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

Course outline 9.1. Introduction 9.2. Basic Mass-Transfer Concepts 9.3. Correlation for Mass-Transfer Coefficient 9.4. Measurement of Interfacial Area 9.5. Correlations for a and D32 9.6. Gas Hold-Up 9.7. Power Consumption 9.8. Determination of Oxygen-Absorption Rate 9.9. Correlation for kLa 9.10. Scale-Up 9.11. Shear-Sensitive Mixing

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

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

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

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

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

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

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.

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.

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.

Oxygen Path From A Bubble To An Immobilized Cell System

Oxygen Path From A Bubble To An Immobilized Cell System

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

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

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

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

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

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.

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)

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)

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

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

Molecular Diffusion in Liquids (溶質濃度CA很低)

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)

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. 3-225, 1973). Convert the experimental value to that corresponding to a temperature of 40°C. (9.5)

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.

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

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

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 :

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

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)

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.

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.

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.

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

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)

Measurement of Interfacial Area

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

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