Linearization 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. 

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 main difference in the three synthesis routes detected so far— DA-SHF, DA-SHCF, and DA-SSCF—is the hydrolysis and fermentation reactor distributions. Then, a comparison of annual fixed costs for reactor tanks is used in this level as a final factor. The reacting volume was estimated by relating the volume flow obtained from the simulations and the dilution rate reported in Table 2.11. The total reactor volume was then estimated as 20% above the reacting volume, and four different tank capacities were considered in order to achieve the total reactor volume (Table 2.12). The tank cost estimations were based on the data reported by Aden et al. (2002) with a linear depreciation in 10 years. Table 2.13 shows the annual fixed cost and the annual production for each option, from which unit costs per gallon of ethanol were estimated. 

The resultant equations are non-linear and in this general case numerical solution techniques must be used. However, there exists a special case where an analytical solution may be obtained. If the increase in biomass concentration during flow through the reactor is small then an average value for the biomass concentration, independent of the distance Z along the fermenter, may be used. The material balance for the substrate over the reactor element may then be written ... 

In batch fermentation, the number of cells of the microorganism present in the reactor typically varies with time in the manner shown in Figure 13.1. Readers should note that the scale of the ordinate is logarithmic while that of the abscissa is linear. Some authors describe the cell growth cycle shown in Figure 13.1 in terms of the four primary phases, while others include two smooth transitions between primary phases as additional growth phases. 

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