Fermenter design
Mahesh Bule
Basic Fermenter Design Criteria
• Microbiological and biochemical characteristics of the
cell system (microbial, mammalian, plant)
• Hydrodynamic characteristics of the bioreactor
• Mass and heat transfer characteristics of the bioreactor
• Kinetics of the cell growth and product formation
• Genetic stability characteristics of the cell system
• Aseptic equipment design
• Control of bioreactor environment (both macro and
micro-environment)
• Implications of bioreactor design on downstream products
separation
• Capital and operating costs of the bioreactor
• Potential for bioreactor scale-up
Requirements of Bioreactors
• There is no universal bioreactor.
• The general requirements of the bioreactor are as follows:
– The design and construction of bioreactors must keep sterility
from the start point to end of the process.
– Optimal mixing with low, uniform shear.
– Adequate mass transfer, oxygen.
– Clearly defined flow conditions.
– Feeding substrate with prevention of under or overdosing.
– Suspension of solids.
– Gentle heat transfer.
– Compliance with design requirements such as: ability to be
sterilized; simple construction; simple measuring, control,
regulating techniques; scale-up; flexibility; long term stability;
compatibility with up- downstream processes; antifoaming
measures.
Fermenter Design
• The basic points of consideration while designing a fermenter:
– Productivity and yield
– Fermenter operability and reliability
– Product purification
– Water management
– Energy requirements
– Waste treatment
• Other few significant things to be taken in account:
– Design in features so that process control will be possible over
reasonable ranges of process variables.
– Operation should be reliable
– Operation should be contamination free
Fermenter design
• To achieve these the fermenter should have:
– Heat and oxygen transfer configuration
– Sterilization procedures
– Foam control
– Fast and thorough cleaning system
– Proper monitoring and control system
• Traditional design is open cylindrical or rectangular vessels made
from wood or stone.
• Most fermentations are now performed in close system to avoid
contamination.
• It should be constructed from non-toxic, corrosion-resistant
materials.
• Small fermentation vessels of a few liters capacity are constructed
from glass and/or stainless steel.
Fermenter design
• Pilot scale and many production vessels are normally made of
stainless steel with polished internal surfaces
• Very large fermenters are often constructed from mild steel lined with
glass or plastic, in order to reduce the cost.
• If aseptic operation is required, all associated pipelines transporting
air, inoculum and nutrients for the fermentation need to be sterilizable,
usually by steam.
• Most vessel cleaning operations are now automated using spray jets,
and called cleaning in place CIP. And located within the vessel.
• Associated pipe work must also be designed to reduce the risk of
microbial contamination. There should be no horizontal pipes or
unnecessary joints and dead stagnant spaces where material can
accumulate; otherwise this may lead to ineffective sterilization.
Fermenter design
• Normally, fermenters up to 1000 L capacity have an external jacket,
and larger vessels have internal coils.
• Pressure gauges and safety pressure valves must be incorporated,
(required during sterilization and operation).
• For transfer of media pumps are used. Centrifugal pumps (generate
high shear forces and path for easy contaminations), magnetically
coupled, jet and peristaltic pumps.
• Alternate methods of liquid transfer are gravity feeding or vessel
pressurization.
• In fermentations operating at high temperatures or containing
volatile compounds, a sterilizable condenser may be required to
prevent evaporation loss.
• Fermenters are often operated under positive pressure to prevent
entry of contaminants.
Summary of bioreactor systems
Bioreactor design
Cell systems used
Products
Air-lift bioreactors
Bacteria, yeast and fungi
SCP, Enzymes, Secondary
metabolites, Surfactants
Fluidized bed bioreactor
Immobilized bacteria, yeast Ethanol, Secondary
and other fungi, Activated
metabolites, Wastewater
sludge
Interferons, Growth factors,
Immobilized (anchored),
Blood factors, Monoclonal
mammalian cells on solid
antibodies, Vaccines,
particles
Proteases, Hormones
Microcarrier bioreactor
Surface Tissue
Mammalian, tissue growth
on solid surface, tissue
engineering
Interferons, Growth factors,
Blood factors, Propagator,
Monoclonal antibodies,
Vaccines, Proteases,
Hormones
Summary of bioreactor systems
(cont’d)
Bioreactor design
Cell systems used
Products
Membrane Bioreactors,
Hollow fibers and
membranes used,
Rotorfermentor
Bacteria, yeast Mammalian
cells, Plant cells
Ethanol, Monoclonal antibodies, Interferons, Growth
factors, Medicinal products
Modified stirred tank
bioreactor
Immobilized bacteria, yeast Ethanol, Monoclonal antiand plant cells
bodies, Interferons, Growth
factors,
Immobilized bacteria, yeast Ethanol, Enzymes,
and other fungi
Medicinal products
Modified packed bed
bioreactor
Tower and loop Bioreactors Bacteria and yeasts
Single cell proteins
Summary of bioreactor systems
(cont’d)
Bioreactor design
Cell systems used
Products
Vacuum bioreactors
Bacteria, yeast and fungi
Ethanol, volatile products
Cyclone bioreactor
Bacteria, yeast and fungi
Photochemical bioreactor
Photosynthetic bacteria,
Algae, Cyano bacteria,
plant cell culture, r-DNA
plant cells
Commodity products and
SCP
Interferons, Growth factors,
Blood factors, Monoclonal
antibodies, Vaccines,
Proteases, Hormones
Surface Tissue
Mammalian, tissue growth
on solid surface, tissue
engineering
SCP, algae, medicinal plant
products, monoclonal antibodies, vaccines and
interferons
Bioreactor configuration
1. Stirred tank bioreactors
Mixing method: Mechanical
agitation
•Baffles are usually used to
reduce vortexing
• Applications: free and
immobilized enzyme reactions
•High shear forces may damage
cells
•Require high energy input
Schematic diagram of a tower bioreactor system
with multiple impellers and liquid down comer and
counter-current air liquid flow
Air
Feed
Perforated
plate
Downcomer
Baffle
Impeller
Product
Air
2. Bubble column bioreactors
Mixing method: Gas
sparging
• Simple design
•Good heat and mass transfer
•Low energy input
Gas-liquid mass transfer
coefficients depend largely on
bubble diameter and gas holdup.
Schematic diagram of a tower bioreactor
system with perforated plates and co-current
air liquid flow
Air exhoust
Broth
outlet
Sampling
nozzles
Jacket
Constant temp.
water bath
Compressed
air
Perforated
plate
Pump
Orifice
Sparger
Air filter
Peristaltic
pump
Medium
inlet
Flow
meter
Medium
reservior
3. Air lift reactors
Mixing method: airlift
• Compared to bubble
column reactors, in an
airlift reactors, there
are two liquid steams:
up-flowing and downflowing steams. Liquid
circulates in an airlift
reactor as a result of
density difference
between riser and
downcomer.
ICI Deep shaft unit
EMLICHHEIM FLOWSHEET
CONDENSATE,
MAE-UP WATER, AND
FLOCCULATING AGENT
CLARIFIER
WASH
WATER
SETTLEMENT RECYCLED
WATER
TANT
RECYCLE SLUDGE
B
SAND
DECANTER
CENTRIFUGE
B
FLOATATION
SOIL AND
SLUDGE
DEEP
SHAFT
AIR
COMPRESSOR
LAGOON
4. Packed bed bioreactor
Packed-bed
reactors are used
with immobilized
or particulate
biocatalysts.
Medium can be
fed either at the
top or bottom and
forms a
continuous liquid
phase.
Packed bed perfusion bioreactor for
mammalian cell culture
5. Trickle-bed bioreactor
The trickle-bed
reactor is another
variation of the
packed bed
reactors.
Liquid is sprayed
onto the top of the
packing and
trickles down
through the bed in
small rivulets.
Trickle bed reactor for treating waste
water
6. Fluidized bed reactor
When the packed beds
are operated in upflow
mode, the bed
expands at high liquid
flow rates due to
upward motion of the
particles.
Internal circulation patterns of fluidized Ca-alginate
beads containing immobilized cells of Z. mobilis. All
dimensions in cm.
Outer draft tube
Inner draft tube
1.176
4 Jets
28.40
26.43
21.30
6.895
0.953
2.876
0.1
2.620
4.530
Miscellaneous reactors
• Vacuum fermenter
• Tray fermenter
• Stirred cascade reactor
Vacuum Fermenter
Chilled
water
Condenser
Level
control
Vacuum
pump
Vacuum
control
Receiving
tank
(product)
Dry ice
bath
Heating
water
Fermenter
Filter
Medium
reservoir
Rheostat
Filter
Metering
pump
Air or O2
Receiving
tank
(bleed)
Tray fermenter
Stirred cascade reactor
Bioreactor Operation Modes
1. Batch Operation
A batch bioreactor is
normally equipped
with an agitator to
mix the reactant, and
the pH of the reactant
is maintained by
employing either
buffer solution or a
pH controller
Change of Cs
with time, t
•A foam breaker may be installed to disperse foam
dCs
rmax CS
r

dt
K m  CS
Batch operation
with stirring
Cs 0
K m ln
 Cs 0  Cs   rmax t
Cs
Bioreactor Operation Modes
-2. Plug-flow mode
In a plug-flow
reactor, the substrate
enters one end of a
cylindrical tube with
is packed with
immobilized enzyme
and the product
steam leaves at the
other end.
An ideal plug-flow reactor can
approximate the long tube,
packed-bed and hollow fiber or
multistaged reactor
F, Cs0
t=0
F, Cs
V
V

F
Residence
time
Continuous operation
without stirring
Cs 0
K m ln
 Cs 0  Cs   rmax t
Cs
Bioreactor Operation Modes
3. Continuous stirred-tank
A continuous stirredtank reactor (CSTR)
is an ideal reactor
which is based on the
assumption that the
reactants are well
mixed.
F, Cs0
F, Cs
V
Continuous
operation with
stirring
Bioreactor Operation Modes
3. Continuous stirred-tank reactor-Con.
Mass balance of substrate:
F, Cs0
Input - Output  Consumptio n  Accumulati on
F, Cs
V
dCs
FCs 0  FCs  rsV  V
dt
Steady state:
dC s
0
dt
MichaelisMenten rate:
rmax C S
r
K m  CS
rmax Cs
FCs 0  FCs  V
0
K m  Cs
Bioreactor Operation Modes
3. Continuous stirred-tank reactor-Con.
Mass balance of substrate:
F, Cs0
F, Cs
rmax Cs
FCs 0  FCs  V
0
K m  Cs
V
rmax Cs
F

V Cs 0  Cs K m  Cs 
F 1

V 
rmax Cs
Cs   K m 
Cs 0  Cs
Aeration and oxygen transfer in
bioreactor systems
• Bio-oxidation of substrate with molecular oxygen as
the final electron acceptor
Oxygen transfer in fermentation
system
GAS FILM
GAS-LIQUD
INTERFACE
O2
O2
AIR BUBBLE
CELL-LIQUD
INTERFACE
INTERNAL
CELL
RESISTANCE
O2
CELL
O2
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
Oxygen transfer
• At Steady-state with no O2 accumulation in the liquid
phase:
• What are the O2 requirements of microorganisms?
– We define: QO2 = Respiration rate coefficient for a given
microorganism.
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
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.
1
2
Q
O
m
a
x
2
1
0
QO 2
Q
8
O
2
6
Q
/
2
O
m
a
x
2
4
2
0
0
K
O
2
2
4
C
L
C
R
I
T
.
6
8 1
0 1
2 1
4 1
6 1
8 2
0
O
x
y
g
en
C
O
N
C
.(CL
)
Respiration coefficient QO2 as a function of the dissolved oxygen 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)
X dt
[Ks = S (g/L), at µmax/2]
Volumetric mass transfer coefficient
kLa and methods of measurement
GAS FILM
GAS-LIQUD
INTERFACE
a
UNIT LIQUID
VOLUME
AIR BUBBLE
O2
CL
O2 TRANSFER
C *L
kL
LIQUID FILM
BULK
LIQUID
PHASE
CELLS
(CONC. X)
OXYGEN
(CONC. C )
L
Schematic diagram of the mass balance of oxygen transfer in unit liquid volume
Mass balance of oxygen in unit liquid
volume
Mass balance of oxygen in unit liquid
volume (cont’d)
Mass balance of oxygen in unit liquid
volume (cont’d)
At all the times CL = constant
Mass balance of oxygen in unit liquid
volume (cont’d)
Mass balance of oxygen in unit
liquid volume (cont’d)
Methods of measurement of kLa in
a bioreactor
Chemical methods of kLa
measurement
The Sulphite Batch Oxidation Method.
F,
SO
23
In flu e n t
M o to r
A ir flo w , ra te
A ir o u tle t
rp m
W a te r o u t
W a te r in
Schematic diagram of a stirred tank batch reactor
Chemical Methods of KLa
Measurement (Cont’d)
●
Liquid Solution = 0.5 M Na2SO3 (Sodium
++
sulphite), with Cu as catalyst.
●
Sparge air through the bioreactor vessel at a
given volumetric flow rate Q and impeller
speed (R.P.M.)
●
-2
Make sure that [SO3 ] is in excess (i.e. 0.5 M
Na2SO3)
Chemical Methods of KLa Measurement (Cont’d)
Chemical Methods of KLa Measurement (Cont’d)
Chemical Methods of KLa Measurement (Cont’d)
Chemical Methods of KLa Measurement (Cont’d)
-2
● The reaction with [SO3 ] is extremely
fast.
● As a result, the O2 gas molecules are
consumed as soon as they diffuse into
the liquid phase.
● Therefore, the D.O. concentration in the
liquid phase, CL  0.
Chemical Methods of KLa Measurement (Cont’d)
Chemical Methods of KLa Measurement (Cont’d)
● Use iodometric titration to measure
-2
[SO3 ] as a function of time, t, as the air
bubbles pass through the bioreactor
vessel at a given R.P.M.
Chemical Methods of KLa Measurement (Cont’d)
8
0
7
0
d[SO3-2]
SLOPE = ~dt
[SO3-2]
t
4
6
T
I
M
E
, t, (m
in
)
8
-2
-2
O
]
d [S
]O [S
3
S L OP E
=
~ -- 3
dt
t
6
0
2
[SO 3 ]
5
0
4
0
3
0
2
0
1
0
0
0
2
Concentration of SO3-2 as a function of oxidation time
Chemical Methods of KLa Measurement (Cont’d)
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
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 Online the D.O. Concentration in the liquid phase of the
Bioreactor.
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)
In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)
10
15
Alkali
pH
rpm
11
12
13
5
Acid
6
Water out
2
7
15
1
30 deg.
water in
DO2
8
9
4
3
14
16
1. Feed
2. Flow meter
3. Ring sparger
4. Impeller
5. Motor
6. Shaft
7. pH probe
8. D.O. probe
9. Baffle
10. To Condenser
11. D.O. meter
12. pH meter
13. Speed controller
14. Water Jacket
15. Thermometer
16. Chart recorder
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.
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.
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.
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 fermentation time.
DO2 CONC. C L (mM O 2/L)
In Situ Measurement of KLa, QO2, and CL*
During Cell Growth in a Bioreactor (Cont’d)
CL STEADY-STATE
CL,CRIT
AIR-OFF
AIR-ON
TIME (MIN)
3-5
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.
CL (mMO2/L)
4
SLOPE = - QO2X
3
2
1
0
0
1
2
3
4
5
6
Time, t (min)
7
8
9
D.O. concentration CL as function of time during AIR-OFF period.
10
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
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
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
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
*
Intercep t = CL
CL (mgO2/L)
3.8
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
[dCL/dt+QO2X]
1.4
1.6
1.8
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 Characteristics of
Poly(glutamic acid) Fermentation by Bacillus subtilis”, Biotechnology and Bioengineering, Vol. 82, No. 3, p. 299-305
(2003).
Agitation requirement in fermentation systems
The dimensions of what is called a “standard” stirred tank
bioreactor vessel with Baffles.
Geometric Ratios for a Standard Bioreactor
Vessel
Impeller
Type
Di/Dt
HL/Dt
Flat-Blade
Turbine
0.33
1.0
Paddle
impeller
0. 3 3
1.0
Marine
Propeller
0.33
1.0
Li/Di
Wi/Di
Hb/Di
Wb/Dt
No. Baffles
0.25
0.2
1.0
0.1
4
-
0.25
1.0
0.1
4
1.0
0.1
4
pitch = Di
Where:
Dt = tank diameter,
HL = liquid height
Di = impeller diameter
Hb = impeller distance from bottom of vessel
Wb = baffle width
Li = impeller blade length
Wi = impeller blade height
Different Impeller Types. (a) Marine-type propellers; (b) Flat-blade turbine, Wi =
Di/5. © Disk flat-blade turbine, Wi = Di/5, Di = 2Dt/3, Li = Di/4; (d) Curved-blade
turbine, Wi = Di/3; (e) Pitched-blade turbine, Wi = Di/8; and (f) Shrouded
turbine, Wi = Di/8.
Mixing Patterns for Flat-Blade Turbine Impeller. Effect of Baffles. Liquid agitation in
presence of a gas-liquid interface, with and without wail baffles: (a) Marine impeller and
(b) Disk flat-blade turbines; (c) in full vessels without a gas-liquid interface (continuous
flow) and without baffles.
Mixing and Power Requirements forNewtonian
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].
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
The power number is given by
NP = Pgc/n3Di5
The impeller Reynolds number is given by
NRe = nDi2/
Where:
NRe = dimensionless Reynolds number
NP = dimensionless Power number
P = Un-gassed power for liquid (no air), W
gc = 1, for SI units system
n = Impeller rotational speed, revolutions per
sec., (s-1)
Di = Impeller diameter, m
 = Density of liquid, kg/m3
 = Viscosity of liquid, (N.m)/(s)
For six-bladed flat-blade turbine impeller (cf.
Fig. 3.3), the mixing becomes fully turbulent at
an impeller Reynolds number NRe = 3,000.
Power number NP = 6 (constant) at NRe > 3,000
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)()
● 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.
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
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