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
μ
X
X
X
X
X X X
X
X
X
critical value
≈ 0.01 mM
D.O.
Figure 1. μ vs dissolved oxygen.
D.O. = dissolved oxygen
Equilibrium solubility of O2
≈ 1 mM
bubble
4
O2
cell
1 2 3
Figure 2. Oxygen pathway.
1)
2)
3)
4)
Diffusion across stagnate gas film
Absorption
Stagnate liquid layer (rate-limiting step)
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].
at equilibrium
3) O2 flux = kl (CO2 − CO2 )
[=]
*
mass transfer
coefficient
mol
area time
bulk liquid
concentration
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)
β
⎛P⎞
kl a = constantU s ⎜ ⎟ where Us is the superficial gas velocity
⎝V ⎠
⎛ length ⎞ ⎛ area ⎞
−1
kl a[=] ⎜
(s-1)
⎟⎜
⎟ = time
⎝ time ⎠ ⎝ volume ⎠
α
U S [ =]
length
(m/s)
time
power
P
=
V volume
(W/m3)
const. = 0.002
α = 0.2
β = 0.7
@ SS, O2 transport = O2 uptake by biomass
biomass growth rate
kl a (C − CO2 ) =
*
O2
μX
YX O
2
dX
< kl aCO* 2 YX O
Crude limit:
2
dt
or
dX
dt
yield coefficient ≈ .4-.9
g cell dry wt.
g O2
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 19
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].
O2 transport in tissues
o
o
r
o
R0
o
o
capillary radius Rc
Figure 3. Krogh cylinder model.
One-dimensional steady-state diffusion:
DO2 ∂ ⎛ ∂CO2 ⎞
⎜r
⎟ = VO2
r ∂r ⎝ ∂r ⎠
Fick's Law
metabolic consumption rate of
oxygen, zero-order
(cylindrical coordinates)
Boundary conditions:
symmetry
no-flux
flux=0 @ r=R0
∂CO2
= 0 @ r=R0
∂r
CO2 = CO2 , plasma @ r=Rc
DO2
Integrate twice:
CO2
CO2 , plasma
⎛
r* ⎞
= 1 + Φ ⎜ r *2 − R*2 − 2 ln * ⎟
R ⎠
⎝
where
r * = r R0 , R* = Rc R0 , Φ =
1 VO2
char. rxn rate
R2
=
4 CO2 , plasma DO2 char. transport rate
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 19
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].
1
CO2
Φ decreasing
CO2 , plasma
r*
Figure 4. Dissolved oxygen vs. radius for various values of
O2 diffuses further before consumption as
When R ≈ 0.05,
*
decreases.
CO2 = 0 @ r * = 1 when Φ ≥ 0.2
~50-100
o
Φ
Φ.
μm
O2
necrotic core
Figure 5. Tumor micrometastases.
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 19
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].