Fed-Batch Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 666

feed rate, 2) exponential feed rate, and 3) exponential and then constant feed rate strategy.
The constant rate is the easiest control strategy and commonly used. The exponential feed
operation can be at any rate, up to the maximum rate in the exponential growth phase of
a batch growth. This is the case that closely resembles a chemostat operation (Chapter 12).
The exponential feed requires the feed rate to increase exponentially and can be demanding
for the feeding system. One way to alleviate the difficulty is to feed exponentially first to
increase the feed rate at an acceptable level and then maintain a constant feed. Usually,
maximum growth rate is not optimal as by-product production can be high, which is the
main drawback of batch fermentation.
During fed-batch operations, besides the substrate and product concentrations change
with time in the reactor, the total reaction mixture (volume) also changes with time. There-
fore, comparing to common desired batch and/or flow reactors, there are at least three
balance equations needing to be dealt with before the problem can be solved.

13.1. DESIGN EQUATIONS

Evaluation of batch reactor performance relies on extensive mass and energy balances. We
have learned in Chapter 3 how mass and energy balances work. Let us apply the mass and
energy balances in this section for a fed-batch reactor. The control volume is shown in
Fig. 13.3 .

13.1.1. Overall Mass Balance in the Reactor

d ðrVÞ

d t

r F Q 0 þ 0 ¼ (13.1)

Q
S F
X F = 0

V , S , X, P

FIGURE 13.3 A schematic of fed-batch reactor. The feed volumetric rate is Q , which is sterile X F ¼ 0 and
contains the substrate at a concentration of S F . The volume of the media in the batch reactor is V , with the biomass
concentration being X , substrate concentration being S and a cellular product concentration of P .