Dynamic model fermentation reactor

In this chapter the dynamics of fermentation reactors for the production of penicillin will be discussed. Since these reactors are usually operated in a fed-batch mode, this mode will be discussed in addition to a continuous operation mode. For the continuous reactor, the nonlinear dynamic model will be linearized to explain the dynamic responses of the reactor concentrations to a change in feed rate. 

Putting these important issues aside, the production of ethanol by batch fermentation is an important example of a batch reactor. The basic regulatory control of a batch ethanol fermentor is not a difficult problem because the heat removal requirements are modest and there is no need for very intense mixing. In this section we develop a very simple dynamic model and present the predicted time trajectories of the important variables such as the concentrations of the cells, ethanol, and glucose. The expert advice of Bjom Tyreus of DuPont is gratefully acknowledged. Sources of models and parameter values are taken from three publications.1 3... 

Consider a simple isothermal fed-batch fermenter with a single bio-reaction where biomass (with concentration X) is produced using some substrate (with concentration 5). Assume that only substrate is fed into the reactor with concentration Sp. If constant physico-chemical properties and the presence of an inert solvent are assumed then the lumped dynamic model of a simple fed-batch fermentor is as follows ... 

Gonzalez-Figueredo, C., De La Torre, L.M., and Sanchez, A. (2010) Dynamic modeling and experimental validation of a solid-state fermentation reactor. lEAC Proc. Vol, 11, 221-226. 

So far, chemical processes have been discussed as well as fermentation reactors. These systems can be characterized by the fact that there are usually no discontinuities in the model equations. In physiological systems, however, there is often a threshold value that has to be succeeded before certain phenomena take place. This causes a threshold non-linearity in the model and therefore these systems can be analyzed well through simulation but theoretically they are difficult to analyze. It is not the purpose of this chapter to discuss different physiological models the two systems that will be selected for illustration of system dynamics are the modeling of glucose-insulin dynamics and cardiovascular modeling approaches. 

The two extreme hypotheses on mixing produce lumped models for the fluid dynamic behavior, whereas real reactors show complex mixing patterns and thus gradients of composition and temperature. It is worthwhile to stress that the fluid dynamic behavior of real reactors strongly depends on their physical dimensions. Moreover, in ideal reactors the chemical reactions are supposed to occur in a single phase (gaseous or liquid), whereas real reactors are often multiphase systems. Two simple examples are the gas-liquid reactors, used to oxidize a reactant dissolved in a liquid solvent and the fermenters, where reactions take place within a solid biomass dispersed in a liquid phase. Real batch reactors are briefly discussed in Chap. 7, in the context of suggestions for future research work. 

---