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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

)

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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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PBR reactor with pressure drop

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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

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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

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PBR

27

2/1

2

2

)W1(y

)W1(y

dWdy

1y0WWhen

y2dWdy

0For

X1TT

y2dWdy

0

Initial condition

0cc

0

P1

1A2