The following kinetic equations can therefore be used describe growth under oxygen limited conditions.
dX dt


K o m
C o

C o
X dC o dt
 
1
Y o
K
 o m

C o
C o
X
Where Co is the concentration of oxygen, µm is the maximum specific growth rate, Yo is the biomass yield from oxygen and
K o is the Monod constant for oxygen uptake.
1

Thus the oxygen uptake rate (OUR) can be described the equation:
OUR

1
Y o
K
 o m

C o
C o
X
The dissolved oxygen concentration in a reactor is thus determined by the balance between the oxygen transfer rate (OTR) and oxygen uptake rate (OUR).
dC o dt dC o

OTR

OUR dt
 k
L a

C
* o

C o


Y o
1
2
K
 o m

C o
C o
X

Steady state analysis
The movement of oxygen from a bubble through the bulk liquid to a cell, can be thought of as a continuous process.
Oxygen enters the bulk liquid and is removed by the cells.
3

The dissolved oxygen concentration in the bulk liquid will quickly reach a steady state and therefore dC o dt

0 and the oxygen transfer rate will equal the oxygen uptake rate
OTR = OUR k
L a

C o
* 
C o


Y o
1
4
K
 o m
C o

C o
X

Critical Oxygen Concentration
•
• C o,cr is the concentration of dissolved oxygen below which a culture is oxygen limited.
Then µ = µ , the cells are not oxygen limited.
5

Integrating the oxygen uptake and oxygen transfer equations
The steady state relationship between oxygen uptake and oxygen transfer:
OTR = OUR k
L a

C o
* 
C o


Y o
1

K o m

C o
C o
X
6

level of mixing
7

Medium viscosity
8

Temperature
9

Interfacial area and oxygen transfer
潘威仁 連耘愷
10