An Approach Considering Both Operation Stability and System's Hopf Bifurcations to Chemical Process Design

In order to consider the inherent safety of chemical processes, researchers proposed many methods and strategies, many quantitative indices have been developed to describe the potential hazard and dangerous of different reaction routes and reactants. In authors' previous paper[1] an integrated quantitative index considering both speed to return to steady state point and capability of resistance to disturbances is introduced. In the other hand, oscillation behavior was observed in both experiment and mathematical simulation in some chemical processes[2-10], in which the concentration of feedstock and product oscillation occur under certain operation conditions. In order to design a more stable process, these potential oscillations should be avoided. And it is reported that the oscillation was caused by the existence of Hopf bifurcations in systems[2, 11]. Since all Hopf singularity points can be identified by using mathematic calculation under given operation condition range, consequently, the Hopf singularity point range can be determined. This paper proposed a design approach to chemical process design, considering both operation point stability and systems Hopf singularity points to improve the process stability and avoid potential oscillation in process. The detailed steps of this approach are described as follows:

(1)    Solve the steady state solution of the dynamic model of chemical process.

(2)    Judge the stability of these solutions and divide the solution curve into parts with different stabilities (stable and unstable).

(3)    Calculate the integrated quantitative stability index of the process system

(4)    Calculate Hopf points under the possible operation condition range.

(5)    Formulate a multi-objective optimization problem for the process design in which the quantitative stability index together with the economic index are considered as objectives and the Hopf points ranges are involved as constraints,

(6)    Obtain the optimal operation conditions.

The proposed approach is applied to a continuous fermentation process and a multi-objective optimization problem considering both economic and stability factors were conducted, and the Hopf points ranges are considered as constraints at the same time in this optimization problem. After calculation, a Pareto set is obtained. The optimization results provide information that is very useful for guiding process design and operation. From this study, conclusions can be drawn:

(1)      Quantitative stability index is useful in multi-objective optimization problem when stability was considered as one of the objectives.

(2)      Hopf singularity points range can be considered as constraints in optimal process design problems to avoid the potential oscillation in process.

References:

1.            Wang, H., et al., An integrated quantitative index of stable steady state points in chemical process design, in Proceedings of the 11th International Symposium on Process Systems Engineering, I.A. Karimi and R. Srinivasan, Editors. 2012, Elsevier B.V.: Singapore

2.           Sridhar, L.N., Elimination of Oscillations in Fermentation Processes. AIChE Journal, 2011. 57(9): p. 2397-2405.

3.            Paz Astudillo, I.C. and C.A. Cardona Alzate, Importance of stability study of continuous systems for ethanol production. Journal of Biotechnology, 2011. 151(1): p. 43-55.

4.            Bai, F.W., W.A. Anderson, and M. Moo-Young, Ethanol fermentation technologies from sugar and starch feedstocks. Biotechnology Advances, 2008. 26(1): p. 89-105.

5.            Bai, F.W., et al., Parameter oscillations in a very high gravity medium continuous ethanol fermentation and their attenuation on a multistage packed column bioreactor system. Biotechnology and Bioengineering, 2004. 88(5): p. 558-566.

6.            McLellan, P.J., A.J. Daugulis, and J.H. Li, The incidence of oscillatory behavior in the continuous fermentation of Zymomonas mobilis. Biotechnology Progress, 1999. 15(4): p. 667-680.

7.            Daugulis, A.J., P.J. McLellan, and J.H. Li, Experimental investigation and modeling of oscillatory behavior in the continuous culture of Zymomonas mobilis. Biotechnology and Bioengineering, 1997. 56(1): p. 99-105.

8.            Sprenger, G.A., Carbohydrate metabolism in Zymomonas mobilis: a catabolic highway with some scenic routes. FEMS Microbiology Letters, 1996. 145(3): p. 301-307.

9.            Ghommidh, C., et al., Oscillatory behaviour of Zymomonas in continuous cultures: A simple stochastic model. Biotechnology Letters, 1989. 11(9): p. 659-664.

10.          Jöbses, I., et al., Fermentation kinetics of Zymomonas mobilis at high ethanol concentrations: oscillations in continuous cultures. Biotechnology and Bioengineering, 1986. 28(6): p. 868-877.

11.          Kuznetsov, Y.A., Elements of applied bifurcation theory. 1998, New York: Springer

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* Corresponding author. Tel.: +86 10 62781499;fax: +86 10 62770304.

E-mail address: dcecbz@tsinghua.edu.cn  (Bingzhen Chen)