Chapter 5

Aeration and Agitation

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 Oxygen transfer in fermentation
system
GAS FILM
GAS-LIQUD
INTERFACE

O2
CELL-LIQUD
O2 INTERFACE INTERNAL
CELL
AIR BUBBLE RESISTANCE
O2 O2 CELL
LIQUID FILM
Dissolved O2
O2 in liquid phase,
nutrients
Electron
(medium mostly
Transport
water)
System +
TCA cycle
LIQUID FILM enzymes

The oxygen transport path to the microorganism. Generalized path of oxygen

from the gas bubble to the microorganism suspended in a liquid is shown. The
various regions where a transport resistance may be encountered are as indicated
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 Oxygen transfer
In general:
QO2 = f(microbial species and type of
cell, age of cell, nutrient conc. in liquid
medium, dissolved O2 conc., temperature,
pH, etc.)
• For a given: 1) type of species of cell
2) age of cell
3) nutrient concentration
4) temperature
5) pH
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 Oxygen transfer
and if O2 concentration, CL, is the limiting factor in cell
growth, then QO2 is a strong function of dissolved O2
concentration CL (= mg O2/L). The relationship between
QO2 and CL is of the Monod type.
12
Q
O2ma
x

10

Q
O2
8
QO 2

Q
O2ma
x
6
/
2

2
K
O2
C
L C
RIT.
0
0 2 4 6 8 10 12 14 16 18 20
O
xyge
nCO
NC.(C
L)

Respiration coefficient QO2 as a function of the dissolved oxygen 15

concentration CL.
• where: KO2 = O2 conc. at QO2 max/2
CL CRIT. = Critical O2 conc. beyond which O2 is
not limiting
QO2 = QO2max = constant
• At CLCRIT. respiration enzymes of Electron Transport System are
saturated with O2.
• When O2 conc. is the “limiting substrate” then

analogous to the Monod equation:

µmax.S
µ = _______ (S = substrate conc. (g/L)
KS + S

µ = 1 dX (h-1) [Ks = S (g/L), at µmax/2]

X dt

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 Volumetric mass transfer coefficient
kLa and methods of measurement
GAS FILM
GAS-LIQUD
INTERFACE

a
UNIT LIQUID
VOLUME

AIR BUBBLE
O2 CL

O2 TRANSFER CELLS
(CONC. X)
kL OXYGEN
C *L BULK
(CONC. C )
L
LIQUID
LIQUID FILM
PHASE

Schematic diagram of the mass balance of oxygen transfer in unit liquid

volume 17
Mass balance of oxygen in unit liquid
volume

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Mass balance of oxygen in unit liquid
volume (cont’d)

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Mass balance of oxygen in unit liquid
volume (cont’d)

At all the times CL = constant

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Mass balance of oxygen in unit liquid
volume (cont’d)

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Mass balance of oxygen in unit
liquid volume (cont’d)

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Methods of measurement of
kLa in a bioreactor

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In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor

Consider a Stirred Tank Bioreactor System,

Where Cell Growth takes Place at a Given Set of
Conditions:
Aeration
Agitation
pH
Temperature
Medium Composition

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 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)

The Bioreactor Vessel is Equipped with:

● The D.O. Probe, Connected to a D.O. Analyzer.
● Chart Recorder:
To Measure Signal from D.O. Probe and Measure
On-line the D.O. Concentration in the liquid phase
of the Bioreactor.

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 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)

● The D.O. Probe Measures the PyO2 Partial Pressure (PyO2)

of dissolved O2 in the liquid phase, which means that it
measures HO2CL.

Where:
HO2 = Henry’s Constant for O2 in Water
CL = D.O. Concentration in the Liquid
Phase (Mass of O2/L)

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 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor
(Cont’d)
15 10

1. Feed
DO2 pH rpm 2. Flow meter
3. Ring sparger
5 4. Impeller
Alkali Acid 11 12 13 5. Motor
6
6. Shaft
7. pH probe
Water out 8. D.O. probe
2
7 8 9. Baffle
15 10. To Condenser
11. D.O. meter
1 12. pH meter
14
30 deg. 13. Speed controller
4 9
water in 14. Water Jacket
3 16 15. Thermometer
16. Chart recorder
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Set up of a Stirred tank Bioreactor with Dissolved Oxygen Probe, pH probe and accessories.
 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)

● Turning air ON and OFF while maintaining the same

R.P.M. we can:
Record the D.O. Probe Output in the Chart
Recorder.
From these Data, we can get
KLa,
QO2,
CL*
at given in-situ Bioreactor Conditions.
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 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)

● The ON-OFF Operation takes 5 min, during which time:

Cell Concentration X (g /L)  Constant.
We make sure that the D.O. Concentration CL
never falls below the critical oxygen concentration
CCRT,which means that the respiration rate
coefficient QO2 = QO2Max = Constant.

● Using the D.O. probe output and a recorder we measure

directly the D.O. concentration as a function of time, t.
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 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)

While we maintain the same R.P.M. of the bioreactor impeller, we

turn the AIR-OFF. During the AIR-OFF period the following
conditions apply:
● Rate of Supply of O2 = 0
● No Air Present in the Bioreactor
● KLa = 0 because a = 0, no air bubbles present
● Using Eq. 2.2 for O2 Mass Balance, we have:

● We know cell concentration X by measuring it. Therefore, we

calculate QO2 because we also measure the slope – QO2X. 30
 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)
• Fig. 2.11 Shows D.O. concentration CL inside the bioreactor = f(t)
when Air is turned Off and On, always keeping the R.P.M. of the
impeller the same to provide good mixing of the liquid phase.

• After a period of about 5 min, a liquid sample is taken from the

bioreactor to measure the cell concentration X (g dry wt./L).

• The KLa, QO2, and CL* values correspond to that specific fermentation
time and given cell growth conditions.

• We can do many AIR-OFF and AIR-ON measurements to get all

three parameters KLa, QO2, and CL* as a function of total batch 31
 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)

AIR-OFF
CL STEADY-STATE
DO2 CONC. CL (mM O 2/L)

CL,CRIT AIR-ON

TIME (MIN) 3-5

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Transient Air-Off, Air-On Experiment in a Bioreactor System
 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)

● During the AIR-OFF period the D.O. concentration CL is plotted

as a function of time t from which we get the slope = - QO2X, as
shown in Fig. 2.12.
4

SLOPE = - QO2X
3
CL (mMO2/L)

0
0 1 2 3 4 5 6 7 8 9 10
Time, t (min)
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D.O. concentration CL as function of time during AIR-OFF period.
 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)

• AIR-ON Period
During this period the following oxygen mass
balance equation applies:

• From the CL vs. time (t) data we can get

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 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)
● Re-arranging KLa equation and solving for CL we get

● By plotting CL vs. at a given fermentation time, t,

we can get the slope which is equal to

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 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)
● and therefore, the value of KLa is found, and the
intercept also gives the value of

● During the Air-On Period:

CL* = Constant
QO2 = Constant
KLa = Constant
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CL, dCL/dt vary with time t
 In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)

4.4
*
Intercept = CL
3.8
CL (mgO2/L)

3.2
SLOPE = -1/kLa
2.6
2.0
1.4
0.8
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
[dC L/dt+QO2X]
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D.O. concentration CL as function of [dCL/dt + QO2X] during AIR-ON period.
 In Situ Measurement of KLa, QO2, and
CL* During Cell Growth in a Bioreactor
(Cont’d)

Dynamic air-on/air-off data during Poly glutamic acid (PGA) production by Bacillus subtilis IFO 3335
(fermentation time = 26 h). Dissolved oxygen concentration CL () as a function of time.

Taken from A. Richard and A. Margaritis, “Rheology, Oxygen Transfer, and Molecular Weight
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Characteristics of Poly(glutamic acid) Fermentation by Bacillus subtilis”, Biotechnology and
Bioengineering, Vol. 82, No. 3, p. 299-305 (2003).
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 Mixing and Power Requirements for
Newtonian Fluids in a Stirred Tank

NP vs. NRe; the power characteristics are shown by the power number, NP, and the
modified Reynolds number, NRe, of single impellers on a shaft. [Adopted from S.
Aiba, A.E. Humphrey and N.F. Millis. “Bubble Aeration and Mechanical Agitation”.
In Biochemical Engineering, 2nd Ed., Academic Press, Inc., New York (1973) 174].
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Last slides figure shows relationship
between NP and
NRe at three different flow regimes:
● Laminar
● Transient
● Fully Turbulent
for three different impeller types:
● Six-bladed flat blade turbine
● Paddle impeller
● Marine Propeller
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Different Types of impellers have different power
characteristics

For six-bladed flat turbine and for turbulent conditions:

NP = 6 = Pgc/n3Di5

or P = (6)(n3Di5)/(gc)

At NRe = 3,000 the corresponding impeller speed is:

n = (3,000)()/(Di2)()
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● Earlier equation is an estimate of the minimum
impeller speed, n, of a 6-flat blade turbine impeller
for the on-set of turbulent flow within the stirred
tank bioreactor vessel.
● Equation also shows that for a fluid of a given
density, :
P  n3Di5

This is an important consideration for bioreactor

vessel scale-up.

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Calculation of the Required Volumetric
Mass Transfer Coefficient, KLa, During
Fermentation, and Gassed Power, Pg.

At Steady-State Operation of an
Aerobic
Fermentation:
OTR = OUR
KLa[CL* - CL] = QO2X 53
For a given QO2, X, and (CL* - CL), KLa can
be calculated using earlier equation

For a given VL and Ug, Pg can be calculated

using the empirical correlation for KLa given

KLa = C [Pg/VL]m [Ug]k

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