(585a) Alkylation of Benzene with Ethene over H-ZSM-5 – A Multiscale Investigation

Gas-solid-reactions in porous media are occurring via a number of elementary steps that are (i) entrance of the reactants into the pore, (ii) multicomponent diffusion towards the active site, (iii) adsorption on the active site, (iv) reaction, (v) desorption of the products from the active site, and (vi) multicomponent diffusion of the products back to the bulk phase. In zeolite catalysis the kinetic diameters of the reactants are often of similar size as the pore diameter. This leads to strongly confined reactants and/or products. When modelling these processes particular care has to be taken of a proper description of the multicomponent diffusion combined with reaction kinetics. Both of these rate phenomena are strongly dependent on the pore topology and are unique for a certain type of zeolite. Due to the complicated nature of the diffusion process the real effectiveness factors for zeolite catalysed reactions are often smaller than those estimated by means of the classical Thiele modulus [1].

In the present study the framework of the Maxwell-Stefan (M-S) equations adapted to diffusion in zeolites [2], combined with an appropriate theory to describe multicomponent adsorption equilibrium is applied to the industrially relevant gas phase alkylation of benzene with ethene in order to get insights into how diffusional limitations affect the observed macroscopic behavior of the reaction system. To make these simulations predictive as many parameters as possible needed to solve the system of differential equations are determined from molecular simulations and quantum chemical calculations. A continuum model is proposed to calculate the intrinsic rate of reaction as function of the local concentration at the active sites that takes the unique pore structure of MFI into account.

The first step of the study was the elucidation of the reaction mechanism using density functional theory (DFT) on cluster models of the active site. For this purpose three different reaction mechanisms ? two one-step schemes and one two-step scheme ? were studied on three cluster models of progressively larger size. In the one-step schemes ethylene protonation and C-C bond formation occur simultaneously. The two-step scheme starts with the formation of a stable ethoxide intermediate which subsequently reacts with benzene to form the reaction product. Activation energies obtained from DFT results were improved by single-point MP2 calculations. The calculated intrinsic activation energies of the one-step schemes are similar to the activation energy of the alkylation step in the two-step scheme. Numerical values of the MP2 corrected activation energies are in reasonable agreement with experimental data. The largest cluster (33 T-atoms) was found to stabilize protonated ethylbenzene as a stable intermediate [3].

While DFT calculations on cluster models are useful for the elucidation of reaction mechanisms for hydrocarbon transformation in zeolites, a quantitative prediction of the rate coefficients can in general not be expected. Reasons are the missing long range part of the electrostatic potential in the zeolite lattice and the underestimation of non-covalent interactions between the adsorbate and the zeolite lattice i.e. dispersion. Since dispersion is an intermolecular electron correlation effect the simplest quantum mechanical method for describing it is second-order Møller-Plesset perturbation theory (MP2). The computational expense of these calculations prevents the application of MP2 to large chemical systems. However, by using hybrid methods quantum chemical modelling approaching chemical accuracy can be achieved. We employ a MP2:DFT multilevel approach [4] to improve the rate coefficients obtained from DFT cluster calculations. This includes the re-optimization of all stationary points obtained with DFT cluster calculations within the full unit cell using plane wave DFT with periodic boundary conditions. Subsequent MP2 and DFT calculations on cluster models of increasing size cut out from the plane wave DFT-optimized unit cell are then used to estimate the missing dispersion interaction by fitting the difference between MP2 and DFT reaction energies to an analytical dispersion term. Moreover, the basis set incompleteness is accounted for by extrapolating MP2 energies obtained with basis sets of increasing size towards the complete basis set limit. Rate coefficients obtained in this way are more likely to be quantitative accurate than those obtained from DFT cluster calculations.

In order to parameterize the M-S equations, molecular dynamics (MD) simulations were carried out for pure ethene in MFI and for ethene-benzene and ethene-ethylbenzene mixtures at a variety of loadings and temperatures. The adsorption isotherms of all species have been obtained from Monte Carlo (MC) simulations in the grand canonical ensemble. For calculating mixture adsorption isotherms the Ideal Adsorption Solution Theory (IAST) [5] was used.

The performance of the proposed continuum model is evaluated by comparing simulation results to kinetic measurements reported in the literature. Experimental activation energies and turnover frequencies are in good agreement with simulated data. Moreover, the continuum model allows investigating separately the influence of (i) the mixture adsorption equilibrium, (ii) the pore architecture, and (iii) the degree of diffusion limitation on the macroscopic reaction orders. The adsorption equilibrium of ethene-benzene mixtures under the industrially relevant process conditions is the first important factor responsible for the difference in the macroscopic reaction orders with respect to ethene and benzene partial pressures. The pore architecture mainly affects the reaction order with respect to the benzene partial pressure. In the absence of diffusion limitation the model predicts an almost first order dependence of the reaction rate on the ethene partial pressure while the exponent associated with the benzene partial pressure is less than 0.5. Diffusion limitation considerably affects the reaction orders. The simulated values of around 0.8 for ethene are in good agreement with experimental data. For benzene the reaction order depends on the temperature and pressure range in which it is determined. It ranges from slightly negative to slightly positive values. The results of this study show that neither Langmuir-Hinshelwood expressions nor empirical power laws offer the flexibility to correlate kinetic measurements of this reaction over a wide range of partial pressures and temperatures. Moreover it is demonstrated that the effectiveness factors predicted from the continuum model are smaller than those calculated using the conventional definition of the Thiele modulus.

References

[1] R. Baur, R. Krishna, Chem. Eng. J. 99 (2004) 105?116.

[2] R. Krishna, J. M. van Baten, Microporous Mesoporous Mater. 109 (2008) 91?108.

[3] N. Hansen, T. Brüggemann, A. T. Bell, F. J. Keil, submitted.

[4] C. Tuma, J. Sauer, Phys. Chem. Chem. Phys. 8 (2006) 3955-3965.

[5] A. L. Myers, J. M. Prausnitz, AIChE J. 11 (1965) 121-130.