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Gas-liquid mass transfer in bioreactors

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Supplying oxygen to aerobic cell is 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

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.

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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.

H

P*C o

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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 liquid film surrounding interface Step 4 - Movement through the bulk liquid by forced

convection and diffusion Step 5-9: Movement through the floc

Step 5 - movement through the liquid 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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Oxygen Path From A Bubble To An Immobilized Cell System

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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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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.

If The bubble contains a low concentration of oxygen,

then the rate of oxygen transfer

out of the bubble will be slow

or even zeroO2

CO2

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Step 3- Diffusion through stagnant liquid film

The movement of solutes through the film 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 which may affect the rate of diffusion of oxygen through the liquid film

Temperature Concentration of oxygen in the bulk liquid Sturation concentration of oxygen in the liquid Concentration of oxygen in the bubble

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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

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Step 5-9: Movement through the floc complete the journey of the oxygen moleculeStep 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 Steps 5 and 7 are slow processes.

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OTRCCakN LLA )*(

NA = Volume-dependent mass transfer(mMO2/Lh)

kL = Transfer coefficient at the phase boundary

a = 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)

Step 3 The interphase oxygen transfer equation

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Molecular Diffusion The movement of component molecules in a mixture under the influence of a concentration difference in the system. Diffusion of molecules occurs in the direction required to destroy the concentration gradient.

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Fick’s Law of diffusion

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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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Concentration profile near a gas-liquid interface

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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 (1) Substitution of NG and NL into Eq. (1) 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 CGi cannot be measured

To define the overall mass-transfer coefficient as follows :

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Film Theory

The two-film theory is a useful model for mass transfer between phases. Mass transfer of solute from one phase to another involves transport from the bulk of one phase to the phase boundary or interface, and then from the interface to the bulk of the second phase.

The film theory is based on the idea that a fluid film or mass-transfer boundary layer forms wherever there is contact between two phases.

Mechanism of Mass Transfer

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According to the film theory, turbulence in each fluid dies out at the phase boundary. A thin film of relatively stagnant fluid exists on either side of the interface; mass transfer through this film is effected solely by molecular diffusion. The concentration of A changes near the interface

Most of the resistance to mass transfer resides in the liquid films rather than in the bulk liquid.

It is generally assumed that there is negligible resistance to transport at the interface itself; this is equivalent to assuming that the phases are in equilibrium at the plane of Mass Transfer contact.

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The difference between CA1i and CA2i at the interface accounts for the possibility that, at equilibrium, A may be more soluble in one phase than in the other. For example, if A were acetic acid in contact at the interface with both water and chloroform, the equilibrium concentration in water would be greater than that in chloroform by a factor of between 5 and 10.

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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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Determination of Oxygen-Absorption RateThe oxygen absorption rate per unit volume qa/v can be estimated by

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Methods of KLa determination

Sodium Sulfite Oxidation Method The sodium sulfite oxidation method (Cooper et al., 1944) is based on the oxidation of sodium sulfite to sodium sulfate in the presence of catalyst (Cu++ or Co++) as

To measure the oxygen-transfer rate in a fermenter, fill the fermenter with a 1 N sodium sulfite solution containing at least 0.003 M Cu++ ion. Turn on the air and start a timer when the first bubbles of air emerge from the sparger.

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Allow the oxidation to continue for 4 to 20 minutes, after which, stop the air stream, agitator, and timer at the same instant, and take a sample.

Mix each sample with an excess of freshly pipetted standard iodine reagent. Titrate with standard sodium thiosulfate solution (Na2S2O3) to a starch indicator end point.

Once the oxygen uptake is measured, the kLa may be calculated by using following Equation. where CL is zero and CL * is the oxygen equilibrium concentration.

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Limitations of sulfite oxidation method

•The solution cannot approximate the physical and chemical properties of a fermentation broth. •An additional problem is that this technique requires high ionic concentrations (1 to 2 mol/L), the presence of which can affect the interfacial area and, in a lesser degree, the mass-transfer coefficient

Dynamic Gassing-out Technique

This technique monitors the change of the oxygen concentration while an oxygen-rich liquid is deoxygenated by passing nitrogen through it. Polarographic electrode is usually used to measure the concentration. The mass balance in a vessel gives

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Direct Measurement In this technique, we directly measure the oxygen content of the gas stream entering and leaving the fermenter by using gaseous oxygen analyzer. The oxygen uptake can be calculated as

Once the oxygen uptake is measured, the kLa can be calculated by using same (above) equation where CL is the oxygen concentration of the liquid in a fermenter and C*L is the concentration of the oxygen which would be in equilibrium with the gas stream. The oxygen concentration of the liquid in a fermenter can be measured by an on-line oxygen sensor.

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Dynamic Technique

By using the dynamic technique (Taguchi and Humphrey, 1966), we can estimate the kLa value for the oxygen transfer during an actual fermentation process with real culture medium and microorganisms. This technique is based on the oxygen material balance in an aerated batch fermenter while microorganisms are actively growing as

While the dissolved oxygen level of the fermenter is steady, if you suddenly turn off the air supply, the oxygen concentration will be decreased with the following rate

since kLa in Eq. is equal to zero. Therefore, by measuring the slope of the CL vs. t curve, we can estimate O2 X r C . If you turn on the airflow again, the dissolved oxygen concentration will be increased according to above equation which can be rearranged to result in a linear relationship as

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