Lecture 16
Chemical Reaction Engineering (CRE) is the
field that studies the rates and mechanisms of
chemical reactions and the design of the reactors in
which they take place.
Web Lecture 16
Class Lecture 25 – Thursday 4/18/2013
 Bioreactors
 Monod Equation
 Yield Coefficients
 Washout
2
Review Last Lecture
Enzymes - Urease
A given enzyme can only catalyze only one reaction. Urea is
decomposed by the enzyme urease, as shown below.
NH 2 CONH
2
 UREASE
2


 2 NH 3  CO 2  UREASE
H O
2
S  E 

PE
H O
The corresponding mechanism is:
E  S  E  S
k1
E  S  E  S
k2
E  S  W  P  E
k3
3
Michaelis Menten Equation
rP   rS 
V max S
KM  S
Bioreactors
rP   rS 
Nutrient (S) +
KM  S
cells
rg   max
4
V max S
more cells + Products
CCCS
K S  CS
Bioreactors
5
Batch Bioreactor
6
Phases of Cell Growth and Division
7
Bioreactors
inoculum
t=0 time 
8
Cells + Substrate  More Cells + Product
Bioreactors
a) Phases of bacteria growth:
I. Lag II. Exponential III. Stationary
b) Monod growth rate law:
rg   max
Lag Phase
lnCc
Stationary
Phase
Death
Phase
Exponential
Growth
Phase
9
0
time
IV. Death
CCCS
K S  CS
Bioreactors
1) Mass Balances
Accumulation =
V
dC C
[In]

v0C C 0
dt
Let
[Out]

v0C C
+ [Growth] 
Vr g
D  v0 / V
1
10
-
dC C
dt
 D ( C C 0  C C )  rg  rd

[Death]
Vr d
Bioreactors
1
2 
dC C
dt
 D ( C C 0  C C )  rg  rd
dC S
dt
 D (C S 0  C S )  rS
Rate Laws:
3 
  C 
max
S
rg  k OBS 
C C
K S  C S 
n
4  k OBS
11
 C 
P
 1  * 
 C P 
Cp*= Product concentration at which all metabolism ceases
Bioreactors
3) Stoichiometry
A) Yield Coefficients
Y 'C
Y 'P
S
S
mass of new cells formed

Y 'S
C
mass of substrate to produce new cells
mass of product

mass of substrate consumed
formed
to form product
B) Maintenance
5  m 
mass of substrate consumed
 rS  rg Y S
12
for ma int ainence
mass of cells  time
C
 rP Y S
P
 mC C

1
Y 'C
S
Bioreactors
3) Stoichiometry
Rate of Substrate Consumption
 rS  rg Y ' S
C
 rP Y ' S
P
 mC C
Can’t separate substrate consumption used for cell
growth from that used for product formations during
exponenial growth.
 rS  rg Y ' S
Y 'S
13
C

C
 mC C
( grams of substrate
consumed)
( grams of cells produced)
Bioreactors
Volume=V
v0
CS0
v
CC
CS
V=V0
1) Mass Balance:
V
14
dC C
dt
 0  v 0 C C  rg  rd  V
(cells)
Bioreactors
V
 0  v 0 C C  rg  rd  V
dC C
dt
V
dC S
 v 0 C S 0  v 0 C S  rS V
dt
D 
15
1


v0
(cells)
(substrate )
(dilution rate)
V
1 
dC C
2 
dC S
3 
dC P
dt
dt
dt
  DC C  rg  rd

 D C S 0  C S   rS
 DC
P
 rP
(product)
Bioreactors
2) Rate Laws:
4 
rg 
 max C S
kS  CS
C C K OBS
n

C P 
 1  * 
C P 

5 
K OBS
6 
rP  Y P / C rg
7 
rS  Y S / C rg  mC C
8 
rD  k D C C
3) Parameters
 max , C P , n , k S , k D , y S / C , y P / C , m , D , C S 0
*

16
m  v 0 C C , m p  v 0 C P , v 0  DV , V
Polymath Setup
1.) d(CC)/d(t)=-D*CC+(rg-rd)
2.) d(CS)/d(t)=-D*(CS0-CS)-Ysg*rg-m*CC
3.) d(CP)/d(t)=-D*CP+YPC*rg
4.) rg=(((1-(CP/Cpstar))**0.52)*mumax*(CS/(KS+CS))*CC
5.) D=0.2
6.) kd=0.01
7.) rd=kd*CC
8.) CS0=250
9.) YPC=5.6
17
10.) m=0.3
11.) mumax=0.33
12.) YSC=12.5
13.) KS=1.7
Bioreactors – Chemostats - CSTRs
1. Steady State - Neglect Death Rate and Cell Maintenance
2. Cell
0   DVC
DC C  rg 
 max C S
K S  CS
D  
CS 
18
 rg V
C
C C  C C
 max C S
K S  CS
DK
S
 max  D
Bioreactors – Chemostats - CSTRs
0  D C S 0  C S V  rS V
3. Substrate
D C S 0  C S    rS  Y S / C rg  Y S / C DC C
C C  YC
19
S
C S 0

DK S 
 C S   YC S  C S 0 

 max  D 

Bioreactors – Chemostats - CSTRs
CC  0
CSTR Washout
m c
CC

v0C C
V
CC
DC C
DW
D
Washout dilution rate
20
V
 DC C

DK S 
 DY C S  C S 0 



D
max


DW 
 max C S 0
K S  CS0
Maximum Product Flow Rate
How does this figure relate to
drinking a lot of fluids when you
have an infection or cold?
DCC
DW 
D max
21
Dmaxpro
d
prod
K S  C S0
  max
D
DW
 max C S 0

1 


KS
K S  C S0




End of Web Lecture 16
End of Class Lecture 25
22