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7.REACTION MECHANISMS,PATHWAYS,BIOREACTIONS AND

BIOREACTORS

Professional Reference Shelf

R7.2 Oxygen-Limited Fermentation

Oxygen is necessary for all aerobic fermentation (by definition) [cf.Equation (7-98)]. Maintaining the appropriate concentration of dissolved

oxygen in fermentation is important for the efficient operation of afermentor. For oxygen-limited systems, it is necessary to design a

fermentor to maximize the oxygen transfer between the injected air bubble

and the cell. Typically, a fermentor contains a gas sparger, heat transfersurfaces, and an impeller, such as the one shown in Text Figure 7-18 for a

batch reactor. A chemostat has a similar configuration, with the addition ofinlet and outlet streams.

Transport Steps. The overall transport mechanism of oxygen to a cell is

very similar to that described for reactant gas in a slurry reactor and asshown in Figure CD7-3. The corresponding oxygen transport and reaction

steps and equations are analogous to the slurry reactor transport steps

discussed in Chapter 12, that is:

(R7.2-

1)

(R7.2-2)

Generally, the diffusional resistance from the bulk liquid to the cell surfaceis ignored. However, depending on the cell size or cell floc size, the transfer

step from the bulk liquid to the cell surface may be rate-limiting; one suchexample is the oxygenation of a culture ofStreptomyces niveus. The

transport of oxygen into a cell occurs by different mechanisms for yeast and

bacteria. In the case of yeast, an oxygen molecule diffuses across an inertcell membrane before being consumed by the cell. The corresponding rate

equations are:

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Analogousto slurry

reactor

steps

Figure R7.2-1

Oxygen transport to microorganisms.

(R7.2-3)

(R7.2-

4)

where:

ac= cell surface area per mass of cell, m2/g

De effective diffusivity across the cell, m2/s

L = thickness of cell membrane, m

Cc= concentration of cells, g/ m3 (analogous to m in a slurry reactor, Text

Chapter 12)

Ci, Cb, C0, Cc= saturation, bulk, external surface, and internal cellconcentrations of oxygen, respectively

Combining Equations (R7.2-2) through (R7.2-4) and rearranging, we obtain

Yeast

(R7.2-

5)

For many yeast cells, diffusion across the cell membrane can be neglected.

In the case of bacteria, the oxygen begins to be consumed as soon as itdiffuses into the cell membrane. In fact, bacteria consume oxygen primarily

atthe cell membrane, where most of the respiratory enzymes are located.

As is the case of the catalyst pellet in the slurry reactor, the rate of oxygenconsumption can be given by the product of the effectiveness factor and the

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rate of reaction that would occur if the entire interior of the cell wereexposed to the concentration at the external surface, C0

The rate law for oxygen consumption (uptake) generally follows eitherMichealis-Menten or first-order kinetics. In many systems it depends on theparticular growth phase of the bacteria cell. Typical respiration rates for

single-cell yeast and bacteria are on the order of 100 to 600 mg O2/g cellh. For first-order kinetics we have

(R7.2-

6)

where kris the specific reaction rate for oxygen uptake, s-1, and h is the

effectiveness factor for diffusion and reaction of oxygen inside the cell.

Combining equations (R7.2-6), (R7.2-2), and (R7.2-3) gives

Bacteria(R7.2-

7)

We can observe from Equations (R7.2-5) and (R7.2-7) that at low cell

concentrations, transport steps C, D, and E (mass transfer of oxygen to andwithin the cell) become rate limiting.

The main variables affecting kLab are the impeller diameter, Di, and speed,

N(rpm); volumetric flow rate of the gas, Q; tank diameter, DT, and height

LT; and power input to impeller, . Many fermentations produce productsthat cause the broth to exhibit non-Newtonian fluid behavior. Consequently,

a characteristic relaxation time, , is included in the correlation for the

mass transfer coefficient between the gas bubble and the bulk liquid, kLab.Representative correlations for kLab are given in Table R7.2-1.

The power input to the fermentor without gas bubbles present ( ) is afunction of system variables:6,7

where the Reynolds number for this system is defined as

(R7.2-8)

When gas is present, the power input, Pg is reduced for a given propellerspeed 8 and is a function of gas flow rate, impeller speed and diameter, and

the Reynolds number. The ration of the power input with gas present, Pg,

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to that without gas present ( ) is

(R7.2-

9)

Table R7.2-1. Mass Transfer Coefficients In Fermentor

1. Low-viscosity broths Van't Reit (1):

Range

Pure Water2-2600dm3

Electrolytic (Solutions)

2-4400

dm3

where = power input per unit volume of vessel and isin units of W/m3

Q = volumetric flow rate, m3/s

DT= tank diameter, m

Vs = superficial gas velocity

2. Non-Newtonian correlations

Perez and Sandall (2):(R7.2-

10)

Yagi and Yoshida (3):

(R7.2-

11)

Ranade and Ulbrecht (4):

(R7.2-

12)

[Comment: These correlations were obtained in tanks having a volume of12 dm3 or less (5).]

Other parameters in the correlations are:

g = gravitational acceleration, m2/s = fluid viscosity, g/m s

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e = effective viscosity, g/m sw= viscosity of water, g/ms

d= viscosity of dispersed phase,g/m s

= surface tension, N/m

N= impeller rotation speed, s-1 = density, g/m3

DAB = diffusivity, m2/s

3. Effect of solids (6):

(1) K. Van't Reit, Fund. Eng. Chem. Proc. Des. Dev., 18, 357 (1979)

(2) J.F. Perez and O.C. Sandall,AIChE J., 20, 770 (1974)

(3) H. Yagi and F. Yoshida, Ind. Eng. CHem. Proc. Des. Dev., 14, 488(1975)

(4) V.R. Ranade and J.J. Ulbrecht,AIChE J., 24, 796 (1978)(5) D.W. Hubbard, L.R. Harris, and M.K. Wierenga, Chem.Eng. Prog., 84(8),

55 (1988)(6) D.B. Mills, R. Bar, and D.J. Kirwan,AIChE J., 33, 1542 (1987)

The functions F1 and F2 are generally given graphically

for different types of fluids and different geometricconfigurations. 9,10

Fermentation Scale Up

2006 by Pearson Education, Inc.Publishing as Prentice Hall PTR

ISBN 0-13-047394-4

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