Post on 11-Jan-2016
1 - 04/21/23
Departm
ent of Chem
ical E
ngineering
Lecture 6
Kjemisk reaksjonsteknikk
Chemical Reaction Engineering
Review of previous lectures Pressure drop in fixed bed reactor PFR reactor design with pressure drop (ε=0)
2 - 04/21/23
Departm
ent of Chem
ical E
ngineering
These topics build upon one another
Mole
Bala
nce
Rate
Law
s
Sto
ich
iom
etr
y
Reaction Engineering
2
Isothermal reactor design
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Departm
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Reactor Mole Balances in terms of conversion
Reactor Differential Algebraic Integral
A
0A
r
XFV
CSTR
A0A rdV
dXF
X
0 A0A r
dXFVPFR
Vrdt
dXN A0A
Vr
dXNt
X
0 A0A Batch
X
t
A0A rdW
dXF
X
0 A0A r
dXFWPBR
X
W3
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Departm
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Gas Phase Flow System:
Concentration Flow System:
0
00A
0
00
0AAA P
P
T
T
X1
X1C
PP
TT
X1
X1FFC
A
A
FC
P
P
T
TX1 0
00
0
0B0A
0
00
B0AB
B P
P
T
T
X1
Xab
C
P
P
TT
X1
Xab
FF
C
4
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Departm
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Note: Pressure drop does NOT affect liquid phase reactionsSample Question:
Analyze the following second order gas phase reaction that occurs isothermally in a PBR:
2AB
A0A rdW
dXF
Mole Balance:Must use the differential form of the mole balance to separate variables:
2AA kCr Second order in A and
irreversible:
Rate Law:
Pressure Drop in Packed Bed Reactors
5
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CA FA
CA 0
1 X 1X
P
P0
T0
TStoichiometry:
CA CA 0
1 X 1X
P
P0
Isothermal, T=T0
2
02
2
0A
20A
P
P
X1
X1
F
kC
dW
dX
Combine:
Need to find (P/P0) as a function of W (or V if you have a PFR)
Pressure Drop in Packed Bed Reactors
6
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TURBULENT
LAMINAR
p3
pc
G75.1D
11501
Dg
G
dz
dPErgun Equation:
Pressure Drop in Packed Bed Reactors
7
P pressure, kPa
Φ porosity (volume of void/total bed volume)
1- Φ (volume of solid/total bed volume)
gc conversion factor. 1.0 for metric system
Dp diameter of particle in bed m
μ viscosity of gas passing through the bed kg/m.s
Z length down the packed bed m
u, superficial velocity m/s
ρ gas density kg/m3
G= ρu superficial mass velocity kg/m2,s
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TURBULENT
LAMINAR
p3
pc
G75.1D
11501
Dg
G
dz
dPErgun Equation:
Pressure Drop in Packed Bed Reactors
8 0
00 T
T
P
P)X1(
0
0
0T
T0 T
T
P
P
F
F
00
00
0mm Constant mass flow:
9 - 04/21/23
Departm
ent of Chem
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0T
T
0
0
p3
pc0 F
F
T
T
P
PG75.1
D
11501
Dg
G
dz
dP
T
0T0
00 F
F
T
T
P
PVariable
Density
G75.1
D
11501
Dg
G
p3
pc00Let
Pressure Drop in Packed Bed Reactors
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0T
T
0
0
cc
0
F
F
T
T
P
P
1AdW
dP
ccbc 1zAzAW Catalyst Weight
0cc
0
P
1
1A
2
Let
Pressure Drop in Packed Bed Reactors
10
b bulk density
c solid catalyst density
porosity (a.k.a., void fraction)
Where
Ac, cross section area
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We will use this form for single reactions:
X1
T
T
PP
1
2dW
PPd
00
0
0T
T
0 F
F
T
T
y2dW
dy
0P
Py
X1T
T
y2dW
dy
0
X1y2dW
dy
Isothermal
case
Pressure Drop in Packed Bed Reactors
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Departm
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The two expressions are coupled ordinary differential equations. We can only solve them simultaneously using an ODE solver such as Polymath. For the special case of isothermal operation and epsilon = 0, we can obtain an analytical solution.
Polymath will combine the mole balance, rate law and stoichiometry.
22
0A
220A y
X1F
X1kC
dW
dX
P,XfdW
dX P,Xf
dW
dP X,yf
dW
dyan
do
r
Pressure Drop in Packed Bed Reactors
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PBR
1) Mole Balance:0A
A
F
r
dW
dX
2) Rate Law:
2
2
20AA y
X1
X1kCr
AB
y
X1
X1C
P
P
X1
X1CC 0A
00AA
13
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PBR
14
2/1
2
2
)W1(y
)W1(y
dWdy
1y0WWhen
y2dW
dy
0For
X1T
T
y2dW
dy
0
Initial condition
0cc
0
P
1
1A
2
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Departm
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W
21W1y
P1
15
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CA CA 0 1 X PP0
CA
2
W
P
No P
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No P
rA kCA2
-rA
3
P
W17
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No P
X4
W
P
18
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0
00 T
T
P
P)X1(
19
P
Py,TT 0
0
y)X1(
1f 0
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Departm
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No P
5
W
P
1.0
20
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Example 1: Gas Phase Reaction in PBR for δ = 0
Gas Phase Reaction in PBR with δ = 0 (Polymath Solution) A + B 2C
Repeat the previous one with equil molar feed of A and B and kA = 1.5dm9/mol2/kg/minα = 0.0099 kg-1
Find X at 100 kg
21
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A + B 2C
min kg mol
dm5.1k
6
1kg 0099.0
kg 100W ?X ?P
1PP D2D 0102 P2
1P Case 2:
Example 1: Gas Phase Reaction in PBR for δ = 0
22
Case 1:
?X ?P
23 - 04/21/23
Departm
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1) Mole Balance:0A
A
F
'r
dW
dX
2) Rate Law: BAA CkC'r
3) yX1CC 0AA
4) yX1CC 0AB
0W 1y
Example 1: Gas Phase Reaction in PBR for δ = 0
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y2dW
dy 5) dWydy2
W1y2
21W1y
W1X1kCyX1kCr 220A
2220AA
0A
220A
F
W1X1kC
dW
dX
Example 1: Gas Phase Reaction in PBR for δ = 0
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dWW1
F
kC
X1
dX
0A
20A
2
2
WW
F
kC
X1
X 2
0A
20A
XX ,WW ,0X ,0W
0.e.i,droppressurewithout 75.0X
droppressurewith 6.0X
Example 1: Gas Phase Reaction in PBR for δ = 0
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26
Example A + B → 2C
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Departm
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ical E
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27
Example A + B → 2C