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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

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cbe 320b biochemical engineering iii course notes
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
TABLE OF CONTENTS

1. Introduction

 Bioprocess Design

 Novel Bioreactor Types

 Design Criteria for Bioreactors

2. Aeration and Oxygen MassTransfer in Bioreactor Systems

 Oxygen Requirements by Microorganisms

 The volumetric Mass Transfer Coefficient KLa and Methods of Measurements

 Empirical Correlations of KLa

slide3
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

slide4
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

slide8
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

______________________________________________________________________

slide9
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

__________________________________________________________

slide10
TABLE 2. Summary of Bioreactor Systems (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

________________________________________________________________________________________

table 2 summary of bioreactor systems cont d
TABLE 2. Summary of Bioreactor Systems (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

________________________________________________________________________________________

slide12
Fig. 1.1. Schematic diagram of a tower bioreactor system with perforated plates and co-current air liquid flow.
slide13
Fig. 1.2. Schematic diagram of a tower bioreactor system with multiple impellers and liquid down comer and counter-current air liquid flow
slide16
FIG. 1.5. Internal circulation patterns of fluidized Ca-alginate beads containing immobilized cells of Z. mobilis. All dimensions in cm.
slide19
 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.)

slide21
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.

slide22
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.

oxidation reduction reaction cont d
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
LIQUID PHASE

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
LIQUID PHASE (CONT’D)

 At Steady-state with no O2 accumulation in the liquid phase:

 What are the O2 requirements of microorganisms?

2 1 oxygen requirements of microorganisms
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.)

slide27
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

slide28

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.

FIG. 2.4. Respiration coefficient QO2 as a function of the dissolved oxygen concentration CL.

slide29
 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

slide30
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.

slide31

TABLE 1. Cell suspensions in glucose. Oxygen uptake determined in constant volume Warburg respirometer

slide32

TABLE 2. Typical values of CL CRIT in the Presence of Substrate

Adopted from R. K. Finn, P.81 in: N. Blakebrough (ed), Biochemical Engineering Science. Vol. 1, Academic Press, Inc., New York, 1967

slide33

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)

slide34

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)

mass balance of oxygen in unit liquid volume
Mass Balance of Oxygen in Unit Liquid Volume

FIG. 2.7 Schematic diagram of the mass balance of oxygen transfer in unit liquid volume

chemical methods of k l a measurement
Chemical Methods of KLa Measurement

FIG. 2.8. Schematicdiagram of a stirred tank batch reactor

chemical methods of k l a measurement cont d51
Chemical Methods of KLa Measurement (Cont’d)

FIG. 2.9. Concentration of SO3-2 as a function of oxidation time

in situ measurement of k l a q o2 and c l during cell growth in a bioreactor cont d
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.

in situ measurement of k l a q o2 and c l during cell growth in a bioreactor cont d55
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 k l a q o2 and c l during cell growth in a bioreactor cont d56
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.

in situ measurement of k l a q o2 and c l during cell growth in a bioreactor cont d57
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 k l a q o2 and c l during cell growth in a bioreactor cont d58
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 CLnever 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 k l a q o2 and c l during cell growth in a bioreactor cont d59
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 k l a q o2 and c l during cell growth in a bioreactor cont d60
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.

in situ measurement of k l a q o2 and c l during cell growth in a bioreactor cont d61
In Situ Measurement of KLa, QO2, and CL* During Cell Growth in a Bioreactor (Cont’d)

FIG. 2.11. Transient Air-Off, Air-On Experiment in a Bioreactor System

in situ measurement of k l a q o2 and c l during cell growth in a bioreactor cont d62
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.

FIG. 2.12. D.O. concentration CL as function of time during AIR-OFF period.

in situ measurement of k l a q o2 and c l during cell growth in a bioreactor cont d63
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 k l a q o2 and c l during cell growth in a bioreactor cont d64
In Situ Measurement of KLa, QO2, and CL* During Cell Growth in a Bioreactor (Cont’d)

● Re-arranging Eq. 2.2 and solving for CL we get Eq. 2.9

● By plotting CL vs. at a givenfermentation time, t,

wecan get the slope which is equal to

in situ measurement of k l a q o2 and c l during cell growth in a bioreactor cont d65
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 k l a q o2 and c l during cell growth in a bioreactor cont d66
In Situ Measurement of KLa, QO2, and CL* During Cell Growth in a Bioreactor (Cont’d)

FIG. 2.13.D.O. concentration CL as function of [dCL/dt + QO2X] during AIR-ON period.

in situ measurement of k l a q o2 and c l during cell growth in a bioreactor cont d67
In Situ Measurement of KLa, QO2, and CL* During Cell Growth in a Bioreactor (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).

in situ measurement of k l a q o2 and c l during cell growth in a bioreactor cont d68
In Situ Measurement of KLa, QO2, and CL* During Cell Growth in a Bioreactor (Cont’d)

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).

in situ measurement of k l a q o2 and c l during cell growth in a bioreactor cont d69
In Situ Measurement of KLa, QO2, and CL* During Cell Growth in a Bioreactor (Cont’d)

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).

slide71
● 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:

slide72

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

FIG. 2.16. Typical stirred tank bioreactor vessel

● Impeller Speed R.P.M.

Aeration Rate Q

Working Liquid Volume VL

of the Vessel

slide73
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

empirical correlations of k l a
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 (Zi2Ci)…………………………………(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)

empirical correlations of k l a75
EMPIRICAL CORRELATIONS 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:

empirical correlations of k l a76
EMPIRICAL CORRELATIONS 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.

slide77
● 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).

FIG. 2.17. A log-log plot of experimental data according to Equ. 2.10.

slide78
● Definition of gas-holdup, Ho, in an agitated and aerated vessel

FIG. 2.18. Typical agitated and aerated stirred tank bioreactor vessel

slide79
● 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)

slide81
● 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
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

slide83

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.

slide84

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.

slide85
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].

slide86
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

slide87
The power number is given by Equ. 3.1

NP = Pgc/n3Di5………………………(3.1)

The impeller Reynolds number is given by Equ. 3.2

NRe = nDi2/……………..................(3.2)

Where:

NRe = dimensionless Reynolds number

NP = dimensionless Power number

slide88
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

slide89
Different Types of impellers have

different power characteristics Fig. 3.3.

For six-bladed flat turbine and for turbulent conditions:

NP = 6 = Pgc/n3Di5

or P = (6)(n3Di5)/(gc)………..(3.3)

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

n = (3,000)()/(Di2)()…(3.4)

slide90
● 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  n3Di5

This is an important consideration for bioreactor

vessel scale-up.

slide91
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

slide92

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/nDi3……………(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).

slide93

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].

slide94
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

slide95
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)

slide96
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.