Continuous Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 656

0.25 h 1 , K (b) Tessier equation: m G ¼ m max ½1 expðKSÞ ,with m max ¼ ¼ 0.005/mg/L.

m G ¼ m max S n

0.25 h 1 , K S ¼ (c) Moser equation: , with m max ¼ 100 mg/L, n ¼ 1.5.

K S þ S n

m max S

0.25 h 1 , K SX ¼

m G ¼ m max ¼

0.04, YF X/S ¼ (d) Contois equation:

S ,with

K SX X þ

0.4 g/g.

Compare and comment on the results.
12.16. Formation of lactic acid from glucose is realized in a continuous culture by
Streptococcus lactis . The following information was obtained from experimental
studies.
S 0 ¼ 0.2 h 1 , K S ¼ 0.002 h 1 ,YF X/S ¼

5 g/L, m max ¼ 200 mg/L, k d ¼ 0.4 g-X/g-S,

0.1 g-P/(g-X/h).
(a) Plot the variations of S , X , P ,D X , and D P with dilution rate.
(b) Determine (graphically) the optimum dilution rate maximizing the productivities
of biomass (D X ) and the product (D P ).
12.17. In a two-stage chemostat system, the volumes of the first and second reactors are
V 1 ¼

m P ¼

300 L, respectively. The first reactor is used for biomass
production and the second is for a secondary metabolite formation. The feed flow
rate to the first reactor is Q

500 L and V 2 ¼

¼ 100 L/h, and the glucose concentration in the

0.3 h 1 , feed is S ¼ 5.0 g/L. Use the following constants for the cells: m max ¼

K S ¼ 0.4 g-cells/g-glucose. Assuming that the endogenous

metabolism rate is proportional to the growth rate and the yield factor includes the
substrate consumption due to extracellular product formation as a result of the
endogenous metabolism.
(a) Determine cell and glucose concentrations in the effluent of the first stage.
(b) Assume that growth is negligible in the second stage due to the exhaustion of
minor nutrients required for cell growth and the specific rate of product formation
is

0.1 g/L, YF X/S ¼

0.6 g-P/g-S. Determine the product and
substrate concentrations in the effluent of the second reactor.
12.18. An industrial wastewater stream is fed to a stirred-tank reactor continuously and the
cells are recycled back to the reactor from the bottom of the sedimentation tank
placed after the reactor. The system parameters are given by: Q

m P ¼ 0.02 g-P/(g-cell $ h) and YF P/S ¼

¼ 100 L/h;

0.25 h 1 ; K S ¼

S 0 ¼ 5000 mg/L; m max ¼ 200 mg/L; R (recycle ratio) ¼ 0.6; c R (cell

concentration factor) ¼ 2; YF X/S ¼ 0.4. The effluent concentration is desired to be

100 mg/L.
(a) Determine the required reactor volume.
(b) Determine the cell concentration in the reactor and in the recycle stream.
(c) If the residence time is 2 h in the sedimentation tank, determine the volume
of the sedimentation tank and cell concentration in the effluent of the
sedimentation tank.
12.19. Consider the batch growth data in Table P12.19 with a complex medium. You have
available three tanks of different volumes: 900, 600, and 300 L. Given a flow rate of
100 L/h, what configuration of tanks would maximize the production of the
secondary metabolite P ?