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1 - 04/19/23
Departm
ent of Chem
ical E
ngineering
Lecture 2
Kjemisk reaksjonsteknikk
Chemical Reaction 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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Departm
ent of Chem
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ngineering
General Mole Balance
General Mole Balance on System Volume V
In Out Generation Accumulation
FA 0 FA rA dV dNA
dt
FA
0
FAGA
System Volume, V
2
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Departm
ent of Chem
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ngineering
Reactor Mole Balance Summary
Reactor Differential Algebraic Integral
V FA 0 FA
rA
CSTR
Vrdt
dNA
A 0
A
A
N
N A
A
Vr
dNtBatch
NA
t
dFA
dVrA
A
A
F
F A
A
dr
dFV
0
PFR
FA
V3
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Departm
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ngineering
fedA moles
reactedA moles X
X ,conversion Define
D a
d C
a
c B
a
b A
ncalculatio of basis asA reactant limiting Choose
D d C c B b A a
Consider the generic reaction
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Departm
ent of Chem
ical E
ngineering
Batch
XN N N
reacted
A Moles
initially
A Moles
remaining
A Moles
0A0AA
dXN0dN 0AA
Vrdt
dXN
dt
dNA0A
A
5
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Departm
ent of Chem
ical E
ngineering
Reactor Mole Balances in terms of conversion
Reactor Differential Algebraic Integral
V FA 0X
rACSTR
FA 0
dX
dV rA
X
AA r
dXFV
0
0PFR
Vrdt
dXN AA 0
0
0
X
AA Vr
dXNtBatch
X
t
FA 0
dX
dW r A
X
AA r
dXFW
0
0PBR
X
W6
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Departm
ent of Chem
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ngineering
Batch reactor
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Departm
ent of Chem
ical E
ngineering
Continuous stirred tank reactor (CSTR)
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Departm
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ical E
ngineering
Continuous stirred tank reactor (CSTR)
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Departm
ent of Chem
ical E
ngineering
Plug flow reactor (PFR)
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Departm
ent of Chem
ical E
ngineering
Plug flow reactor (PFR)
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Departm
ent of Chem
ical E
ngineering
Levenspiel Plots
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:
12
)X(gr
F
A
0A
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Departm
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ngineering
Levenspiel Plots
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Departm
ent of Chem
ical E
ngineering
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)
Other numerical methods are: Trapezoidal Rule (uses two data points) Simpson’s Three-Eight’s Rule (uses four data points) Five-Point Quadrature Formula
)X(r
1
)2/X(r
4
)0(r
1F
3
xdX
r
FV
AAA0A
X
0 A
0A
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Departm
ent of Chem
ical E
ngineering
Reactors in Series
Given: rA as a function of conversion, one can also design any sequence of reactors:
reactorfirst tofedA of moles
ipoint toup reactedA of molesXi
Only valid if there are no side streams.
Molecule Flow rate of species A at point i:
i0AAi XFF 15
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Departm
ent of Chem
ical E
ngineering
Reactors in Series
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Departm
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ngineering
Reactors in Series
Reactor 1:
1001 XFFF AAA
1
10
1
1000
1
101
A
A
A
AAA
A
AA
r
XF
r
XFFF
r
FFV
17
V1
A
0A
r
F
X
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Departm
ent of Chem
ical E
ngineering
Reactors in Series
Reactor 2:
dXr
FV
X
X A
A
2
1
02
18
V2
A
0A
r
F
X
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Departm
ent of Chem
ical E
ngineering
Reactors in Series
Reactor 3:
0
0
33300200
3332
VrXFFXFF
VrFF
AAAAA
AAA
V3 FA 0 X3 X2
rA 3
19
V3
A
0A
r
F
X
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Departm
ent of Chem
ical E
ngineering
Reactors in Series
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Departm
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ngineering
Important Definitions
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
Space time is the time necessary to process one reactor volume of fluid at entrance conditions.
V
0
S-1
