Monod growth kinetics exponential phase

FIGURE 2-27 Cell density versus time in a batch culture. During the lag phase, the cells become acclimated. During the exponential phase, the number of cells increases exponentially as described by Monod growth kinetics, see Eq. [2-73]. During the stationary phase, cell density is constant for some time before the culture declines due to substrate depletion, waste accumulation, and/or excessive cell density. 

A limiting case of Monod kinetics has Ks = 0 so that cell growth is zero order with respect to substrate concentration. Rework Example 12.7 for this situation, but do remember to stop cell growth when S = 0. Compare your results for X and p with those of Example 12.7. Make the comparison at the end of the exponential phase. 

The ability of Monod s empirical relation to fit kinetic data for biochemical reactions has its foundations in generalizations of two phenomena frequently observed for fermentation processes (1) nature places a cap on the quantity of microorganism that can be achieved during the exponential phase of growth in a bioreactor operating in a batch mode and (2) as the concentration of the limiting substrate approaches zero, the rate laws for biochemical reactions approach pseudo-first-order behavior with respect to that substrate. The cap indicated on the cell growth rate has been associated with the natural limit on the maximum rate at which replication of DNA can be achieved. 

Table 6.1 shows the ACSL program and Figure 6.6 shows the results. Comparison of Figure 6.6 with Figure 6.1 shows that Monod kinetics can predict the cell growth from the start of the exponential growth phase to the stationary phase. 

In contrast, with the differential method of analysis, only a single experiment need be carried out. However, in this experiment x(t) and s t) are simultaneously measured. As suggested in Fig. 4.19, measurements made at about 2-hour intervals are sufficient from the beginning of the experiment to the beginning of the exponential growth phase. In the range where Monod kinetics are to be characterized in effect, measurements should be repeated every few minutes (this is also the reason why, for example, semicontinuous addition... 

The rate of biomass production, i.e., the increase in the number of cells during the exponential growth phase, is described by the empirical Monod-kinetics, which are shaped after the Michaelis-Menten kinetics for enzymatic reactions ... 

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