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.
Today’s lecture
 Enzyme Kinetics
 Noncompetitive Inhibition
 Bioreactors
 Monod Equation
 Yield Coefficients
 Washout
2
Last lecture
A given enzyme can only catalyze only one reaction. Urea is
decomposed by the enzyme urease, as shown below.
HO
2
NH2CONH2 UREASE

2NH3  CO2 UREASE
H O
2
S  E 

P  E
The corresponding mechanism is:

k1
E  
S 
E S
E  S  E  S
k2
E  S  W  P  E
k3
3
Michaelis Menten Equation
Vmax S
rP  rS 
Km  S
Lecture 16 - Bioreactors
Nutrient +
Nutrient +
4
+ Products
cells
more cells + Products
Bioreactors
5
6
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
Stationar
y Phase

Death
Phase
Exponential
Growth
Phase
9
0
time
CC CS
K   CS
IV. Death
Bioreactors
Mass Balances:
Accumulation =
In
dC C
V
 v 0CC0
dt
Let D  v0 / V
10
- Out + Growth - Death
 v 0CC
 Vrg
 Vrd
Bioreactors
1
dCC
 D(CC 0  CC )  rg  rd
dt
2
dCS
 D(CS0  CS )  rS
dt
Rate Laws:
3
 maxCS 
rg  kOBS 
CC
K S  CS 
 CP 
 1 * 
 CP 
n
4 kOBS
11
Cp*= Product Concentration at which all metabolism ceases

Bioreactors
Stoichiometry:
A.)Yield Coefficients
YC S
mass of new cells formed

mass of substrate to produce new cells
YP S 
YS C
mass of product formed
mass of substrateconsumedto form product
B.) Maintenance
5
12
mass of substrate consumed for maintainence
m
mass of cells  time
 rS  rg YS C  rP YS P  mCC
1

YC S
Bioreactors
Volume=V
v0
CS0
v
CC
CS
V=V0
1) Mass balance:
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

dCC
V
 0  v0CC  rg  rd V
dt
(cells)
Bioreactors


dCC
 DCC  rg  rd
1
dt
1 v0
D 
(dilution rat e)
 V
dCS
V
 v 0CS 0  v 0CS  rSV
(substrate)
dt
dCS
 DCS 0  CS  rS
2
dt
dCP
 DCP  rP
(product)
3
dt
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Bioreactors
2) Rates:
4  rg 
5 KOBS
maxCS
k S  CS
CC KOBS
 CP n
 1  * 
 CP 
6 rP  YP /C rg
7 rS  YS /C rg  m CC
8 rD  kD CC
3) Parameters:
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 max , C*P , n, k S , k D , yS / C , y P / C , m, D, CS0
  v 0 CC , m
 p  v 0CP , v 0  DV, V
m
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
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0  DVCC  rg V
 maxCS
DCC  rg 
CC  CC
K S  CS
 maxCS
D
K S  CS
DKS
CS 
 max  D
Bioreactors – Chemostats - CSTRs
3. Substrate
0  DCS0  CS V  rSV
DCS0  CS   rS  YS/ Crg  YS/ CDCC

DKS 
CC  YC S CS0  CS   YC S CS0 

 max  D 

18
Bioreactors
CSTR Washout
CC  0
 c v 0CC
m

 DC C
V
V
CC
CC

DKS 
DCC  DYC S CS0 

 max  D 

 maxCS0
D
DW 
K S  CS 0
DW
Washout dilution rate
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Maximum Product Flow Rate
How does this figure relate to
drinking a lot of fluids when
you have an infection or cold?
DCC
 maxCS0
DW 
K S  CS 0
D maxprod
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Dmaxprod
DW

K
S
  max 1 
K S  CS0

D




End of Lecture 16
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