lecture 11 kjemisk reaksjonsteknikk chemical reaction ...folk.ntnu.no/audunfor/5....
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1 - 27/09/2012
Departm
ent of Chem
ical Engineering
Lecture 11Kjemisk
reaksjonsteknikk
Chemical Reaction Engineering
Review of previous lectures
Kinetic data analysis of heterogeneous reactions
1.
Characterization of Pt catalysts2.
Kinetic study, find a kinetic expression and kinetic parameter3.
Catalytic reactor design
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7-Step Procedure for CRE Data analyses (1)
1. Postulate a rate law
A. Power law models fro homogeneous reactions
B. Langmuir-Hinshelwood models for heterogeneous reactions
2. Select reactor type and corresponding mole balance A.If batch reactor, use mole balance on Reactant A
B.If differential PBR, use mole balance on product P (A →P)
BAA CkCr
2)1( BBAA
BAA PKPK
PkPr
dtdCr A
A
WC
WFr PP
A
0
dtdCr A
A
WC
WFr PP
A
0
1. Postulate a rate law
A. Power law models for homogeneous reactions
B. Langmuir-Hinshelwood models for heterogeneous reactions
2. Select reactor type and corresponding mole balance A.If batch reactor, use mole balance on Reactant A
B.If differential PBR, use mole balance on product P (A →P)
WC
WFr PP
A
0
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7-Step Procedure for CRE Data analyses (2)
3. Process your data in terms of the measured variables (e.g. NA
, CA
, or PA
). If necessary, rewrite your mole balance in terms of your measured variables
4. Look for simplification For example, if one of the reactants is in excess, assume its concentration is constant,. If the gas phase mole fraction of reactant A is small, set ε=0
5. For a batch reactor, calculate –rA
as a function of concentration CA
to determine the reaction order:A.Differential analysisB.Integral methodC.Nonlinear regression
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7-Step Procedure for CRE Data analyses (3)
6.
For differential PBR, calculate –rA
as a function of CA
or PA
A. Calculate as a function of reactant concentration CA
or partial pressure PA
B. Choose a model, e.g.,
C. Use nonlinear regression to find the best model and model
parameters
7. Analyze your rate law model for “goodness of fit”. Calculate a correlation coefficient.
WC
WFr PP
A
0
AA
AA PK
kPr
1
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Example: Scaling up of toluene hydrogen process
Hydrogen and toluene are reacted over a Pt catalysts supported on crystalline silica-alumina to form methane and benzene.
C3
H5
CH3
+H2
→
C6
H6
+ CH4
We wish to design a packed bed reactor to process a feed consisting of 20% toluene and 80 % hydrogen. Toluene is fed at a rate of 50 mol/min at a temperature of 640 oC
and
a pressure of 40 atm.
Step 1, Characterization of Pt catalystsStep 2, Kinetic study, find a kinetic expression and kinetic
parameterStep 3, Catalytic reactor design
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Determination of active site numbers
The concentration of active sites on the catalyst surface is typically determined by H2
or CO chemisorption.
The chemisorption
of H2
at 298 K on Pt catalysts 1) determine Langmuir-isotherm. 2) determine the Pt surface area or dispersion
0
0.5
1
1.5
2
2.5
0 50 100 150 200 250
P (mmHg)
H2
ads (
CM
3 STP
)
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Associative adsorption
2
2
1 H
HA KP
KP
2
111
HV
t
KPCC
** 22 HH ka
2*2 HDHa kPk
1* A
Linearization of Langmuir-isotherm
0
5
10
15
20
25
0 0.02 0.04 0.06 0.08 0.1 0.12
1/P (mmHP-1)
1/C
v (g/
mm
mol
)
8 - 27/09/2012
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Dissociative adsorption
2/12
2/12
)(1)(
H
HH KP
KP
2/12 )(
111
HV
t
H KPCC
*2*22 HH ka
22*2 HDHa kPk
1* A
Linearization of Langmuir-isotherm
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4
1/P0.5 (mmHP-1)
1/C
v (g/
mm
mol
)1/CT
slop=1/(CT
K0.5)
CT
=0.137 mmol/gcat
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Kinetic Modeling and Analysis
1) Select a proper reactor for kinetic study
2) Perform kinetic study and design kinetic experiments
3) Developing an algebraic rate expression consistent with experimental observations
2) Analyzing the rate expression in a such manner that the rate expression parameters can readily be determined from experimental data
3) Find a mechanism and rate determining step consistent with the experimental data (for
non-elementary reactions)
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We select differential fixed bed reactor for the kinetic study
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Data from a differential reactor
-rT Partial pressure (atm)Run
mmol
toluene/gcat
.hr Toluene Hydrogen Methane Benzeneset A
1 71 1 1 1 02 71.3 1 1 4 0
Set B2 71.1 1 1 0 13 71.3 1 1 0 4
Set C4 71.8 1 1 0 05 142 1 2 0 06 284 1 3 0 0
Set D7 47 0.5 1 0 08 71.3 1 1 0 09 117 5 1 0 010 127 10 1 0 011 131 15 1 0 012 133 20 1 0 0
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Turn over frequency (TOF)
cat
cat
T
A
gmmol
hrgmmol
CrTOF
sTOF 1146.0
3600*135.071
TOFCr TA
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Dependence of methane and benzene
0
10
20
30
40
50
60
70
80
0 1 2 3 4 5
PM (atm)
-rA
(mm
ol/g
cat.h
r)
0
10
20
30
40
50
60
70
80
0 1 2 3 4 5
PB (atm)
-rA
(mm
ol/g
cat.h
r)
....1
...
MM
A PKr
....1
...
BB
A PKr
KM
PM
<<1 KB
PB
<<1
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Dependence of toluene
0
20
40
60
80
100
120
140
0 5 10 15 20 25
PT (atm)
-rA
(mm
ol/g
cat.h
r)
....1
TT
TA PK
Pr
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Dependence of hydrogen
0
50
100
150
200
250
300
0 1 2 3 4 5
PH2 (atm)
-rA
(mm
ol/g
cat.h
r)
....1 22
2
HH
HA PK
Pr KH2
PH2
<< 1
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Proposed reaction mechanism
AdsorptionT(g) + * ↔ T*
Surface reaction H2
(g) + T* ↔ B* +M(g)Desorption B* ↔ B(g) +*
)( *T
TTATD K
Pkr
)( 2S
MBTHSTD K
PPkr
1** TBT
TT
THT PK
PkPr
1
2
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Determination of kinetic parameters
0
0.005
0.01
0.015
0.02
0.025
0 0.5 1 1.5 2 2.5
1/PT (atm-1)
1/-r
A (g
cat.h
r/mm
ol)
THH
T
T PkPkPK
r 22
11
0071.02
H
T
kPK
007.01
2
HkP
Slope=
k=142.9 hratmgmmol
cat2
k=1 atm-1
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PBR reactor
1) Mole balance
T
TH
TT
THT P
PPPK
PkPr
19.142
1222) Rate law
3) Stoichiometry: XFF AA 10
AA rdWdXF 0
X
XCC TT
110
011112 HTBM
00 Ty
0TT 0PP
)1()1( 000 xPxRTCRTCP TTTT
022 ,HH PP
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PBR reactor
000
2 1)1(1
TTH
ToT
FdWdx
XPkPxPK
0
02
002 1
1
TH
T
TH FdWdx
kPK
XPkP
))1ln(( 02
0 xxPKPkP
FW TTToH
T
4) Combine:
5. Evaluation
)1(1
1002
0 xPKXPkP
dWdxF
ToT
THT
gatm
atmatmatm
hratmgmmol
hrmolW
cat
8.656))8.01ln(8.0811(8329.142
min/60min/50
2
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TURBULENT
LAMINAR
p3
pc
G75.1D11501
DgG
dzdPErgun Equation:
Pressure Drop in Packed Bed Reactors
21
P pressure, kPaϕ
porosity (volume of void/total bed volume)1-
ϕ (volume of solid/total bed volume)
gc
conversion factor. 1.0 for metric systemDp
diameter of particle in bed mμ
viscosity of gas passing through the bed kg/m.sZ length down the packed bed mu, superficial velocity m/sρ
gas density
kg/m3
G= ρu =superficial mass velocity kg/m2,s
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TURBULENT
LAMINAR
p3
pc
G75.1D11501
DgG
dzdPErgun Equation:
Pressure Drop in Packed Bed Reactors
22 0
00 T
TPP)X1(
0
0
0T
T0 T
TPP
FF
00
00
0mm Constant mass flow:
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0T
T
0
0
p3
pc0 FF
TT
PPG75.1
D11501
DgG
dzdP
T
0T0
00 F
FTT
PP
Variable Density
G75.1
D11501
DgG
p3
pc00Let
Pressure Drop in Packed Bed Reactors
23
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0T
T
0
0
cc
0
FF
TT
PP
1AdWdP
ccbc 1zAzAW Catalyst Weight
0cc
0
P1
1A2
Let
Pressure Drop in Packed Bed Reactors
24
b bulk density c solid catalyst density porosity (a.k .a., void fraction )
Where
Ac , cross section area , z length of the reactor
25 - 27/09/2012
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We will use this form for single reactions:
X1
TT
PP1
2dWPPd
00
0
0T
T
0 FF
TT
y2dWdy
0P
Py
X1TT
y2dWdy
0
X1y2dW
dy
Isothermal
case
Pressure Drop in Packed Bed Reactors
25
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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 ε= 0, we can obtain an analytical solution.
Polymath will combine the mole balance, rate law and stoichiometry.
P,XfdWdX
P,XfdWdP
X,yfdWdy
and or
Pressure Drop in Packed Bed Reactors
26
yxPK
yXPkPdWdxF
ToT
THT )1(1
1002
0