion Ri+. The protonation of olefins is described via the protonation of a reference olefin Or.3,10 These reference olefins are either 2methylalkenes4 or 1-alkenes8 for C4 and C3 olefins. Step 3a is the rate-determining step of a reaction pathway for cracking. The product carbenium ion R+p and the gas-phase olefin Ol are formed from the larger carbenium ion R+i . The reaction rate for the cracking reaction from an educt carbenium ion of type m to a product carbenium ion of type n is a first-order reaction4 at the concentration of the educt carbenium ion on the surface ̃ (m; n) only depends on CR+i . The single-event rate constant kCR the types of carbenium ions involved in the cracking reaction, whereas the number of single events ne is accounting for structural differences between certain carbenium ions.3,4,8 The dimerization reaction between the carbenium ion R+i and a gas 11796


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Industrial & Engineering Chemistry Research K̃ eq, thus ensuring the microscopic reversibility.14 The following equation is used to calculate the single-event rate constant for dimerization from the single-event rate constant for cracking.14

R R i+ =

k

+

j=1

−

∑ rDIM(R i+ , Ov ; R k+) k

All carbenium ions in the reaction network are considered by the summation over the index k.14 Rate-determining steps forming the carbenium ion R+i from carbenium ion R+k are added to the rate of formation of carbenium ion R+i ; others consuming it are subtracted. The olefin Ov is arbitrary and does not affect the rate of the rate-determining step for cracking.4 The flow rates of the olefins considered in the reaction network are obtained by solving the design equation for an isothermal plug flow reactor.4,14,31 Because of the equilibrium between isomers of one carbon number, the rates of formation of all olefins with one carbon number are added by summation over the number of isomers niso for that carbon number.

No change in the symmetry number of educts and products is assumed for physisorption; thus, Kphys,Oi is equal to the corresponding single-event equilibrium constant. The different reference olefins in Figure 7 are labeled to clarify from which olefin they are stemming, with Oir being the reference olefin of olefin Oi. By equating the reaction rate of the dimerization pathway and the reaction rate for the corresponding cracking pathway, it can be shown that the equilibrium condition between the gas phase olefins is obtained. This proves that microscopic reversibility between different reaction pathways is ensured. The fact that all double-bond and skeletal isomerization reactions are in thermodynamic equilibrium is used to implement the experimentally observed quasi-equilibrium between isomers in the derivation of the reaction rate.14 Therefore, the molar flows of all isomers corresponding to one carbon number are combined, and the equilibrium mole fractions of these isomers are determined under one experimental condition. To obtain the molar flow of one specific olefin for calculating the reaction rate, the molar flow of all isomers with this carbon number is multiplied with the mole fraction of this olefin in isomerization equilibrium. Thus, for example, the molar flow of 1-butene is obtained from the molar flow of all butene isomers multiplied with the mole fraction of 1-butene in equilibrium among 1-butene, cis-2-butene, trans-2butene, and isobutene. Consequently, the number of differential equations necessary to calculate the reaction rate of all butene isomers is reduced to one. When considering larger olefins, such as decenes, this reduction becomes more advantageous. This procedure is comparable to the a posteriori lumping applied by Cochegrue et al.30 or by Guillaume et al.,9 who also consider equilibria between isomerization reactions. The rate of formation of an olefin ROi is obtained by summing up the reaction rates of the different reaction pathways consuming or forming olefin Oi.14

dFOCN dW

n iso

=

∑ RO

i

(4)

i=1

Thus, the molar flow rate FOCN of all olefins with the carbon number CN is obtained, with which the flow rate of a separate olefin is calculated from its mole fraction in isomerization equilibrium among isomers with one carbon number. This ordinary differential equation is solved by integrating the molar flow FOCN over the mass of catalyst W.

6. THERMODYNAMIC DATA Because of the significant increase in the number of olefin isomers with carbon number, experimental thermodynamic data is only available for olefins up to C6. To obtain Gibbs energies of larger olefins, estimation schemes have to be used. For this task, the Benson contribution method is applied to calculate thermodynamic data for C7−C12 olefins.32,33 Because experimental Gibbs energies proved to be more accurate in the calculation of equilibrium compositions, experimental thermodynamic data from Alberty and Gehrig34 are used in the calculation of equilibrium constants for C2− C6 olefins. To be used together, Gibbs energies from both sources are referred to gaseous H2 and graphite.34−36 In the calculation of equilibria, cis and trans isomers are distinguished because cis and trans isomers have different enthalpies.32,34 Thus, an isomer group of cis and trans isomers is formed to account for the resulting different Gibbs energies.37 ⎛ ⎛ −ΔGcis ⎞ ⎛ −ΔGtrans ⎞⎞ ⎟ + exp⎜ ⎟⎟ ΔG IG = −RT ln⎜exp⎜ ⎝ RT ⎠⎠ ⎝ ⎝ RT ⎠

nDIM

∑ rj(Rl+; R q+ , Oi) − ∑ rj(Rl+ , Oi ; R q+) + R R

∑

Ov ; R i+)

(3)

(1)

R Oi =

k

rDIM(R k+ ,

k

̃ (n ; m ) kDIM = K̃RDS ̃ (m ; n) k CR K̃ eqK phys, Ow K̃ prot(Orw , m) K̃ isom(Ow ; Orw) = K̃ prot(Ori , n) K̃ isom(Oi ; Ori) K phys, Oi

nCR

∑ rCR(R k+; R i+ , Ov) − ∑ rCR(R i+; R k+ , Ov)

(5)

This Gibbs energy of an isomer group ΔGIG is used to calculate equilibrium constants in the model when cis and trans isomers are involved in the reaction.14 Thermodynamic data for physisorption and protonation are taken from theoretical calculations by Nguyen et al.,38 who give linear correlations to determine the thermodynamic data for physisorption and protonation on ZSM-5.38 For protonation, a discrimination between 1-alkenes as well as 2/3/4-alkenes is applied,38 but only the data for 1-alkenes are used to describe physisorption.14 The physisorption data from Nguyen et al.38 corresponds to linear olefins. For the description of linear and branched olefins in the reaction network, the physisorption

+ i

j=1

(2)

Using the sum over the number of cracking reactions nCR, the formation of olefin Oi from cracking of the educt carbenium ion R+l to the product carbenium ion R+q and olefin Oi is considered. The consumption of Oi is taken into account via the sum over all dimerization reactions nDIM. Reaction rates of carbenium ions stemming from olefin Oi are comprehended by RR+i , which is explained below:14 11797


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Industrial & Engineering Chemistry Research parameters for 1-alkenes38 seem to be better suited; thus, only these are applied.14 For isobutene, separate thermodynamic data are used, which have been also taken from Nguyen et al.39

to the values of the parameters. The values of the activation energies are physically consistent because lower activation energies are obtained when more stable carbenium ions are involved in the elementary reaction.4,8,42 Using the parameters given in Table 2, a good agreement between modeling and experimental results is obtained as shown in the parity plots for ethene, propene, butenes, pentenes, and C6−C12 olefins in Figure 8. The proposed single-event kinetic model for 1-pentene cracking on ZSM-5 reproduces the experimental data points over a wide temperature range of 100 K as well as for two different partial pressures and flow rates at the reactor inlet. The mole fractions of the olefins, from which the parity plots in Figure 8 are determined, are plotted over the modified residence time at all experimental conditions given in Figures S3−S7. The modified residence time (or contact time) is calculated by dividing the catalyst mass with the initial molar flows at the reactor inlet (of nitrogen and 1-pentene). The influence of the reaction network on the parameter estimation results is tested by comparing a variety of different reaction networks. Therefore, alternative reaction networks with more than two methyl side groups at maximum with hydrocarbons containing quaternary carbon atoms and different assumptions regarding the formation of ethene and primary product carbenium ions or a different maximum carbon number for olefins are evaluated. These reaction networks are listed in Table S3. Comparing the residuals between model and experimental data as well as the confidence intervals, the reaction network RN1 from Table S3 used for determining the kinetic parameters shown in Table 2 and the parity plot in Figure 8 proved best. A slightly smaller sum of squares of residuals is obtained with considering 14 carbon atoms as the maximum carbon number, as shown in Table S4 for the parameter estimation results with reaction network RN8. Because only minor improvements result from considering 14 instead of 12 carbon atoms as the maximum carbon number, 12 carbon atoms are a reasonable limit for the maximum size of olefins in the reaction network. Different assumptions in the reaction network regarding the formation of primary product carbenium ions in cracking reactions also lead to the consideration of the activation energy ECR a (t; p). A reaction network considering the formation of primary carbenium ions only when no other possibilities for cracking are available, i.e., in case of linear pentenes, results in a slightly worse description of the experimental data than a reaction network including all reaction possibilities via secondary to primary carbenium ions. One advantage of a microkinetic model is the fact that the resulting kinetic parameters could be also used for different reaction conditions. Because the single-event kinetic model presented here is based on elementary reactions, the obtained kinetic parameters are fundamental, so extrapolation should be possible. To investigate this further, data points at higher temperatures, which were not included in the parameter estimation, are compared to model predictions. The results are shown in Figure 9 with the molar flows at the reactor outlet divided by the molar flow of 1-pentene at the inlet being plotted at different temperatures for low conversions. A good agreement between model predictions and experimental data is observed in Figure 9 until temperatures of approximately 800 K. At higher temperatures, a qualitative description of the trends in the experimental data is still obtained with the kinetic model. Here, however, an over-

7. PARAMETER ESTIMATION The existence of thermodynamic equilibria between all isomers of one carbon number further reduces the number of singleevent rate constants to be determined from the experimental data; thus, only the single-event rate constants for cracking have to be estimated. With quaternary carbon atoms being excluded from the reaction network, cracking reactions with tertiary product carbenium ions become impossible. This leads to five unknown kinetic parameters in the model, which are the four CR CR activation energies for cracking, ECR a (s; p), Ea (t; p), Ea (s; s) CR and Ea (t; s), as well as the pre-exponential factor. A reparametrization of the single-event rate constant is applied with the mean temperature of 683 K being used as the reference temperature.40,41 ̃ (m ; n) = ACR k CR

⎛ E CR (m ; n) ⎞ T ⎟ exp⎜ − a Tref RTref ⎠ ⎝

⎛ E CR (m ; n) ⎛ 1 1 ⎞⎞ exp⎜⎜ − a ⎜ − ⎟⎟⎟ R Tref ⎠⎠ ⎝T ⎝

(6)

The temperature dependence of the pre-exponential factor is also expressed via the reference temperature Tref. The preexponential factor in the single-event kinetic approach is calculated from the Boltzmann constant, the temperature, the Planck’s constant, and the intrinsic entropy difference between reactant and transition state.22,42−44 ACR =

⎛ ΔS 0,̂ ≠ ⎞ kBT ⎟⎟ exp⎜⎜ ℏ ⎝ R ⎠

(7)

Thus, the linear temperature dependence of the preexponential factor in the calculation of the single-event rate constant is based on the derivation of the single-event kinetic approach. A Levenberg−Marquardt algorithm is applied to minimize the sum of squares of residuals between mole fractions in the reactor predicted by the model and the experimental data.40 Therefore, the solver lsqnonlin is used in MATLAB with ode15s being applied to determine the molar flows of olefins in the reactor model. At the reactor inlet, the molar flows of the feed containing 1pentene and nitrogen are set as initial conditions. Because of the high purity of the 1-pentene feed of 99%, impurities in the feed are neglected. The estimated activation energies and the pre-exponential factor are given in Table 2 with their corresponding 95% confidence intervals. All kinetic parameters are significant, and the confidence intervals are small compared Table 2. Estimated Pre-Exponential Factor and Activation Energies for 1-Pentene Cracking on ZSM-5 with 95% Confidence Intervals ACR ECR a (s; p) ECR a (t; p) ECR a (s; s) ECR a (t; s)

2.18 × 1016 ± 3.0 × 1015 s−1 229.6 ± 0.9 kJ/mol 211.8 ± 1.4 kJ/mol 199.7 ± 0.8 kJ/mol 171.2 ± 0.8 kJ/mol 11798


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Figure 8. Parity plots between model and experimental data for ethene, propene, butenes, pentenes as well as C6−C12 olefins with single-event rate constants calculated from Table 2.

suitability of the applied procedure to model the influence of the zeolite via excluding reaction pathways with sterically demanding olefins from the reaction network. Parameter estimation results obtained with different reaction networks yield a worse description of the experimental dependencies, as shown in Table S4. Thus, comparing different reaction networks shows that all the considered elementary reactions are relevant to describe the reactivity. The reaction networks with olefins containing quaternary carbon atoms or more than two methyl side groups are least suited as indicated by the sum of squares of residuals in Table S4. The confidence intervals of activation energies obtained with sterically demanding olefins, e.g., containing quaternary carbon atoms, in the reaction network include zero. This further supports the assumptions made on steric constraints in the zeolite pores and the methodology of incorporating the influence of the catalyst into the kinetic model. The implementation of thermodynamic equilibria between all isomers of one carbon number in the derivation of the reaction rate drastically reduces the number of kinetic parameters to one pre-exponential factor and four activation energies. Thus, significant kinetic constants with small confidence intervals in Table 2 are determined from the experimental data set. The shown procedure is based on the assumption of equilibrated isomerization reactions. This assumption is not strictly valid for the different pentene isomers at low conversions, as displayed in Figure 1. However, an improvement of the model predictions by estimating kinetic parameters for isomerization reactions is not expected, which is why the assumption of equilibrated isomerization can be maintained. The number of kinetic parameters is further reduced by expressing the single-event rate constant for dimerization reactions via the single-event rate constant for cracking, which is used in the rate equation of the reverse reaction pathway. In Table 1, dimerization pathways are described by an Eley− Rideal mechanism with a carbenium ion being adsorbed on the zeolite and reacting with a gas-phase olefin. A Langmuir− Hinshelwood mechanism would also be possible. However, the

Figure 9. Extrapolation of the kinetic model to data points at higher temperatures, which were not included in the parameter estimation, using kinetic parameters from Table 2.

prediction of ethene and propene in conjunction with an underprediction of butenes as well as C6−C12 olefins is observed. This is shown in Figure S8 for additional data points until 843 K.

8. DISCUSSION OF THE RESULTS The influence of the catalyst is considered in the model by excluding reaction pathways, which are possible only in the gas phase because of steric constraints in the pores of ZSM-5.14 The assumptions which olefins are present in the reaction network are based on experimental observations.12,17 As shown in Figure 4, the experimentally obtained global equilibrium distribution of C2−C12 olefins is reproduced under these assumptions.19 Thus, the proposed reaction network with the considered olefins describes the approach to equilibrium in the kinetic model at long residence times according to experimental data.19 Consequently, a good agreement between modeling and experimental results is also observed at high conversions in Figure 8. Thus, the considered elementary reactions capture the reactivity to the observed product distribution. This proves the 11799


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A minor scattering around the diagonal is also observed in the parity plot for the mole fraction of ethene in Figure 8. This results from the partial pressure dependence because for the higher partial pressure of 70.3 mbar an overprediction is observed, and for 42.7 mbar, an underprediction is observed. This correlation is evident from Figure S3. Because of the low absolute deviations in the mole fraction of ethene in Figure 8, no systematic deviation between modeling and experimental results is assumed in this case. At the lowest temperature of 633 K, minor deviations between modeling and experimental results lead to some scatter in the parity plots in Figure 8, especially for propene and the C6−C12 olefins. This can be concluded from Figures S3−S7. Taking the accuracy of reproduction measurements into account, which is shown in Figure S9, this scatter is considered significant. The estimation of Gibbs energies for C7−C12 olefins according to the Benson contribution method32 is regarded as the reason for these deviations at 633 K. At low temperatures, the equilibrium favors dimerization reactions; thus, the reactions of the feed mainly proceed via the formation of a C10 intermediate and its subsequent cracking. Consequently, the influence of estimated Gibbs energies for the C7−C12 olefins is comparably larger at this lowest temperature, indicating that the observed deviations are due to the estimates of thermodynamic data for C7−C12 olefins. Considering the good parity observed in Figure 8 and the ability to use the kinetic parameters for extrapolation purposes as shown in Figure 9, these deviations are not regarded to affect the model validity. As shown in Figure 9, the temperature dependence of the rate constants obtained with the pre-exponential factor and activation energies from Table 2 allows the extrapolation beyond the experimentally covered temperature range. Fundamental kinetic parameters can be obtained with the single-event kinetic modeling approach.3 Thus, using data points not included in the parameter estimation, the ability of the kinetic model for extrapolation purposes can be shown by Figure 9. Judging from the agreement with experimental data and the extrapolation, the kinetic parameters in Table 2 can be considered as fundamental for olefin cracking. The good agreement between modeling and experimental results in Figure 8 is not achieved by an overparametrization of the kinetic model because only four activation energies and one pre-exponential factor are used. For example, compared to a power-law approach for the derivation of the reaction rate, intrinsic kinetic parameters for 1-pentene cracking on ZSM-5 are obtained with the single-event kinetic model. These are valid over a wide range of experimental conditions, with different temperatures, partial pressures of 1-pentene in the feed, flow rates at the reactor inlet, and residence times being varied in the experimental data set. In the present model, intracrystalline diffusion was not considered, although it might play a significant role when studying reactions on ZSM-5. To prevent diffusion effects from distorting the kinetic data, the same crystallite size was used for every experiment. Furthermore, the pellet size remained constant throughout all measurements. For the crystallite size given in section 2.1, the Weisz−Prater criterion was calculated. Because its value is several magnitudes smaller than unity even for the highest crystallite sizes and temperatures, diffusional effects should be negligible. Nevertheless, it might be possible that the experimental results are not totally free of intracrystal-

estimated kinetic parameters are reasonable, which is why the assumed mechanism seems to be appropriate. The estimated value for the pre-exponential factor in Table 2 of 2 × 1016 s−1 is considered as comparatively high. An order on the magnitude of 1 × 1013 s−1 is expected for an elementary reaction on the catalyst surface.45 Kumar et al.43 also report preexponential factors in the range of 2 × 1016 s−1, for example, for demethylation or deprotonation in the methanol to olefins process on ZSM-5. This value refers to a monomolecular reaction without significant entropy change. During the cracking reactions studied in this work, the entropy is changing significantly. A reason for the high pre-exponential factor in Table 2 might be the use of calculated thermodynamic data38 for physisorption and protonation of olefins on ZSM-5. For example, higher or lower values for the physisorption entropies of all olefins in ZSM-5 directly affect the estimated preexponential factor, as can be seen from the rate equations in Table 1. The values of the activation energies are, however, consistent, and they decrease with more stable carbenium ions being involved in the elementary reaction. Thus, ECR a (s; p) is CR CR CR larger than ECR a (t; p), Ea (s; s) larger than Ea (t; s), and Ea (t; p) is larger than ECR (t; s) (Table 2). a The kinetic parameters estimated for 1-pentene cracking can be compared to experimental46 and theoretical47 activation energies for olefin cracking from literature. Chen et al.46 studied butene, pentene, and hexene feeds on ZSM-5 at conversions below 15%. Mazar et al.47 calculated activation energies for cracking from theory. Both46,47 obtain activation energies for cracking that are in most cases comparable to the values given in Table 2. The estimated activation energies in Table 2 reflect the different reaction pathways shown in Figure 5. Monomolecular cracking of pentenes to ethene and propene is favored by high temperatures, and because of this, ECR a (s; p) has the highest activation energy. In contrast to that, low temperatures favor the reaction pathways via dimerization and subsequent cracking, which proceed via lower activation energies. Dimerization reactions are also influenced, however, by the corresponding equilibrium constant, e.g., between pentenes and decenes, which decreases with increasing temperature. These dependencies can be concluded from the experimental selectivities in Figure 3 as well as the estimated activation energies. Higher partial pressures of the reactant (Figures S3− S7) have a comparable effect on the dimerization equilibrium and the reaction pathways in Figure 5 as lower temperatures. Thus, the kinetic modeling gives mechanistic insight into the complex reaction pathways in olefins cracking on ZSM-5 and allows quantification of the effects of different reaction conditions with the estimated parameters. Using these kinetic parameters, a good reproduction of the experimental data is obtained in Figure 8. The largest relative deviations in Figure 8 are observed in the parity plot for the C6−C12 olefins. The determination of mole fractions for C6−C12 olefins has, however, also the greatest experimental uncertainty because of the large number of different peaks in the GC chromatogram. Because the absolute mole fractions of the combined C6−C12 olefins are relatively low for most of the experimental conditions, the separate peaks in the GC chromatogram also have comparatively small areas. Thus, the comparatively large relative deviations between model and experiment for the C6−C12 olefins in Figure 8 are not regarded to be systematic. 11800


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Industrial & Engineering Chemistry Research line diffusion effects, taking into account the very small pores of the zeolite.

Notes

9. CONCLUSIONS Using the single-event kinetic modeling approach, kinetic parameters for the cracking of 1-pentene on ZSM-5 are estimated from an experimental data set. The influence of the catalyst was implemented in the kinetic model via steric constraints being imposed on sterically demanding olefins by the pore size of ZSM-5. The assumptions according to which olefins are excluded from the reaction network compared to the free gas phase are based on experimental observations.12,17 With these, the equilibrium distribution19 of olefins on ZSM-5 can be described. The assumption of equilibrated isomerization reactions in the derivation of the reaction rate for 1-pentene cracking reduces the number of kinetic parameters. By this procedure, an overparameterization of the kinetic model is avoided without reducing the complexity of the reaction network. As a further consequence, the remaining five kinetic parameters can be estimated significantly with small confidence intervals. The good agreement between modeling and experimental results shows that the underlying reaction network is appropriate to describe the reactivity of 1-pentene on ZSM-5. The exclusion of different species is confirmed and allows insight into mechanistic pathways on the catalyst, leading to the observed product distribution. Furthermore, the influence of temperature on product distribution can be shown with the kinetic model: Higher temperatures lead to an increase of monomolecular cracking reactions, which is manifested in a higher yield of propene and ethene because these two are the only possible products for monomolecular pentene cracking. This pathway has to proceed via energetically unfavored primary ethyl carbenium ions, which means that monomolecular cracking shows higher activation energies. In contrast, lower temperatures favor dimerization reactions, the products of which then undergo subsequent cracking. Such reaction pathways led to a product distribution containing more butenes and hexenes, but less ethene: When there are energetically more favored pathways possible, ethene formation is not significant. In summary, the temperature dependence of the selectivities can be deduced from the estimated activation energies. The single-event kinetic modeling approach is based on elementary reactions; thus, fundamental kinetic parameters are obtained that are also valid outside of the range of experimentally covered conditions. This allows the use of the kinetic model for optimization purposes of the product distribution and to find reactor configurations that maximize or minimize the yields of certain olefins.

ACKNOWLEDGMENTS We acknowledge the financial support from Clariant Produkte (Deutschland) GmbH and fruitful discussions in the framework of MuniCat. T.v.A. and S.S. acknowledge the support from the TUM Graduate School.

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The authors declare no competing financial interest.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b02629. Experimental data used for parameter estimation and comparison of different reaction networks. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 11801

LIST OF SYMBOLS ACR = Pre-exponential factor for the single-event rate constant (s−1) CR+i = Concentration of carbenium ion R+i on the zeolite surface (mol/kgcat) COi = Concentration of physisorbed olefin Oi on the zeolite surface (mol/kgcat) Ct = Total concentration of acid sites on the zeolite (mol/ kgcat) ECR a (s; p) = Activation energy for cracking with secondary educt carbenium ion to primary product carbenium (J/mol) ECR a (t; p) = Activation energy for cracking with tertiary educt carbenium ion to primary product carbenium (J/mol) ECR a (s; s) = Activation energy for cracking with secondary educt carbenium ion to secondary product carbenium (J/ mol) ECR a (t; s) = Activation energy for cracking with tertiary educt carbenium ion to secondary product carbenium (J/mol) F = Molar flow of feed olefin and inert at the reactor inlet (mol/s) FOCN = Molar flow of all olefin isomers OCN with carbon number CN in the reactor (mol/s) ΔGcis = Gibbs energy of cis isomer (J/mol) ΔGIG = Gibbs energy of an isomer group consisting of cis and trans isomer (J/mol) ΔGtrans = Gibbs energy of trans isomer (J/mol) ℏ = Planck’s constant (J/s) kB = Boltzmann constant (J/K) ̃ (m; n) = Single-event rate constant for cracking reaction kCR between educt carbenium ion of type m to product carbenium ion of type n (1/s) ̃ (m; n) = Single-event rate constant for dimerization kDIM reaction between educt carbenium ion of type m to product carbenium ion of type n (1/bar s) K̃ isom(Oi; Or) = Single-event equilibrium constant for isomerization of olefin Oi to reference olefin Or (-) Kphys,Oi = Equilibrium constant for physisorption of olefin Oi (1/bar) K̃ prot(Or; m) = Single-event equilibrium constant for protonation of reference olefin Or to carbenium ion of type m (-) K̃ prot(Ori , m) = Single-event equilibrium constant for protonation of reference olefin Or corresponding to olefin Oi to carbenium ion of type m (-) K̃ RDS = Single-event equilibrium constant of the ratedetermining step of a reaction pathway (1/bar) m = Type of carbenium ion: tertiary, secondary or primary (-) n = Type of carbenium ion: tertiary, secondary or primary (-) ne = Number of single events (-) nCR = Number of all cracking reactions in the reaction network (-) DOI: 10.1021/acs.iecr.5b02629 Ind. Eng. Chem. Res. 2015, 54, 11792−11803

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nDIM = Number of all dimerization reactions in the reaction network (-) niso = Number of olefin isomers for one carbon number (-) pOv = Partial pressure of olefin Ov (bar) rCR(m; n) = Reaction rate for cracking as rate-determining step from educt carbenium ion of type m to product carbenium ion of type n (mol/kgcat s) rCR(R+k ; R+i , Ov) = Reaction rate for cracking as ratedetermining step from educt carbenium ion R+k to product carbenium ion R+i and olefin Ov (mol/kgcat s) rDIM(m; n) = Reaction rate for dimerization as ratedetermining step from educt carbenium ion of type m to product carbenium ion of type n (mol/kgcat s) rDIM(R+i , Ov; R+k ) = Reaction rate for dimerization as ratedetermining step from educt carbenium ion R+i and olefin Ov to product carbenium ion R+k (mol/kgcat s) R = Universal gas constant (J/mol K) ROi = Rate of formation of olefin Oi (mol/kgcat s) RR+i = Rate of formation of carbenium ion R+i (mol/kgcat s) ΔŜ0,≠ = Intrinsic entropy difference between reactant and transition state (J/mol K) σOi = Symmetry number of olefin Oi (-) σR+i = Symmetry number of carbenium ion R+i (-) T = Temperature (K) Tref = Reference temperature, mean of experimental temperatures (K) W = Weight of catalyst in the reactor (kgcat)

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NOTE ADDED AFTER ASAP PUBLICATION This paper was published ASAP November 19, 2015. Corrections were made to the List of Symbols section, and the paper was reposted December 2, 2015.

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Single-Event Kinetic Model for 1-Pentene Cracking ... - ACS Publications

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