Continuous Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 611

r X max

Growth rate
(from batch data)

r X

Cell mass balance
Slope =

D

r X = D ( X - X 0 )

0

0

X 0 X X

FIGURE 12.4 A sketch of cell mass balance on the cell mass concentration vs cell growth rate plane.

m net is the net specific growth rate, which is given by
m net ¼ m G k d

where

(12.5)
m G and k d are growth and death rate constants, respectively (h 1 ). Equation (12.3) can be rear-
ranged as

DðX X 0 Þ¼ðm G k d ÞX (12.6)

Usually, the feed media are sterile, X 0 ¼ 0, thus Eqn (12.6) gives rise to two solutions

X ¼ 0 (12.7)

or

(12.8)
Since we built the reactor to culture the cells, the trivial solution Eqn (12.7) is not a desired
solution. More often, this trivial solution is omitted. However, as we will see later, this solu-
tion could be the only solution realizable in some cases, for example when the flow rate is too
high (washout).
Figure 12.5 shows a schematic of the cell mass balance on the

D ¼ m net ¼ m G k d

m net vs S plane. Clearly, the
cell mass balance line is a horizontal line with fixed net specific growth rate equal to the dilu-
tion rate. Figures 12.4 and 12.5 show that cell mass balance can be represented differently
depending on the rate data available.
Furthermore, if the endogenous metabolism or death rate is negligible as compared to the
growth rate ( k d << m G )

(12.9)
Therefore, cells are removed in a chemostat at a rate equal to their (net) growth rate,
and the (net) growth rate of cells equals the dilution rate. This property allows the investi-
gator to manipulate net growth rate as an independent parameter and makes the chemostat
a powerful experimental tool. In simple terms, the growth rate can be controlled by the
dilution rate.

D ¼ m G