Elements of
Chemical Reaction Engineering
6th Edition



Home

Essentials of
Chemical Reaction Engineering
Second Edition

  Select  Chapter  >>     TOC     Preface     1     2     3     4     5     6     7     8     9     10     11     12     13     14     15     16     17     18     Appendices  
›

By Chapter Hide

  • Objectives
  • Living Example Problems
  • Extra Help
  • - Summary Notes
  • - LearnChemE Screencasts
  • - FAQs
  • - Interactive Computer Modules
  • Additional Material
  • Self Test
  • i>Clicker Questions
  • Professional Reference Shelf

By Concept Hide

  • Interactive Modules
  • -Web Modules
  • -Interactive Computer Games
  • Living Example Problems

U of M Hide

  • Asynchronous Learning
  • ChE 344
  • ChE 528

Chapter 9: Reaction Mechanisms, Pathways, Bioreactions and Bioreactors

Professional Reference Shelf

The following information is taken from the 4th edition of Elements of Chemical Reaction Engineering, so the equation numbers correspond to those found in that book

R9.4 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 a fermentor. 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 transfer surfaces, 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 of inlet 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 as shown 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:

  
 

 
  IMAGE 07eq120.gif

(R7.2-1)

(R7.2-2)
 


Generally, the diffusional resistance from the bulk liquid to the cell surface is 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 such example is the oxygenation of a culture of Streptomyces 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 inert cell membrane before being consumed by the cell. The corresponding rate equations are:

 
     

Analogous to slurry reactor steps

Figure R7.2-1
Oxygen transport to microorganisms.

 
     
 

IMAGE 07eq121.gif

(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 cell concentrations of oxygen, respectively

 
     
 

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

  
     

Yeast

IMAGE 07eq122.gif

(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 it diffuses into the cell membrane. In fact, bacteria consume oxygen primarily at the 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 oxygen consumption can be given by the product of the effectiveness factor and the rate of reaction that would occur if the entire interior of the cell were exposed to the concentration at the external surface, C0

  
     
 

IMAGE 07eq123.gif

 
     
 

The rate law for oxygen consumption (uptake) generally follows either Michealis-Menten or first-order kinetics. In many systems it depends on the particular 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 cellmiddoth. For first-order kinetics we have

  
     
  IMAGE 07eq124.gif

(R7.2-6)
 

where kr is 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

IMAGE 07eq125.gif

(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 and within 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,pi with ~. Many fermentations produce products that cause the broth to exhibit non-Newtonian fluid behavior. Consequently, a characteristic relaxation time,time2, 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 (p with ~) is a function of system variables:6,7

  
     
 

image 07eq126.gif

 
     
 

where the Reynolds number for this system is defined as

  
     
 

image 07eq127.gif

(R7.2-8)
     

When gas is present, the power input, Pg is reduced for a given propeller speed 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, to that without gas present () is

  
     
 

image 07eq128.gif

(R7.2-9)
     
     
  Table R7.2-1. Mass Transfer Coefficients In Fermentor

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

Range

    Pure Water

2-2600 dm3

    Electrolytic (Solutions)IMAGE 07eq129a2.gif

2-4400 dm3

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

Q = volumetric flow rate, m3/s
DT = tank diameter, m
Vs = superficial gas velocityIMAGE 07eq129a3.gif

 
 

2. Non-Newtonian correlations		  
     
    Perez and Sandall (2):
image 07eq129b.gif

(R7.2-10)

 
    Yagi and Yoshida (3):
IMAGE 07eq129c.gif

(R7.2-11)
 

 
    Ranade and Ulbrecht (4):
    IMAGE 07eq129d.gif

(R7.2-12)

 

    [Comment: These correlations were obtained in tanks having a volume of 12 dm3 or less (5).]







 

Other parameters in the correlations are:

     

g = gravitational acceleration, m2/s

  

mu gif = fluid viscosity, g/mmiddots
   

mu gife = effective viscosity, g/mmiddots

  

mu gifw= viscosity of water, g/mmiddots
     

mu gifd = viscosity of dispersed phase, g/mmiddots

  

sigma.gif = surface tension, N/m
     

N = impeller rotation speed, s-1

  

rho gif = density, g/m3
     

DAB = diffusivity, m2/s

    
   

 

   3. Effect of solids (6):

IMAGE 07eq129f.gif

(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 geometric configurations. 9,10

Fermentation Scale Up