(295e) Comparison of Different Simplification Methods for Complex Reaction Networks

Comparison of Different Simplification Methods for Complex
Reaction Networks

Lei Zhang, Tong Qiu,
Bingzhen Chen*

Department of Chemical
Engineering, Tsinghua University, Beijing, China

Abstract

To develop a more reliable and
robust model, elementary reaction networks are widely studied and used in
chemical engineering, combustion science, atmosphere simulation and etc. The
elementary reaction model was first proposed by Rice and Herzfeld [1] in 1934.
Elementary reaction model usually contains thousands of reactions and hundreds
of species, and it remains a problem to determine the reaction rate constants
until an automatic reaction network generation technique, such as RMG [2], is
fully developed. But there still exist a large amount of unimportant reactions
in the automatic generated model. So reaction network simplification is needed
to reduce the model and CPU time before the reaction model is used.

In this paper, three
different simplification methods: principle
component analysis (PCA), computational singular perturbation (CSP) and
reaction rate analysis are taken to make a simplification for a naphtha steam
cracking reaction model containing 1273 elementary reactions and 114 species
(Model 1), respectively. This model was established by authors earlier. Based
on the simplification results, a comparison of these three methods has been
provided in terms of their efficiency.

PCA was introduced to
kinetic model by Vajda [3] in 1985. It is an eigenvalue-eigenvector analysis
used to extract meaningful kinetic information from linear sensitivity
coefficients computed for several species of a reacting system at several time
points. According to the eigenvalue-eigenvector analysis of Jacobian matrix and
linear transformation from the reactions to the principle components, small
principle components can be neglected from the reaction network. 169 reactions
are removed using PCA (Model 2) and the errors compared with the original
reaction model are less than 0.74%.

The theory of CSP uses
the eigenvalues of Jacobian matrix to order the trial modes, and provides a
refinement procedure to improve the decoupling of the trial fast and slow
subspaces [4]. Events whose time scales are shorter than ¦¤t are considered fast
modes, and all others are considered the slow modes. A simplified reaction
model can be obtained from neglecting the fast mode reactions. 41 reactions are
removed using CSP (Model 3) and the errors are less than 0.16%.

The average reaction rate along
the reactor shows the level of importance for the reaction in the model. So the
direct way of simplify the reaction model is to set a limit to the reaction rate
for all reactions. If the reaction whose average reaction rate less than the
specified reaction rate limit, it can be neglected. The reaction rate limit
controls the error caused by the simplification and different simplified models
will be generated for different reaction rate limits. Here, 312 reactions are
removed using reaction rate analysis (Model 4) and the errors are less than
0.13%. Meanwhile, as this method needn't use the information from Jacobian
matrix, so it is easier to be implemented compared with other two methods.

In summary, in PCA method, as the
principle components are the linear transformation from the reactions, so important
reactions may be included in the unimportant principle components; In CSP
method, all the Jacobian matrixes of every point along the reactor have to be
considered, so the computation is time consuming. Table 1 shows the
simplification results of PCA, CSP and reaction rate analysis methods. It can
be seen from the simplification results that the
reaction rate analysis can
be considered as an efficient and fast way for reaction network simplification.

Table
1. Results
of PCA, CSP and reaction rate analysis simplification model

Model 1: The
original reaction model; Model 2: Simplified reaction model using PCA; Model 3:
Simplified reaction model using CSP; Model 4: Simplified reaction model using
reaction rate analysis.

Key Words: Reaction network
simplification, Reaction rate analysis, Principle component analysis,
Computational singular perturbation, Elementary reaction network

References:

[1]   Rice, F. O., and
K. F. Herzfeld. "The thermal decomposition of organic compounds from the
standpoint of free radicals. VI. The mechanism of some chain reactions." Journal
of the American Chemical Society 56.2 (1934): 284-289.

[2]   William H. Green,
et al.; "RMG - Reaction Mechanism Generator v4.0",
2013, http://rmg.sourceforge.net/

[3]   Vajda, S., et
al.. "Principal Component Analysis of Kinetic-Models." International
Journal of Chemical Kinetics 17.1 (1985): 55-81.

[4]   Lam, S. H., and
D. A. Goussis. "The CSP method for simplifying kinetics." International
Journal of Chemical Kinetics 26.4 (1994): 461-486.