AT CHURCH STRETTON SCHOOL Shropshire Council Reference : CSTR 014 & CSTR 018.
Part II, Measures Other Than Conversion I · 2. Applications/Examples of the CRE Algorithm II...
Transcript of Part II, Measures Other Than Conversion I · 2. Applications/Examples of the CRE Algorithm II...
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Part II, Measures Other Than Conversion I
Apr/07 2011 Spring 1
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Part II, Measures Other Than Conversion II
Apr/07 2011 Spring 2
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2. Applications/Examples of the CRE Algorithm I
Apr/07 2011 Spring 3
Gas Phase
Elementary
Reaction
Additional Information
Only A fed P0 = 8.2 atm
T0 = 500 K CA0 = 0.2 mol/dm3
k = 0.5 dm3/mol·s vo = 2.5 dm3/s
Solve for X = 0.9 for A is limiting
2A → B
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2. Applications/Examples of the CRE Algorithm II
Apr/07 2011 Spring 4
Reactor Mole Balance Rate Law Stoichiometry
Batch
CSTR
PFR
X
A
AVr
dXNt
00
A
A
r
XFV
0
X
A
Ar
dXFV
00
2
AkCrA
2
AkCrA
2
AkCrA
Gas:
V = V0
Gas:
T =T0, P =P0
Gas:
T =T0, P =P0
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2. Applications/Examples of the CRE Algorithm III
Apr/07 2011 Spring 5
Reactor Stoichiometry 2
Batch
CSTR
PFR
Per mole A ?
Per mole A
A → ½B
ε = 1.0(1- ½) = -0.5
Per mole A
A → ½B
ε = 1.0(1- ½) = -0.5
)1(
)1(
A0
0
A0AA
XC
V
XN
V
NC
)ε1(
)1(
)ε1(
)1(
A0
0
A0AA
X
XC
Xv
XF
v
FC
![Page 6: Part II, Measures Other Than Conversion I · 2. Applications/Examples of the CRE Algorithm II Apr/07 2011 Spring 4 Reactor Mole Balance Rate Law Stoichiometry Batch CSTR PFR ³ X](https://reader033.fdocuments.us/reader033/viewer/2022042214/5eb95456e4749f1f1e68a21b/html5/thumbnails/6.jpg)
2. Applications/Examples of the CRE Algorithm IV
Apr/07 2011 Spring 6
Reactor Stoichiometry 3
Batch
CSTR
PFR
2
)2
1(
A0
0
A0B
B
XC
V
XN
V
NC
)ε1(2
)ε1(
)2
1(
A0
0
A0B
B
X
XC
Xv
XF
v
FC
![Page 7: Part II, Measures Other Than Conversion I · 2. Applications/Examples of the CRE Algorithm II Apr/07 2011 Spring 4 Reactor Mole Balance Rate Law Stoichiometry Batch CSTR PFR ³ X](https://reader033.fdocuments.us/reader033/viewer/2022042214/5eb95456e4749f1f1e68a21b/html5/thumbnails/7.jpg)
2. Applications/Examples of the CRE Algorithm V
Apr/07 2011 Spring 7
Reactor Combine Integration
Batch
CSTR
PFR
X
dXXkC
t0 2
A0 )1(
11
22
A0
2
0
)1(
)5.01(
XkC
XXFV A
X
dXX
X
kC
FV
0 2
2
2
A0
A0
)1(
)5.01(
)1(
1
A0 X
X
kCt
X
XX
X
kC
FV
1
)ε1(ε
)1ln()ε1(ε2
222
A0
A0
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2. Applications/Examples of the CRE Algorithm VI
Apr/07 2011 Spring 8
Reactor Evaluate For X = 0.9
Batch
CSTR
PFR
kCA0 = (0.5)(0.2)
= 0.1 s-1
kC2A0 = (0.5)(0.2)2
= 0.02mol/dm3·s
FA0 = CA0·v0
= (0.2)(2.5) = 0.5 mol/s
t = 90 s
V = 680.6 dm3
τ = V/v0 = 272.3 s
V = 90.7 dm3
τ = V/v0 = 36.3 s
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7. Mole Balances on 4 Basic Reactors I
Apr/07 2011 Spring 9
o Liquid phase
Batch and
CSTR and
PFR and
PBR and
AA r
dt
dC A
B ra
b
dt
dC
A
AA00 )(
r
CCvV
A
BB00
)/(
)(
rab
CCvV
AA
0 rdV
dCv A
B0 r
a
b
dV
dCv
'
AA
0 rdW
dCv '
AB
0 ra
b
dW
dCv
D C B A a
d
a
c
a
b
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7. Mole Balances on 4 Basic Reactors II
Apr/07 2011 Spring 10
o Gas phase 1
T
T
P
P
F
Fvv 0
0T
T00
T
T
P
P
F
F
v
F
v
FC 0
0T
T0
0
AAA
0
0T0
0
0T
T0AT0A ,
RT
PC
T
T
P
P
F
F
v
FCC
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7. Mole Balances on 4 Basic Reactors III
Apr/07 2011 Spring 11
o Gas phase 2
1. Mole balances
BatchCSTR PFR
D C B A a
d
a
c
a
b
Vrdt
dNA
A
Vrdt
dNB
B
Vrdt
dNC
C
Vrdt
dND
D
A
AA0
r
FFV
B
BB0
r
FFV
C
CC0
r
FFV
D
DD0
r
FFV
AA r
dV
dF
BB r
dV
dF
CC r
dV
dF
DD r
dV
dF
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7. Mole Balances on 4 Basic Reactors IV
Apr/07 2011 Spring 12
o Gas phase 3
2. Rate law
3. Stoichiometry
- Relative rate
- Then
- Concentration
β
B
α
AAA CCkr
d
r
c
r
b
r
a
r DCBA
AB ra
br
AC ra
cr AD r
a
dr
yT
T
F
FCC
0
T
AT0A y
T
T
F
FCC
0
T
B0TB y
T
T
F
FCC
0
T
CT0C
yT
T
F
FCC
0
T
D0TD
000T
T ,2 P
Py
T
T
F
F
ydW
dy
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7. Mole Balances on 4 Basic Reactors V
Apr/07 2011 Spring 13
o Gas phase 4
- Total molar flow rate
4. Combine
- Specify parameter values
- Specify entering numbers
IDCBAT FFFFFF
β
T
B
α
T
Aβα
T0AA
F
F
F
FCk
dV
dFβ
T
B
α
T
Aβα
T0AB
F
F
F
FCk
a
b
dV
dF
β
T
B
α
T
Aβα
T0AC
F
F
F
FCk
a
c
dV
dFβ
T
B
α
T
Aβα
T0AD
F
F
F
FCk
a
d
dV
dF
dcbaTCk ,,,,βα,,, ,0T0A
0000 ,,, DCBA FFFF
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8. Microreactors I
Apr/07 2011 Spring 14
o Description
- High surface area-to-volume ratio in their micro
structure regions
• 100μm width, 20,000μm length (2 cm)
• high surface area-to-volume ratio
☞ ca. 10,000 m2/m3
reduce or eliminate heat & mass transfer resistances
• to study intrinsic kinetics of reactions isothermally
• production of toxic or explosive intermediates
• shorter residence time
• narrow residence time distribution
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8. Microreactors II
Apr/07 2011 Spring 15
o Example
- 32 microreaction system in parallel produce 2000 t/yr
- Lab-on-a-chip
p 204, Ex 4-7
OHCHO-RO21 OHCH-R 2Ag22
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9. Membrane Reactors I
Apr/07 2011 Spring 16
o Description
- Really just a plug-flow reactor
• contains an additional cylinder of some porous material
within it, kind of like the tube within the shell of a shell-
and-tube heat exchanger
• this porous inner cylinder is the membrane that gives the
membrane reactor its name
- The membrane is a barrier that only allows certain
components to pass through it
• selectivity of the membrane is controlled by its pore
diameter, which can be on the order of Angstroms, for
microporous layers, or on the order of microns for
macroporous layers
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9. Membrane Reactors II
Apr/07 2011 Spring 17
o What is it?
- Combine reaction
with separation to
increase
conversion and/or
selectivity
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9. Membrane Reactors III
Apr/07 2011 Spring 18
o Typical reactors 1
- IMRCF (Inert Membrane Reactor with Catalyst Pellets
on the Feed Side)
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9. Membrane Reactors IV
Apr/07 2011 Spring 19
o Typical reactors 2
- CMR (Catalytic Membrane Reactor)
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9. Membrane Reactors V
Apr/07 2011 Spring 20
o Modeling 1
- IMRCF
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9. Membrane Reactors VI
Apr/07 2011 Spring 21
o Modeling 2
- Change the algorithm a little, V → W (= ρbV)
• mole balance for A
• mole balance for C
• mole balance for B
AA r
dV
dF
CC r
dV
dF
BBB Rr
dV
dF
0
Accu.Gen.Diffusion
byOut
flowby
Out
flowby
In
BBBB
VRVRFF
VVV
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9. Membrane Reactors VII
Apr/07 2011 Spring 22
o Modeling 3
- Rate of molar flux B out through the membrane
- Rate of transport B out through the membrane
- Let kC = k’Ca and CBS ≈ 0,
p 211, Ex 4-8
)( BSB
'
CB CCkW
)( BSB
'
CBB CCakaWR
DL
D
DLa
4
4
π
π
Volume
Area2
BCB CkR
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9. Membrane Reactors VIII
Apr/07 2011 Spring 23
o Enhance selectivity
- Fed species to the reactor through the sides of
membrane
BBB Rr
dV
dF
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10. Unsteady-State Operation of Stirred
Reactors I
Apr/07 2011 Spring 24
o Startup of a CSTR 1
- Mole balance equation
- For batch reactor, conversion means little
- 1st order rxn
- With initial conditions CA = 0 at t = 0
dt
dNVrFF A
AAA0
dt
dCrCC A
AAA0 ττ
ττ
τ1 A0A
A CC
k
dt
dC
τ
t)τ1(exp1
τ1
A0A k
k
CC
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10. Unsteady-State Operation of Stirred
Reactors II
Apr/07 2011 Spring 25
o Startup of a CSTR 2
- Steady state analysis
• assume time to reach 99% of st-st conc., CAS
• CA0 = 0.99CAS
• for slow rxn with small k (1 » τk)
• for rapid rxn with large k (1 « τk)
☞ most 1st-order system, st-st achieved in 3 ~ 4 space time
k
CC
τ1
A0AS
kt
τ1
τ6.4S
τ6.4S t
kt /6.4S
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10. Unsteady-State Operation of Stirred
Reactors III
Apr/07 2011 Spring 26
o Semibatch reactor 1
- Motivation
• to obtain high selectivity
• maintain A at high conc.
• feed B as low as possible
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10. Unsteady-State Operation of Stirred
Reactors IV
Apr/07 2011 Spring 27
o Semibatch reactor 2
- Mole balance equation 1
dt
dNtVr A
A )(00
Accum
of Rate
Generation
of Rate
out
Rate
in
Rate
dt
dVC
dt
VdC
dt
VCdVr A
AAA
)(
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10. Unsteady-State Operation of Stirred
Reactors V
Apr/07 2011 Spring 28
o Semibatch reactor 3
- Mole balance equation 2
- Since the reactor is being filled, V varies
dt
Vdv
)ρ(00ρ
Accum
of Rate
Generation
of Rate
out
Rate
in
Rate
00
dt
dVC
dt
VdC
dt
VCdVr A
AAA
)(
![Page 29: Part II, Measures Other Than Conversion I · 2. Applications/Examples of the CRE Algorithm II Apr/07 2011 Spring 4 Reactor Mole Balance Rate Law Stoichiometry Batch CSTR PFR ³ X](https://reader033.fdocuments.us/reader033/viewer/2022042214/5eb95456e4749f1f1e68a21b/html5/thumbnails/29.jpg)
10. Unsteady-State Operation of Stirred
Reactors VI
Apr/07 2011 Spring 29
o Semibatch reactor 4
- Constant density
- With initial condition V = V0 at t = 0
- Balance on A can be rewritten as
- For B, we have generation term, rBV
• balance on B can be
0vtd
Vd
tvVV 00
A0
AA C
V
vr
dt
dC
V
CCvr
dt
dC )( BB00B
B
![Page 30: Part II, Measures Other Than Conversion I · 2. Applications/Examples of the CRE Algorithm II Apr/07 2011 Spring 4 Reactor Mole Balance Rate Law Stoichiometry Batch CSTR PFR ³ X](https://reader033.fdocuments.us/reader033/viewer/2022042214/5eb95456e4749f1f1e68a21b/html5/thumbnails/30.jpg)
10. Unsteady-State Operation of Stirred
Reactors VII
Apr/07 2011 Spring 30
o Semibatch reactor 5
- Design equations in terms of conversion 1
• for species A
• for species B
XNNN
tt
A0A0A
time toup
reactedA of
moles of #
initially
vatin theA of
moles of #
at time
vatin theA of
moles of #
XNdtFNN
tt
t
Bi A00
0BB
time toup
reacted B of
moles of #
vat the to
added B of
moles of #
initially
vatin the B of
moles of #
at time
vatin the B of
moles of #
A + B C + D
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10. Unsteady-State Operation of Stirred
Reactors VIII
Apr/07 2011 Spring 31
o Semibatch reactor 6
- Design equations in terms of conversion 2
• for a constant molar feed rate & no B initially
• mole balance on species A
• for a reversible 2nd order rxn
• recalling
XNtFN 0A0BB
dt
dXN
dt
dNVr A0
AA
C
DCBAA
K
CCCCkr
tvV
XN
V
NC
00
0AAA
)1(
tvV
XNtFN
V
NC i
00
0A0BBBB
tvV
XNC
00
0AC
tvV
XNC
00
0AD
tvV
KXNXNtFNXk
dt
dX i
00
C
2
0A0A0BB )/())(1(
tvVV 00
A + B C + D
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10. Unsteady-State Operation of Stirred
Reactors IX
Apr/07 2011 Spring 32
o Semibatch reactor 7
- Equilibrium conversion 1
• at time t, equilibrium conversion
• for
A + B C + D
ee
ee
ee
ee
ee
ee
NN
NN
V
N
V
N
V
N
V
N
CC
CCK
BA
DC
BA
DC
BA
DCC
XNtFN ABB 00
)1
( then,
))(1())(1(
))((
2
C
0BC
0A
0A0B
2
0A
0A0B0A
0A0AC
e
ee
ee
e
ee
ee
X
XXK
FK
Nt
XNtFX
XN
XNtFXN
XNXNK
![Page 33: Part II, Measures Other Than Conversion I · 2. Applications/Examples of the CRE Algorithm II Apr/07 2011 Spring 4 Reactor Mole Balance Rate Law Stoichiometry Batch CSTR PFR ³ X](https://reader033.fdocuments.us/reader033/viewer/2022042214/5eb95456e4749f1f1e68a21b/html5/thumbnails/33.jpg)
10. Unsteady-State Operation of Stirred
Reactors X
Apr/07 2011 Spring 33
o Semibatch reactor 8
- Equilibrium conversion 2
• at a semibatch reactor
A + B C + D
)1(2
)1(411
C
0A
0BCC
2
0A
0BC
0A
B0C
K
N
tFKK
N
tFK
N
tFK
X e
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10. Unsteady-State Operation of Stirred
Reactors XI
Apr/07 2011 Spring 34
o Reactive distillation
- Applicable to reversible, liquid phase reactions
• the equilibrium point lies far to
the left and little product is formed
• if one or more of the products are removed more of
the product will be formed because of Le Chatlier's
Principle