Biochemical engineering notes for biotechnology applications

CBE 320b BIOCHEMICAL
ENGINEERING III COURSE NOTES
Instructor: Dr. A. Margaritis, Ph.D., P.Eng., F.C.I.C.
Professor of Biochemical Engineering
http://www.eng.uwo.ca/people/amargaritis/
DEPARTMENT OF CHEMICAL AND BIOCHEMICAL
ENGINEERING
The University of Western Ontario
Faculty of Engineering
©A. Margaritis 2006-2007

TABLE OF CONTENTS
1. Introduction
 Bioprocess Design
 Novel Bioreactor Types
 Design Criteria for Bioreactors
2. Aeration and Oxygen Mass
Transfer in Bioreactor
Systems
 Oxygen Requirements by Microorganisms
 The volumetric Mass Transfer Coefficient KLa
and Methods of Measurements
 Empirical Correlations of KLa

3. Agitation of Bioreactor
Systems
4. Scale-up of Bioreactor
Systems
 Scale-up Criteria
 Example of Geometric Scale-up
5. Sterilization of Liquid Media
 Kinetics of Thermal Death of Microorganisms
 Batch Sterilization of Liquid Media
 Continuous Sterilization of Liquid Media
 Examples of Design for Continuous Liquid
Medium Sterilization in a Tubular Sterilizer

6. Air Sterilization by Fibrous
Bed Filters
 Mechanisms of Air Filtration and Design of
Fibrous Packed Beds
 Example of Design of Fibrous Packed Bed for
Air Sterilization

GENERALIZED VIEW OF
BIOPROCESS
RAW MATERIALS
UPSTREAM PROCESSES
Inoculum
Preparation
Equipment
Sterilization
Media Formulation
and
Sterilization
BIOREACTOR - FERMENTER
Reaction Kinetics
and Bioactivity
Transport Phenomena
and Fluid Properties
Instrumentation
and Control
DOWNSTREAM PROCESSES
Separation
Recovery and
Purification
Waste Recovery,
Reuse and Treatment
THE BOTTOM LINE
REGULATION ECONOMICS HEALTH AND SAFETY

TYPICAL BIOPROCESS FLOW SHEET
RAW MATERIAS
Nutrients and Reactants
in Aqueous Solution
(may contain insoluble
organic and/or inorganic
materials)
Air
CELL SEPARATION
1). CELL DISTRUPTION
2). PRODUCT EXTRACTION
PRODUCT
CONCENTRATION
PROCESS
FINAL PRODUCT
DRYING
PURIFICATION
PRODUCT
SEPARATION
PREPARATION
OF BIOMASS
Innoculum Stages
FOAM CONTROL
Antifoam Addition
pH CONTROL
Acid-Alkali Addition
Extracellular
product
Intracellular
product
STERILIZATION
BIOREACTOR
Free Cells,
Immoblized Cells
or
Enzyme Bioreactor
PRODUCT RECOVERY

TABLE 1. Basic Bioreactor 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
______________________________________________________________________

TABLE 2. Summary of Bioreactor Systems
__________________________________________________________
Bioreactor Cell Systems Products
Design used
__________________________________________________________
 Air-Lift Bioreactor Bacteria, Yeast and SCP, Enzymes, Secondary
other fungi metabolites, Surfactants
 Fluidized-Bed Immobilized bacteria, Ethanol, Secondary
Bioreactor yeast and other fungi, metabolites, Wastewater
Activated sludge treatment
 Microcarrier Immobilized (anchored) Interferons, Growth factors,
Bioreactor mammalian cells on Blood factors, Monoclonal
solid particles antibodies, Vaccines, Proteases,
Hormones
 Surface Tissue mammalian, tissue Interferons, Growth factors,
Propagator growth on solid surface, Blood factors,
tissue engineering Monoclonal antibodies,
Vaccines, Proteases, Hormones
__________________________________________________________

(Cont’d)
____________________________________________________________________________________________________
Bioreactor Cell Systems used Products
Design
________________________________________________________________________________________
 Membrane Bioreactors, Bacteria, Yeasts, Ethanol, Monoclonal anti-
Hollow fibers and Mammalian cells, Plant bodies, Interferons, Growth
membranes used, cells factors, Medicinal products
Rotorfermentor
 Modified Stirred Immobilized Bacteria, Ethanol, Monoclonal anti-
Tank Bioreactor Yeast, Plant cells bodies, Interferons, Growth
factors
 Modified Packed- Immobilized Bacteria, Ethanol, Enzymes, Medicinal
Bed Bioreactor Yeasts and other fungi products
 Tower and Loop Bacteria, Yeasts Single Cell Protein (SCP)
Bioreactors
________________________________________________________________________________________

(Cont’d)
_______________________________________
_____
Bioreactor Cell System used Products
design
__________________________________________________________________________________________________________
___________
 Vacuum Bioreactors Bacteria, Yeasts, Fungi Ethanol, Volatile
products
 Cyclone Bioreactors Bacteria, Yeasts, Fungi Commodity products,
SCP
 Photochemical Photosynthetic bacteria, SCP, Algae, Medicinal
Bioreactors Algae, Cyano bacteria, plant products,
Plant Cell culture, r-DNA Monoclonal antibodies,
plant cells Vaccines, Interferons
________________________________________________________________________________________

Fig. 1.1. Schematic diagram of a tower bioreactor system with
perforated plates and co-current air liquid flow.
Medium
inlet
Air filter
Orifice
Compressed
air
Flow
meter
Peristaltic
pump
Medium
reservior
Constant temp.
water bath
Air exhoust
Pump
Jacket
Perforated
plate
Sparger
Broth
outlet
Sampling
nozzles

Fig. 1.2. Schematic diagram of a tower bioreactor system
with multiple impellers and liquid down comer and
counter-current air liquid flow
Perforated
plate
Downcomer
Baffle
Impeller
Feed
Air
Product
Air

Fig. 1.3. ICI Deep Shaft Unit
AIR
PROCESS
AIR
OUTLET
RISER
DOWN-
COMER
SHAFT
LINING
INLET
SLUDGE
RECYCLE
START
-UP AIR

FIG. 1.4. EMLICHHEIM FLOWSHEET
AIR
COMPRESSOR
DEEP
SHAFT
B
FLOATATION
LAGOON
B
SAND
WASH
WATER
CLARIFIER
RECYCLE SLUDGE
RECYCLED
WATER
SETTLEMENT
TANT
CONDENSATE,
MAE-UP WATER, AND
FLOCCULATING AGENT
DECANTER
CENTRIFUGE
SOIL AND
SLUDGE

FIG. 1.5. Internal circulation patterns of fluidized Ca-alginate beads
containing immobilized cells of Z. mobilis. All dimensions in cm.
0.1
0.953
6.895
21.30
28.40
2.876
26.43
1.176 2.620 4.530
Outer draft tube
Inner draft tube
4 Jets

FIG. 1.6. Vacuum Fermenter
Dry ice
bath
Metering
pump
Receiving
tank
(bleed)
Filter
Filter
Fermenter
Vacuum
control
Receiving
tank
(product)
Condenser
Level
control
Heating
water
Medium
reservoir
Rheostat
Vacuum
pump
Air or O2
Chilled
water

2. Aeration and Oxygen Mass
Transfer in Bioreactor
Systems

 Living Cells:
Bacteria,
Yeasts,
Plant cells,
Fungi,
Mammalian Cells
Require Molecular Oxygen O2 as
final Electron Acceptor in Bioxidation
of Substrates (Sugars, Fats, Proteins,
etc.)

Substrate O2
Electrons H2O
Products of
Oxidation
CO2
Products
Cell mass
FIG. 2.1. Bio-oxidation of Substrate with Molecular
Oxygen as the Final Electron Acceptor

OXIDATION-REDUCTION REACTION
 Glucose is oxidized to make CO2
 Oxygen is reduced to make H2O
 Fig. 2.1. Shows the biochemical pathway for
aerobic oxidation of carbohydrates, fatty
acids, and amino acids (AA) via the Tri-
carboxylic acid cycle (T.A.C.) and electron
Transport System.
 Molecular oxygen O2 accepts all the
electrons released from the substrates during
aerobic metabolism.

FIG. 2.2. Aerobic oxidation of carbohydrates, fatty acids, and amino acids via the TCA
cycle and the Electron Transport System (ETS) through which electrons are transported
and accepted by molecular oxygen (O2).
ATP is produced from the phosphorylation of ADP. The ETS is
composed of the following: FP1 = NADH; FP2 = succinate
dehydrogenase; Q = Co-enzyme Q; Cytochrome b, c, a, and a3.
The final electron acceptor O2 is reduced to water. Oxygen comes
from the liquid phase and diffuses through the cell.
Pyruvate
Acetyl CoA
alpha-
Ketoglutarate
Marate
Isocitrate
Fumarate
Succinate
2H
2H
2H
2H
2H
2H
Citrate
CO2
CO2 NAD FPi
FPi
ADP+Pi
Q b
ADP+Pi
ATP ATP
c a a3
O2
H2O
ADP+Pi
CO2
Oxaloacetate
Amino acids
Fatty acids
Respiratory chain phosphorylation
--Electron transport along the respiratory chain--

OXIDATION-REDUCTION REACTION
(CONT’D)
 Question: How do we ensure that we
provide enough O2 so that the cell
growth in a bioreactor is not limiting?
 Answer: Must ensure that O2 is
transferred fast enough from the air
bubbles (gas phase) to the liquid phase
(usually water) where all cells are
present and growing.

LIQUID PHASE
O2
O2
O2
O2
Dissolved O2
in liquid phase,
nutrients
(medium mostly
water)
AIR BUBBLE
LIQUID FILM
CELL
O2
INTERNAL
CELL
RESISTANCE
LIQUID FILM
CELL-LIQUD
INTERFACE
Electron
Transport
System +
TCA cycle
enzymes
GAS FILM
GAS-LIQUD
INTERFACE
FIG. 2.3. 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

LIQUID PHASE (CONT’D)
 At Steady-state with no O2
accumulation in the liquid phase:
 What are the O2 requirements of
microorganisms?
Rate of O2 Transfer (OTR) = Rate of O2 Uptake (OUR)
(Air bubbles Liquid) by Growing Cells

2.1 OXYGEN REQUIREMENTS OF
MICROORGANISMS
We define: QO2 = Respiration rate coefficient for
a given microorganism.
Units of QO2:
(mass of O2 consumed) ÷ (unit wt. of dry biomass) .
(time)
“Biomass” means the “mass of cells” in a
bioreactor vessel.
Some units of QO2:
mM O2/(g dry wt. of biomass) (hr.)
gO2/(g dry wt.) (hr.)
LO2/(mg dry wt.) (hr.)

CONVERSION FACTORS:
1 M O2 = 32 x 10-6 g O2
1 L = 1 x 10-6 L at S.T.P.
1 mole O2 = 22.4 L O2 at S.T.P.
 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

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.
O
x
y
g
e
n
C
O
N
C
.
(
C
L
)
Q
O
2
0
2
4
6
8
1
0
1
2
0 2 4 6 8 1
0 1
2 1
4 1
6 1
8 2
0
Q
O
2
m
a
x
K
O
2
Q
O
2
m
a
x
/
2
Q
O
2
C
L
C
R
I
T
.
FIG. 2.4. 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) [Ks = S (g/L), at µmax/2]
X dt
 
1
.
2
.
2
2
2
L
L
MAX
C
C
Q
Q







 Table 1 shows typical values of QO2 measured by
Warburg respirometer.
 Table 2 shows typical data for critical oxygen
concentration CL,CRIT. (mmol O2/L).
 FIG. 2 shows the variation of QO2 with
fermentation time for the microorganism
Bacillus subtilis, where QO2 reaches a maximum
value during the exponential growth phase.
 FIG.3 shows the effect of agitation rate (revolutions
per minute) on the value of QO2 for the bacterium
Nocardia erythropolis, growing on hexadecane to
produce biosurfactants.

________________________________________________________________________
Microbial Species Temp. Culture Resp. Rate Coeff.
(o
C) age (hr.) QO2 (µL O2)/
(mg dry wt.) (hr.)
_____________________________________________________________
B. aerogenes 36; 30 17; 48 47; 50
Azotobacter choococcum 22 36 2,000-10,000
A. subtilis (cells) 37 6-8 170
C. subtilis (spores) 32 98-147 10
Corynebacteria species 30 48-96 67
E. coli 40; 32 20 200; 272
L. bulgaricus 45; 37 8 55; 34
Micrococcus luteus 35 30-34 15
Microbacterium avium 37 84 1
Mycobacterium tuberculosis 38 252 4
Pseudomonas fluorescens 26 30 58
________________________________________________________________________
TABLE 1. Cell suspensions in glucose. Oxygen uptake determined in
constant volume Warburg respirometer

________________________________________________________________________
Microorganism Temp. (o
C) CL CRIT.
(mmol O2)/L
_____________________________________________________________
Azotobacter vinelandii 30 0.018-0.049
E. coli 37.8 0.0082
E. coli 15 0.0031
Serratia marcescens 31  0.015
Pseudomonas denitrificans 30  0.009
Yeast 34.8 0.0046
Yeast 20 0.0037
Penicillium chrysogenum 24  0.022
Penicillium chrysogenum 30  0.009
Aspergillus oryzae 30  0.020
________________________________________________________________________
 Adopted from R. K. Finn, P.81 in: N. Blakebrough (ed),
Biochemical Engineering Science. Vol. 1, Academic Press, Inc., New
York, 1967
TABLE 2. Typical values of CL CRIT in the Presence of Substrate

FIG. 2. 5a: Oxygen uptake rate, QO2X () and broth viscosity (▲)during batch aerobic fermentation of Bacillus subtilis. b: Respiration
rate coefficient, QO2 () and volumetric mass transfer coefficient, KLa ().
Taken from A.Richard and A. Margaritis, “Rheology, Oxygen Transfer, and Molecular Weight Characteristics of Poly(glutamic acid)
Fermentation by B. subtilis”, Biotechnology and Bioengineering, Vol. 82 No. 3, p. 299-305, (2003)

FIG. 2.6. Effect of agitation on the respiration coefficient (QO2) in a 20 L batch
fermentation of Nocardia erythropolis. () 250 r.p.m, () 375 r.p.m, () 500 r.p.m.
(Adopted from Kennedy et al. In Dev. Ind. Microbiol., 20 (1978) 623-630)

2.2 THE VOLUMETRIC MASS
TRANSFER COEFFICIENT
kLa AND METHODS OF
MEASUREMENT

Mass Balance of Oxygen in Unit Liquid
Volume
AIR BUBBLE
LIQUID FILM
GAS FILM
GAS-LIQUD
INTERFACE
L
k
a
C L
*
UNIT LIQUID
VOLUME
CELLS
(CONC. X)
O2 C L
OXYGEN
(CONC. C )
L
BULK
LIQUID
PHASE
O2 TRANSFER
FIG. 2.7 Schematic diagram of the mass balance of oxygen transfer in unit liquid volume

Volume (Cont’d)
Rate of = net rate of O2
Accumulation supply from air
of O2 bubbles – rate of
O2 consumption by
cells
dCL
dt
= kLa(C*L - CL) - QO2X......(2.2)

Volume (Cont’d)
where: dCL/dt in (mmol O2/L.h)
kLa in (h-1
)
C*
L, CL in (mmol O2/L)
QO2 in (mmol O2/(g dry
wt. cell)(h)
X in (g dry wt. Cell/L)

Volume (Cont’d)
At steady state:
dCL
dt
kLa(C*L - CL) = QO2X.........(2.3)
= 0
At all times CL = constant

Volume (Cont’d)
Oxygen transfer rate from air
bubbles to liquid = OTR
OTR = kLa (C*
L – CL)
OTR
kLa =
(C*L - CL)
......(2.4)

Volume (Cont’d)
For a given OTR and CL
*
(= PyO2/H), please note that as
kLa increases, then CL also increases.
Where:
CL
*
= saturated oxygen conc. (mole O2/Lit)
P = total pressure inside air bubble (atm)
yO2 = mole fraction of oxygen in air (0.21)
H = Henry’s constant (atm.Lit/mole O2)
This is an important way of controlling the dissolved
oxygen concentration CL which also affects the metabolic
activity of aerobic cells their rate of growth and the rate
of production of different metabolic products.
For pure oxygen, yO2 = 1.00

Methods of Measurement of KLa
in a Bioreactor
Two basic methods for Measuring
KLa
● Chemical methods (no cells present)
● Physical Methods (with/without
cells)

Chemical Methods of KLa
Measurement
The Sulphite Batch Oxidation Method.
SO
3
2-
F,
Water out
Water in
rpm
Motor
Influent
Air flow, rate
Air outlet
FIG. 2.8. 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.)
● Make sure that [SO3
-2
] is in excess (i.e. 0.5 M
Na2SO3)

Chemical Methods of KLa Measurement
(Cont’d)
 Oxygen oxidizes the sulphite ion to
sulphate.
SO3-2 + 1
2
O2
Cu++
SO4-2 .......(2.5)
(SULPHITE) (SULPHATE)
 The rate of chemical reaction is extremely
fast.
 The controlling step is diffusion of O2
molecules through the liquid film
surrounding the air bubbles.

(Cont’d)
Rate of reaction = R = k2[O2][SO3-2]
~ k1[O2] =
= -
i.e. k1 ~ k2[SO3-2]
= constant
2
d[SO3-2]
1
dt

(Cont’d)
 i.e. R is zero order to sulphite concentration
[SO3
-2
] because it is in excess.
? From stoichiometry shown in Eq. (2.5)
dt
1 d[SO3-2]
2
R = (- ) = (KLa)(CL* - CL)...(2.6)

(Cont’d)
● The reaction with [SO3
-2
] 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.

(Cont’d)
● Equation (2.6) becomes:
R = (KLa)(CL*) = (KLa)( )
PyO2
H = (- 1
2
)
d[SO3-2]
dt
......(2.7)
● Assuming a perfeftly mixed vessel,

(Cont’d)
● Use iodometric titration to measure
[SO3
-2
] as a function of time, t, as the
air bubbles pass through the
bioreactor vessel at a given R.P.M.

(Cont’d)
SLOPE = - ~ -
d[SO3-2]
dt t
[SO3-2]
T
I
M
E
, t
, (
m
i
n
)
[
S
O
3
-
2
]
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
0 2 4 6 8
S L OP E = -
~ -
d [S O
3
-2
]
d t t
[S O
3
-2
]
FIG. 2.9. Concentration of SO3
-2 as a function of oxidation time

(Cont’d)
● For a given:
Aeration rate Q
Agitation Speed R.P.M.
Total air pressure P
● Volumetric mass transfer coefficient
KL
a can be calculated from Equation
(2.7) as:
KLa =
)(H)
(- )(
2 t
[SO3-2]
1
PyO2
......(2.8)
-

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

CL
(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.

CL
(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

In Situ Measurement of KLa, QO2,
and CL
* During Cell Growth in a
Bioreactor (Cont’d)
Fig. 2.10 Set up of a Stirred tank Bioreactor with Dissolved Oxygen Probe, pH probe and
accessories.
Acid
DO2
1
4 9
pH
7 8
12
11
2
10
6
14
rpm
Alkali 13
15
15
16
5
3
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
Water out
30 deg.
water in

CL
● 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.

CL
(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

CL
(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.
dCL
dt = 0 - QO2X

CL
(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.

CL
(Cont’d)
TIME (MIN)
DO
2
CONC.
C
L
(mM
O
2
/L)
AIR-OFF
AIR-ON
CL,CRIT
3 - 5
CL STEADY-STATE
FIG. 2.11. Transient Air-Off, Air-On Experiment in a Bioreactor System

CL
● 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.
Time, t (min)
C
L
(mMO
2
/L)
0
1
2
3
4
0 1 2 3 4 5 6 7 8 9 10
SLOPE = - Q
O2X
FIG. 2.12. D.O. concentration CL as function of time during AIR-OFF period.

CL
(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
dCL
dt = KLa (CL* - CL) - QO2X
dCL
dt ~ t
CL

CL
(Cont’d)
● Re-arranging Eq. 2.2 and solving for CL we get Eq. 2.9
● By plotting CL vs. at a given fermentation time, t,
we can get the slope which is equal to
dCL
dt + CL*.....(2.9)
CL =
KLa
1
- QO2X +
dCL
dt +QO2X
KLa
1
-

CL
(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
PyO2
H
CL* =

CL
[dCL/dt+QO2X]
C
L
(mgO
2
/L)
0.8
1.4
2.0
2.6
3.2
3.8
4.4
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
SLOPE = -1/kLa
Intercept = C
L
*
FIG. 2.13. D.O. concentration CL as function of [dCL/dt + QO2X] during AIR-ON period.

CL
(Cont’d)
● Figures 2.8 and 2.9 show batch aerobic fermentation results in a
stirred tank bioreactor system for the production of the
biopolymer poly(glutamic acid) produced by Bacillus subtilis
obtained by A. Richard and A. Margaritis.
● Reference: A. Richard and A. Margaritis (2003), “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 .
● Please read chapter 8, “Bioproducts and Economics” pp. 609-685,
in Book “Biochemical Engineering” by H.W. Blanch and D.S.
Clark, Marcel Dekker, Inc., New York (1996). This material is
useful for the Plant Design Course, CBE 497 (4th year).

and CL
FIG. 2.14. Batch fermentation kinetics of Bacillus subtilis IFO 3335 during polyglutamic acid production. Biomass, X (); dissolved
oxygen concentration, CL (□); Polyglutamic acid (PGA) concentration, P (▲).
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).

and CL
FIG. 2.15. 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).

2.3. EMPIRICAL CORRELATIONS
OF KLa

● A large number of Empirical
Correlations Exist for KL and KLa for
Agitated and Aerated Bioreactor
Vessels.
● General Background Reading:
Textbook by H.W. Blanch and D.S.
Clark “Biochemical Engineering”,
Chapter 5. Transport Processes,
pp. 343-415. Publisher: Marcel Dekker,
Inc., New York, 1996.
● Consider a Stirred Tank Bioreactor
Vessel at a given:

P
g
VL
DT
L
H
AIR, Q
Q = Vol. air flow rate
@S.T.P.
DT = Tank diameter
HL = Liquid height (un-
gassed)
VL = Working Liquid
volume (un-gassed)
Pg = Gassed power
P = Un-gassed power
● Impeller Speed R.P.M.
Aeration Rate Q
Working Liquid Volume VL
of the Vessel
FIG. 2.16. Typical stirred tank bioreactor vessel

Most Empirical Correlations for KLa have the
following form
Where:
● KLa = Vol. mass transfer coefficient
● Pg = Gassed power supplied by
mechanical impeller for mixing of
bioreactor vessel.
● VL = Liquid working volume of
bioreactor vessel
KLa = C
Pg
VL
m
Ug
k
................(2.10)

EMPIRICAL CORRELATIONS
OF KLa
● Ug = Superficial air velocity
● m, k = Exponents, constants
● The values for C, m, and k depend greatly on the ionic strength of the
aqueous phase in the bioreactor.
● Ionic strength, I, of the solution in the bioreactor is defined by Equation 2.11.
I = ½ (Zi
2Ci)…………………………………(2.11)
● Where:
I = Ionic strength of solution, (g ions/L)
Zi = Electric charge of ionic species i, present in the solution
e.g.
SO4
-2 = has Zi = -2
Na+ has Zi = +1
Ag+ has Zi = +1
Ci = Concentration of ionic species in the solution = (g-ions/L)
Cross-sectional area of
bioreactor vessel
Vol. air flow rate @ S.T.P.
=

OF KLa
Constants C, m, and k also depend on:
● Temperature, T
● pH
● Physical properties of the solution
● Presence of other nutrients
● For Pure Water at pH = 7, T = 25 oC, the following
empirical correlation applies:
KLa = (0.026)
Pg
VL
0.4
Ug
0.5
....(2.12)

OF KLa
Where:
KLa = Vol. mass transfer coefficient (s-1)
Pg = Gassed power (W)
Ug = Superficial air velocity (m s-1)
Note: The values of C = 0.026, exponents
0.4 and 0.5 in Eq. 2.12 can be used
only with the units of KLa, Pg and
Ug specified above.

● A log-log plot of experimental data according to Equation
2.10 is shown in the following figure.
● Taking the log on both sides of Eq. 2.10, we get
log (KLa) = log (C) + k log (Ug) + m log (Pg/VL).
log (Pg/VL)
log
K
L
a
SLOPE = m
Ug = CONSTANT
FIG. 2.17. A log-log plot of experimental data according to Equ. 2.10.

● Definition of gas-holdup, Ho, in an agitated and
aerated vessel
T
V
AIR
LIQUID PHASE,
VL
AIR BUBBLES,
Vg (DISPERSED
PHASE)
Ho = gas hold-up =
Volume occupied by gas phase
Total volume
(VT) Total volume = Liquid Volume (VL)+Gas volume (Vg)
Ho =
Vg
Vg +VL
.........................(2.13)
FIG. 2.18. Typical agitated and aerated stirred tank bioreactor vessel

● Assuming a monodispersed size distribution of air
bubbles each having the same diameter dB, then the
gas hold-up Ho is related to the interfacial specific
gas-liquid area and dB according to Eq. 2.14.
Where:
● Ho = dimensionless
● dB = bubble diameter, m
● a = interfacial specific area, m2/m3 = m-1
● Eq. 2.14 can be used as an approximation for a
rough estimate of specific interfacial area a (m2/m3
of total volume)
.........................(2.14)
dB
6Ho
a =

3. AGITATION OF BIOREACTOR
SYSTEMS

● Fig. 3.1 shows the dimensions of what is called a
“standard” stirred tank bioreactor vessel with
Baffles.
FIG. 3.1. Standard Stirred Tank Bioreactor Geometry [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].

Geometric Ratios for a Standard Bioreactor
Vessel
Impeller Di/Dt HL/Dt Li/Di Wi/Di Hb/Di Wb/Dt No. Baffles
Type
Flat-Blade 0.33 1.0 0.25 0.2 1.0 0.1 4
Turbine
Paddle 0. 3 3 1.0 - 0.25 1.0 0.1 4
impeller
Marine 0.33 1.0 pitch = Di 1.0 0.1 4
Propeller
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

FIG. 3.2 A. 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.

FIG. 3.2 B. 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.

3.1 Mixing and Power Requirements for
Newtonian Fluids in a Stirred Tank
FIG. 3.3 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].

Fig. 3.3 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 Equ.
3.1
NP = Pgc/n3Di
5………………………(3.1)
The impeller Reynolds number is given
by Equ. 3.2
NRe = nDi
2/……………..................(3.2)
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 Fig. 3.3.
For six-bladed flat turbine and for
turbulent conditions:
NP = 6 = Pgc/n3Di
5
or P = (6)(n3Di
5)/(gc)………..(3.3)
At NRe = 3,000 the corresponding
impeller speed is:
n = (3,000)()/(Di
2)()…(3.4)

● Eq. 3.4 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.
● Eq. 3.3 shows that for a fluid of a given density,
:
P  n3Di
5
This is an important consideration for bioreactor
vessel scale-up.

Eq. 3.1 is used to find the un-gassed power, P, at
a given:
impeller diameter, Di and
impeller speed, n.
For aerobic fermentation (aerated) bioreactors:
Pg (gassed) < P (un-gassed) power
since eff (effective density) < 
Pg/P < 1

The aeration number, Na, is defined by Equ. 3.5 and is
used to quantify the power ratio Pg/P as a function of
aeration rate Qg, as shown in Fig. 3.4.
For water:
Na = Qg/nDi
3……………(3.5)
Where:
Na = aeration number (dimensionless)
Qg = Volumetric flow rate of air (m3 at STP/s)
n = impeller rotational speed, revolutions per
second (s-1).
Di = impeller diameter (m).

FIG. 3.4 Power requirements for agitation in a gassed system. The ordinate and abscissa are
degree of power decrease, Pg/P, and the aeration number, Na. Parameters are the types of
impellers, whose representative geometrical ratios in agitated vessels are also shown in the
figure. [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) 176].

Fig. 3.4 shows the relationship between
Pg/P ratio and Aeration Number, Na,
for three types of mechanical impellers:
● Flat-blade turbine (A)
● Vaned disk impeller with
different vanes (np = 4, 6, 8, 16)
curves, B, C, D, E
● Paddle impeller

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…….(3.6)

For a given QO2, X, and (CL
* - CL), KLa can
be calculated using Eq. 3.6.
For a given VL and Ug, Pg can be calculated
using the empirical correlation for KLa given
by Eq. 3.7.
KLa = C [Pg/VL]m [Ug]k……………3.7
Figs. 3.3 and 3.4 are used in combination to find the
correct rotational impeller speed, n, to deliver the
required Pg at a given Ug, for the required value of
KLa.

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