How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 597

8 0.8

7 0.7

6 0.6

5 0.5

4 0.4

X

P

3 0.3

2 0.2

0.1

1

0 0

0 2 4 6 8 10 12 14 16 18

t , h

FIGURE E11-3.1

Batch operations are not controlled operations. There is no control being exerted on to the
system after fermentation started other than external environment. In the same time, there is
less chance of introducing unwanted material into the system. This is also the reason that drug
productions are usually batch. We have learnt how to solve a batch reactor problem in Chapter
4. In this section, we shall use an example to refresh our understanding on batch fermentation.

Example 11-3 . Optimum Reactor Size
Production of a secondary metabolite has been characterized using a small batch reactor and
the kinetic data is shown in Fig. E11-3.1 . You are to design a reactor to produce 2Mg/year of the
product P. Batch production mode is chosen based on the approved drug production method.
Identical reaction conditions (same seed culture concentrations, pH, and temperature) will be
used as those for generating the data in Fig. E11-3.1 . Experience is that for each batch of opera-
tions, there are 6 h additional time needed for reactor loading, preparation, unloading after reac-
tion, and reactor cleaning. Determine the minimum reactor size required for this production.
Solution . The kinetic data have not been treated to obtain mathematical expressions. We
shall attempt to use a graphical method to solve this problem. Minimizing the reactor size is
equivalent to maximize the productivity of P. The productivity of P is given by

P P 0
t B

P P ¼ (E11-3.1)

where P is the product concentration at a total batch time t B (the sum of reaction time t and
preparation time t P ), while P 0 is the product concentration in the feed (or initial stream). To
maximize P P , we set

t B min

dP
dt B ðP P 0 Þ
t B

t B min ¼

t B

dP P
dt B

0 ¼ (E11-3.2)