1. 攪拌與通氣 Agitation and Aeration
生化工程(Biochemical Engineering)
攪拌與通氣 Agitation and Aeration
國立宜蘭大學
食品科學系
馮臨惠

2. Course outline 9.1. Introduction 9.2. Basic Mass-Transfer Concepts
Correlation for Mass-Transfer Coefficient
Measurement of Interfacial Area
Correlations for a and D32
Gas Hold-Up
Power Consumption
Determination of Oxygen-Absorption Rate
Correlation for kLa
9.10. Scale-Up
9.11. Shear-Sensitive Mixing

3. Typical Bioprocessing
Stock Culture
Raw Materials
Shake Flasks
Medium Formulation
Seed Fermenter
Sterilization
Fermenter
Air
Recovery
Purification
Products

4. Aeration and Agitation
Important factor in a fermenters
Provision for adequate mixing of its contents
Mixing in fermentation
to disperse the air bubbles
to suspend the cells
to enhance heat and mass transfer in the medium
All relate to Gas-liquid mass transfer

5. Definition of Fermentation
Early
The production of alcohol and lactic acids
General
Anaerobic microbial conversion processes
Industrial
All microbial conversion processes including aerobic cultivations.

6. Introduction Aeration
Aeration refers to the process of introducing air to increase oxygen concentration in liquids
Aeration may be performed by bubbling air through the liquid, spraying the liquid into the air or agitation of the liquid to increase surface absorption
Gas-liquid mass transfer in bioreactors

7. Introduction Background
The aerobic fermentation：
the primary method of product formation
very few anaerobic fermentation (lactic acid bacteria)
Supplying oxygen to aerobic cells：
a significant challenge
The problem：oxygen is poorly soluble in water
The solubility of oxygen in pure water is
8 mg/L at 4oC (sucrose is soluble to 600 g/L)
The solubility of oxygen decreases as with
increasing temperature and concentration of solutes in the solution

8. Introduction Background
The factors affect oxygen transfer
How fermentation systems can be designed
to maximize dissolved oxygen concentration in bioreactors
The supply of oxygen
the rate limiting step in an aerobic fermentation
Satisfy oxygen demands
constitute a large proportion of the operating and capital cost of a industrial scale fermentation system

9. Introduction Gas exchange and mass transfer (Crueger and Crueger, 1990)
The most critical factors in the operation of a large scale fermenter is the provision of adequate gas exchange.
Oxygen is the most important gaseous substrate for microbial metabolism
Carbon dioxide is the most important gaseous metabolic product.
When oxygen is required as a microbial substrate, it is frequently a limiting factor in fermentation.

10. Introduction Gas exchange and mass transfer (Crueger and Crueger, 1990)
Because of its low solubility, only 0.3 mM 02, equivalent to 9 ppm, dissolves in one liter of water at 20℃ in an air/water mixture
Due to the influence of the culture ingredients, the maximal oxygen content is actually lower than it would be in pure water.
The solubility of gases follows Henry's Law in the gas pressure range over which fermenters are operated.

11. Henry's Law
Describes the solubility of O2 in nutrient solution in relation to the O2 partial pressure in the gas phase
C* is the oxygen saturation concentration of the nutrient solution, Po is the partial pressure of the gas in the gas phase and H is Henry's constant, which is specific for the gas and the liquid phase
Aeration with air 9 mg O2/L dissolves in water, with pure oxygen 43 mg O2/L.

12. Oxygen Path From A Bubble To An Immobilized Cell System

13. Oxygen Path From A Bubble To An Immobilized Cell System

14. The oxygen transfer process
Step 1 - Diffusion through the bubble to the gas-liquid interface
Step 2 - Diffusion across the gas-liquid interface
Step 3 - Diffusion through the bubble boundary layer
Step 4 - Movement through the bulk liquid by forced convection and diffusion
Step 5-9: Movement through the floc
Step 5 - movement through the boundary layer surrounding the microbial slime
Step 6 - entry into the slime
Step 7 - movement through the slime
Step 8 - movement across the cell membrane
Step 9 - reaction

15. The oxygen transfer process
Step 1
Diffusion through the bubble to the gas-liquid interface
Gas molecules move quickly
they are evenly distributed throughout the bubble. O2

16. The oxygen transfer process
Step 2 - Diffusion across the gas-liquid interface
This step will be very rapid if the concentration of oxygen in the bubble high. High oxygen concentrations in the bubble (as measured in terms of partial pressure) will push the oxygen molecules across the interface, into the boundary layer.
If the medium is rich in CO2 , then the carbon dioxide will be pushed into the bubble.
The bubble contains a low concentration of oxygen,
then the rate of oxygen transfer
out of the bubble will be slow
or even zero O2
CO2

17. The oxygen transfer process
Step 3- Diffusion through the bubble boundary layer
The movement of solutes through the boundary layer is slow. Solutes move through the liquid by diffusion.
The movement of the molecule will be driven by the concentration gradient across the boundary layer.
Factors affect the rate of diffusion of oxygen through the boundary layer, including :
temperature
concentration of oxygen in the bulk liquid
saturation concentration of oxygen in the liquid
concentration of oxygen in the bubble
size of the molecule and
viscosity of the medium

18. The oxygen transfer process
Step 4 Movement through the bulk liquid by forced convection and diffusion
The rate of movement of an oxygen molecule through the bulk liquid is dependent on
the degree of mixing (relative to the volume of the reactor)
viscosity of the medium O2

19. The oxygen transfer process
Step 5-9: Movement through the floc
complete the journey of the oxygen molecule
Step 5 - movement through the boundary layer surrounding the microbial slime.
Step 6 - entry into the slime
Step 7 - movement through the slime
Step 8 - movement across the cell membrane
Step 9 - reaction
Steps 5 and 7 are slow processes.

20. The oxygen transfer process
If only
suspended cells are involved
the level of mixing in the bulk liquid is sufficiently high
Then
the rate limiting step in the oxygen transfer process is
the movement of the oxygen molecules through the bubble boundary layer. (Step 3)

21. The oxygen transfer process
Step 3
The interphase oxygen transfer equation
NA = Volume-dependent mass transfer(mMO2/Lh)
kL = Transfer coefficient at the phase boundary
a = Specific exchange surface
kLa = Volumetric oxygen transfer coefficient (h-1)
C* = Saturation value of the dissolved gas in the phase boundary
CL = Concentration of the dissolved gas (mM/L)
OTR = O2 Transfer Rate (mM O2/Lh)

22. The transfer of mass Fick’s Law of diffusion
The oxygen transfer process
The transfer of mass Fick’s Law of diffusion
D ：the diffusivity (the movement of mass)
成分A在成分B之擴散係數

23. Molecular Diffusion in Liquids
When the concentration of a component varies from one point to another
the component has a tendency to flow in the direction that will reduce the local differences in concentration

24. Molecular Diffusion in Liquids
(溶質濃度CA很低)

25. Diffusivity
The kinetic theory of liquids is much less advanced than that of gases
The correlation for diffusivities in liquids is not as reliable as that for gases
The Wilke-Chang correlation (for dilute solutions of nonelectrolytes)
(9.4)

26. Diffusivity Othmer and Thakar correlation (the solvent is water)
Example 9.1 ：Estimate the diffusivity for oxygen in water at 25°C. Compare the predictions from the Wilke-Chang and Othmer-Thakar correlations with the experimental value of 2.5×10−9 m2/s (Perry and Chilton, p , 1973). Convert the experimental value to that corresponding to a temperature of 40°C.
(9.5)

27. Mass-Transfer Coefficient (kL & kG)
where
CS is the dissolved concentration of the solute in the bulk liquid
k is the mass transfer coefficient for the solute through the boundary layer
A is the total interfacial area and
Cs* is the concentration of the solute in the boundary layer.

28. Figure 9.3 Concentration profile near a gas-liquid interface and an equilibrium curve.

29. Mass-Transfer Coefficient (kL & kG)
Since the amount of solute transferred from the gas phase to the interface must equal that from the interface to the liquid phase,
NG =NL (9.8)
Substitution of Eq. (9.6) and Eq. (9.7) into Eq. (9.8) gives

30. Mass-Transfer Coefficient (kL & kG)
It is hard to determine the mass-transfer coefficient
Because the interfacial concentrations, CLi or CGi cannot be measure
To define the overall mass-transfer coefficient as follows :

31. Figure 9.4 The equilibrium curve explaining the meaning of G C * andGL *

32. Mass-Transfer Coefficient (kL & kG)
For sparingly soluble gases, the slope of the equilibrium curve is very steep
M is much greater than 1 and from Eq. (9.14)
KL ≈kL (9.15)
Similarly, for the gas-phase mass-transfer coefficient,
KG ≈kG (9.16)

33. Mechanism of Mass Transfer
The two-film theory (雙膜理論)
The penetration theory (滲透理論)
The surface renewal theory (表面更新理論)
Read textbook p. 9-8 ~ 9-9
All these theories require knowledge of one unknown parameter, the effective film thickness Zf, the exposure time te, or the fractional rate of surface renewal s. Little is known about these properties, so as theories, all three are incomplete.

34. Correlation for Mass-Transfer Coefficient
Mass-transfer coefficient is a function of physical properties and vessel geometry
Because of the complexity of hydrodynamics in multiphase
mixing, it is difficult, if not impossible, to derive a useful correlation based on a purely theoretical basis
It is common to obtain an empirical correlation for the mass-transfer coefficient by fitting experimental data. The correlations are usually expressed by dimensionless groups since they are dimensionally consistent and also useful for scale-up processes.

35. Sauter-mean diameter D32
D32 can be calculated from measured drop-size distribution from the following relationship
Example 9.3 Determine appropriate dimensionless parameters that can relate the mass transfer coefficient by applying the Buckingham-Pi theorem.

36. Dimensionless Number for Mass Transfer Correlations
(9.21)
(9.22)
(9.23)

37. For small bubbles (D < 2.5 mm)
Correlations for Mass Transfer Coefficients (Calderbank & Moo-Young, 1961)
For small bubbles (D < 2.5 mm)
(9.26)
For large bubbles (D > 2.5 mm)
(9.28)

38. Measurement of Interfacial Area

39. Correlations for interfacial area
Gas Sparging with No Mechanical Agitation
Gas Sparging with Mechanical Agitation

40. Correlations for gas hold-up
Gas Sparging with No Mechanical Agitation
Gas Sparging with Mechanical Agitation