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攪拌與通氣Agitation and Aeration

國立宜蘭大學食品科學系馮臨惠

生化工程 (Biochemical Engineering)

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Course outline9.1. Introduction9.2. Basic Mass-Transfer Concepts 9.3. Correlation for Mass-Transfer Coefficient9.4. Measurement of Interfacial Area9.5. Correlations for a and D329.6. Gas Hold-Up9.7. Power Consumption9.8. Determination of Oxygen-Absorption Rate9.9. Correlation for kLa9.10. Scale-Up9.11. Shear-Sensitive Mixing

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Typical Bioprocessing Stock Culture Raw Materials

Shake Flasks

Seed Fermenter

Medium Formulation

Sterilization

  Fermenter

Recovery

Purification Products

Air

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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

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Definition of FermentationEarly

The production of alcohol and lactic acidsGeneral

Anaerobic microbial conversion processesIndustrial

All microbial conversion processes including aerobic cultivations.

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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

http://www.foodprocessing-technology.com/glossary/aeration.html

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IntroductionBackground 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

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IntroductionBackground 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

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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.

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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.

Introduction Gas exchange and mass transfer (Crueger and Crueger, 1990)

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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.

HP

*C o

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Oxygen Path From A Bubble To An Immobilized Cell System

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Oxygen Path From A Bubble To An Immobilized Cell System

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The oxygen transfer process Step 1 - Diffusion through the bubble to the gas-liquid interfa

ce 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 convecti

on 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 slimeStep 7 - movement through the slimeStep 8 - movement across the cell membraneStep 9 - reaction

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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

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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

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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

The oxygen transfer process

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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

The oxygen transfer process

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Step 5-9: Movement through the floc complete the journey of the oxygen moleculeStep 5 - movement through the boundary layer surroundi

ng the microbial slime. Step 6 - entry into the slimeStep 7 - movement through the slimeStep 8 - movement across the cell membraneStep 9 - reaction Steps 5 and 7 are slow processes.

The oxygen transfer process

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If only suspended cells are involved the level of mixing in the bulk liquid is

sufficiently highThen the rate limiting step in the oxygen transfer

process is the movement of the oxygen molecules

through the bubble boundary layer. (Step 3)

The oxygen transfer process

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OTRCCakN LLA )*(

NA = Volume-dependent mass transfer(mMO2/Lh)kL = Transfer coefficient at the phase boundarya = Specific exchange surfacekLa = Volumetric oxygen transfer coefficient (h-1) C* = Saturation value of the dissolved gas in the phase boundaryCL = Concentration of the dissolved gas (mM/L)OTR = O2 Transfer Rate (mM O2/Lh)

The oxygen transfer processStep 3 The interphase oxygen transfer equation

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The transfer of massFick’s Law of diffusion

D ： the diffusivity (the movement of mass)成分 A在成分 B之擴散係數

dzdCDJ

Am A

ABA

]/[/length

volumemassDArea

timemassAB

])([2

timelengthDAB

The oxygen transfer process

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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

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Molecular Diffusion in Liquids

(溶質濃度 CA很低 )

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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)

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Diffusivity Othmer and Thakar correlation (the solvent is wate

r)

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. 3-225, 1973). Convert the experimental value to that corresponding to a temperature of 40°C.

(9.5)

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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.

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

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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

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Mass-Transfer Coefficient (kL & kG)

It is hard to determine the mass-transfer coefficient

Because the interfacial concentrations, CLi or CG

i cannot be measure To define the overall mass-transfer coefficient a

s follows :

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

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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)

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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 unknow

n 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.

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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.

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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.

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Dimensionless Number for Mass Transfer Correlations

32total mass transfer diffusive mass transfer

LSh

AB

k DND

= =

/momentum diffusivity mass diffusivity

c cSc

AB

ND

= =

332

2

gravitation force viscous force

cGr

c

D gN

= =

(9.21)

(9.22)

(9.23)

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Correlations for Mass Transfer Coefficients (Calderbank & Moo-Young, 1961)

3/13/131.0 GrScSh NNN

1/3 1/32.0 0.31Sh Sc GrN N N= +

(9.26)

(9.28)

For small bubbles (D < 2.5 mm)

For large bubbles (D > 2.5 mm)

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Measurement of Interfacial Area

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Correlations for interfacial area

Gas Sparging with No Mechanical Agitation

Gas Sparging with Mechanical Agitation

0.10.5 321.13

2

1 3

CC LC

L

gDg DaD H

1/ 20.4 0.2

0 0.6 1.44 scm

t

VP vaV

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Correlations for gas hold-upGas Sparging with No Mechanical Agitation

Gas Sparging with Mechanical Agitation

1/2 1/ 20.4 0.2

4

0.6 +(2.16 10 )s scm

t t

V H VP vHV V

1/121/8 32

24 0.20

(1 )sCC c

Cc

VgDH g DgDH