(505e) First Principles Based Kinetic Modeling of Industrial Catalytic Reactions: Hydrogenation of Mono Aromatic Compounds

Introduction

The development
and optimization of chemical processes requires accurate reaction models that
are applicable over a wide range of process conditions. For many years the
construction of kinetic models for industrial catalytic reactions has been
largely based on indirect experimental observations and chemical intuition and often
does not take into account the elementary step kinetics. This can limit the
applicability of the model to a restricted range of process conditions. For
complex, multistep catalytic reactions such as benzene hydrogenation, a large
number of kinetic models can be proposed based on various model hypotheses,
each containing a significant number of kinetic and thermodynamic parameters.
This makes model discrimination and parameter estimation based on experimental
data very difficult. In this work, we explore the capabilities of first
principles modeling as a new tool for the development of reaction models for industrial
catalytic reactions. The catalytic hydrogenation of aromatics of Pt was
selected as a test case in view of its relevance for a variety of industrial
processes, such as hydrocracking, hydrogenation, catalytic reforming and nylon
production. In addition, the multistep reaction mechanism poses a challenge to
kinetic modeling. To validate the first principles based kinetic model, lab scale
intrinsic kinetic data were collected for toluene hydrogenation over a 0.5 wt%
Pt/ZSM-22 hydrocracking catalyst¹ and an industrial hydrocracking
unit was simulated.

Method

First principles
calculations were used to construct the kinetic model and to determine the
kinetic and thermodynamic parameters. Relativistic density functional theory
with the Becke Perdew functional and a Slater double zeta quality basis set was
applied as implemented in ADF². The catalyst was represented by a Pt(14,8)
cluster model with the Pt-Pt distance constrained at the bulk value of 277 pm.
It was found that this approach yields reasonably accurate values for adsorption
and activation energies, both in comparison with experimental and periodic slab
calculations³.

Toluene
hydrogenation was studied in a gas phase continuous stirred tank reactor¹.
Nitrogen was used to vary the H₂ and toluene partial pressures under
which conversion was measurable and not transport limited as confirmed by Weisz
modili of about 10^-2. The concentration of active sites C_t
was calculated from the number of accessible Pt atoms and amount to 0.8 10^-2
mol kg_cat^-1.

Results

Model construction.
A number of fundamental concepts for the analysis of catalytic reaction
mechanisms was introduced by Boudart³. These concepts, i.e. catalytic
cycle, rate determining step (RDS) and most abundant reaction intermediate
(MARI), help in the construction of Langmuir-Hishelwood-Hougen-Watson (LHHW)
type kinetic models. Based on the ab initio reaction path analysis³,
the following hypotheses could be formulated:

(i) the
chemisorption of the reactants hydrogen and molecular aromatic is competitive

(ii) desorption
of the hydrogenated product is irreversible because of the low adsorption
energy

(iii) hydrogenation
follows a single dominant reaction path where the addition of the fifth
hydrogen is the rate determining step. Along the dominant reaction path the
activation energies for every step are at least 20 kJ/mol lower than for any of
the competing paths branching from the dominant path³. Along the
dominant reaction path, the activation energy for the fifth hydrogenation step,
104 kJ/mol, is significantly higher than the activation energy for any of the
other steps, which are between 72 and 88 kJ/mol. Assuming similar
pre-exponential factors, the fifth step can therefore be considered rate
determining.

(iv) the
chemisorbed reactants, hydrogen and aromatic, are the thermodynamic sink of the
reaction path and can be considered Most Abundant Reaction Intermediates (MARI)

Based on these
hypotheses, a LHHW kinetic model was derived, enabling easy interpretation and
evaluation of the parameters appearing in the rate equation:

                                             (1)

where p_A
and p_H2 are the reactant partial pressures. Taking into account the
temperature dependency, nine parameters appear in the rate equation: the
concentration of active sites C_t, which was obtained experimentally,
the rate coefficient of the rate determining step k₅ (2 parameters),
the product of the equilibrium coefficients for the surface reactions, (2
parameters), and the adsorption coefficients for toluene, K_A, and
for hydrogen, K_H2 (2 parameters each).

All kinetic and
thermodynamic parameters were obtained from first principles, combining the DFT
calculations with statistical mechanics, and are listed in Table 1. The
hydrogen adsorption enthalpy is strongly coverage dependent (e.g. ref. 5).
Instead of assigning the low coverage DFT value of ?94 kJ/mol, the hydrogen
adsorption enthalpy was treated as an adjustable parameter, DH_ads(H₂). The reaction
enthalpy for the product of the equilibrium coefficients, ,
also varies with the hydrogen adsorption enthalpy since 4 adsorbed hydrogen
atoms are consumed in going from the reactants A* and 4 H* to the intermediate AH₄*.

The kinetic
model (1) was implemented in a reactor model and the coverage dependent
hydrogen chemisorption enthalpy was optimized to accurately describe lab scale
experimental data for gas phase hydrogenation of toluene. The resulting value
of ?63.6 ± 0.9 kJ/mol falls between the high and low coverage values,
consistent with a simulated surface coverages between 55 and 85%. As shown in
the parity diagram, Figure 1, the ab initio based LHHW model captures the main
trends in the reaction rates. The model predicts reaction orders for the inlet
partial pressure of hydrogen and toluene ranging from 1.6 to 2.2 and from -0.3
to +0.7 respectively, in agreement with experimental values which range from
1.3 to 1.8 and from -0.3 to +0.3 respectively. Also the experimentally observed
maximum in the reaction rate versus temperature is predicted by the ab initio
model.

Industrial
hydrocracker simulation. The first principles based kinetic model was
implemented in a reactor model for the simulation of an industrial hydrocracker⁶.
The reactor is operated in trickle bed regime with co-current downflow of the
vapor and the liquid phase. The reactor model accounts for possible mass and
heat transfer gradients at the vapor liquid interface and internal mass
transfer gradients in the catalyst.

The simulation
indicates that the hydrogenation of aromatics occurs mainly in the first part
of the reactor. This leads to hot spot formation and liquid phase hydrogen
depletion in the first decimeters of the reactor, Figure 2. The higher the
aromatic content, the more pronounced these effects. For the highest aromatic
content, i.e., higher than 15%, a regime is established in which the interphase
hydrogen mass transfer becomes rate limiting. This is evident from the
development of a shoulder in the liquid phase temperature profile and from the
delayed recovery of the liquid phase hydrogen flux from the initial depletion,
Figure 2.

Conclusion

A fundamental LHHW
kinetic model for the hydrogenation of monoring aromatics over platinum
catalysts was constructed, based on detailed first principles density
functional calculations. The model parameters were obtained from the first
principles calculations and from statistical mechanics. Our first principles
based kinetic model rather accurately describes lab scale kinetic data for the
hydrogenation of toluene over a 0.5 wt% Pt/ZSM-22 catalyst. The incorporation
of this kinetic model in the simulation of an industrial hydrocracker revealed
effects such as hot spot formation and liquid phase hydrogen depletion near the
entrance of the reactor. For higher aromatic contents hydrogen interphase mass
transfer becomes rate limiting.

References

[1]              
J. W. Thybaut, M. Saeys, G. B. Marin, Chem. Eng. J. 90 (2002) 117.

[2]              
G. te Velde, F. M. Bickelhaupt, E. J. Baerends, C.
Fonseca Guerra, S. J. A. Van Gisbergen, J. G. Snijders, T. Ziegler, J. Comp. Chem.
22 (2001) 931.

[3]              
M. Saeys, M.-F. Reyniers, M. Neurock, G. B. Marin, J. Phys. Chem. B 109 (2005) 2064.

[4]              
Boudart, M., Djéga-Mariadassou, G., Kinetics of Heterogeneous
Catalytic Reactions, Princeton University Press: Princeton (1984)

[5]              
S.G. Podkolzin, R. Alcala, J.J. de Pablo, J.A. Dumesic, J. Phys. Chem. B
106 (2002) 9604.

[6]              
G.G. Martens, G.B. Marin, AIChE J. 47 (2001) 1607.

Table 1
First principles derived kinetic and thermodynamic parameters for the LHHW rate
equation (1).

Figure 1.
Parity diagram for the methylcyclohexane outlet flow rate; Line: Experimental,
Dots: Calculated based on first principles kinetic model equation (eq. 1) and
parameters from Table 1.

Figure 2.
Effect of the total aromatic feed content on: a) the liquid phase temperature
and b) the liquid phase hydrogen molar flux as a function of the axial position
in the reactor at 520 K, 12 MPa and a hydrogen to hydrocarbon ratio of 25 for an
LHSV of 4.6 m_L³ (m³_cat h)^-1.