Design of Fermentation Processes
367
9.1.5 Fed-Batch Operation
As indicated in table 9.1 the operation of bioreactors in semi batch mode is very popular in the
fermentation industry.
The reactor is
started as a batch, and a suitably large biomass
concentration is obtained by consumption of the initial substrate. The rate of product formation is
typically low or even zero during the batch cultivation. At a certain time, usually when the
substrate level has decreased to a very low level, a feed of (usually very concentrated) substrate
is initiated. At the same time an
inducer
may be added to switch on the metabolic pathways that
lead to the desired product. During the whole
fed batch
period no product is withdrawn from the
reactor, and the medium volume keeps increasing. At the end of the fed batch period a certain
portion of the reactor volume may be withdrawn and sent to down-stream processing. New
substrate is added, and after a batch period a second fed batch period is started. This is
repeated
fed batch
operation. It will work satisfactorily if the remainder of biomass used to grow up a new
culture has not been weakened, and perhaps producing the desired product with a low yield.
When a time-varying feed stream
v(t)
containing one or more of the substrates at a constant
concentration
cf
is admitted to a stirred tank reactor without withdrawal of a corresponding effluent
stream, the mass balances become
=
+C~T
=
+
+ c/ v(0
(9.52)
dt
dt
dt
dt
7
The mass balances for the fed-batch operational mode therefore become
dc
~dt
= q(c) + ^ ^ - ( c /
V(t)
f
c)
(9.53)
There is a striking similarity between Eq. (9.53) and the mass balances for a stirred tank reactor. In
Eq. (9.53), the dilution rate
D
= v(r) /
V(t)
is, of course, a function of time, and the fed-batch model
is in principle a purely transient model, although most results can safely be derived assuming that
the growth is balanced.
One may visualize the fed-batch as a control problem: Subject to certain constraints it is possible to
choose the control function
v(t)
such that a given goal is reached. This goal may be defined at the
end of the fermentation process where
V{t)
has reached a specified value. This end-point control
problem is a classical problem of control theory: e.g., to choose
sf
and the initial values
s0
and
x0
that characterize the state when the fed-batch process v(r) is initiated so that a given state
(x^s)
is
reached in the shortest possible time. The chemical engineering literature abounds with solutions of
this kind of problem. Typical references are Menawat
et al.
(1987) and Palanki
et ai
(1993). We
shall, however, choose to study two simpler problems where the control action is applied with the
purpose of achieving certain metabolic conditions for the cell culture at every instant during the
fermentation. The concept of an instantaneous control action is illustrated in sufficient generality
with only one growth-limiting substrate and the biomass as the state vector. To simplify the
discussion maintenance free kinetics will be used.
previous page 390 Bioreaction Engineering Principles, Second Edition  read online next page 392 Bioreaction Engineering Principles, Second Edition  read online Home Toggle text on/off