(435e) Methane Steam Reforming Unraveled By the Microkinetic Engine, a User-Friendly Kinetic Modelling Tool

Kinetic
modelling forms the bridge between the phenomena occurring at the molecular and
reactor scale. It results in a mathematical representation of the underlying
reaction mechanisms which ratify or debunk the assumptions made. This turns it
an important activity in chemical engineering because it allows the
optimization and intensification of industrial chemical processes. From an
industrial point of view, global kinetic models such as power law or
Langmuir-Hinshelwood-Hougen-Watson (LHHW) models
often provide sufficient, reliable information for process control and
optimization. However, decreasing margins and increasing computational
capabilities open up perspectives for more fundamental kinetic modelling for
industry which, up to recently, was only exploited by academia. In addition,
the shift towards ‘green’ production processes underlines the need for a more
detailed understanding of the more complex nature of biomass conversion.

Dedicated
software with various features is available to construct such (micro)kinetic
models. However, there is a significant induction period for novices in the
field of kinetic modelling since a good knowledge of chemistry, mathematics,
statistics and (chemo)informatics is required. In order to make fundamental
kinetic modelling more accessible and to reduce the time spent for model
construction, a user-friendly tool has been developed: the MicroKinetic
Engine (µKE).

MicroKinetic Engine (µKE)

The
µKE is a software package for the simulation and regression of chemical
kinetics and even non-chemical applications such as solar cells. This package
has been developed during the last decade at the Laboratory for Chemical
Technology, Ghent University and was originally constructed for the detailed
kinetic modelling of heterogeneously catalyzed reactions. In order to simulate
different reactor types, both differential and algebraic solvers are integrated
in the software’s library. To enable model regression to experimental data, two
deterministic regression routines are included, i.e., the Rosenbrock
[1] and Levenberg-Marquardt algorithm [2]. A
Graphical User Interface (GUI), see Figure 1 (left), is wrapped around all
these routines such that no programming effort whatsoever is required from the
µKE user, making it very distinct from other chemical modelling tools such as
Athena Visual Studio [3] or Chemkin [4].

Figure 1.
Graphical User Interface of the MicroKinetic Engine.
Left: window for problem definitions, right: window for automatic network
generation

The
µKE consists of an onion structure as indicated in Figure
2. At its core, the µKE has the kinetic model which expresses the
reaction rates of every (elementary) step included in the reaction network. By
default, the law of mass action is applied to describe these reaction rates,
but also power laws or user defined rates can be included. Due to the latter,
also applications other than chemical kinetics can be handled by the µKE, for
example simulating a solar cell’s performance as a function of its properties
and the applied voltage. These rate equations are subsequently incorporated in
a reactor model which describes the mass balance of all components over the
selected reactor type. The corresponding set of algebraic and/or differential equations
is solved using DASPK3.0 [5] in order to calculate the individual outlet flow
rates. If regression is required, an additional shell is activated in which the
Rosenbrock method performs a first estimation effort,
after which the Levenberg-Marquardt algorithm is
called to further optimize the parameter estimates. Both regression algorithms
are based on the minimization of the (weighted) residual sum of squares of the
responses in order to determine optimal parameter estimates.

Figure 2. Structure of the MicroKinetic Engine

The
input of the µKE comprises (initial) parameter values, experimental data,
including independent and dependent variables, and the proposed reaction
network for chemical kinetics. The reaction network can be constructed either
manually via the GUI, or automatically based on the integration with the
Reaction Network Generator (ReNGeP) [6] or, by extension, by any other network
generation program, see Figure 1 (right). The µKE automatically converts the
reaction network into the corresponding rate equations which are subsequently
substituted in the reactor model. Instead of a reaction network, user-defined
equations can be given which are applicable to both chemical and non-chemical
systems. The output of the optimization procedure consists of the model
predictions and, in case of regression, an extended statistical analysis and
the corresponding optimal parameter estimates. In case of reversible steps, the
parameter estimates are determined such that thermodynamic consistency is
assured for each of the reaction steps. Additionally, the µKE identifies
quasi-equilibrated reaction steps while no assumptions have to be made a
priori on rate-determining step(s) or quasi-equilibria. If required, a rate
of production analysis is performed by the µKE providing an additional layer of
insight in the reaction network included.

Methane
steam reforming

To
demonstrate the features and versatility of the µKE, methane steam reforming is
selected as a case study. To model the reaction mechanism of this industrially
relevant process, a LHHW type kinetic model is proposed. The model is regressed
to the experimental data acquired by Oyama et al.. The dataset comprises 80
experiments, performed in a tubular packed bed reactor at a total pressure of
0.4 MPa in a temperature range from 893 to 943 K with space times ranging from
0.82 to 5.76 kg s mol^-1 and CH₄ to H₂O molar
ratios between 0.125 and 0.7. In some experiments, CO, CO₂ and/or H₂
were added to the feed. The catalyst is an industrial SiO₂-MgO
supported Ni catalyst.

The
reaction network used for the kinetic model is shown in Figure 3. The
adsorption/desorption steps are assumed to be in quasi-equilibrium, without
making a priori any other assumptions about the surface reactions. The
weighted regression of this adequate model was found to be globally significant
(F_cal = 10325 and F_tab
= 2) with statistically significant parameter estimates, see Table 1. The model
showed an acceptable performance combined with a clear physical meaning, see
Figure 4.

Figure 3.
Reaction network for the Langmuir-Hinshelwood kinetic model for methane steam
reforming.

Figure 4.
Methane conversion as a function of the water inlet pressure at a total
pressure of 0.4 MPa and a temperature of 923 K. Symbols: experimentally
observed with blue =  40 kPa inlet partial
pressure of CH₄ (p_CH4,in) or a space time of 2.88 kg s
mol^-1, red = 80 kPa p_CH4,in or
1.44 kg s mol^-1, green = 120 kPa p_CH4,in
or 0.96 kg s mol^-1, full line: simulated via weighted regression.

Table 1.
95% confidence interval of the model parameters of the Langmuir-Hinshelwood
model.

A
rate of production analysis (RPA) is performed with the µKE, based on the parameter
estimates of the Langmuir-Hinshelwood model. In the selected experiment for the
RPA a mixture containing 120 kPa CH₄, 200 kPa H₂O and 80 kPa N₂
(inert) is fed to the reactor at a temperature of 923 K and a space time of
0.96 kg_cat s mol^-1, resulting
in a conversion of 30 % and selectivities to CO and CO₂ equal to 30
and 70% respectively. The visual representation of the RPA at the beginning and
the end of the reactor is shown in Figure 5. Based on the RPA, it is clear that
both at the beginning and the end of the reactor the forward steps are most
dominant as indicated by the differences in arrow thickness in Figure 5.
Throughout the reactor the water-gas shift reaction gains importance.

Conclusion

Through
the case study of methane steam reforming, the µKE has proved to be a well
performing and strongly user-friendly software package for the simulation and
regression of chemical kinetics. With minor user intervention, regressions
could be performed providing, in an automated manner, the statistical
interpretation of these results, such that the user can focus on their physical
interpretation. A rate of production analysis was successfully carried out at
two positions in the reactor and indicated the sequence of the steam reforming
followed by the water-gas shift reaction. Additionally, both reactions are
close to being irreversible.

Figure 5.
Visual representation of the rate of production analysis of the
Langmuir-Hinshelwood model. Left: forward steps, right: reverse steps, top: at
reactor inlet, bottom, at reactor outlet. Experimental conditions: inlet flow
containing 120 kPa CH₄, 200 kPa H₂O and 80 kPa N₂
at a temperature of 923 K and a space time of 0.96 kg_cat
s mol^-1, resulting in a conversion of 30 % and selectivities to CO
and CO₂ equal to 30 and 70 % respectively.

References

[1] H.H. Rosenbrock,
AN AUTOMATIC METHOD FOR FINDING THE GREATEST OR LEAST VALUE OF A FUNCTION, Comput. J., 3 (1960) 175-184.

[2] D.W. Marquardt, AN ALGORITHM
FOR LEAST-SQUARES ESTIMATION OF NONLINEAR PARAMETERS, Journal of the Society
for Industrial and Applied Mathematics, 11 (1963) 431-441.

[3] Athena Visual Studio, http://www.athenavisual.com/.

[4]
Chemkin, http://www.reactiondesign.com/products/chemkin/chemkin-2/.

[5]
S. Li, L. Petzold, DASPK 3.0, https://techtransfer.universityofcalifornia.edu/NCD/10326.html.

[6]
J.W. Thybaut, G.B. Marin, Single-Event MicroKinetics:
Catalyst design for complex reaction networks, J. Catal.,
308 (2013) 352-362.