10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup

Lecture 19: Oxygen transfer in fermentors

This lecture covers: Applications of gas-liquid transport with reaction

Gas-liquid mass transfer in bioreactors Microbial cells often grown aerobically in stirred tank reactors -oxygen supply is often limiting

X

D.O.

μ

X

X X

X X

X X X X

critical value ≈ 0.01 mM

Figure 1. μ vs dissolved oxygen. D.O. = dissolved oxygen Equilibrium solubility of O2 1 mM ≈

O2

2 3

4

1

cell

bubble

Figure 2. Oxygen pathway.

1) Diffusion across stagnate gas film 2) Absorption 3) Stagnate liquid layer (rate-limiting step) 4) Diffusion and convection

Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

3) O2 flux = −k C( )* [=]l O2 2C O

mol

area time

What is the value for the interfacial area? Important system parameters:

- liquid physical properties (surface tension, viscosity) - power input/volume (stirring, propeller size) - superficial gas velocity

empirical correlations (TIB 1:113 ’83)

= α ⎛ ⎞P β

kl sa constantU ⎜ ⎟ where U⎝ ⎠V s is the superficial gas velocity

⎛ ⎞length ⎛ area ⎞k a[ ]= =⎜ ⎟⎜ ⎟ time−1 (s-1) l⎝ ⎠time ⎝ volume ⎠

lengthUS [ ]= (m/s) time

P power= (W/m3)

V volume

const. = 0.002 α = 0.2 β = 0.7

@ SS, O2 transport = O2 uptake by biomass

at equilibrium

mass transfer bulk liquid coefficient concentration

biomass growth rate

10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 19 Prof. K. Dane Wittrup Page 2 of 4 Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

2 2

2

*( )X

O

l O OXk a C C

Yμ

− =

Crude limit:

g

dX< k a *

l OC X2Y

dt O2

or dX

dt

≈yield coefficient .4-.9

2

cell dry t.

w

g O

O2 transport in tissues

o

o

o

o

o

capillary radius Rc

R0r

Figure 3. Krogh cylinder model. One-dimensional steady-state diffusion:

2 2

2

Fick's Law

O OO

D Cr V

r r r∂⎛ ⎞∂

=⎜ ⎟∂ ∂⎝ ⎠

metabolic consumption rate of oxygen, zero-order

(cylindrical coordinates) Boundary conditions: symmetry no-flux flux=0 @ r=R0

2

20O

O

CD

r∂

=∂

@ r=R0

2 2 ,O O plasmaC C= @ r=Rc

Integrate twice:

2

2

**2 *2

*,

1 2O

O plasma

C rr RC R

⎛ ⎞= +Φ − −⎜ ⎟

⎝ ⎠ln

where *0r r , R= *

0cR R R= , 2

2 2

2

,

14

char. rxn rate

char. transport rate

O

O plasma O

V RC D

Φ = =

10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 19 Prof. K. Dane Wittrup Page 3 of 4 Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 19 Prof. K. Dane Wittrup Page 4 of 4 Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

Figure 4. Dissolved oxygen vs. radius for various values of Φ .

r*

2

2 ,

O

O plasma

CC

1

Φ decreasing

O2 diffuses further before consumption as Φ decreases. When *R ≈ 0.05, 0 @

2OC = *r = 1 when Φ ≥ 0.2

O2

necrotic core

~50-100 mμ

o

Figure 5. Tumor micrometastases.