Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 857

16.24. Organism A grows on substrate S and produces product P, which is the only substrate
that organism B can utilize. The batch kinetics gives rise to
d X A

d t ¼ m Amax S K S þS X A

d X B

d t ¼ m Bmax P K P þP X B

d P

d t ¼ YF P=A m Amax S YF B=P m Bmax P

1

K S þS X A K P þP X B

YF P = A

d S
d t ¼ YF A=S m Amax S

1

YF P=S m Amax S K S þS X A K S þS X A

Assume the following parameter values:
m Amax ¼ 0.18 h 1 ; m Bmax ¼ 0.29 h 1 , K S ¼ 0.42 g/L, K P ¼ 0.30 g/L, YF A/S ¼ 0.30 g/g,

YF B/S ¼ 0.5 g/g, YF P/S ¼ 1.0 g/g, YF P/A ¼ 4.0 g/g, S 0 ¼ 10 g/L.
Determine the behavior of these two organisms in a chemostat. Plot S, P, X A , and X B
versus dilution rate. Discuss what happens to organism B as the dilution rate
approaches the washout dilution rate for organism A.
16.25. An activated-sludge waste treatment system ( Fig. P16.25 ) is required to reduce the
amount of BOD 5 from 1 to 0.02 g/L at the exit. The sedimentation unit concentrates
biomass by a factor of 3. Kinetic parameters are

m max ¼ 0.2 h 1 ; K S ¼ 0.08 g/L, YF X/S ¼
0.50 g-MLVSS/g-BOD 5 , k d ¼ 0.01 h 1 . The flow of wastewater is 10,000 l/h and the
size of the treatment basin is 50,000 L.
(a) What is the value of the net specific growth rate of cells, m net ?

(b) What value of the recycle ratio must be used?

Q , S 0

(1 - y s ) Q

X , S

Waste water

Effluent

S e , X e

(1 + R ) Q

V, X, S

Air

RQ
S R ,

Sedimentation
unit

X R

( R + y s ) Q

Activated sludge reactor

S R = S e

X R = c R X

y s Q, S R , X R

Excess sludge

FIGURE P16.25 Schematic of an activated sludge waste treatment system.