# (291h) Top-Down Kinetic Modeling: A Transient Solution Strategy to Assess Benzene Hydrogenation Kinetics

- Conference: AIChE Annual Meeting
- Year: 2019
- Proceeding: 2019 AIChE Annual Meeting
- Group: Catalysis and Reaction Engineering Division
- Session:
- Time: Tuesday, November 12, 2019 - 10:06am-10:24am

4.0pt;margin-left:17.85pt;text-align:justify;text-indent:-17.85pt;line-height:

150%">**1. ****Introduction**

150%">A

top-down methodology can be applied to the kinetic modeling of chemical

reactions by gradually extending the complexity of the considered mechanism

with relevant elementary steps. The MicroKinetic Engine (μKE) is a

user-friendly software tool developed for this purpose within the Laboratory

for Chemical Technology at Ghent University [1], which enables the construction

and evaluation of (micro)kinetic models. The software has originally been

developed to perform steady-state simulations, as well as regression with steady-state

experimental intrinsic kinetic data [2,3]. The inclusion of a time-dependent

term as an additional independent variable now allows assessing transient phenomena

using the µKE, including the time integration towards a steady-state solution. The

latter feature proved to be essential for the application of the top-down

methodology to benzene hydrogenation, starting from simple power law kinetics

till more detailed models.

4.0pt;margin-left:17.85pt;text-align:justify;text-indent:-17.85pt;line-height:

150%">**2. ****Method**

150%">Initially

developed for allowing kinetic modeling of (complex) catalytic reaction

networks [1], the μKE now incorporates the component mass balances in

transient terms for continuous stirred-tank reactors (CSTR). By avoiding the

pseudo-steady state approximation for the surface intermediates, the CSTR can

now be described by a set of ordinary differential equations (ODEs), where the

initial conditions (at 0 s, before reactants are fed) are known, thus

facilitating the approach to a steady-state solution. For the considered

mechanism, quasi-equilibrated reactions were identified, accordingly reducing the

number of differential equations. The method of lines coupled with backward

differentiation formulas was used for ODEs integration. Both the Rosenbrock and

Levenberg‒Marquardt algorithms [4,5] were employed during the nonlinear

parameter regression against the experimental data obtained at steady-state.

4.0pt;margin-left:17.85pt;text-align:justify;text-indent:-17.85pt;line-height:

150%">**3. ****Results
and discussion**

150%">For the hydrogenation of benzene, the top-down kinetic modelling

methodology was applied. From a single overall reaction based on power law

kinetics to a more detailed model with the relevant elementary steps, passing

through a reactants adsorption model, the behavior of the hydrogenation of

benzene could be reproduced. Table 1 shows the three mechanisms tested: a power

law model, a reactants adsorption model and a Langmuir-Hinshelwood model, while

a graphical representation of the model performances is given in Figure 1. Although

the parameter estimates obtained for the power law model were statistically

significant, without any binary correlation coefficients exceeding 0.95, and

the regression was also globally significant with an *F* value of 7.4·10^{4},

greatly exceeding the tabulated one of 3.9 (Table 1), the model simulated concentrations

do not reproduce the experimental data well [6]. The addition of the

dissociative adsorption of hydrogen and the adsorption of benzene, as

quasi-equilibrated reactions, to the model, leading to the reactants adsorption

model, resulted in a better agreement between model simulated and the

experimentally obtained concentrations. The regression was again globally

significant with an F-value of 2.9·10^{5}, greatly exceeding the tabulated

one of 3.2 (Table 1), while the parameters were also statistically significant and

did not have binary correlation coefficients exceeding 0.95. The Langmuir-Hinshelwood

model is obtained after adding the desorption of cyclohexane, also as a

quasi-equilibrated step, to the model. The model simulated concentrations now

reproduce the experimental data well. The parameters were again statistically

significant and did not have binary correlation coefficients exceeding 0.95. The

*F *value for the global significance of the regression amounts to 4.8·10^{5}

which considerably exceeds the tabulated one, i.e., 3.0. From the three

considered mechanisms, the concentrations simulated with the Langmuir-Hinshelwood

model reproduce more accurately the experimentally obtained concentrations,

while describing the reaction network in more detail.

4.0pt;margin-left:17.85pt;text-align:justify;text-indent:-17.85pt;line-height:

150%">**4. ****Conclusions
and future work**

150%">A

top-down kinetic modelling methodology coupled

with a transient solution strategy was applied to the hydrogenation of benzene.

From the three considered mechanisms, the Langmuir-Hinshelwood

model was suspected to be the best performing one, reproducing the

experimental data accurately while describing the reaction network in detail.

The statistical basis of the three regressions will be further evaluated. The

top-down methodology is suitable for mechanism elucidation, as proven here, and

can be exploited for more complex mechanisms using μKE. With the increase

of the complexity, i.e., by increasing the number of surface species in detailed

reaction networks, the mathematical effort intensifies, thus demanding the aide

of transient strategies, available in the μKE. The advantages of transient

solution strategy over the steady-state strategy will be further explored.

margin-left:0cm;text-align:justify;line-height:150%">**References**

[1] K.

Metaxas, J. W. Thybaut, G. Morra, D. Farrusseng, C. Mirodatos, G.B. Marin. Top.

Catal., 53 (2010) 64‒76.

[2] N.

Kageyama, B. R. Devocht, A. Takagaki, K. Toch, J. W. Thybaut, G. B. Marin, S.

T. Oyama.
" arial>Ind. Eng. Chem. Res. 56 (2017) 1148–58.

[3] C.

Sprung, P. N. Kechagiopoulos, J. W. Thybaut, B. Arstad, U. Olsbye, G. B. Marin.

Appl. Catal. A: Gen. 492 (2015) 231–42.

[4] H.

Rosenbrock. Comput. J. 3 (1960) 175–84.

[5]

D.W. Marquardt. SIAM J. Appl. Math. 11 (1963) 431–41.

[6] T.

Bera, J. W. Thybaut, G. B. Marin.
line-height:150%;font-family:" arial>Ind. Eng. Chem. Res. 50 (2011)

12933–45.

150%">** **