Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 690587, 18 pages
Research Article

Modeling and Parameter Identification Involving 3-Hydroxypropionaldehyde Inhibitory Effects in Glycerol Continuous Fermentation

School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, China

Received 9 July 2012; Accepted 21 September 2012

Academic Editor: Gerhard-Wilhelm Weber

Copyright © 2012 Zhaohua Gong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Mathematical modeling and parameter estimation are critical steps in the optimization of biotechnological processes. In the 1,3-propanediol (1,3-PD) production by glycerol fermentation process under anaerobic conditions, 3-hydroxypropionaldehyde (3-HPA) accumulation would arouse an irreversible cessation of the fermentation process. Considering 3-HPA inhibitions to cells growth and to activities of enzymes, we propose a novel mathematical model to describe glycerol continuous cultures. Some properties of the above model are discussed. On the basis of the concentrations of extracellular substances, a parameter identification model is established to determine the kinetic parameters in the presented system. Through the penalty function technique combined with an extension of the state space method, an improved genetic algorithm is then constructed to solve the parameter identification model. An illustrative numerical example shows the appropriateness of the proposed model and the validity of optimization algorithm. Since it is difficult to measure the concentrations of intracellular substances, a quantitative robustness analysis method is given to infer whether the model is plausible for the intracellular substances. Numerical results show that the proposed model is of good robustness.