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 4/14/2011
 Bioreactors
 Monod Equation
 Yield Coefficients
 Washout
2
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
Michaelis Menten Equation
E  S  E  S
VmaxS
rP  rS 
KM  S
k2
E  S  W  P  E
k3
3
rP  rS 
Nutrient (S) +
KM  S
cells
rg  max
4
VmaxS
more cells + Products
CC CS
K S  CS
5
6
7
inoculum
t=0 time 
8
Cells + Substrate  More Cells + Product
a) Phases of Bacteria growth:
I. Lag II. Exponential
III. Stationary
CC CS
b) Monod growth rate law: r  
g
max
Lag Phase
lnCc
K S  CS
Stationar
y Phase
Death
Phase
Exponential
Growth
Phase
9
0
time
IV. Death
Accumulation = [In] - [Out] + [Growth] - [Death]
dCC
V
 v0CC 0  v0CC  Vrg  Vrd
dt
Let D  v0 / V
dCC
1
 D(CC 0  CC )  rg  rd
dt
10
dCC
1
 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

m ass of new cells form ed
Y 'C S 
m ass of substrateto producenew cells
Y 'P S 
5
12
1
Y 'S C 
Y 'C S
m ass of product form ed
m ass of substrateconsum edto form product
mass of substrate consumed for maintainence
m
mass of cells  time
 rS  rgYS C  rPYS P  mCC
 rS  rgY '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  rgY 'S C mCC
(grams of substrateconsumed)
Y 'S C 
(grams of cells produced)
13
Volume=V
v0
CS0
v
CC
CS
V=V0
1) Mass balance:
14
dC C
V
 0  v0CC  rg  rd V
dt
(cells)
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
dCP
3
 DCP  rP
(product)
dt
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:
max , CP* , n, k S , k D , yS / C , yP / C , m, D, CS 0
16
m  v0CC , m p  v0CP , v0  DV , V
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
1. Steady State - Neglect Death Rate and Cell Maintenance
2. Cell
18
0  DVCC  rgV
maxCS
DCC  rg 
CC  CC
K S  CS
 maxCS
D
K S  CS
DK S
CS 
 max  D
3. Substrate
0  DCS 0  CS V  rSV
DCS 0  CS   rS  YS / C rg  YS / C DCC

DKS 
CC  YC S CS 0  CS   YC S CS 0 

max  D 

19
CSTRWashout
CC  0
m c v0CC

 DC C
V
V
CC
CC

DKS 
DCC  DYC S CS 0 

max  D 

D
DW
Washout dilution rate
20
 maxCS 0
DW 
K S  CS 0
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
21
Dmaxprod
DW

K
S
  max 1 
K S  CS0

D




22