Chapter 6
Multiple Reactions
Overview
• Multiple reactions types
• Define “Selectivity”. How it can be used in the
design?
• Solve engineering problems with multiple
reactions
6.1 Definitions
• 6.1.1 Types of reactions
There are four types of multiple reactions
1. Parallel reactions (competing reactions) where the reactant
is consumed by two different reaction pathways to form
k1
A


B
different products
k2
A 
C
e.g oxidation of ethylene to ethylene oxide
2. Series reactions (consecutive reactions) where the reactant
forms an intermediate product, which reacts further to form
another product
e.g EO with NH3 to form mono, di and triethanolamine
k1
k2
A 
B 
C
3. Complex reactions are reactions that involve a
combination of both series and parallel
reactions
e.g formation of butadiene from ethanol
A B C  D
AC  E
4. Independent reactions are reactions that
occur at the same time independently
e.g cracking of crude oil to form gasoline
A BC
DEF
• We want to minimize the formation of
undesired products and maximize the
formation of desired products to reduce the
cost of separating undesired from desired
products
kD
A 
Desired
kU
A 
Undesired
or
kU
kD
A 
Desired 
Undesired
Selectivity
• Selectivity quantifies the formation of desired wrt
undesired products
• Instantaneous selectivity
S D /U 
rate of formation of desired
r
 D
rate of formation of undesired rU
• Overall selectivity
S D /U
Exit molar rate of desired
FD


Exit molar rate of undesired FU
ND

NU
• For a batch reactor
S D /U
• For CSTR
S D /U  S D /U
Yield
• Yield is defined as the ratio of the reaction rate of a
given product to that of the key reactant
rD
• Instantaneous yield
Y 
D
• Overall yield
• For a batch reactor
• For CSTR
YD 
 rA
FD
FA0  FA
ND
YD 
N A0  N A
YD  YD
6.2Parallel Reactions
• We examine ways to maximize SD/U for parallel
reactions
kD
A 
D
kU
A 
U
1
rD  k D C A
rU  kU C A
2

2
 rA  rD  rU  k D C A 1  kU C A
S D /U
rD k D 1  2


CA
rU kU
rD k D a
  CA
rU kU
let 1   2  a  S D /U
• Case 1: α1>α2
• Keep the conc of reactant A as high as possible
– If gas phase no inerts and high pressure are used
– If liquid phase use of diluents is minimized
– Batch or PFR is used because conc drops progressively
while in CSTR the conc is always at the lowest exit
value
rD
kD
let  2  1  b  S D /U  
• Case 2: α1<α2
rU kU C Ab
• Keep the conc of reactant A as low as possible
– Diluting the feed with inerts
– Recyle reactor product
– CSTR is used
• The sensitivity of the selectivity to the
temperature can be determined from the
reaction rates ratio
S D /U
•
•
•
•
•
k D AD [( ED  EU ) / RT ]
  e
kU AU
Case 3: ED>EU
kD and rD↑ with temperature than Ku
Keep temperature as high as possible
Case 4: EU>ED
Operate at low possible temperature
6.3 Reactions in series
For the sequence where B is the desired product
k1
k2
A  B  C
• If the first reaction is slow and the second
reaction is fast it will difficult to produce B
• If the first reaction is fast and the second
reaction is slow large yield of B can be
achieved
• For series reactions space time (in flow
reactor) and real time in batch reactor is the
most important variable
• The reactions can be rewritten as
A  B and B  C
k1
k2
• Applying on A and B mole balance, rate law,
stoichiometry, combine and evaluate
algorithm
C A  C A0 e  k1 
 e  k1   e  k2  

C B  k1C A0 
 k 2  k1 
C
CC  A0 k 2 (1  e  k1  )  k1 (1  e  k2 )
k 2  k1

CC  C A0  C A  C B

Optimum yield of B (maximum CB)
k1C A0
dC B
e  k1 '
0
(k1
 k 2 e  k2 ' )
d '
k 2  k1
At this maximum value of CB τ, W and X can be
solved for as follows
1
k1
 'opt 
ln
k1  k 2 k 2
0
k
ln 1
k1  k 2 k 2
C A0  C A
k  '
X opt 
 1  e 1 opt
C A0
Wopt 
k1 /( k1  k 2 )
  k  k1 /(k1 k2 ) 
 k1 
1
  1   
X opt  1  exp  ln  
  k 2 

 k2 
6.4 Complex Reactions
The algorithm for complex reactions is
1. Number each reaction
2. Write mole balance on each and every species
3. Write the net reaction rate for each species
4. Write rate law for one species in every reaction
5. Relate the reaction rates for each species
6. Combine the rates in terms of conc
7. Write stoichiometry (conc in terms of flow rates)
8. Write pressure drop in terms flow rates
9. Combine and solve ODE
• The net reaction rate for species j is the sum
of all reaction rates in which j appears
• Where q is the number of reactions
q
rj   rij
• Rate law is required fori one species in each
reaction
rij  kij f i (C A , CB C j Cn )
• For the reaction aA  bB  cC  dD
• The reaction rate of each species can be
related to eachrother
as
r
r
r
iA
iB
 ai  bi

iC
ci

iD
di
• For liquid phase
• For gas phase
Cj 
Fj
0
 Fi  P T0
FT 0  Fi  P T0


Cj   
 CT 0  
0  FT  P0 T
 FT  P0 T
n
FT   F j
j 1
CT 0 
• Then
P0
RT0
Fj
F1
F2
r1  fn1 (C1 , C2 C j )  fn1 (CT 0 , CT 0
CT 0
)
FT
FT 0
FT 0
Fj
F1
F2
r2  fn2 (C1 , C2 C j )  fn2 (CT 0 , CT 0
CT 0
)
FT
FT 0
FT 0
• Where fn represents the net rate of formation
6.5 Multiple Reactions in PFR/PBR
• Combining mole balance, rate laws, and
stoichiometry for species 1 to j in the gas
phase
m
Fj 

dF1
F1
 r1   ri1  fn1  CT 0
,  CT 0 
dV
FT
FT 
i


Fj 

F1
 rj   rij  fn j  CT 0
,  CT 0 
dV
FT
FT 
i

dF j
q
• Coupled j ODEs must be solved simultaneously
using numerical package (Polymath)
6.6 Multiple Reactions in CSTR
• Recall the design CSTR equation
F j 0  F j  rjV
• For q gas phase reactions with N species, the following set
of algebraic equations
 F1

FN
F10  F1  r1V  V . f1  CT 0 ,  ,
CT 0 
FT
 FT


 F1

FN
FN 0  FN  rNV  V . f N  CT 0 ,  ,
CT 0 
FT
 FT

• These equations must be solved simultaneously using
numerical package (Polymath)