Continuous Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 654

Q , S , X

Q 1 , S 1 , X 1

Q 1 , S , X

Q , S 0 , X 0

V 1 , S , X

V 2 , S 1 , X 1

FIGURE P12.7 A schematic of a two-stage chemostat system.

12.8. In a chemostat you know that if a culture obeys the Monod equation, the residual
substrate is independent of the feed substrate concentration. You observe that in your
chemostat an increase in S 0 causes an increase in the residual substrate concentration.
Your friend suggests that you consider whether the Contois equation may describe the
situation better. The Contois equation is:

m max S
K SX X þ S

m ¼

(a) Derive an expression for S in terms of D, m max , K SX , and X for a steady-state CSTR

(chemostat).
(b) Derive an equation for S as a function of S 0 ,D, K SX ,YF X/S , and m max .

(c) If S 0 increases twofold, by how much will S increase?
12.9. Plot the response of a culture to diauxic growth on glucose and lactose based on the
following:
m glucose ¼

1.0 h 1 ; 0.5; enzyme induction

requires 30 min to complete. Plot cell mass, glucose, and lactose concentrations,
assuming initial values of 2 g/L glucose, 3 g/L lactose, and 0.10 g/L cells.
12.10. Pseudomonas putida with

m lactose ¼ 0.6/h; YF glucose ¼ YF 1actose ¼

0.5 h 1 is cultivated in a continuous culture under m max ¼

0.28 h 1 . The carbon and energy source in the feed is
lactose with a concentration of S 0 ¼

aerobic conditions where D ¼

2 g/L. The effluent lactose concentration is desired

to be S

¼

0.1 g/L. If the growth rate is limited by oxygen transfer, by using the
following information:

C ¼ 8 YF X = S ¼ 0:45 g-X = g S ; YF X = O 2 ¼ 0:25 g X = g O and mg = L

2

(a) Determine the steady-state biomass concentration ( X ) and the specific rate of
oxygen consumption (

m O2 ).
(b) What should be the oxygen transfer coefficient ( k L a ) in order to overcome oxygen
transfer limitation (i.e. C L 2 mg/L)?

12.11. Table P12.11 shows data obtained from oxidation of pesticides present in
wastewater by a mixed culture of microorganisms in a continuously operating
aeration tank.

¼