Continuous Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 617

Combine with the Monod equation

m G ¼ m max S

(E12-1.4)

K S þ S

we obtain

K S ðD þ k d Þ
m max D k d

S ¼ (E12-1.5)

Thus, from the mass balance of the cells in the chemostat, we are able to relate the substrate
concentration with the dilution rate with the given kinetic model (Monod equation).
We next perform a mass balance on the substrate in the chemostat:

QðS 0 SÞ m G X

d ðVSÞ

d

YF X = S V ¼

(E12-1.6)

t

Again at steady state, nothing would change with time,

X ¼ DYF X = S S 0 S

(E12-1.7)

m G

Substitute Eqns (E12-1.3) and (E12-1.5) into Eqn (E12-1.7) , we obtain

X ¼ DYF X = S
D þ k d

D þ k d
m max D k d

S 0 K S (E12-1.8)

Equations (E12-1.5) and (E12-1.8) define the chemostat operation. Now it is a matter of fitting
the experimental data to these two equations to obtain the kinetic parameters.

TABLE E12-1.2 Parametric Estimation Results

Error 2 or
(

S C calculated
from Eqn
(E12-1.5) , g/L

X c calculated
from Eqn
(E12-1.8) , g/L

Error
weighting
factor,

SLS C ) 2

2

S ,

mg/L

X ,

mg/L

u

D, h L 1 XLX c ) 2 D ( u

0 3.394824 0

0.02 5.770941 193.014

0.05 9.6 301 9.575349 301.1293 0.077482 10

0.08 13.70043 349.0995

0.1 16.7 366 16.64925 368.0817 4.59119 10

0.2 33.5 407 34.38288 407.2729 78.02232 10

0.3 59.4 408 59.32796 412.1521 17.75862 10

0.4 101 404 97.00599 400.4078 28.85616 1

0.5 169 371 160.5069 369.4652 74.48863 1

( Continued )