Optimization of a continuous fermentation process producing 1,3-propane diol with Hopf singularity and unstable operating points as constraints

Abstract

Oscillatory behavior was observed in both experiments and mathematical simulation during continuous fermentation of Klebsiella pneumoniae, in which biomass, product and substrate oscillations existed under certain operating conditions. These oscillations were caused by the existence of Hopf bifurcations in the system. Multiple steady states were also observed in this process. To design a stable process and achieve high product quality, these potential oscillations and unstable operating condition points should be avoided. In this paper, a quantitative index to describe potential risk distribution of operating point around Hopf point is proposed, and then the operating conditions were optimized to identify stable operating points with the Hopf singularity and unstable operating points range as a constraint. In addition, a framework of operating condition optimization considering Hopf singularity points and unstable operating points is proposed for inherently stable process design.