(291h) Top-Down Kinetic Modeling: A Transient Solution Strategy to Assess Benzene Hydrogenation Kinetics
AIChE Annual Meeting
2019
2019 AIChE Annual Meeting
Catalysis and Reaction Engineering Division
Reaction Path Analysis
Tuesday, November 12, 2019 - 10:06am to 10:24am
1. Introduction
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. 2. Method 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. 3. Results
and discussion 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 7.4·104,
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 2.9·105, 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 4.8·105
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. Conclusions
and future work 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. References
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. 2. Method 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. 3. Results
and discussion 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 7.4·104,
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 2.9·105, 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 4.8·105
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. Conclusionsand future work 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. 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. 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. Ind. Eng. Chem. Res. 50 (2011)
12933–45.