kinetics & catalysis of the water-gas-shift...

Kinetics & Catalysis of theWater-Gas-Shift Reaction:

A Microkinetic and Graph Theoretic Approach

March 31, 2006

Caitlin A. Callaghan

A PhD Defense

Fuel Cell CenterDepartment of Chemical EngineeringWorcester Polytechnic InstituteWorcester, MA 01609

Research Objectives• Develop a predictive microkinetic model for LTS

and HTS water gas shift catalysts– Identify the slow steps– Develop reduced kinetic model

• Simulate the reaction for various metal catalysts

• Eventual goals:– detailed kinetic analysis– a priori design of WGS catalysts in fuel reformers for

fuel cells

That was thenThat was then……

• Catalyst design via trial and error• Mechanisms not comprehensive,

involving only a few elementary reaction steps

• Kinetic analysis of a mechanism based on arbitrary assumptions (i.e., RLS, QE, etc.)

This is nowThis is now……

• Comprehensive mechanism• Systematic methodology for mechanistic

analysis – RR Graph theory– Kirchhoff’s Laws

• Rational basis for catalyst design

AccomplishmentsAccomplishments

• Comprehensive mechanism• RR Graph Theory

– Graphical depiction of complete mechanism– Application of network theory (i.e., Kirchhoff’s

Laws)– Systematic simplification and reduction– QE reactions, RLSs identified

OutlineOutline

• Why study the WGSR?• Catalytic Kinetic Analysis

– LHHW Approach– Microkinetic Approach

• Reaction Route Graphs– RR Graph Theory– Network Reduction & Analysis

• Future Work

Why Study theWhy Study theWaterWater--GasGas--ShiftShift

Reaction?Reaction?

The Fuel CellThe Fuel CellImportance

• Environmental Issues:– Depletion of fossil fuels– Harmful by-products released during combustion

in power production

• Fuel Cells provide an alternative to traditional methods of obtaining power.

… Fuel Cells…a cleaner, more efficient alternative

The Fuel CellThe Fuel CellHow does it work?

Simple Concept:

H2 + O2

H2O + electricity

Where does HWhere does H22 come from?come from?

Burner

FuelTank

AIR

EXHAUST

H2OFUEL CELL

FUEL

Reformer(ATR or SR)

HTSReactor

LTSReactor

PreferentialOxidation

(PrOx)

Generator+

-

Saturator

Radiator

Battery

Cathode Anode

Effect of CO on PEM Fuel Cell Effect of CO on PEM Fuel Cell PerformancePerformance

S. Gottesfeld, and J. Pafford, J. Electrochem. Soc., 135, 2651 (1988).

Why is the WGSR important?– Many industrial applications:

• Ammonia synthesis• Methanol synthesis• Hydrogen production

– WGSR is the greatest catalytic challenge in fuel processing– Recovers lost energy– The ideal catalyst must have sufficient activity and durability

start-up, shutdownair exposureover a wide temperature range

Why is the WGSR studied?– Detailed understanding of mechanism and kinetics is lacking– At present, development of catalyst is by trial and error and

substantial experimentation with limited success– Design of catalyst via simulation is attractive

The WaterThe Water--GasGas--Shift ReactionShift Reaction

H2O + CO H2 + CO2

The WGS Reaction:

Catalytic KineticCatalytic KineticAnalysisAnalysis

LHHW Approach (1)LHHW Approach (1)

• Single RRmechanism

• Single RLS assumed

• Remaining steps at QE

s1: A + S A·S QEs2: A·S B·S RLSs3: B·S B + S QE

B2 A

AOR

A A

11

1

t

A B

PC k PK P

rK P K P

⎛ ⎞−⎜ ⎟

⎝ ⎠=+ +

LHHW Approach (2)LHHW Approach (2)

• Boudart (1984)– 2 RLS– Single RR

• Ovesen, et al. (1996)– 3 RLS– Single RR

CO·S + O·S CO2·S + S

OH·S + S O·S + H·S

H2O·S + S OH·S + H·S

Redox Reaction Mechanism

O·S + CO CO2 + S

H2O + S O·S + H2

Two-Step Redox Reaction Mechanism

Boudart, M.; Djega-Mariadassou, G. Kinetics of Heterogeneous Catalytic Reactions; Princeton University Press: Princeton, 1984.; Ovesen, C. V., et al., J. Catal. 1996, 158, 170.

Microkinetic Approach (1)Microkinetic Approach (1)

• More comprehensive mechanism

• Obtain kinetics, theoretically

• Assume a reactor type

CO(g)

+ H2O(g)

CO2(g)

+ H2(g)

H2O

OHCO H2

OCO2 H

Catalyst Surface

• Solve material balances for all species (including intermediates) using “black box” approach

Dumesic, J. A., et al. The Microkinetics of Heterogeneous Catalysis; ACS, 1993.Stoltze, P., Progress in Surface Science 2000, 65, 65.

Microkinetic Approach (2)Microkinetic Approach (2)

s 13: H2O·S + O·S 2OH·S

s 12: HCOO·S + O·S CO2·S + OH·S

s 11: HCOO·S + S CO2·S + H·S

s 10: CO·S + OH·S CO2·S + H·S

s 9: OH·S + S O·S + H·S

s 8: CO·S + OH·S HCOO·S + S

s 7: CO·S + O·S CO2·S + S

s 6: H2O·S + S OH·S + H·S

s 5: H2·S H2 + S

s 4: H·S + H·S H2·S + S

s 3: CO2·S CO2 + S

s 2: CO + S CO·S

s1: H2O + S H2O·S

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 3 6 9 12 15

Time (s)

Spec

ies

Cov

erag

eCO·S

H2O·S

H·S

Fishtik, I.; Datta, R., Surf. Sci. 2002, 512, 229.

Reaction RouteReaction RouteGraphsGraphs

RR RR GraphsGraphs

A RR graph may be viewed as several hikes through a mountain range:

Valleys are the energy levels of reactants and productsElementary reaction is a hike from one valley to adjacent valleyTrek over a mountain pass represents overcoming the energy barrier

Reaction Route Graph TheoryReaction Route Graph Theory

Powerful new tool in graphical and mathematical depiction of reaction mechanisms

New method for mechanistic and kinetic interpretation

“RR graph” differs from “Reaction Graphs”– Branches elementary reaction steps– Nodes multiple species, connectivity of elementary reaction

steps

Reaction Route Analysis, Reduction and Simplification – Enumeration of direct reaction routes– Dominant reaction routes via network analysis– RDS, QSSA, MARI assumptions based on a rigorous De Donder

affinity analysis– Derivation of explicit and accurate rate expressions for dominant

reaction routes

Ref. Fishtik, I., C. A. Callaghan, et al. (2004). J. Phys. Chem. B 108: 5671-5682. Fishtik, I., C. A. Callaghan, et al. (2004). J. Phys. Chem. B 108: 5683-5697. Fishtik, I., C. A. Callaghan, et al. (2005). J. Phys. Chem. B 109: 2710-2722.

RRRR Graph TopologyGraph Topology

A + B

C

s1 s2 s5

s3 s4

s5

s1 s2

s3 s4

s5OR

s1: A + S A·Ss2: B + S B·Ss3: A·S + B·S C·S + Ss4: C·S C + SOR: A + B C

s3: A·S + B·S C·S + Ss4: C·S C + S–s5: C + 2S A·S + B·S OR: 0 0

Full Route

s1: A + S A·Ss2: B + S B·Ss3: A·S + B·S C·S + Ss4: C·S C + Ss5: A·S + B·S C + 2S

Mechanism: A + B C

Empty Route

Eρ ρΛ Elementary Reaction Steps

Eρ ρΛ

s1 0 1.5 106 CO + S CO·S 12.0 1014 s2 0 106 H2O + S H2O·S 13.6 1014 s3 25.4 1013 H2O·S + S OH·S + H·S 1.6 1013 s4 10.7 1013 CO·S + O·S CO2·S + S 28.0 1013 s5 0 1013 CO·S + OH·S HCOO·S + S 20.4 1013 s6 15.5 1013 OH·S + S O·S + H·S 20.7 1013 s7 0 1013 CO·S + OH·S CO2·S + H·S 22.5 1013 s8 1.4 1013 HCOO·S + S CO2·S + H·S 3.5 1013 s9 4.0 1013 HCOO·S + O·S CO2·S + OH·S 0.9 1013 s10 29.0 1013 H2O·S + O·S 2OH·S 0 1013 s11 26.3 1013 H2O·S + H·S OH·S + H2·S 0 1013 s12 1.3 1013 OH·S + H·S O·S + H2·S 4.0 1013 s13 0.9 1013 HCOO·S + OH·S CO2·S + H2O·S 26.8 1013 s14 14.6 1013 HCOO·S + H·S CO2·S + H2·S 14.2 1013 s15 5.3 4 1012 CO2·S CO2 + S 0 106 s16 15.3 1013 H·S + H·S H2·S + S 12.8 1013 s17 5.5 6 1012 H2·S H2 + S 0 106 s18 15.3 6 1012 H·S + H·S H2 + S 7.3 106

Adsorptionand

DesorptionSteps

Surface Energetics for Cu(111) Catalyst:

Activation energies:kcal/mol

Pre-exponential factors:atm-1s-1 (ads/des) s-1 (surface)

Rate, Affinity & ResistanceRate, Affinity & Resistance• DeDonder Relation:

• Reaction Affinity:

• Reaction Rate (Ohm’s Law):

( )1 1 expr

r r rr

ρρ ρ ρ ρ

ρ

⎛ ⎞⎡ ⎤= − = − −⎜ ⎟ ⎣ ⎦⎜ ⎟

⎝ ⎠A

1 1 1

ln ln ln lnqn n

i i o o k k i ii k i

AK P

RTρ

ρ ρ ρ ρ ρ ρν µ α θ α θ β= = =

− = − = = − + + +∑ ∑ ∑A

rR

ρρ

ρ

=A

(conventional)

ln1

rr

Rr r r

ρ

ρρ

ρ ρ ρ

⎛ ⎞⎜ ⎟⎝ ⎠= =

−

RESISTANCE

net reaction rate

forward reaction rate

reaction affinity

Kirchhoff’s Current Law– Analogous to conservation of mass

Kirchhoff’s Voltage Law– Analogous to thermodynamic consistency

Ohm’s Law– Viewed in terms of the De Donder Relation

Electrical AnalogyElectrical Analogya

b

cd

ea b c d e 0r r r r r− + − + =

f g h i 0− − =A +A A Af g

i h

Rr

ρρ

ρ

A=

Constructing the Constructing the RRRR GraphGraph

1. Select the shortest MINIMAL FROR = s1+s2+s3+s15+s7+s18

s1 s2 s3 s15 s7 s18

s18 s7 s15 s3 s2 s1

1


2. Add the shortest MINIMAL ER to include all elementary reaction steps

s4 + s6 – s7 = 0s5 + s8 – s7 = 0s5 + s9 – s4 = 0s6 + s16 – s12 = 0s8 + s16 – s14 = 0s16 + s17 – s18 = 0

2

s1 s2 s3 s15 s7 s18

s18 s7 s15 s3 s2 s1s4

s5

s4

s5s9

s9

s6

s6

s12

s12

s8

s8

s14

s14

s17

s17 s16

s16

All but 3 steps included!

s5

s16


3. Add remaining steps to fused RR graphs3 + s16 – s11 = 0s6 + s10 – s3 = 0s3 + s13 – s8 = 0

3

s1 s2 s3 s15 s7 s18

s18s7 s15 s3 s2 s1s4

s5

s4

s9

s9

s6

s6

s12

s12

s8

s8

s14

s14

s17

s17 s16

s11

s11

s10 s10

s13s13


4. Balance the terminal nodes with the OR4

RR RR NetworkNetwork

RRRR enumerationenumerationFR1: s1 + s2 + s3 + s7 + s15 + s18 = OR

FR2: s1 + s2 + s7 + s11 + s15 + s17 = OR

FR3: s1 + s2 + s3 + s4 + s6 + s15 + s18 = OR

FR4: s1 + s2 + s3 + s5 + s8 + s15 + s18 = OR

FR5: s1 + s2 + s4 + s6 + s11 + s15 + s17 = OR

FR6: s1 + s2 + s3 + s4 + s12 + s15 + s17 = OR

FR7: s1 + s2 + s3 + s5 + s14 + s15 + s17 = OR

FR8: s1 + s2 + s3 + s7 + s15 + s16 + s17 = OR

FR9: s1 + s2 + s5 + s8 + s11 + s15 + s17 = OR

FR10: s1 + s2 + s7 + s8 – s13 + s15 + s18 = OR

FR250: s1 + s2 + s4 – s10 – 2s13 + 2s14 + s15 + 2s17 – s18 = OR

FR251: s1 + s2 + s5 + 2s10 + 2s12 + s13 + s15 – 2s16 + s18 = OR

FR252: s1 + s2 + s5 + 2s10 + 2s12 + s13 + s15 + 2s17 – s18 = OR

ER1: s4 + s6 – s7 = 0

ER2: s4 – s5 – s9 = 0

ER3: s5 – s7 + s8 = 0

ER4: s6 – s8 + s9 = 0

ER5: s3 – s6 – s10 = 0

ER6: s3 – s8 + s13 = 0

ER7: s3 – s11 + s16 = 0

ER8: s6 – s12 + s16 = 0

ER9: s8 – s14 + s16 = 0

ER10: s9 + s12 – s14 = 0

ER115: s5 – s7 + s9 – s10 + s11 + s17 – s18 = 0

ER116: s4 – s7 – s10 – s13 + s14 + s17 – s18 = 0

ER117: s5 – s7 + s10 + s12 + s13 + s17 – s18 = 0

Network ReductionNetwork Reduction

• Consider the effect of s18

Parallel PathwaysParallel Pathways

100

1010

1020s4+s6-s7

R4 + R6R7

100

1010

1020s5-s7+s8

R5 + R8R7

100

1010

1020s4-s5-s9

R5 + R9R4

100

1015

1030s3-s6-s10

R6 + R10R3

100

1020s3-s8+s13

R3 + R13R8

100

1020s6-s8+s9

R6 + R9R8

100

1010

1020s3-s11+s16

R3 + R16R11

100

1010

1020

s6-s12+s16

R6 + R16R12

100

1010

1020s8-s14+s16

R8 + R16R14

10-3

10-2

10-1

100s16+s17-s18

R16 + R17R18

273 473 673 873100

1015

1030s10-s11+s12

R10 + R12R11

273 473 673 873100

1010

1020s11+s13-s14

R11 + R13R14

273 473 673 873100

1010

1020s9+s12-s14

R9 + R12R14

273 473 673 873100

1015

1030s9-s10-s13

Res

ista

nce

(1/ra

te(s

-1))

R10 + R13R9

Temperature (K)

Complete MechanismComplete Mechanismw/ and w/o s18

273 373 473 573 673 773 8730

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Con

vers

ion

of C

O

Temperature (K)

Overall MechanismEquilibriumw/o s18

Network Reduction (1)Network Reduction (1)

• Consider the effect of s18

• Similarly, s10 and s13 are not kinetically significant, as indicated in previous studies*.

• Thus far, mechanism reduced to 15 steps previously considered*.

• Now…

*Fishtik, et al., J. Phys Chem. B 108 (2004), 5683.


CO2 inlet 0.00

H2 inlet 0.00

CO inlet 0.10

H2O inlet 0.10

Experimental ConditionsSpace time

1.80 s

Simulations based on energetics of Cu(111)

R1 R2 R3

R14 R5

R15 R17

R12

R8R16

R9R6

R11 R7

R4

AOR

(a)n1 n2 n3 n4

n5

n6

n7 n8

n9 n10

n3 to n6R3 + R16 vs. R11

n6 to n7R6 + R9 vs. R8

Parallel PathwaysParallel Pathways

100

1010

1020s4+s6-s7

R4 + R6R7

100

1010

1020s5-s7+s8

R5 + R8R7

100

1010

1020s4-s5-s9

R5 + R9R4

100

1015

1030s3-s6-s10

R6 + R10R3

100

1020s3-s8+s13

R3 + R13R8

100

1020s6-s8+s9

R6 + R9R8

100

1010

1020s3-s11+s16

R3 + R16R11

100

1010

1020

s6-s12+s16

R6 + R16R12

100

1010

1020s8-s14+s16

R8 + R16R14

10-3

10-2

10-1

100s16+s17-s18

R16 + R17R18

273 473 673 873100

1015

1030s10-s11+s12

R10 + R12R11

273 473 673 873100

1010

1020s11+s13-s14

R11 + R13R14

273 473 673 873100

1010

1020s9+s12-s14

R9 + R12R14

273 473 673 873100

1015

1030s9-s10-s13

Res

ista

nce

(1/ra

te(s

-1))

R10 + R13R9

Temperature (K)


CO2 inlet 0.00

H2 inlet 0.00

CO inlet 0.10

H2Oinlet 0.10

Experimental ConditionsSpace time

1.80 s


R1 R2 R3

R14 R5

R15 R17

R12

R8R16 R7

R4

AOR

(c)n1 n2 n3 n4

n5

n6

n7 n8

n9 n10

n4 to n7R8 + R16 vs. R14

COCO HH22OOs1 s2

s3

s5

s16

Formate RR

COCO22

s15

HH22

s17

s7

s12

ModifiedRedox RR

AssociativeRR

s8s4

C

C

O

H

H OH

C

O

OH

H

H

H H

H H

O O

C

O

O

C

O

O

CO O

H H C

O

O

s6

Redox RR

s4

H H

COCO HH22OOs1 s2

s3

s5

s16

Formate RR

COCO22

s15

HH22

s17

s7

s12

ModifiedRedox RR

AssociativeRR

s8s4

C

C

O

C

O

H

H OH

H OH

C

O

C

O

OH

HH

HH

HH HH

HH H

O OO O

C

O

C

O

C

O

O

C

O

OC

O

C

O

C

O

OO

CO O

CO OO O

HH HH C

O

C

O

C

O

O

s6

Redox RR

s4

H HHH H

WGSR Energy DiagramWGSR Energy Diagram

Based on energetics of Cu(111)

n1

Pote

ntia

l Ene

rgy

(kca

l/ mol

)

0

10

20

30

40

50

-10

-20

-30

-40

-50

Reaction Coordinate

s17s15

s12

s16

s4

s3s1

s2s5

s8

s7

n2

n3

n4 n7

n5 n6

n8

n9

n10

from the reduced RR network

Quasi Equilibrium & RDSQuasi Equilibrium & RDS


273 373 473 573 673 773 87310

-10

10-5

100

105

1010

1015

Temperature (K)

Res

ista

nce

(1/ra

te(s

-1))

R3

R15, R17

R2

R1

273 373 473 573 673 773 87310

-4

10-2

100

102

104

106

108

1010

1012

Temperature (K)

Res

ista

nce

(rat

e(s

-1))

R7(R5+R8)

R7+R5+R8

R16

Reduced Rate ExpressionReduced Rate Expression

rOR = r8 + r10 + r15

where

( )2

2

0 1/ 2H

1 H O 2 1/ 24 5

1

1 COP

K P K PK K

θ =

+ + +

(OHS is the QSS species.)

2

2

2 2 2

2

2

1/ 2H2 6 2 12 17 CO

3 2 H O 0 5 7 1 CO 12 1/216 17 4 2 12 17 CO 12 H CO H

1/ 2H3 4 2 12 17 CO

12 5 7 1 CO1/23 16 174 2 12 17 CO 12 H

( )( )

1

( )( )

OR

P k K K K Pk K P θ k k K P k

K K k K K K P k P P Pr

KPk k K K K Pk k k K P

K K Kk K K K P k P

⎡ ⎤+ +⎢ ⎥

+⎢ ⎥⎣ ⎦= −⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟+ + +

⎜ ⎟+⎢ ⎥⎝ ⎠⎣ ⎦

2H O COP P⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

Experimental ValidationExperimental Validation

Data Acquisition

Vent to Hood

ArAr

digital signaldigital signalmaterial flowmaterial flow

CO

MFC

CO

MFC

H2

MFC

H2

MFC

N2

MFC

N2

MFC

MFC Readout

Furnace

Packed Bed Reactor Condenser

Bypass

Data Acquisition

Gas Chromatograph

DI H2O

MFC

CO2

MFC

MFC

CO2

Syringe Pump

Vaporizing Section

Simulation of Microkinetic Model Simulation of Microkinetic Model for Cu(111)for Cu(111)

Experimental Conditions

Space time:

1.80 s

FEED:

COinlet = 0.10

H2Oinlet = 0.10

CO2 inlet = 0.00

H2 inlet = 0.00

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400 500 600

Temperature (oC)

Con

vers

ion

of C

O

Experiment

Equilibrium

Simplified Model

Simulation of Microkinetic Model Simulation of Microkinetic Model for Fe(110)for Fe(110)

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400 500 600Temperature (oC)

Con

vers

ion

of C

O

ExperimentFe15modelEquilibrium

FeExperimental Conditions

Space time:

1.34 s

FEED:

COinlet = 0.10

H2Oinlet = 0.10

CO2 inlet = 0.00

H2 inlet = 0.00

Simulation of Microkinetic Model Simulation of Microkinetic Model for Ni(111)for Ni(111)

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400 500 600

Temperature (oC)

Con

vers

ion

of C

O

Experiment

EquilibriumMicrokinetic Model

NiExperimental Conditions

Space time:

1.80 s

FEED:

COinlet = 0.11

H2Oinlet = 0.256

CO2 inlet = 0.068

H2 inlet = 0.256

ConclusionsConclusions• Reaction network analysis is a useful tool for

reduction, simplification and rationalization of the microkinetic model.

• A direct analogy between a reaction network and electrical network exists.

• This analogy allows the application of Kirchhoff’s Laws and mechanism reduction

• Application of the formalism to the WGS reaction confirmed the reduced model developed earlier based solely on a numerical RR analysis

• Reasonable comparison with experimental results

Future WorkFuture Work

The next stepsThe next steps……

• Elementary Reaction Kinetics– How can we improve the model?

• Reaction Route Graphs/Network Analysis– Where else can we apply the methodology?

• Experimental– What about methane production?

Elementary Reaction KineticsElementary Reaction KineticsReaction Energetics

• Transition State Complex identification• Activation Energies

– Ab Initio, semi-empirical methods• Pre-exponential factors

– Statistical Mechanics– Lund’s Methodology– Ab Initio

Elementary Reaction KineticsElementary Reaction KineticsStatistical Mechanics

Partition Function Parameters and Calculation Results (T = 190oC) [12,16]

Species H2 H·S H2O H2O·S O·S OH·S CO CO·S CO2 CO2·S HCOO·S m kg 3.32E-27 2.99E-26 4.65E-26 7.31E-26

ω? cm-1 1121 460 391 280 343 410 340

ω|| cm-1 928 48 508 49 24 31 36

ω cm-1 4405.3 1594.6 1600 670 2170 2089 1343 1343 760

3657.1 3370 667 667 1330

3755.8 745 2349 2349 1640

2910

1043

1377

1377

σ 2 2 1 2

B cm-1 60.8 1.93 0.39

IAIBIC kg3m6 5.77E-141

Ee kJ/mol -35 -40.7 -306 -359 -243 309.6 -132.2 -186.1 -359 -431 554

zt 3.34E+05 1.13E-02 9.03E+06 2.88E+01 2.53E-01 4.79E+01 1.75E+07 1.61E+02 3.45E+07 7.90E+01 7.21E+01 zv 1.06E-03 1.00E+00 8.37E-07 1.55E-04 1.00E+00 4.03E-01 3.43E-02 3.90E-02 1.33E-03 1.33E-03 1.09E-07 zr 2.65E+00 1.00E+00 8.30E+01 1.00E+00 1.00E+00 1.00E+00 1.67E+02 1.00E+00 4.12E+02 1.00E+00 1.00E+00 ze 8.86E+03 3.89E+04 3.25E+34 3.09E+40 2.55E+27 1.21E-35 8.13E+14 9.76E+20 4.08E+48 3.09E+40 3.29E-63 z 8.33E+06 4.41E+02 2.04E+37 1.38E+38 6.46E+26 2.33E-34 8.15E+22 6.11E+21 7.71E+55 3.24E+39 2.58E-68

Ref. Ovesen, et al. J. Catal. 1992, 134, 445; Ovesen, et al. J. Catal. 1996, 158, 170.

0AB

ABA S B S

expB B

B

zk T k T Sh z z h k⋅ ⋅

′′ ⎛ ⎞∆Λ = = ⎜ ⎟′′ ′′ ⎝ ⎠

‡‡

Elementary Reaction KineticsElementary Reaction KineticsLund’s Methodology

Lund, C., Ind. Eng. Chem. Res. 1996, 35, 2531.

( ) ( ), · , ,g gf i S f i trans iS S S∆ = ∆ −

( )

( )32

, 3

25 ln2g

gasi Btrans i gas

R Tm k TS R

h Pπ⎡ ⎤⎛ ⎞

⎢ ⎥⎜ ⎟= + ×⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

exp jj j

SR

⎛ ⎞∆Λ = Λ −⎜ ⎟⎜ ⎟

⎝ ⎠

Lund Dumesic Forward Reverse Forward Reverse

s1 1.00E+06 8.01E+16 1.50E+06 1.00E+14s2 1.00E+06 2.02E+14 1.00E+06 1.00E+14s3 1.00E+13 8.25E+12 1.00E+13 1.00E+13s4 1.00E+13 2.38E+13 1.00E+13 1.00E+13s5 1.00E+13 2.90E+12 1.00E+13 1.00E+13s6 1.00E+13 6.80E+13 1.00E+13 1.00E+13s7 1.00E+13 1.62E+14 1.00E+13 1.00E+13s8 1.00E+13 5.59E+14 1.00E+13 1.00E+13s9 1.00E+13 8.23E+13 1.00E+13 1.00E+13s10 1.00E+13 1.21E+12 1.00E+13 1.00E+13s11 1.00E+13 7.05E+12 1.00E+13 1.00E+13s12 1.00E+13 5.81E+13 1.00E+13 1.00E+13s13 1.00E+13 6.78E+14 1.00E+13 1.00E+13s14 1.00E+13 4.78E+14 1.00E+13 1.00E+13s15 1.00E+13 7.59E+03 4.00E+12 1.00E+06s16 1.00E+13 8.54E+12 1.00E+13 1.00E+13s17 1.00E+13 1.81E+04 6.00E+12 1.00E+06s18 1.00E+13 1.55E+04 6.00E+12 1.00E+06

ExperimentalExperimentalPrecious Metal Catalysts

PtPt PdPd

RhRh RuRu

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

600 650 700 750 800 850 900 950 1000

Temperature (K)

Con

vers

ion

of C

O, H

2

Feed 1, X(CO)

Feed 2, X(H2)

Feed 3, X(CO)

0

0.1

0.2

0.3

0.4

0.5

0.6

400 500 600 700 800 900 1000

Temperature (K)

Con

vers

ion

CO

, H2

Feed 1, X(CO)

Feed 2, X(H2)

Feed 3 X(CO)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

400 500 600 700 800 900 1000Temperature (K)

Con

vers

ion

of C

O, H

2

Feed 1, X(CO)

Feed 2, X(H2)

Feed 3, X(CO)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

600 650 700 750 800 850 900 950 1000

Temperature (K)

Con

vers

ion

of C

O,H

2

Feed 1, X(CO)

Feed 2, X(H2)

Feed 3, X(CO)

ExperimentalExperimentalMethanation

• The precious metal catalysts produced methane as a by-product of the WGS reaction…– Where did it come from?– How can we correct for

it?– Will a multiple OR RR

graph yield a model that will account for the production of CH4?

C + 2H2 CH4

CO2 + 4H2 CH4 + 2H2O

CO + 3H2 CH4 + H2O

2CO + 2H2 CO2 + CH4

CO2 + 2H2 C + 2H2O

CO + H2 C + H2O

2CO C + CO2

Possible Side Reactions of the WGS Reaction

Xue, E.; O'Keeffe, M. O.; Ross, J. R. H., Catal. Today 1996, 30, 107.

Reaction Route GraphsReaction Route GraphsMultiple OR Graphs

• Extension of RR graph theory to reaction mechanisms comprising multiple OR reactions– Steam Reforming Process:

CH4 + H2O CO + 3H2 (MSR)

CH4 + ½ O2 CO + 2 H2 (CPOX)

CO + H2O CO2 + H2 (WGS)

• How are the individual OR linked via their RRgraphs?

AcknowledgementsAcknowledgements

• Prof. Ravindra Datta, Advisor• Prof. Ilie Fishtik, Co-Advisor• Prof. Nikolas K. Kazantzis• Prof. Joseph D. Fehribach• Prof. Jennifer L. Wilcox• Dr. A. Alan Burke• Dr. Nikhil Jalani, Saurabh Vilekar, James Liu, Katherine Fay• Dr. Pyoungho Choi, Dr. Jingxin Zhang, Dr. Tony Thampan• Joe Kaupu, Sandy Natale, Jack Ferraro and Doug White• Students, Faculty and Staff of the Chemical Engineering Department• My family• …and everyone else I’ve met along the way!

• General Motors’ GM Fellowship• Office of Naval Research/University Laboratory Initiative Program

I would like to thank the following individuals for their assistance, support, guidance and inspiration during the time I have worked on this research.

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