lecture 8
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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.
Lecture 8
Lecture 8 – Tuesday 2/5/2013
2
Block 1: Mole BalancesBlock 2: Rate LawsBlock 3: StoichiometryBlock 4: Combine
Pressure DropLiquid Phase ReactionsGas Phase Reactions
Engineering Analysis of Pressure Drop
Gas Phase Flow System:
Concentration Flow System:
0
00
0
00
0
11
1
1PP
TT
XXC
PP
TTX
XFFC AAAA
A
AFC
PP
TTX 0
00 1
0
00
0
00
0
11 PP
TT
X
XabC
PP
TTX
XabF
FCBABA
BB
Pressure Drop in PBRs
3
Pressure Drop in PBRs
4
Note: Pressure Drop does NOT affect liquid phase reactions
Sample Question:Analyze the following second order gas phase reaction
that occurs isothermally in a PBR:AB
Mole BalancesMust use the differential form of the mole balance to separate variables:
Rate LawsSecond order in A and irreversible:
AA rdWdXF 0
2AA kCr
CA FA
CA 0
1 X 1X
PP0
T0
TStoichiometry
CA CA 01 X 1X
PP0
Isothermal, T=T0
2
02
2
0
20
11
PP
XX
FkC
dWdX
A
A
Combine:
Need to find (P/P0) as a function of W (or V if you have a PFR)
5
Pressure Drop in PBRs
TURBULENT
LAMINAR
ppc
GDDg
GdzdP 75.111501
3
Ergun Equation:
60
00 )1(
TT
PPX
0
0
00 T
TPP
FF
T
T
00
00
0
mm Constant mass flow:
Pressure Drop in PBRs
00
03
0
75.111501
T
T
ppc FF
TT
PPG
DDgG
dzdP
T
T
FF
TT
PP 00
00 Variable Density
G
DDgG
ppc
75.1115013
00
Let
7
Pressure Drop in PBRs
00
00
1 T
T
cc FF
TT
PP
AdWdP
ccbc zAzAW 1Catalyst Weight
0
0 112
PA cc
Let
8
Pressure Drop in PBRs
b bulk density
c solid catalyst density
porosity (a.k.a., void fraction )
Where
(1 ) solid fraction
We will use this form for single reactions:
X
TT
PPdWPPd
112 00
0
002 T
T
FF
TT
ydWdy
0PPy
XTT
ydWdy
12 0
XydW
dy 1
2 Isothermal case9
Pressure Drop in PBRs
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 Balances, Rate Laws and Stoichiometry.
22
0
220
11 y
XFXkC
dWdX
A
A
PXfdWdX , PXf
dWdP , Xyf
dWdy ,and or
10
Pressure Drop in PBRs
11
2/1
2
2
)1(
)1(
10
)1(2
0
Wy
Wy
dWdy
yWWhen
XydW
dyFor
Packed Bed Reactors
W
P
1
12
Pressure Drop in a PBR
13
Concentration Profile in a PBR2
No P
CA CA 0 1 X PP0
CA
W
P
14
Reaction Rate in a PBR3
No P
2
2 2
0
(1 )A APr kC k XP
-rA
P
W
15
Conversion in a PBR4
No P
X
W
P
16
Flow Rate in a PBR5
No P
W
P
1
PP
For
00
:0
0
f
17
0TT
0
00 1
TT
PPX
0 1(1 )
fX y
PPy 0
Example 1:Gas Phase Reaction in PBR for δ=0
18
Gas Phase reaction in PBR with δ = 0 (Analytical Solution)
A + B 2C
Repeat the previous one with equimolar feed of A and B and:
kA = 1.5dm6/mol/kg/minα = 0.0099 kg-1
Find X at 100 kg
00 BA CC
0AC
0BC
?X
Example 1:Gas Phase Reaction in PBR for δ=0
19
1) Mole Balance0
'
A
A
Fr
dWdX
2) Rate Law BAA CkCr '
3) Stoichiometry yXCC AA 10
yXCC AB 10
Example 1:Gas Phase Reaction in PBR for δ=0
20
ydWdy
2
, dWydy 2
Wy 12
211 Wy
WXkCyXkCr AAA 111 220
2220
0
220 11
A
A
FWXkC
dWdX
0W 1y,
4) Combine
Example 1:Gas Phase Reaction in PBR for δ=0
21
dWW
FkC
XdX
A
A
11 0
20
2
21
2
0
20 WW
FkC
XX
A
A
XXWWXW , ,0 ,0
0.., 75.0
6.0
eidroppressurewithoutX
droppressurewithX
Example 2:Gas Phase Reaction in PBR for δ≠0
22
The reaction A + 2B C
is carried out in a packed bed reactor in which there is pressure drop. The feed is stoichiometric in A and B.
Plot the conversion and pressure ratio y = P/P0 as a function of catalyst weight up to 100 kg.
Additional InformationkA = 6 dm9/mol2/kg/minα = 0.02 kg-1
Example 2:Gas Phase Reaction in PBR for δ≠0
23
A + 2B C
1) Mole Balance0A
A
Fr
dWdX
2) Rate Law 2BAA CkCr
3) Stoichiometry: Gas, Isothermal
PPX 0
0 1
yX
XCC AA
11
0
Example 2:Gas Phase Reaction in PBR for δ≠0
24
4) y
XXCC B
AB
1
20
5) XydW
dy 1
2
6) yXf
1
0
Initial values: W=0, X=0, y=1 Final values: W=100Combine with Polymath. If δ≠0, polymath must be used to solve.
7)
02.0,6,2,232]2[
31]211[
00
0
kFC
y
AA
A
Example 2:Gas Phase Reaction in PBR for δ≠0
25
Example 2:Gas Phase Reaction in PBR for δ≠0
26
27
T = T0
Robert the Worrier wonders: What if we increase the catalyst size by a factor of 2?
Pressure DropEngineering Analysis
29
𝜌0=𝑀𝑊∗𝐶𝑇 0=𝑀𝑊∗𝑃0
𝑅𝑇0
𝛼=2𝑅𝑇0
𝐴𝐶𝜌𝐶𝑔𝐶 𝑃02 𝐷𝑃 𝜙3𝑀𝑊
𝐺[150 (1−𝜙 )𝜇𝐷𝑃
+1.75𝐺]𝛼≈ ( 1
𝑃0 )2
Pressure DropEngineering Analysis
30
Pressure DropEngineering Analysis
31
Mole Balance
Rate Laws
Stoichiometry
Isothermal Design
Heat Effects
32
End of Lecture 8
33
Pressure Drop - Summary
34
Pressure DropLiquid Phase Reactions
Pressure Drop does not affect concentrations in lquid phase reactions.
Gas Phase ReactionsEpsilon does not equal to zero
d(P)/d(W)=… Polymath will combine with d(X)/d(W) =… for you
Epsilon = 0 and isothermalP=f(W)Combine then separate variables (X,W) and integrate
Engineering Analysis of Pressure Drop
Pressure Change – Molar Flow Rate
35
cc
0
0
0T
T0
1ATT
PP
FF
dWdP
cc0
00T
T0
1AyPTT
FF
dWdy
CC0
0
1AP2
00T
T
TT
FF
y2dWdy
Use for heat effects, multiple rxns
X1FF
0T
T Isothermal: T = T0 X1y2dW
dX
Example 1:Gas Phase Reaction in PBR for δ=0
36
A + B 2C
Case 1:
Case 2:
0AC
0BC??
XP
001
6
,0099.0,min
5.1 AB CCkgkgmoldmk
?,?,100 PXkgW
?,?,21,2 01021 PXPPDD PP
PBR
37
0
1/20
'
0 and (1 )
A A
A A B
AA
T
A B
dXF rdW
r kC CFC yF
C C
T T y W
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