Unraveling Diffusion and Other Shape Selectivity ... - ACS Publications

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Unraveling Diffusion and Other Shape Selectivity Effects in ZSM5 Using n‑Hexane Hydroconversion Single-Event Microkinetics B. D. Vandegehuchte, J. W. Thybaut,* and G. B. Marin Laboratory for Chemical Technology, Ghent University, Technologiepark 914, Ghent B-9052, Belgium S Supporting Information *

ABSTRACT: Potentially dominant factors governing the shape selectivity in n-hexane hydroconversion over a Pt/H-ZSM5 catalyst were evaluated by means of single-event microkinetic (SEMK) model regression against experimental data. The observed product distribution could be adequately modeled, and a corresponding physically meaningful interpretation could be made only when accounting for intracrystalline diffusion limitations for each hexane isomer involved in the reaction network, rather than considering physisorption effects or transition-state shape selectivity. Simultaneous diffusion and reaction inside the catalyst crystallites were expressed via Fick’s second law, while the alkane Fick diffusion coefficients were assessed by explicitly accounting for mixture nonideality effects. A 3-fold lower diffusion coefficient was found to be required for 3-methylpentane compared with 2-methylpentane to explain the typically high selectivity toward the latter alkane. Once formed inside the catalyst crystallite, dimethylbutane isomers remained nearly immobile as was evident from their significantly lower diffusion coefficients. Reaction at the crystallite external surface was primarily responsible for the marginal conversion toward the former species, as observed experimentally. cracking products formed exclusively from (s;s) β-scission are reminiscent of the negligible formation of tribranched isomer species inside the zeolite framework.19,23,25,26 Instead, cracking of intrinsically less reactive monobranched and especially dibranched isomer species has been proposed.18,21,27 The production of dibranched alkanes is, however, hardly noticeable from the hydrocracking product distribution. This is the result of the nearly fully constrained diffusion of these species through the ZSM5 framework.10,11,14,20,28 The latter may result in an apparently pronounced debranching and/or cracking reactivity upon the formation of these dibranched isomers, and provides an explanation for the peculiarly high cracking affinity of the catalyst at the expense of feed isomerization.9 While product and transition-state shape selectivity within a ZSM5 framework are well-recognized for dibranched and tribranched hydrocarbons, respectively, the deviation from thermodynamic equilibrium within the monobranched alkane isomer lump has not yet been fully resolved. Earlier experimental work proposed transition-state shape selectivity in the branching of the n-alkane reactant over a protonated cyclopropane (PCP) transition state as the primary cause of the typically higher selectivity toward the 2-methyl-branched isomer.3,18,19,23 In those works, no pronounced differences in the effective diffusion coefficients of monobranched decanes were observed, and hence, intracrystalline diffusion effects were not taken into account. Conversely, Kinger and Vinek22 ruled out transition-state shape selectivity by taking into account

1. INTRODUCTION Shape selectivity is often exploited in catalysis to fine-tune the product distribution of a target reaction to the market demands.1,2 Zeolites are ideally suited for this endeavor thanks to their well-defined framework structures, exhibiting narrow pore size distributions with pore dimensions commonly approaching the kinetic diameters of hydrocarbons. Zeolites with 10-membered pore apertures, such as ZSM22 and ZSM5, have been successfully optimized for selective hydroconversion toward products in the distillate and in the naphtha range, respectively.3 ZSM5 is a pentasyl-based zeolite that is widely applied in the petroleum industry thanks to its high stability and catalytic activity.4,5 It is composed of 1.0 nm elliptical straight channels (0.51 nm × 0.55 nm) and 1.2 nm circular sinusoidal channels (0.53 nm × 0.56 nm) that perpendicularly intersect.6,7 Cavities formed at the channel intersections have a diameter of about 0.85 nm.8 The pore dimensions approach the molecular diameters of cyclic and branched hydrocarbons,9−11 which potentially results in a complex interplay of reactant, product, and/or transition-state shape selectivity impacting the catalyst performance in numerous industrially relevant processes such as benzene alkylation, toluene disproportionation, methanol to olefins conversion, olefin oligomerization, methane aromatization, catalytic cracking, and, as already mentioned, hydrocracking.1,12−15 Recently, pore mouth catalysis was identified in the selective hydrogenation of fatty acids over Pt/H-ZSM5, which emphasizes once more its versatility in countless catalytic processes.16,17 The branched isomer yields obtained from n-alkane hydrocracking over a ZSM5 catalyst are usually much lower in comparison with the product distribution obtained over a large-pore (US)Y catalyst.3,18−21 Therefore, molecular weight reduction of linear alkanes is mostly achieved by the use of ZSM5 catalysts rather than feed isomerization.8,22−24 The high yields of © 2014 American Chemical Society

Special Issue: Alı ́rio Rodrigues Festschrift Received: Revised: Accepted: Published: 15333

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in hydrocarbon conversion over one of the most frequently applied zeolite catalysts in industry would allow a comprehensive analysis of the observed product slate and, moreover, advance considerably the model-guided synthesis of related materials.

fast intramolecular alkyl shifts, which, over non-shape-selective catalysts, establish thermodynamic equilibrium within the isomer lump from moderate feed conversions on.29,30 Instead, the authors proposed intracrystalline mass transport limitations, which were less pronounced as the methyl branch was located toward the end of the molecular carbon chain. In the more recent literature, distinctly higher diffusion coefficients were indeed found for the 2-methyl alkane compared with any other methyl-branched isomer.31−35 In the same context, it was convincingly demonstrated that the shape selectivity involved in n-decane hydroconversion over MFI frameworks could be significantly attenuated by synthesizing nanosheets.36 The latter observation is reminiscent of mass transport limitations, which become more pronounced as the length of the diffusion path through the catalyst crystallite increases. Subtle differences in van der Waals interactions with the MFI framework were observed from gravimetric and chromatographic measurements.37,38 The strongest stabilization by physisorption was observed for the n-alkane, which according to Monte Carlo simulations39 is significantly favored in the lower temperature range. 2-Methylpentane and 3-methylpentane showed quite similar physisorption behavior in MFI frameworks at kinetically relevant temperatures that is slightly weaker than that of the corresponding n-alkane.34,35,37,38,40 A similar conclusion could be drawn for both dimethylbutanes. Differences in physisorption parameters are commonly denoted as physisorption selectivity exhibited by the catalyst.41 Whether or not physisorption selectivity is responsible for the peculiar isomer selectivities observed during alkane hydroconversion on ZSM5 catalysts remains, however, an unresolved matter to date. The aim of this work was to identify the dominant factors in the shape selectivity during n-hexane hydroconversion over Pt/H-ZSM5. This was accomplished by performing fundamental model regression against experimental data while systematically incorporating intracrystalline diffusion limitations, transition-state shape selectivity, and physisorption selectivity. Physisorption selectivity is not categorized as a shape selectivity effect induced by steric effects,42 but it is inherent to the catalyst nonetheless and could strongly impact the product distribution. Other reported forms of shape selectivity observed on ZSM5 catalysts, such as pore mouth catalysis in fatty acid hydrogenation,16 were not considered in this work. The reaction kinetics was assessed following the single-event microkinetic (SEMK) methodology, which is based upon the reaction family concept.43−46 The SEMK model allows the catalyst role in the overall kinetics to be identified via so-called “catalyst descriptors”, which are model parameters that specifically account for the catalyst properties.47 Doing so brings a SEMK-model-based catalyst design within reach that is merely based on a sensitivity analysis with respect to the catalyst descriptors, as recently demonstrated for Pt/H-ZSM22 in alkane hydroisomerization48 and for Pt/H-ZSM5 in xylene isomerization.49 n-Hexane was chosen as the model component because, unlike any larger feed alkane, no cracking of dibranched hexane isomers is expected. The latter can convert toward lighter alkane fragments over unstable primary ions, which is experimentally not observed. As a result, a product distribution that almost exclusively comprises 2-methyl- and 3methylpentane is obtained,28,50 and the typically higher isomerization affinity toward 2-methylpentane could be investigated up to high feed conversions while avoiding excessive cracking. A clear understanding of the shape selectivity involved

2. PROCEDURES 2.1. Catalytic Activity Testing and Data Treatment. A commercially available H-ZSM5 catalyst (CBV 2802) with a Si/Al ratio of 13751 was loaded with 0.5 wt % platinum by incipient wetness using an aqueous Pt(NH4)3Cl2 solution. The catalyst crystallite dimensions ranged from 0.4 to 0.8 μm.37 The zeolite powder was calcined ex situ under flowing oxygen at 823 K for 1 h. Afterward, the catalyst was shaped into pellets with diameters of 400−710 μm by sequential compressing, crushing, and sieving. A total of 4.85 g of catalyst was loaded into a Berty-type bench-scale continuously stirred tank reactor (CSTR).29,52,53 The catalyst was reduced in situ under flowing hydrogen at 673 K for 4 h to convert Pt into its metallic form. A total of 25 n-hexane hydroconversion experiments were carried out at 503−523 K, 1−3 MPa, hydrogen-to-hydrocarbon inlet molar ratios of 50−100, and space times ranging from 94 to 429 kg s mol−1. No catalyst deactivation was observed during experimentation. The reactor effluent was analyzed by means of a Hewlett-Packard 5890 Series II gas chromatograph equipped with a flame ionization detector and a nonpolar capillary column coated with a 0.25 μm polydimethylsiloxane film. The measured effluent compositions were converted into molar outlet flow rates afterward by satisfying a 100% atomic carbon balance. The latter was verified by means of methane that was added to reactor effluent as internal standard.53 The total n-hexane (nC6) conversion is defined as X tot =

Fn0C6 − FnC6 Fn0C6

(1)

where F denotes the experimental flow rate. The yield of a particular hexane isomer product i is defined as Xi =

Fi 0 FnC 6

(2)

The total isomer yield Xiso is determined as the sum of all of the individual isomer product yields, and the total cracking product yield is defined as Xcra = X tot − X iso

(3)

2.2. Parameter Estimation. An initial estimation of the model parameters was performed by means of an in-housewritten Rosenbrock algorithm that is robust against divergence.54 The Levenberg−Marquardt method, which ensures quadratic convergence around the optimum parameter values,55 was subsequently applied. The ordinary least squares (OLS) option of ODRPACK version 2.01 (available online at NETLIB56) was selected for this purpose. Additional code was added to retrieve the F value for global regression significance and the variance−covariance matrix between the parameter estimates. The weighted sum of squared differences (SSQ) between the experimental (F) and modeled (F̂) outlet flow rates (eq 4) was minimized by adjusting the model parameter vector b to approach the real parameter vector β. Both dimethylbutane outlet flow rates were lumped into a single response for 15334

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alkane i, the following rate expression is obtained for its further isomerization or cracking:46,58

objective function minimization, resulting in a total of four responses. nobs nresp

b

SSQ = ∑ ∑ wi(Fi , j − Fi ,̂ j)2 → min

rk = kk (4)

j=1 i=1

n

(5)

2.3. Reactor Model. An ideal CSTR operation was assumed, resulting in a set of algebraic equations in the outlet flow rates of each product alkane. For example, the equation for response i is Fi ̂ − Fi0 − R i(Fi )̂ W = 0

n

The parameters in eq 7 are explained in the Nomenclature. To simulate the physisorption behavior, a single-site Langmuir isotherm could be used rather than a dual-site Langmuir isotherm, which is commonly adopted in the literature for n-hexane physisorption in MFI frameworks,40,60,61 as verified in section 2.4.2. The dehydrogenation equilibrium coefficients (Kdeh) in eq 7 were calculated from pure-component thermodynamic data obtained from TRC tables. 62 Other parameters in eq 7 are determined by the catalyst properties (i.e., Cacid, Cs, KL, and Kpro) and are therefore taken as “catalyst descriptors”. On the other hand, the isomerization and cracking rate coefficients depend on the reaction kinetics and are taken as the “kinetic descriptors”.47 Instead of calculating each rate coefficient separately, the approach used here introduced the SEMK methodology, which categorizes the isomerization and cracking reactions in reaction families according to the elementary step type and the reactant and product ion type. Unique single-event rate coefficients were defined for each reaction family and were found to be catalyst-independent.45,46,58 Differences in the rate coefficients of elementary steps within the same reaction family originate from symmetry effects, which are accurately captured by the so-called “number of single events”, ne, a factor quantifying the number of structurally indistinguishable ways the elementary step can occur. By virtue of the SEMK methodology, the rate coefficients of a methyl shift/PCP branching/β-scission reaction can be expressed as the product of a kinetic contribution and a structural contribution:

n

n

n

(7)

(∑kobs F )−1 =1 i,k ∑ j =resp1 (∑kobs F )−1 =1 j,k

2

n

∑vole 1 + ∑upar K Lp + ∑upar C sK proK dehK Lp (p )−1 =1 u u =1 =1 u v ,k u,v u u H 2

The weighing factors wi are the diagonal elements of the inverse of the variance−covariance matrix of the experimental errors in the responses. When no replicate experiments are available, the weighing factors can be calculated as follows: wi =

−1 deh L C acidCisKjpro , k K i , j K i pi (pH )

(6)

where W represents the catalyst mass and Ri the net production rate of alkane i. The set of algebraic equations was solved using the DNSQE subroutine available at NETLIB.56 The outlet flow rates of n-hexane and hydrogen were determined a posteriori from the atomic carbon and hydrogen balances, respectively. 2.4. SEMK Model for n-Hexane Hydroconversion. 2.4.1. Rate Equation and Single-Event Concept. A SEMK approach was followed to describe the reaction kinetics observed from experiments. A more detailed elaboration of the SEMK methodology for n-alkane hydroconversion is given in the Supporting Information. The acid-catalyzed part of the n-hexane hydroconversion reaction network is depicted in Figure 1.44,46 Free carbenium ions were assumed to be pro-

MS/PCP/ β

β kmMS/PCP/ = nekm̃ 1; m2 1; m 2

(8)

where m1 and m2 are the types of carbenium ion involved as the reactant and product, respectively. Following the reaction network in Figure 1, the reaction families concerned in the present work comprise (s;s) methyl shift; (s;s), (s;t), (t;s), and (t;t) PCP branching; and (s;s) β-scission. Hydride shifts are not taken into account, as the carbenium ion concentrations are fully determined by protonation equilibria. The number of single events for each of the elementary steps was calculated by an in-house-written algorithm based on Boolean matrix representations for the reactant ion and the transition state.63 The single-event activation entropies in the rate coefficients were approximated from the net gains in degrees of translational freedom induced by the corresponding reactions.45 The activation energies were determined earlier from model regression of n-octane hydroconversion over a Pt/H-USY catalyst58 and are reported in Table 1. 2.4.2. Catalyst Descriptors. The catalyst descriptors in eq 7 are the physisorption saturation concentration (Cs), the Langmuir physisorption coefficient (KL), the total acid site concentration (C acid), and the protonation equilibrium coefficient (Kpro). The physisorption saturation concentration for n-hexane was determined from the ratio of the catalyst micropore volume and the sorbate molar volume calculated via the Hankinson−Brobst−Thomson method at the considered reaction temperature.64 The catalyst micropore volume was approximated as 1.9 × 102 cm3 kg−1, as reported for silicalite by

Figure 1. Carbenium ion chemistry involved in n-hexane hydroconversion, including hydride shift (HS), 1,2-methyl shift (MS), PCP branching (PCP), and β-scission (β).

tonated intermediates following earlier experimental evidence and microkinetic modeling results.57,58 Hydride shift (HS) and methyl shift (MS) are denoted as type A isomerization and induce no change in reactant branching degree.30 Type B isomerization involves consecutive PCP transition state formation and C−C bond scission within the PCP structure.59 The 4-methylpent-2-yl carbenium ion is additionally susceptible to β-scission toward a prop-2-yl ion and propylene. Reactions involving primary ion formation were not considered because of the unstable nature of the latter. Physisorption, dehydrogenation, and protonation were considered to be quasi-equilibrated, implying that the acidcatalyzed reaction steps are rate-determining. The reaction rates of the latter steps can be expressed as a function of the reactant alkane partial pressure. For example, for reactant carbenium ion k originating from alkene j that in turn was formed from 15335

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Table 1. Activation Energies of the Rate-Determining Reaction Families Involved in n-Hexane Hydroconversion As Determined for a Pt/H-USY Catalyst (Si/Al = 30)58 reaction family

activation energy (kJ mol−1)

(s;s) alkyl shift (s;s) PCP branching (s;t) PCP branching (t;s) PCP branching (t;t) PCP branching (s;s) β-scission

77.5 108.7 98.6 129.5 127.9 142.7

Stach et al.65 The differences in the micropore volumes of silicalite and high-silica ZSM5 zeolites are not significant. Ferreira et al.61 found a difference of only 1 cm3 kg−1 between the micropore volumes of silicalite and ZSM5 with a Si/Al ratio of 100. Therefore, the micropore volume as determined for silicalite could reasonably be adopted for the catalyst used in this work. The total acid site concentration was determined as 0.12 mol kg−1 from the catalyst Si/Al ratio by assuming that a Brønsted acid site accessible for protonation can be related to each Al atom present in the framework. The latter was confirmed in various experimental studies.66,67 The presence of 0.5 wt % Pt was assumed not to affect the catalyst’s structural properties in a significant way, as implicitly assumed in many hydroconversion studies. Jimenez et al.68 found earlier that the BET surface areas of ZSM5 and other zeolites were only marginally altered after incorporation of highly dispersed Pt particles, aiming at a nominal loading of 0.5 wt %. The Langmuir physisorption coefficient is related to the Henry coefficient via the physisorption saturation coefficient, and it follows a van’t Hoff relationship with the temperature: KL =

⎛ ΔSphys ⎛ ΔHphys ° ⎞ ° ⎞ H −1 ⎜ ⎟ ⎜ ⎟ 0.5( ) exp exp − = p ° RT ⎠ Cs ⎝ R ⎠ ⎝

Figure 2. Single-site (dotted curve) and dual-site (solid curve) Langmuir isotherms for (a) n-hexane and (b) 2-methylpentane at 503 K. The single-site Langmuir physisorption isotherm was calculated according to eq 10 using the physisorption parameters reported by Denayer et al.37 and the catalyst micropore volume reported by Stach et al.65 The dual-site Langmuir isotherm was calculated according to eq 11 using the physisorption parameters reported by Zhu et al.40 and the saturation concentrations reported in an earlier publication by the same authors.75 The individual Langmuir isotherms for site types A and B contributing to the dual-site Langmuir behavior are depicted as dashed lines. The reactant partial pressure range applied in this work is indicated in gray.

(9)

The peculiar framework structure of ZSM5 consisting of two types of 10-membered pore channels, could induce preferential physisorption of methylpentanes at the channel intersections,40 and of n-hexane in the sinusoidal channels at relatively high pressures. The latter phenomenon is often denoted as “commensurate freezing”69,70 and could lead to an inflection point in the physisorption isotherm.40,60,61,71 However, such physisorption behavior was not observed in experimental studies applying high temperatures and low partial pressures such as the ones used in the present work.32,37,72,73 As commented earlier, a single-site Langmuir isotherm was implicitly assumed in eq 7 in reference to earlier work on non-shape-selective catalysts.58,74 Figure 2 shows the comparison between a single-site Langmuir isotherm (eq 10) and a dual-site Langmuir isotherm (eq 11) for n-hexane and 2-methylpentane physisorption at 503 K over the reactant partial pressure range considered in this work. The single-site Langmuir isotherm parameters were determined by Denayer et al.37 for a ZSM5 catalyst with an identical Si/Al ratio, and the dual-site Langmuir isotherm parameters were reported by Zhu et al.40 for silicalite. Ci =

Ci =

In eq 11, two types of physisorption sites are distinguished, A and B, which correspond to sites located in the channels and at the channel intersections. Under the reaction conditions considered in this work, no dual-site physisorption behavior is expected at any feed conversion according to Figure 2. It should be noted that the impact of the catalyst’s Si/Al ratio was not taken into account in the physisorption parameters determined for the dual-site Langmuir isotherm. Arik et al.73 and Ferreira et al.61 found a 1.6−2 kJ mol−1 difference in the standard enthalpies of physisorption of n-hexane on silicalite and a highsilicate ZSM5 such as the one used in this work. Accounting for such differences would only give rise to a slightly different sorbate concentration for the dual-site isotherm depicted in Figure 2, and not have any impact on the conclusion that n-hexane and its isomers exhibit single-site physisorption behavior under the reaction conditions applied in this work. A single-site Langmuir isotherm was therefore used further on. The alkene standard protonation entropy is determined a priori from the standard translational entropy of the alkene, corresponding to three degrees of freedom, and the standard physisorption entropy.45 The alkene standard protonation enthalpy solely depends on the type of carbenium ion formed upon protonation and has been established as an accurate

CisK iLpi n

1 + ∑upar K Lp =1 u u Cis,AK iL,Api n

1 + ∑upar K L,Apu =1 u

(10)

+

Cis,BK iL,Bpi n

1 + ∑upar K L,Bp =1 u u

(11) 15336

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Figure 3. (a) Experimental (symbols) and simulated (lines) n-hexane conversion (eq 1) as a function of the space time at 503 K (open symbols) and 523 K (solid symbols): 1 MPa (diamonds), 2 MPa (squares), and 3 MPa (circles) at inlet hydrogen-to-hydrocarbon molar ratios between 50 and 100. (b) Expanded view of the 503 K data from (a): 2 MPa (open symbols/black lines) and 3 MPa (gray solid symbols/gray lines) at inlet hydrogento-hydrocarbon molar ratios of 50 (squares), 75 (diamonds), and 100 (circles). The simulated n-hexane conversions were obtained using the SEMK model incorporating diffusion limitations (section 4.1.1) with the estimated diffusion coefficients reported in Table 3 (solid line).

descriptor for the catalyst average acid strength.46,76,77 The alkene standard protonation enthalpy for secondary ion formation is estimated via model regression. Because of the low impact of tertiary carbenium ions on the n-hexane hydroconversion kinetics (vide Figure 1), the alkene standard protonation enthalpy for tertiary ion formation was assumed to be 30 kJ mol−1 more negative than that for secondary ion formation.58,78

3. EXPERIMENTAL RESULTS In the investigated range of operating conditions (vide section 2.1), the total n-hexane conversion ranged from 13% to 57%. Figure 3a shows that the feed conversion increased with the space time as well as with the reaction temperature. The yields of 2-methylpentane and 3-methylpentane followed the same trend. The dibranched butane yields never exceeded 1%. Propane was the only detectable cracking product, indicating that metal-catalyzed C−C bond scission, also denoted as hydrogenolysis, did not occur. The cracking product yield amounted to only 2%, implying that the reactivity of 2-methylpentane toward (s;s) β-scission was marginal regardless of the reaction temperature. This follows directly from the high activation energy for this reaction family [about 30 kJ mol−1 higher than that required for (s;s) PCP branching; vide Table 1].58 Cracking becomes more pronounced for n-heptane and heavier reactants, where the feed isomers can undergo type B β-scission (i.e., involving a tertiary carbenium ion).20,23 The ideality of the hydrocracking conditions were verified on the basis of the data represented in Figure 3a. The n-hexane conversion showed an inverse relationship with the total pressure, as expected in the case of quasi-equilibration of the alkane dehydrogenation step (vide section 2.4).79 A similar conclusion could be drawn from Figure 3b, which visualizes the effect of changing the inlet hydrogen-to-hydrocarbon molar ratio on the n-hexane conversion. Increasing hydrogen partial pressures favor alkene hydrogenation toward alkanes, hence reducing the concentration of reactive intermediates and the hydrocracking conversion.79 The 2-methylpentane production significantly exceeded that of 3-methylpentane, as shown in Figure 4.28,50 The 2-methylpentane/3-methylpentane yield ratio remained above 1.8 even up to considerable n-hexane conversions of about 50% before approaching the thermodynamic equilibrium ratio of 1.6.

Figure 4. Experimental (symbols) and simulated (lines) yields of 2-methylpentane (squares), 3-methylpentane (circles), and dimethylbutane (diamonds) as functions of the total n-hexane conversion. The n-hexane conversion and the isomer yields were calculated via eqs 1 and 2, respectively, and were simulated with the general SEMK model described in section 2.4 using the Langmuir physisorption parameters determined by Cavalcante and Ruthven38 and Denayer et al.37 and reported in Table 2 (short-dashed lines), with the SEMK model incorporating diffusion limitations (section 4.1.1) using the estimated diffusion coefficients reported in Table 3 (solid lines), and with the SEMK model using the estimated Langmuir physisorption coefficients reported in Table 2 (section 4.3.1) (long-dashed lines).

In contrast, the 2-methylpentane/3-methylpentane yield ratio quickly evolved from 1 to the thermodynamic equilibrium ratio on bifunctional H-Y and USY zeolite catalysts.46 As commented in the Introduction, the origin of the peculiar isomer product distribution observed over ZSM5 zeolites has already been attributed to several forms of shape selectivity induced by the catalyst framework.18,22,38

4. QUANTIFICATION OF SHAPE SELECTIVITY EFFECTS BY SEMK MODELING In the present section, intracrystalline diffusion, transition-state shape selectivity, and physisorption selectivity were implemented in the SEMK model elaborated in section 2.4 to describe the experimental data and evaluate the dominant factors in the observed selectivity effects. A best possible compromise between the statistical and physical significance of the model as a whole and of the individual parameter estimates is pursued. 4.1. Intracrystalline Diffusion Limitations. 4.1.1. Model Development. The potentially significant impact of mass 15337

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mass balance with time for each alkane until no significant concentration changes occur:82,89

transport limitations on the observed reaction kinetics has been recognized in the field of catalysis for a long time.80 Slowly diffusing reactants that simultaneously undergo fast reactions induce an incomplete utilization of the catalyst crystallite, as internally located active sites may be out of reach for the reactants.13 As a result, the apparent reaction orders and activation energies deviate from the intrinsic ones.81 In the case of irreducible transport phenomena, such a deviation may be avoided by using a fundamental model that unambiguously accounts for intracrystalline diffusion phenomena in addition to the intrinsic reaction kinetics. Klemm and Emig82 determined the Fick diffusion coefficients of xylene isomers during transient isomerization experiments over an H-ZSM5 catalyst. More recently, Hansen et al.83 modeled benzene alkylation data over H-ZSM5 by means of kinetic Monte Carlo simulations with diffusion coefficients determined from molecular dynamics (MD). A theoretical study by Roberts and Lamb84 found that diffusion limitations could very well result in a change in product selectivities from reversible reactions such that thermodynamic equilibrium is no longer established. More specifically for n-nonane hydroconversion, Kinger and Vinek22 attributed the preferred formation of 2-methyloctane compared with other monobranched isomers to such a diffusion effect. As commented in the Introduction, the fact that dimethylbutanes are practically immobile would be indicative of their pronounced tendency to debranch to a 2-methylpentyl ion upon formation.20,28 Average Net Production Rate. The net production rates as required for the corresponding mass balance (vide eq 6) were obtained by averaging the pointwise net production rates over the catalyst crystallite. For this purpose, a number of equidistant grid points was defined, and a trapezoidal discretization procedure was followed for integration. For example, the average net production rate R̅ i of component i is given by s+1 R̅ i = 2ngrid

∂Ci ∂C ⎞ 1 ∂⎛ = s ⎜y s Di i ⎟ + R i ∂t ∂y ⎠ y ∂y ⎝

where Ci and Di represent the concentration and the Fick diffusion coefficient of sorbate i, respectively. The introduction of (i) a dimensionless length ξ, defined by

ξ=

j=1

θi =

s+1 R i(y0 ) 2n ucell

(15)

Ci Cis

(16)

yields a partial differential equation for each sorbate species considered (i.e., n-hexane, its structural isomers, and propane): Cis

∂θi 4C s ⎛ s ∂θ ∂Di ∂θi ∂ 2θ ⎞ = − 2i ⎜ Di i + + Di 2i ⎟ + R i ∂t ∂ξ ∂ξ L ⎝ ξ ∂ξ ∂ξ ⎠ (17)

where i = 1, ..., npar. The boundary conditions are θi = θisurf at ξ = 1 ⎫ ⎪ ⎬∀t ∂θi = 0 at ξ = 0 ⎪ ∂ξ ⎭

(18)

and the initial conditions are ⎪ θi = θisurf at ξ = 1⎫ ⎬ at t = 0 at ξ ≠ 1⎪ θi = 0 ⎭

(19)

The boundary conditions imply a symmetric concentration profile over the crystallite. Initially, the sorbate concentration equals zero at any point inside the crystallite and θsurf at the i external surface, as illustrated in Figure 5 for component i. A total of 40 internal grid points were used in this work. A spherical crystallite geometry was assumed, as in many other works,82,83,90 because it can be considered as the most adequate approximation of the real geometry in case of small crystallite sizes.2 L in eq 15 then equals the equivalent spherical diameter, which was taken to be 0.5 μm. The derivatives of the pore occupancy and the Fick diffusion coefficient with respect to the dimensionless length ξ in eq 17 were approximated via the central difference method. Time integration was carried out with the DVODE subroutine available at NETLIB56 until the relative differences in the concentration profiles dropped below a user-defined tolerance of 0.01%. No influence of hydrogen on the diffusion behavior of the sorbate alkanes was considered, and hence, eqs 17−19 need to be solved only for the alkanes in the reaction network. Permeation experiments performed by Kapteijn et al.91 demonstrated that, indeed, the mass transport of a hydrocarbon such as n-butane, and hydrogen through silicalite was close to unaffected by the presence of the other diffusing species under reaction conditions such as the ones considered in this work. Multicomponent Diffusion through a Microporous Structure. Diffusion through a microporous substrate is generally dominated by strong physisorption effects over conventional

(12)

where ngrid is the number of intracrystalline grid points, Ri is the net production rate of component i at a specific location inside the crystallite, yj is the length coordinate with respect to grid point j, and s is the crystallite shape factor, which equals 0, 1, or 2 for a slab, cylindrical, or spherical geometry, respectively.85 The trapezoidal discretization procedure in eq 12 would overestimate the reaction at the crystallite external surface, which might contribute to the overall reaction kinetics.66,86 This contribution is separately taken into account by setting ngrid equal to nucell, the maximum number of ZSM5 unit cells (∼2 nm)87 in the catalyst crystallite: R isurf ≈

2y L

where L is the crystallite length, and (ii) the pore occupancy of component i, θi, which is related to its concentration via its saturation concentration Csi ,

ngrid

∑ [R i(yj )yj s + R i(yj + 1)yj + 1s ]

(14)

(13)

The net production rate in the continuity equation (eq 6) hence equals the sum of the net production rate averaged over the catalyst crystallite (following eq 12) and the net production rate evaluated at the external surface (eq 13). Because of the low exothermicity exhibited during alkane hydroconversion, no energy balance was considered in the model. For the expression of a non-isothermal problem, the reader is referred to the work of Cardoso and Rodrigues.88 Intracrystalline Concentration Profile. The steady-state sorbate concentration at a specific grid point inside the catalyst crystallite is determined by integrating the non-steady-state 15338

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where D̃ i0 is the corrected diffusion coefficient at zero occupancy. In eq 21, the pore occupancy of each component is considered, implying that the other sorbate molecules can occupy potential physisorption sites of component i.89 In order to keep the model complexity to an acceptable level, no “drag” effects between diffusing species were included in the present work. In case of strong confinement, as expected with hexane isomers in ZSM5, such interspecies correlation effects are likely to be weaker, and the diffusion is primarily determined by sorbate−sorbent interactions.99 Explicitly accounting for force balances on the diffusing species as elaborated in the Stefan− Maxwell theory will be the subject of a separate work. No Arrhenius relationship of the corrected diffusion coefficients with the reaction temperature was incorporated, considering the relatively low diffusional activation energies determined in the literature100−103 and the limited temperature range over which the experimental data were acquired in this work. The mixture nonideality incorporated into the thermodynamic correction factor in eq 20 is defined by the component fugacity f i:97

Figure 5. Illustration of the discretized pore occupancy profiles of component i at t = 0 (open symbols) and at steady-state (solid symbols) obtained by integration of eq 17 with the boundary and initial conditions given in eqs 18 and 19, respectively.

bulk and Knudsen diffusion. Such a diffusion regime was earlier denoted as “configurational diffusion”.92 The corresponding Fick diffusion coefficient in eq 17 following Fick’s law is usually a complex function of the pore occupancy, which limits its capability to accurately describe mass transport in this regime.93 The Stefan−Maxwell theory is often followed instead as it enables multicomponent diffusion phenomena to be physically interpreted in terms of pure-component data.94 The Stefan−Maxwell theory was found to be particularly useful in describing multicomponent diffusion through silicalite and high-silica H-ZSM5 catalysts such as the one used in this work.95 The Fick diffusion coefficient Di of component i is expressed as the product of a corrected diffusion coefficient D̃ i and a thermodynamic correction factor Γi related to the mixture nonideality: Di = Dĩ Γi

Γi =

Γi = 1 +

n j=1

C js ⎞ θj⎟ Cis ⎟⎠

(22)

θi n

C js

1 − ∑ j = 1 C s θj

(23)

i

Equation 23 accounts for differences in saturation concentrations between the diffusing species and ensures a total pore occupancy that cannot exceed 1 relative to the saturation concentration of component i.105 Model Regression. The net production rate in eq 17 was determined via the SEMK model described in section 2.4 using literature-reported physisorption parameter values, which are shown in Table 2. The dehydrogenation equilibrium between alkanes and alkenes at each internal grid point implies highly dispersed platinum particles over the crystallite. Incipient wetness techniques such as the one used in this work give rise to Pt particles in the subnanometer range that primarily reside within the zeolite framework.106 Only catalyst samples with a Pt loading exceeding 2 wt % showed metal particles located on the external crystallite surface. Martens and Jacobs107 observed a sudden change in the n-decane hydroconversion product distribution over Pt/H-ZSM5 only at Pt concentrations of 1 wt % on. The establishment of ideal hydrocracking at each point inside the catalyst crystallite was therefore assumed to be valid.

(20)

∑

∂ ln Ci

On the basis of the Langmuir isotherm in eq 10, the thermodynamic correction factor can be expressed as a function of the pore occupancy:104

This expression is derived from a force balance over each species in the diffusing mixture. Consequently, the corrected diffusion coefficient could be related to the inverse of a drag coefficient assessing the extent of friction with the catalyst surface and other species.92 The corrected diffusion coefficient depends on the pore occupancy, physisorption site heterogeneity, and channel connectivity.96 A complex function of the above properties is not further elaborated in the present work in order to maintain the focus on identifying the dominant shape-selective effects in n-hexane hydroconversion on Pt/H-ZSM5. The corrected diffusion coefficient is expressed as a linearly decreasing function of θi as applied in earlier research:97,98 ⎛ Dĩ = Dĩ 0⎜⎜1 − ⎝

∂ ln fi

(21)

Table 2. Reported Standard Physisorption Enthalpies, Physisorption Saturation Concentrations, and Langmuir Physisorption Coefficients37,38,65 and Langmuir Physisorption Coefficients Estimated Using the SEMK Model Described in Section 4.3.1 for n-Hexane and Its Isomers on H-ZSM5 (Si/Al = 137) at 503 K

a

component

−ΔH°phys (kJ mol−1)

Cs (10−1 mol kg−1)

KL (10−5 Pa−1)

estimated KL (10−5 Pa−1)

n-hexane 2-methylpentane 3-methylpentane 2,2-dimethylbutane 2,3-dimethylbutane

68.8 66.8 66.0 63.9 63.4

7.0 5.6 4.8 3.2 2.1

10.3 7.5 7.5 6.6 9.5

10.3a 7.5a 10.0 ± 0.4b (9.5 ± 0.7) × 103 (8.0 ± 6.7) × 103

Fixed parameter. b95% confidence interval. 15339

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Both dimethylbutanes were simulated as nearly completely immobile inside the crystallite upon formation. The observed dimethylbutane yields, which experimentally amounted up to only 0.1%, could be acsribed only to reaction at the crystallite external surface via eq 13 according to the methodology presented in section 4.1.1. The simulated dimethylbutane yields remained within the same order of magnitude of the corresponding experimental data. As demonstrated above, the peculiar n-hexane hydroconversion product distribution obtained on Pt/H-ZSM5 could be accurately described by incorporating the diffusion coefficients reported in Table 3. Large discrepancies exist in reported diffusion coefficients measured by different techniques. The latter were often ascribed to various factors disguising the observed diffusion, such as intercrystallite energy barriers,110,113−115 heat transfer effects upon physisorption,114,116 carrier gas effects,117 and crystal defects,118 among others. Microscopic techniques such as pulsed-field-gradient NMR spectroscopy and quasi-elastic neutron scattering are often considered to be less prone to the above effects, and probably as a result, the diffusion coefficients measured via these techniques are usually 3−4 orders of magnitude higher than those obtained from macroscopic measurements.108,109 However, the current “mean-field” approach (eq 21) leads to corrected diffusion coefficient estimates that relate well with values obtained from macroscopic measurement techniques such as uptake,31 chromatography,32 infrared mapping,119 and TAP.117 A similar observation was made by Hansen et al.,83 who ultimately applied corrected diffusion coefficients for all aromatic species involved in benzene alkylation with ethylene, which were more than 3 orders of magnitude lower than those initially simulated from MD, the latter technique agreeing well with results from microscopic measurements.120,121 The reason why the species diffusion coefficients obtained in this and in Hansen’s work correlate better with the reported values specifically obtained from macroscopic measurement techniques is not fully resolved yet. Equation 20, whether or not complemented with a mean-field approach such as in eq 21, has been applied to numerous microscopic and macroscopic physisorption studies.7,71,102,111,120,122,123 There remained similar discrepancies between the results obtained using these two groups of techniques as commented above, and as in this work, these discrepancies could not be ascribed to the methodology used to extract the diffusion parameters from the experimental data. The SEMK model described in section 4.1.1 is both physically and statistically significant and consequently allows information on the intracrystalline diffusion phenomena involved to be extracted. Figure 6 shows the pore occupancies of n-hexane, 2-methylpentane, 3-methylpentane, and dimethylbutane relative to their saturation concentrations (vide eq 16) at total n-hexane conversions of (a) 10% and (b) 50%. The right-hand side of Figure 6 shows the corresponding net production rates evaluated at each grid point. It should be noted that the occupancy profile and consequently the net production rate profile are symmetrical and are only presented partly. No pronounced mass transport limitations were simulated for n-hexane, resulting in a nearly uniform profile. A slightly steeper curvature of the occupancy profile was observed for 3-methylpentane compared with 2-methylpentane originating from the 3-fold lower diffusion coefficient of the former species. As a result, the net production rate of 3-methylpentane remains lower than that of 2-methylpentane

Together with the alkene standard protonation enthalpy for secondary ion formation, the corrected diffusion coefficients of n-hexane, 2-methylpentane and 3-methylpentane at zero occupancy were estimated via model regression. Considering the large discrepancies between alkane diffusion coefficients measured from different experimental techniques,101,108,109 a broad range of orders of magnitude, i.e., 10−12 to 10−17 m2 s−1, were screened as initial values. The diffusion coefficients of both dimethylbranched species were arbitrarily fixed on a value which is 2 orders of magnitude lower than the diffusion coefficients of the methylpentanes.110,111 No diffusion limitations were considered for propane. 4.1.2. Model Validation. Application of the modeling methodology described in section 4.1.1 resulted in a globally significant regression as evidenced by an F value of 2000 which exceeds the tabulated value by 3 orders of magnitude. The diffusion coefficients of n-hexane, 2-methylpentane, and 3-methylpentane were significantly estimated (vide Table 3) Table 3. Corrected Diffusion Coefficients for n-Hexane, 2-Methylpentane, and 3-Methylpentane Estimated Using the SEMK Model Described in Section 4.1.1

a

component

D̃ 0 (10−16 m2 s−1)

n-hexane 2-methylpentane 3-methylpentane

22.3 ± 0.1a 12.9 ± 0.2 4.1 ± 0.1

95% confidence interval.

and exhibited no pronounced correlation. With these values, together with the activation energies reported in Table 1, the Langmuir physisorption parameters reported in Table 2, and an estimated alkene standard protonation enthalpy for secondary ion formation of −70.2 ± 0.2 kJ mol−1, the catalyst activity for n-hexane conversion could be accurately reproduced, as demonstrated in Figure 3. Slight deviations from the experimental data at 503 K are observed at 2 MPa with an inlet hydrogen-tohydrocarbon molar ratio of 100 and at 3 MPa with an inlet hydrogen-to-hydrocarbon molar ratio of 50, and could be due to shortcomings of the model at relatively high occupancies. Nevertheless, the model was able to qualitatively predict the effect of a changing reaction condition on the overall n-hexane conversion in all cases. The yields of 2-methylpentane and 3-methylpentane were satisfactorily reproduced (vide Figure 4). The estimated diffusion coefficient of 3-methylpentane was about 3 times lower than that of 2-methylpentane. This implies more pronounced transport limitations within the catalyst crystallites for the former species. The latter was ascribed to the longer tail in 2-methylpentane, which brings the sorbate into a more favorable configuration for diffusion through the micropores.31,35 As a result, thermodynamic equilibrium between the two species is not established as observed experimentally. A 2−3-fold higher diffusion coefficient for 2-methylpentane compared with its monomethyl isomer was confirmed from the sparse comparative studies available in literature.31,32,35 Jama et al.32 reported a 6 times higher diffusion coefficient for n-hexane compared with 3-methylpentane, which also agrees well with the results presented here. Ferreira and coworkers11,112 and Zhu et al.35 found a range of 1.1 to 3 for the diffusion coefficient ratio of n-hexane and 2-methylpentane, which well includes the estimated value in this work. 15340

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where D is averaged over the crystallite length scale while k is evaluated at the crystallite external surface. It should be noted that D is determined via eqs 20 and 21 and hence varies with the total n-hexane conversion. Particularly for a spherical crystallite geometry, Aris124 determined the following analytical expression for the effectiveness factor as a function of the Thiele modulus defined in eq 24: η=

3ϕ coth 3ϕ − 1 3ϕ2

(25)

The variation of the effectiveness factor with the Thiele modulus is depicted in Figure 7 for both the PCP branching

Figure 7. Effectiveness factor (eq 25) as a function of the Thiele modulus (eq 24) for the PCP branching (solid gray) and methyl shift (gray hatched) reactions in the n-hexane hydroconversion network (Figure 1) involving an n-hexyl (nC6), 2-methylpentyl (2MC5), 3methylpentyl (3MC5), or dimethylbutyl (DMC4) carbenium ion reactant, calculated with the SEMK model described in section 4.1.1 using the estimated diffusion coefficients reported in Table 3.

Figure 6. Simulated pore occupancies (left, solid symbols) and net production rates (right, open symbols) for n-hexane (squares), 2methylpentane (circles), 3-methylpentane (diamonds), and dimethylbutanes (triangles) in the catalyst crystallite as a function of the dimensionless length coordinate at (a) 503 K and 2 MPa with an inlet hydrogen-to-hydrocarbon molar ratio of 50 and a total n-hexane conversion of 10% and (b) 523 K and 1 MPa with an inlet hydrogento-hydrocarbon molar ratio of 50 and a conversion of 50%. To this purpose, the SEMK model described in section 4.1.1 with the estimated diffusion coefficients reported in Table 3 was applied.

and methyl shift reactions in the reaction network (vide Figure 1). Only a limited extent of mass transport limitations was found earlier for n-hexane, resulting in a relatively low Thiele modulus for isomerization toward any methylpentane and correspondingly an effectiveness factor close to 1. A similar conclusion could be drawn for PCP branching reactions involving a monobranched alkane reactant. On the other hand, diffusion limitations are more significant for the fast methyl shift reactions, especially in the case of a 3-methylpentyl ion reactant. Any reaction involving a dimethyl-branched ion reactant is strongly diffusion-limited because of the low diffusion coefficient of the corresponding alkane. Figure 7 contains information on the apparent kinetics of any isomerization reaction involved in the reaction scheme given that the reactants were fed from the bulk phase. However, no further information could be extracted regarding the potentially sluggish transport of the reaction product toward the bulk phase. Figure 8 shows the net production rates of n-hexane, 2-methylpentane, and 3-methylpentane averaged over the catalyst crystallite and evaluated at the crystallite surface. While differences between the two rates were rather limited for n-hexane, distinct discrepancies were observed for both hexane isomers. Because of the higher diffusion coefficient of 2-methylpentane, the production of this species is initially preferred. Reaction at the external surface mainly forms 3-methylpentane via rapid methyl shifts, leading to a negative net production rate of 2-methylpentane. Conversely, reaction in the catalyst micropores indicates an increased production of 2-methylpentane in the entire conversion range and could only

at any point inside the crystallite except near the surface boundary. As a result of fast 1,2-methyl shifts, unconstrained reaction at the crystallite external surface strives to establish thermodynamic equilibrium between the two components, resulting in a negative net production rate for 2-methylpentane. Strong variations in intracrystalline concentrations were observed for dimethylbutanes. The observed yields toward these species are almost exclusively the result of reaction at the crystallite external surface. An apparent discontinuity emerges near the crystallite surface boundary as a result of the significant differences between the unconstrained reaction at the external surface and the reaction inside the crystallite. In the latter case, the net formation of a species should compensate for the diffusion toward the neighboring grid points at steady state (vide eq 14). The discontinuity near the surface boundary would ultimately vanish upon the application of a larger number of intracrystalline grid points at which Fick’s second law of diffusion is to be integrated. The Thiele modulus (ϕ) and the corresponding effectiveness factor (η) are rigorous measures of the impact of diffusion phenomena on the apparent kinetics. Equation 7 suggests a nearly first-order dependence of the reaction rate on the physisorbed alkane concentration, and hence, the Thiele modulus expression for a first-order reaction is applied:124 ϕ=

L 2(s + 1)

k D

(24) 15341

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Figure 8. Average net production rates (black lines) and net production rates evaluated at the crystallite external surface (gray lines) of n-hexane (solid lines), 2-methylpentane (long-dashed lines), and 3-methylpentane (short-dashed lines) as functions of the total n-hexane conversion (eq 1), calculated with the SEMK model described in section 4.1.1 using the estimated diffusion coefficients reported in Table 3.

Figure 9. Simplified representation of the PCP branching reactions and transition states involved in n-hexane hydroconversion.

only significantly estimated parameter, in contrast to any of the activation energies for PCP branching. Intramolecular methyl shifts in the n-hexane hydroconversion mechanism (Figure 1) induced fast establishment of thermodynamic equilibrium between 2-methylpentane and 3-methylpentane. Better agreement between model and experiment could be achieved only by additionally imposing considerably stronger restrictions on the formation of the three-center, two-electron bond transition state of the 1,2-methyl shift reactions. However, this is physically not evident since the carbon−carbon bond distances in the transition-state structures for both 1,2-methyl shifts and PCP branching are comparable, as determined from ab initio calculations.126,127 Weitkamp et al.19 investigated the monobranched isomer distribution from n-nonane to n-hexadecane hydrocracking over Pt/H-ZSM5 at low feed conversions between 1 and 10%. In this conversion range, transition-state shape selectivity could have induced some degree of deviation from thermodynamic equilibrium within the monobranched isomer lump. However, from intermediate conversions onward as observed under the reaction conditions applied in this work and in view of the PCP branching reactions in Figure 9, the peculiar n-hexane hydroconversion performance of Pt/H-ZSM5 could not be primarily ascribed to transition-state shape selectivity. 4.3. Physisorption Selectivity. 4.3.1. Model Development. Physisorption selectivity exhibited by a catalyst can typically be understood by differences between the Langmuir physisorption parameters and/or physisorption saturation concentrations of the various sorbate molecules involved. Denayer et al.37 determined the Langmuir physisorption parameters for n-hexane and all of its isomers on an H-ZSM5 catalyst with an identical Si/Al ratio of 137. Subtle differences between the standard physisorption enthalpies of the hexane isomers were measured (vide Table 2). A similar observation was made in other experimental studies on silicalite at various operating temperatures.34,38,40 Propane physisorption is negligible because of its low Langmuir physisorption coefficient, which, according to its dependence on the sorbate carbon number,60,112 would be more than 1 order of magnitude lower than the coefficient for any of the hexane isomers. The physisorption saturation concentration varies with the sorbate branching degree in the case of confining pore frameworks. Cavalcante and Ruthven38 and Zhu et al.40 found that the maximum sorbate capacities of silicalite for 2-methylpentane and

be the result of the isomerization of 3-methylpentane. The latter indeed exhibits a low net production rate relative to the value expected if diffusion limitations were absent. Apparently, the 3-fold lower corrected diffusion coefficient for 3methylpentane compared with 2-methylpentane alone already gives rise to a hydroconversion pattern substantially different from that observed over non-shape-selective catalysts. Overall, the experimental n-hexane hydroconversion data could be reasonably well described by incorporating intracrystalline diffusion effects, as elaborated above. Other forms of shape selectivity that determine the hydroconversion performance of ZSM5 catalysts have been proposed in the literature, and these are evaluated in the subsequent sections. 4.2. Transition-State Shape Selectivity. 4.2.1. Model Development. Pioneering research on alkane hydroconversion over ZSM5 zeolite catalysts attributed the higher selectivity toward the 2-methyl isomer to transition-state shape selectivity in the formation of the PCP complex during n-alkane isomerization.3,18,19,23 These authors considered the fact that the PCP complex (∼0.43 nm)125 is less confined when located at a terminal position in the alkyl chain, to be an explanation for the preferential formation of the 2-methyl alkane over any other monobranched isomer. Figure 9 gives a simplified representation of the transition states involved in the PCP branching reactions in Figure 1 and constitutes a first indication that no pronounced differences in isomerization rates starting from n-hex-2-yl ion and n-hex-3-yl ion are to be expected. Transition-state shape selectivity for a particular reaction was implemented in the SEMK model by increasing the corresponding activation energy for that reaction only. The activation energies for the PCP branching reaction families are reported in Table 1 and are typically 25−30 kJ mol−1 higher than those of 1,2-methyl shifts involving reactant and product ions of the same type.58 The activation energy of each PCP branching reaction involving a different reactant ion and/or transition state was estimated via SEMK model regression while assuming the corresponding activation energy reported in Table 1 as the initial and minimum value. Thermodynamic consistency between forward and reverse reactions was enforced. 4.2.2. Model Validation. The F value for global model significance amounted to only 885. The alkene standard protonation enthalpy for secondary ion formation constituted the 15342

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literature-reported physisorption parameters are also shown in Figure 4. In this case, the catalyst practically behaved as a nonshape-selective catalyst, leading to a considerable production of dimethylbutanes. The latter were barely above the detection limits, and hence, their negligible production is not reflected by their Langmuir physisorption coefficient reported in the literature. The Langmuir physisorption coefficient of 3-methylpentane increased about 30% relative to its initial value and approached the coefficient for n-hexane at 503 K. As a result, the conversion toward both 2-methylpentane and 3-methylpentane could be accurately reproduced (vide Figure 4). However, a distinctly higher Langmuir physisorption coefficient for 3-methylpentane was not observed in any experimental study. Conversely, the physisorption of 2-methylpentane was always similar to that of 3-methylpentane or even slightly favored.35,37,38,40,128 Together with the unrealistically high Langmuir physisorption coefficients estimated for 2,2-dimethylbutane and 2,3-dimethylbutane that mathematically compensate for the lack of diffusion phenomena incorporated in the model, the current SEMK model fails to provide a physically relevant explanation of the peculiar n-hexane hydroconversion product selectivities observed on Pt/H-ZSM5. Despite the lower F value obtained from model regression in section 4.1.2, the incorporation of intracrystalline diffusion limitations in the SEMK model turned out to be vital to physically interpret the experimental data, and hence, mass transport limitations for any hexane isomer can be designated as the dominant shape selectivity effect exhibited by the ZSM5 framework.

3-methylpentane were about 70−80% of the capacity measured for n-hexane. The latter was attributed to less favorable packing of branched species inside the pore channels.128 Even lower values for the physisorption saturation concentration for 2,2dimethylbutane and 2,3-dimethylbutane were measured. Monte Carlo simulation results were in line with these experimental findings, as they indicated a maximum physisorption loading of eight n-hexane molecules per ZSM5 unit cell at 300 K, which contrasted with a maximum loading of about six molecules per unit cell for 2-methylpentane and only four molecules per unit cell for 2,2-dimethylbutane.60,129,130 A 2,2-dimethylbutane physisorption saturation concentration equal to half of the value calculated for n-hexane was experimentally confirmed by other authors,112,131 suggesting that 2,2-dimethylbutane exclusively resides at the channel intersections within the pore framework. The physisorption saturation concentration of n-hexane was determined from the catalyst micropore volume and the sorbate molar volume at the reaction temperature considered (vide section 2.4.2). Differences among the physisorption saturation concentrations of n-hexane and its isomers on ZSM5 are, however, not reflected by differences in the molar volumes. Therefore, the relative difference between the saturation concentration of each hexane isomer and that of n-hexane as reported by Cavalcante and Ruthven38 was taken as a scaling factor to calculate the saturation concentration of each hexane isomer (vide Table 2 at 503 K). Physisorption of n-hexane is slightly favored over any of its isomers because of a higher absolute value of the standard physisorption enthalpy and physisorption saturation concentration.34,38,40 Following the Langmuir isotherm used in this work (eq 10), both effects induce a higher sorbate concentration compared with the other hexane species. The Langmuir physisorption coefficients and physisorption saturation concentrations reported in Table 2 were implemented in the SEMK model for n-hexane hydroconversion described in section 2.4. The alkene standard protonation enthalpy for secondary carbenium ion formation was estimated during model regression along with the Langmuir physisorption coefficients of 3-methylpentane and both dimethylbutanes. The Langmuir physisorption coefficient of n-hexane was not varied because it exhibited a strong correlation with the alkene standard protonation enthalpy. For the same reason, the Langmuir physisorption coefficient of 2-methylpentane was fixed, as it was strongly correlated with the coefficient of 3-methylpentane in optimizing the 2-methylpentane/3-methylpentane yield ratio. 4.3.2. Model Validation. The F value for global model regression significance amounted to 2900, exceeding the one obtained when accounting for intracrystalline diffusion limitations (vide section 4.1.2). The alkene standard protonation enthalpy was estimated to be 70.9 ± 0.3 kJ mol−1. A slightly better agreement between the experimental and simulated n-hexane conversion (not shown) and isomer yields (Figure 4) could be obtained with the estimated Langmuir physisorption parameters reported in Table 2. It is evident that the estimates of the physisorption coefficients of both dimethylbutanes are extremely high and mathematically result into an immediate debranching toward 2-methylpentane, regardless of their saturation concentrations. Such high physisorption coefficients were not observed in any experimental nor theoretical study and therefore could not provide a physical interpretation of the low affinity of ZSM5 toward dibranched alkane production. For comparison, the simulated isomer yields obtained with the

5. CONCLUSIONS A single-event microkinetic assessment of n-hexane hydroconversion on ZSM5 has allowed a quantitative determination of the origin of the peculiar shape selectivity effects that were observed. 2-Methylpentane yields and selectivities systematically exceeding those of 3-methylpentane, and even those expected from thermodynamic equilibrium were obtained. 2,2Dimethylbutane and 2,3-dimethylbutane were produced only to a negligible extent. On the basis of a combined statistical and physical assessment of the performance of alternative SEMK models, intracrystalline diffusion limitations but not transitionstate shape selectivity or physisorption selectivity effects, were found to be at the origin of the observed selectivity effects. Pronounced differences between the diffusion coefficients of the species involved can be related to the pore dimensions of the ZSM5 framework, which approach the sorbate molecular diameters. Corrected diffusion coefficient estimates at zero pore occupancy that were implemented in a “mean-field” approach to describe multicomponent diffusion inside the catalyst crystallite, were in line with reported values from macroscopic measurement techniques. A 3-fold lower corrected diffusion coefficient of 3-methylpentane compared with 2-methylpentane resulted in significantly hindered mass transport of the former species. Both 2,2-dimethylbutane and 2,3-dimethylbutane were found to be nearly immobile upon formation and debranched to a 2-methylpentane rather than diffusing out of the catalyst micropores toward the bulk phase. The marginal conversion toward these species could almost exclusively be attributed to reaction at the crystallite external surface. This study has presented an assessment of the dominant shape-selective effects involved in n-hexane hydroconversion over Pt/H-ZSM5 and could serve as a benchmark in analyzing the performance of ZSM5-based materials in any reaction 15343

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s s ΔS° SSQ T t t W w X y

involving species of similar molecular diameter. In addition, this work has developed a general modeling methodology that is able to simultaneously incorporate the fundamental kinetics of complex reaction networks via the SEMK methodology and diffusion through a catalyst crystallite. Further unraveling of the diffusion phenomenon in terms of catalyst descriptors that fundamentally assess the dependence of the sorbate diffusion coefficient on the catalyst framework properties, would open up a route toward model-guided design of advanced microporous materials for any reaction in which reactants and/or products are sensitive to intracrystalline mass transport limitations.

■

Greek Symbols

ASSOCIATED CONTENT

β Γ η θ ξ σ ϕ

* Supporting Information S

A more detailed elaboration of the SEMK methodology for n-alkane hydroconversion. This material is available free of charge via the Internet at http://pubs.acs.org.

■

secondary carbenium ion crystallite shape factor standard entropy [J mol−1 K−1] sum of squares temperature [K] tertiary carbenium ion time [s] catalyst mass [kg] weighting factor conversion length coordinate [m]

AUTHOR INFORMATION

Corresponding Author

real parameter vector thermodynamic correction factor effectiveness factor pore occupancy dimensionless length global symmetry number Thiele modulus

*Tel.: + 32 9 331 17 52. E-mail: [email protected].

Superscripts

Notes

0 A,B acid β HS MS PCP s surf

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Research Board of Ghent University (BOF), the Interuniversity Attraction Poles Programme Belgian State - Belgian Science Policy, and the “Long Term Structural Methusalem Funding by the Flemish Government”. Dr. Indranil Choudhury is acknowledged for the acquisition of the experimental data set.

■

Subscripts

cra i,j,k,u,v iso phys R tot

NOMENCLATURE

Roman Symbols

b C D D̃ F F̂ H ΔH° Kdeh KL Kpro k k̃ L m ne ngrid nobs nole npar nresp nucell p p° R R R̅ r

initial physisorption site types acid sites β-scission hydride shift methyl shift PCP branching saturation at the external surface

model parameter vector concentration [mol kg−1] Fick diffusion coefficient [m2 s−1] corrected diffusion coefficient [m2 s−1] experimental flow rate [mol s−1] calculated flow rate [mol s−1] Henry coefficient [mol kg−1 Pa−1] standard enthalpy [J mol−1] dehydrogenation equilibrium coefficient [MPa] Langmuir physisorption coefficient [MPa−1] protonation equilibrium coefficient [kg mol−1] rate coefficient [s−1] single-event rate coefficient [s−1] crystallite length [m] type of carbenium ion number of single events number of grid points number of observations number of alkenes number of alkanes number of responses number of ZSM5 unit cells partial pressure [MPa] atmospheric pressure [Pa] universal gas constant [J mol−1 K−1] net rate of production [mol kg−1 s−1] average net rate of production [mol kg−1 s−1] reaction rate [mol kg−1 s−1]

■

cracking component indices isomerization physisorption reactant ion total

REFERENCES

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