316635 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 ждt 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 | Model 2 | error/% | Model 3 | error/% | Model 4 | error/% | |
Reaction Num. | 1273 | 1104 | - | 1232 | - | 961 | - |
Computation time/s | - | 25460 | - | 2730 | - | 9 | - |
C2H4 | 33.8782 | 33.8711 | -0.02 | 33.8899 | 0.03 | 33.8862 | 0.02 |
CH4 | 18.7021 | 18.6895 | -0.07 | 18.7025 | 0.002 | 18.7013 | -0.004 |
C3H6 | 11.2494 | 11.235 | -0.13 | 11.2417 | -0.07 | 11.2451 | -0.04 |
C4H6 | 3.9427 | 3.9627 | 0.51 | 3.945 | 0.06 | 3.9421 | -0.02 |
IC4H8 | 1.4277 | 1.4171 | -0.74 | 1.426 | -0.12 | 1.4259 | -0.13 |
C2H6 | 3.7208 | 3.7035 | -0.46 | 3.7228 | 0.05 | 3.7217 | 0.02 |
NC4H8 | 0.0608 | 0.0607 | -0.16 | 0.0607 | -0.16 | 0.0608 | 0 |
H2 | 0.6166 | 0.6164 | -0.03 | 0.6162 | -0.06 | 0.6165 | -0.02 |
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.
* Corresponding author. Tel.: +86 10 62781499; fax: +86 10 62770304.
E-mail address: dcecbz@tsinghua.edu.cn (Bingzhen Chen)
See more of this Group/Topical: Computing and Systems Technology Division