design of reactor
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Design of Reactor
By; Eko Ariyanto, ST., MChemEng
8 November 2007 (Week II)
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dVrdXF AAA )(0
PFR
dt
dXNVr AAA 0)(
Batch
t CA 0 dXA(rA )0XA
AX
A
AA
rdXC
vV
00
0
0A
For constant density systems:
identical performance equation
the same Vis needed to do the job
Single
reactions design batch / plug reactor / CSTR -
Vv0 CA0VFA0
CA0XArA
CSTR
FA0XA (rA )V
We need acomparativestudy
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Single reactions design- CSTR (mixed) / plug reactor -
n
AA
A kCdt
dN
Vr
1General nth order rate equation:30n
n
A
n
AAA
n
AA
AA
mA
Am
X
XX
kCr
XC
F
VC
)1(
)1(11
0
0
0
0
AA
AAA
X
XCC
1
10
p CA0V
FA0
p
CA0dXA
rA0XA 1
kCA0n1
(1 AXA )ndXA
(1 XA )n0
XA
mixed
plug
(1)
2)
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Single reactions design- CSTR (mixed) / plug reactor -
CA0n1
m
CA0n1
p
CA 0
nV
FA 0
m
CA 0
nV
FA0
p
XA1 AXA
1 XA
n
m
1 AXA1 XA
n
dXA0
XA
p
0
0
0 A
A
F
VC
v
VDividing (1) / (2) and
0A
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Single reactions design- CSTR (mixed) / plug reactor -
CA0n1
m
CA0n1 p
XA
1 XA n
m
1 XA 1n
1
n 1
p
CA0n1
m
CA 0n1
p
XA
1 XA
m
ln(1 XA )p
0A
1n 1n
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Single reactions design- CSTR (mixed) / plug reactor -
m
p
Vm
Vp
XA
1 XA n
m
1 XA 1n
1
n 1
p
Plot for various XA and comparethe performance
For equal quantities (FA0) ofthe same feed (CA0):
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Single reactions design- mixed reactor systems / 1st order rxn. -
1
/1
0
N
N
ireactorsN
C
C
k
NN
C
C
kp
0ln1
N
Series of N mixed
Plug flow
p
N
p
N
V
V
RA
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Single reactions design- plug reactor systems -
X1,X2,...XN
Consider:
Nplug flow reactors connected in series
Conversion of component A leaving reactor 1,2,3N
V
FA0
dXA
rAXAiXAf
Vi
FA0
dXA
rXi1Xifor ithreactor
V
F0
Vi
F0i1
N
V1 V2 ...VNF0
dX
r
X0
X1dX
r
X1
X2 ...dX
rXN1XN
dX
rX0XN
N reactors in series
N plug reactor in series conversion = single plug reactor conversion
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Design of parallel reactions- product distribution -
A
Decomposition of A
1
1
a
AR
R Ckdt
dCr
R
S
1k
2k
2
2aA
SS Ck
dtdCr
21
2
1 aa
A
S
R
S
R Ck
k
dC
dC
r
r
2121 ,,, aakk ct. (specific system, given temp.)
adjust & controlAC
(desired product)
(unwanted product)
maximise!!!
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Design of parallel reactions- product distribution -
A
Decomposition of A
1
1
a
AR
R Ckdt
dCr
R
S
1k
2k
2
2aA
SS Ck
dtdCr
21
2
1 aa
A
S
R
S
R Ck
k
dC
dC
r
r
2121 ,,, aakk ct. (specific system, given temp.)
adjust & controlAC
(desired product)
(unwanted product)
maximise!!!
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Design of parallel reactions- adjusting CA -
CA low CA high
Mixed flow reactor
Maintaining high conversion
Increasing inerts in feed
Decreasing the pressure ingas-phase systems
Batch / PFR
Maintaining low conversion
Removing inerts in feed
Increasing the pressure ingas-phase systems
CA low or high?
21
2
1 aaA
S
R
S
R Ckk
dCdC
rr
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Design of parallel reactions- adjusting CA -
AR
S
1k
2k
(desired)
(unwanted)
21
2
1 aa
A
S
R
S
R Ck
k
dC
dC
r
r
021
aa CA should be high Batch / plug flow reactor smallsize reactor
CA should be lowMixed flow reactor large size
reactor
21aa .
1
2 ctk
k
dC
dC
r
r
S
R
S
R Product distrib. unaffected by CA
021
aa
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Design of parallel reactions- adjusting k2/k1 -
AR
S
1k
2k
(desired)
(unwanted)
21
2
1 aaA
S
R
S
R Ckk
dCdC
rr
2 ways: Changing the temperature level of operation later!
Using a catalyst selectivity feature the most effective way!
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Design of parallel reactions- summary -
AR
S
1k
2k
(desired)
(unwanted)
High reactant concentration favours the high order reaction
Low reactant concentration
favours the lower order reaction
No effect of concentration reactions with the same order
1
1aA
RR Ck
dtdCr
2
2
a
AS
S Ckdt
dCr
Reactants concentration = key controlling variable:
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Design of parallel reactions- other parallel reactions -
BA R
S
1k
2k
(desired)
(unwanted)
rR dCRdt
k1CA1CB
1
22
2
BA
S
S
CCkdt
dCr
BA
2121
2
1 BAS
R
S
R CC
k
k
dC
dC
r
rMaximise!!!
021
021
021
021
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Design of parallel reactions- contacting patterns -
Batch process
021
021
021
021
021
021
2121
2
1 BAS
R
S
R CCk
k
dC
dC
r
r
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Design of parallel reactions- contacting patterns -
Continuous process
021
021
021
021
021
021
2121
2
1 BAS
R
S
R CCkk
dCdC
rr
Slide 19Slide 25
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Design of parallel reactions- contacting patterns -
Example 1:For the following reactions:
BA TR
US
1k
2k
(desired)
(unwanted)
3.05.1
1 BATR CCk
dt
dC
dt
dC
8.15.02 BA
US CCkdtdC
dtdC BA
Order the contacting schemes from most desirable to least desirable
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Design of parallel reactions- contacting patterns -
Example 1 Solution:
rR k1CA1.5
CB0.3
rS k2CA0.5
CB1.8
rR
rS
k1
k2
CACB1.5
Maximise CA high, CB low (most important)
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Design of parallel reactions- fractional yield -
A RKnowing the rate equations - we can determine the product distribution &reactor size
Instantaneous fractional yield of R
moles R formedmoles A reacted
dCR
dCA
Overall fractional yield of R
all R formedall A reacted
CRf
CA 0 CAf C
Rf
(CA )in reactor
Selectivity
selectivity moles of desired product formed
moles of undesired material formed
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Design of parallel reactions- fractional yield for PFR / MFR -
PFR CA is changing through the reactor
CAf composition everywhere
p 1
CA0 CAfdCACA0
CAf 1CA
dCACA0
CAf
MFR
m evaluated at CAf
m dpdCA
at CAf
p 1
CAmdCACA0
CAf
PFR / MFR relationships
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Design of parallel reactions- fractional yield for series of MFR -
MFR in series Overall yield = sum (fractional yields) weighted by theamount of reaction occurring in each vessel
N mixed 1(CA0 CA1)2(CA1 CA2) ...N(CA,N1 CA,N)
CA0 CAN
CRf (CA0 CAf)
For any type of reactor:
Very useful!!!
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Design of parallel reactions- graphical representation of CRf -
p 1CAdCACA0
CAf
CRf (CA0 CAf)
m evaluated at CAf
CRf (CA0 CAf)
CRf
CRf
CRf
N mixed 1(CA0 CA1) ...N(CA,N1 CA ,N)
CA0 CAN
CRf (CA0 CAf)
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Design of parallel reactions- graphical representation / types of flow -
Which type of flow gives the best product distribution?
Mixed flow isbest
Plug flow is best
Mixed up to CA1follow by plugflow
the largest area
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Design of parallel reactions- product distribution -
Example 2:Consider the aqueous reactions:
(desired)
(unwanted)
CRf=?
BA1k
2k
S
R
dCR
dt1.0CA
1.5CB0.3
dCS
dt1.0C
A
0.5CB
1.8
Equal volumetric flow rates of A and B
Each stream has C=20 mol/lof reactant
90% conversion of A
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Design of parallel reactions- product distribution -
Example 2 Solution:
R
A
dCR
dCR dCS
1.0CA1.5
CB0.3
1.0CA1.5
CB0.3 1.0CA
0.5CB
1.8
CA
CA CB1.5
Af
A
C
CA
AfA
p dCCC 00
1
a) Plug Flow
)1(0 AAAf XCC
BA1k
2k
S
R
10
1 5.0
1
10 5.1 19
1
110
1
A
A
AA
AAp
C
dC
CC
dCC
BA CC
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Design of parallel reactions- contacting patterns -
Example 2 Solution:
p 1
9
dCA
1 CA0.51
10
CA0.5 x CA x
2
dCA 2xdx
p
1
9
2xdx
1 x110
2
9 dx
dx
1 x110
1
10
0.32
CRf (CA0 CAf) 9(0.32) lmolCRf /86.2
CSf (1 )(CA0 CAf) 9(10.32) lmolCSf /14.6
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Design of parallel reactions- contacting patterns -
Example 2 Solution:
lmolCRf /5.4
lmolCSf /5.4
b) Mixed Flow
m evaluated at CAf
5.01
15.05.1
ABA
Aexit
CCC
C
BA CC
)5.0(9)( 0 AfARf CCC
)5.01(9))(1( 0 AfASf CCC
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Design of parallel reactions- contacting patterns -
Example 2 Solution:
lmolCRf /85.7
lmolCSf /15.1
c) Plug flow A Mixed flow B
)87.0(9)( 0 AfARf CCC
)87.01(9))(1( 0 AfASf CCC
Af
A
C
CA
AfA
p dCCC 00
1
87.0118
1
)1(18
1
119
1 19
1
19
1
1
19 5.1
1
19 5.1
A
AA
A
AA
BA
AAp
C
dCdC
C
dCC
CC
dCC
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Design of parallel reactions- contacting patterns -
Example 2 Solution:Summary
Plug Flow:
Mixed Flow:
Plug A / Mixed B
32.0 AR
5.0 AR
87.0 AR
lmolCRf /86.2
lmolCRf
/85.7
lmolCRf /5.4
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