Fed-Batch Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 670

13 .2. IDEAL ISOTHERMAL FED-BATCH REACTO RS

Each balance equation governs the change of composition for one component (or temper-
ature) in the reactor. These compositions affect each other in the reactor due to the work of the
cells as well as the feed in an interactive manner. Therefore, Eqns (13.9) , (13.17) , and (13.19)
need to be solved simultaneously to determine the cell biomass, substrate, and extracellular
product concentrations in the reactor. An automatic integrator such as the ODExLIMS is
useful in this regard.
Figs. 13.4 through 13.8 show how the biomass production (or accumulation) XV , substrate
accumulation SV, and the concentrations of the substrate S and biomass X in the reactor for
different feed (constant feed rate vs exponential feed rate), growth (without maintenance or
a constant specific death rate), and initial conditions. These figures can help us understand
how the growth can be controlled by a feed stream.
Fig. 13.4 shows the reactor contents change for a constant feed rate equal to

m max V 0 .Here
m max is the maximum growth rate in the Monod growth equation, which is assumed to be
valid. The saturation constant K S ¼ 0.05 S F . At the start, the concentrations of the biomass

FIGURE 13.4 Biomass production and substrate accumulation in the reactor as a function of time for constant
feed rate of Q ¼ m max V 0 . The initial conditions are S 0 ¼ S F and X 0 ¼ 1.05 YF X/S S F . The Monod saturation constant

K S ¼ 0.05 S F .