Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 838

(a) Both species can coexist if there is a common substrate concentration at which both
growth rate of A and growth rate of B are equal, and equal to the dilution rate. That is,

D ¼ m A ¼ m B (E16-7.1)

The growth rates are given by
m A ¼ m Amax S

1 : 5 m Bmax S
3K SB þS K SA þS ¼

(E16-7.2)

and

m B ¼ m Bmax S
K SB þS

(E16-7.3)

Solving Eqns (E16-7.1) through (E16-7.3) , we obtain
S ¼ 3 K SB and D ¼ m A ¼ m B ¼ 0:75 m B max
Therefore, there is a solution to the coexistence problem. It is possible to maintain both
species in the reactor. A sketch of the solution is shown in Fig. E16-7 .

(b) Refer to Fig. E16-7 , because species A has high growth rate that species B, only species A
will survive. At the same dilution rate, the substrate concentration will be driven lower
than species B can survive,
(c) Refer to Fig. E16-7 , because species B has higher growth rate at low substrate
concentrations, species B will remain in the reactor.
(d) The coexistence point cannot be maintained sustainably as it is not a stable solution.
It is clear than when the dilution rate fluctuates away from 0.75 m Bmax , one of the

1.4 1.4

µ A

1.2 1.2

µ B

1.0 1.0

Co-existence 0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2

0.0 0.0

0 1 2 3 4 5 1 0 1 0 0

Common Substrate Concentration, K SB

FIGURE E16-7