Lecture 2
Kjemisk reaksjonsteknikk
Chemical Reaction Engineering
Department of Chemical Engineering





Review of Lecture 1
Definition of Conversion, X
Design Equations in Terms of X
Size CSTRs and PFRs given –rA= f(X)
Conversion for Reactors in Series
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General Mole Balance
System
Volume, V
FA0
GA
FA
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General Mole Balance on System Volume V
In
 Out  Generation
FA 0  FA

 r dV
A
 Accumulation
dN A

dt
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Reactor Mole Balance Summary
Reactor
Batch
Differential
Integral
t
dN A
 rAV
dt
NA

N A0
dN A
rAV
NA
t
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FA 0  FA
V 
rA
CSTR
PFR
Algebraic
dFA
 
rA
dV
V 
FA

FA 0
FA
dFA
drA
V
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Consider the generic reaction
a AbB
 c C  d D
Chooselimit ingreact antA as basis of calculat ion
b
c
d
A B
 C  D
a
a
a
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Define conversion, X
molesA react ed
X
molesA fed
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Batch
Moles A  Moles A  Moles A 
remaining  init ially   react ed 

 
 

NA
 N A0
 N A0X
dN A  0  N A0dX
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dN A
dX
 N A0
 rA V
dt
dt
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Reactor Mole Balances in terms
of conversion
Reactor
Differential
Algebraic
Integral
X
X
Batch
N A0
V 
CSTR
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PFR
dX
t  N A0 
 rAV
0
dX
  r AV
dt
dX
FA 0
 rA
dV 
t
FA 0 X
rA
X
V  FA0 
0
dX
 rA
X
PBR

FA 0
dX
 rA
dW
X
W  FA 0 
0
dX
 rA
W
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Batch reactor
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Continuous stirred tank reactor (CSTR)
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Continuous stirred tank reactor (CSTR)
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Plug flow reactor (PFR)
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Plug flow reactor (PFR)
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Levenspiel Plots
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Reactor Sizing
Given –rA as a function of conversion, -rA= f(X),
one can size any type of reactor. We do this by
constructing a Levenspiel plot. Here we plot
either (FA0/-rA) or (1/-rA) as a function of X. For
(FA0/-rA) vs. X, the volume of a CSTR and the
volume of a PFR can be represented as the
shaded areas in the Levenspiel Plots shown as:
FA 0
 g(X)
 rA
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Levenspiel Plots
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Numerical Evaluations of Integrals
 The integral to calculate the PFR volume can be
evaluated using method as Simpson’s One-Third Rule:
(See Appendix A.4)
 1
FA 0
x
4
1 
V
dX 
FA 0 




r
3

r
(
0
)

r
(
X
/
2
)

r
(
X
)
A
A
A
 A

0
X
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Other numerical methods are:
 Trapezoidal Rule (uses two data points)
 Simpson’s Three-Eight’s Rule (uses four data points)
 Five-Point Quadrature Formula
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Reactors in Series
Given: rA as a function of conversion, one can also design any sequence of
reactors:
moles of A reacted up to point i
Xi 
moles of A fed to first reactor
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Only valid if there are no side streams.
Molecule Flow rate of species A at point i:
FAi  FA0Xi
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Reactors in Series
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Reactors in Series
Reactor 1:
FA1  FA0  FA0 X1
FA0  FA1 FA0  FA0  FA0 X 1  FA0 X 1
V1 


 rA1
 rA1
 rA1
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FA 0
 rA
V1
X
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Reactors in Series
Reactor 2:
X2
FA 0
V2  
dX
 rA
X1
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FA 0
 rA
V2
X
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Reactors in Series
Reactor 3:
FA2  FA3  rA3V3  0
FA0  FA0 X 2   FA0  FA0 X 3   rA3V3  0
V3 
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FA 0 X 3  X 2 
rA 3
V3
FA 0
 rA
X
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Reactors in Series
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Space time  is the time necessary to process one reactor volume
of fluid at entrance conditions.

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
Important Definitions
V
0
S-1
Space velocity:
SV = v0/V (s-1)=1/ 
Space velocity is normally given at the standard
conditions (STP).
Liquid hourly space velocity (LHSV= v0,liquid/V)
Gas hourly space velocity (GHSV) = v0,gas/V
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