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.
2O
NH2 CONH2  UREASE H

 2 NH3  CO2  UREASE
2O
S  E H

P  E
The corresponding mechanism is:
E  S  E  S
k1
E  S  E  S
k2
E  S  W  P  E
k3
3
Michaelis Menten Equation
Vmax S
rP  rS 
KM  S
Bioreactors
rP   rS 
Nutrient (S) +
cells
rg   max
4
Vmax S
KM  S
more cells + Products
CC C S
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
CC C S
K S  CS
Bioreactors
1) Mass Balances
Accumulation =
[In]
-
dCC
V
dt
 v0CC 0
[Out]
 v0CC
+ [Growth] -
 Vrg
Let D  v0 / V
dCC
1
 D(CC 0  CC )  rg  rd
dt
10
[Death]
 Vrd
Bioreactors
dCC
1
 D(CC 0  CC )  rg  rd
dt
2
dCS
 D(CS 0  CS )  rS
dt
Rate Laws:
3
 max CS 
rg  kOBS 
CC
K S  CS 
 CP 
 1  * 
 CP 
n
4  kOBS
11
Cp*= Product concentration at which all metabolism ceases

Bioreactors
3) Stoichiometry
A) Yield Coefficients
mass of new cells formed
Y 'C S 
mass of substrate to produce new cells
Y 'P S 
1
Y 'S C 
Y 'C S
mass of product formed
mass of substrate consumed to form product
B) Maintenance
5
mass of substrate consumed for maint ainence
m
mass of cells time
 rS  rg YS C  rPYS P  mCC
12
Bioreactors
3) Stoichiometry
Rate of Substrate Consumption
 rS  rg Y 'S C  rPY 'S P  mCC
Can’t separate substrate consumption used for cell
growth from that used for product formations during
exponenial growth.
 rS  rg Y 'S C  mCC
(grams of substrate consumed)
Y 'S C 
(grams of cells produced)
13
Bioreactors
Volume=V
v0
CS0
v
CC
CS
V=V0
1) Mass Balance:
14
dCC
V
 0  v0CC  rg  rd V
dt
(cells)
Bioreactors
15
dCC
V
 0  v0CC  rg  rd V
(cells)
dt
dCS
V
 v0CS 0  v0CS  rSV
(substrate)
dt
1 v0
D 
(dilution rate)
 V
dCC
1
  DCC  rg  rd 
dt
dCS
2
 DCS 0  CS   rS
dt
dC P
3
 DC P  rP
(product)
dt
Bioreactors
2) Rate Laws:
4  rg 
5 KOBS
max CS
kS  CS
CC KOBS
 CP n
 1  * 
 CP 
6 rP  YP /C rg
7 rS  YS /C rg  mCC
8 rD  kD CC
3) Parameters

16
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
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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   DVCC  rgV
 max CS
DCC  rg 
CC  CC
K S  CS
 max C S
D
K S  CS
DK S
CS 
 max  D
18
Bioreactors – Chemostats - CSTRs
3. Substrate
0  DCS 0  CS V  rSV
DCS 0  CS   rS  YS / C rg  YS / C DC C

DK S 
CC  YC S CS 0  CS   YC S CS 0 

max  D 

19
Bioreactors – Chemostats - CSTRs
CC  0
CSTR Washout
m c v0CC

 DCC
V
V
CC

DK S 
DCC  DYC S CS 0 

max  D 

CC
DW
D
Washout dilution rate
20
 max C S 0
DW 
K S  CS 0
Maximum Product Flow Rate
How does this figure relate to
drinking a lot of fluids when you
have an infection or cold?
DCC
 max CS0
DW 
K S  CS0
D max prod
21
Dmaxpro
d

K
S
  max 1 
K S  CS0

D
DW




End of Web Lecture 16
End of Class Lecture 25
22