visualization, reduction and simplification of a water gas shift mechanism through the application...

Visualization, reduction and Visualization, reduction and simplification of simplification of

a water gas shift mechanism a water gas shift mechanism through the application of through the application of

reaction route graphsreaction route graphs

CA CallaghanCA Callaghan, I Fishtik, and R Datta, I Fishtik, and R Datta

Fuel Cell CenterFuel Cell CenterDepartment of Chemical Engineering Department of Chemical Engineering

Worcester Polytechnic InstituteWorcester Polytechnic InstituteWorcester, MA 01609-2280, USAWorcester, MA 01609-2280, USA

22

Introduction and Introduction and MotivationMotivation

Predicted elementary kineticsPredicted elementary kinetics can provide r can provide reliable eliable microkinetic models.microkinetic models.

Reaction network analysis, developed by us, is a Reaction network analysis, developed by us, is a useful tool for reduction, simplification and useful tool for reduction, simplification and rationalization of the microkinetic model.rationalization of the microkinetic model.

Analogy between a reaction network and electrical Analogy between a reaction network and electrical network exists and provides a useful interpretation of network exists and provides a useful interpretation of kinetics and mechanism via Kirchhoff’s Lawskinetics and mechanism via Kirchhoff’s Laws

Example: the analysis of the WGS reaction Example: the analysis of the WGS reaction mechanismmechanism

33

What are Reaction Route What are Reaction Route Graphs?Graphs?

“RRgraph” 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.

A RR graph may be viewed as several hikes through a mountain range:– Valleys are the energy levels of

reactants and products– Elementary reaction is a hike from

one valley to adjacent valley– Trek over a mountain pass

represents overcoming the energy barrier

44

The electrical analogyThe electrical analogy

Kirchhoff’s Current LawKirchhoff’s Current Law– Analogous to Analogous to conservation of massconservation of mass

Kirchhoff’s Voltage LawKirchhoff’s Voltage Law– Analogous to Analogous to thermodynamic consistencythermodynamic consistency

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

ab

c

d

ea b c d e 0r r r r r

f g h i 0 A + A A Af g

i h

Rr

A=

55

Defining the RR graph Defining the RR graph topologytopology

FFull ull RRoutes (outes (FRFRs):s):– a a RRRR in which the desired in which the desired OROR is produced is produced

EEmpty mpty RRoutes (outes (ERERs):s):– a a RRRR in which a zero in which a zero OROR is produced (a cycle) is produced (a cycle)

IIntermediate ntermediate NNodes (odes (ININs):s):– a node including ONLY the elementary reaction stepsa node including ONLY the elementary reaction steps

TTerminal erminal NNodes (odes (TNTNs):s):– a node including the a node including the OROR in addition to the elementary in addition to the elementary

reaction steps reaction steps

66

EXAMPLE: the WGSR EXAMPLE: the WGSR mechanismmechanism

Adsorption of COAdsorption of H2ODesorption of CO2

Desorption of H2

E

A

Elementary Reactions EI

AI

ΔH

s1: 0 106 CO + S COS 12.0 1014 -12.0 a,b s2: 0 106 H2O + S H2OS 13.6 1014 -13.6 a,b s3: 5.3 4 1012 CO2S CO2 + S 0 106 5.3 a,b s4: 15.3 1013 HS + HS H2S + S 12.8 1013 2.5 a s5: 5.5 6 1012 H2S H2 + S 0 106 5.5 a,b s6: 25.4 1013 H2OS + S OHS + HS 1.6 1013 23.8 a s7: 10.7 1013 COS + OS CO2S + S 28.0 1013 -17.3 a s8: 0 1013 COS + OHS HCOOS + S 20.4 1013 -20.4 a s9: 15.5 1013 OHS + S OS + HS 20.7 1013 -5.2 a s10: 0 1013 COS + OHS CO2S + HS 22.5 1013 -22.5 a s11: 1.4 1013 HCOOS + S CO2S + HS 3.5 1013 -2.1 a

s12: 4.0 1013 HCOOS + OS CO2S + OHS 0.9 1013 3.1 a

s13: 29.0 1013 H2OS + OS 2OHS 0 1013 29.0 a s14 : 26.3 1013 H2OS + HS OHS + H2S 0 1013 26.3 a s15 : 1.3 1013 OHS + HS OS + H2S 4.0 1013 -2.7 a s16: 0.9 1013 HCOOS + OHS CO2S + H2OS 26.8 1013 -25.9 a

s17: 14.6 1013 HCOOS + HS CO2S + H2S 14.2 1013 0.4 a a - activation energies in kcal/mol (θ 0 limit) estimated according to Shustorovich & Sellers (1998) and coinciding with the estimations made in Ovesen, et al. (1996); pre-exponential factors from Dumesic, et al. (1993).

b – pre-exponential factors adjusted so as to fit the thermodynamics of the overall reaction; The units of the pre-exponential factors are Pa-1s-1 for adsorption/desorption reactions and s-1 for surface reactions.

On Cu(111)

77

Topological characteristicsTopological characteristics

Full Reaction RoutesFull Reaction RoutesFR1: OR = s1 + s2 + s3 + s4 + s5 + s6 + s10

FR2: OR = s1 + s2 + s3 + s4 + s5 + s6 + s7 + s9

FR3: OR = s1 + s2 + s3 + s4 + s5 + s6 + s8 + s11

FR4: OR = s1 + s2 + s3 + s5 + s6 + s7 + s15

FR5: OR = s1 + s2 + s3 + s5 + s6 + s7 + s9 - s11 + s17

Example: the water gas shift reaction

Empty Reaction RoutesEmpty Reaction RoutesER1: 0 = -s4 - s6 + s14

ER2: 0 = -s4 - s9 + s15

ER3: 0 = -s8 + s10 - s11

ER4: 0 = -s4 - s11 + s12 + s15

ER5: 0 = -s4 + s8 - s10 + s17

Intermediate NodesIntermediate NodesIN1: r2 - r6 - r13 - r14 + r16

IN2: r1 - r7 - r8 - r10

IN3: -r3 + r7 + r10 + r11 + r12 + r16 +r17

IN4: r4 - r5 + r14 + r15 + r17

IN5: r6 - r8 - r9 - r10 + r12 + 2r13 + r14 - r15 - r16

Terminal NodesTerminal NodesTNTN11: -: -ss9 9 - - ss1010 - - ss1111 + + ss1313 - - ss1515 - - ss1616 - - ss1717 + OR + OR

TNTN22: : ss88 - - ss1111 - - ss1212 - - ss1616 - - ss1717 + OR + OR

TNTN33: -: -ss7 7 - - ss1010 - - ss1111 - - ss1212 - - ss1616 - - ss1717 + OR + OR

TNTN44: : ss66 + + ss1313 + + ss1414 - - ss1616 + OR + OR

TNTN55: -: -ss55 + OR + OR

88

Constructing the RR GraphConstructing the RR Graph

1.1. Select the Select the shortest MINIMALshortest MINIMAL FR FR

OR = s1+s2+s3+s5+s10+s14

s1 s2 s14 s10 s3 s5

s5 s3 s10 s14 s2 s1

1


99


2.2. Add the Add the shortest MINIMAL ERshortest MINIMAL ER to to include all elementary reaction include all elementary reaction stepssteps

s1 s2 s14 s10 s3 s5

s5 s3 s10 s14 s2 s1

s4 + s6 – s14 = 0

s17 s12

s12 s17

s15

s15

s6

s6

s4

s4

s9

s9

s7

s8

s7

s8s11

s11

s7 + s9 – s10 = 0s4 + s11 – s17 = 0s4 + s9 – s15 = 0s12 + s15 – s17 = 0s7 + s8 – s12 = 0

Only s13 and s16

are left to be included

2


1010


3.3. Add remaining steps to fused RR Add remaining steps to fused RR graphgraph

s1 s2 s14 s10 s3 s5

s5 s3 s10 s14 s2 s1

s17 s12

s12 s17

s15

s15

s6

s6

s4

s4

s9

s9

s7

s8

s7

s8s11

s11

s12 + s13 – s16 = 0s13 – s14 + s15 = 0

s13s13s16

s16

3


1111


4.4. Balance the terminal nodes with Balance the terminal nodes with the ORthe ORs1 s2 s14 s10 s3 s5

s5 s3 s10 s14 s2 s1

s17

s12s12

s17

s15

s15

s6

s6

s4 s4

s9

s9s7

s8

s7

s11s8

s11

s13

s13

s16

s16

OR

OR

4


1212

Analysis, reduction and Analysis, reduction and simplificationsimplification

We may eliminate We may eliminate ss1313 and and ss1616 from from the RR graph; they are the RR graph; they are not not kinetically significantkinetically significant steps steps

This results in This results in TWOTWO symmetric sub- symmetric sub-graphs; we only need onegraphs; we only need one


R1 R2 R6

R17 R8

R3 R5

R15

R11R4

R12R9

R14 R10

R7

AOR

1313


Experimental Conditions: Space time = 1.80 sFEED: COinlet = 0.10; H2Oinlet = 0.10

CO2 inlet = 0.00; H2 inlet = 0.00

273 373 473 573 673 773 87310

-5

100

105

1010

1015

Temperature (K)

Re

sis

tan

ce

(ra

te-1

)

R14

R4 + R6

R4 + R6 vs. R14


273 373 473 573 673 773 8730

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Co

nv

ers

ion

of

CO

Temperature (K)

Complete MechanismMechanism without s

14

Effect of R14 on Conversion

R1 R2 R6

R17 R8

R3 R5

R15

R11R4

R12R9

R14 R10

R7

AOR

1414




CO2 inlet = 0.00; H2 inlet = 0.00

273 373 473 573 673 773 87310

-5

100

105

1010

1015

1020

1025

Temperature (K)

Re

sis

tan

ce

(ra

te-1

)

R17

R4 + R11

R4 + R11 vs. R17

273 373 473 573 673 773 8730

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Co

nv

ers

ion

of

CO

Temperature (K)


17

Effect of R17 on Conversion

R1 R2 R6

R17 R8

R3 R5

R15

R11R4

R12R9

R10

R7

AOR

1515




CO2 inlet = 0.00; H2 inlet = 0.00

273 373 473 573 673 773 87310

-5

100

105

1010

1015

1020

1025

Temperature (K)

Re

sis

tan

ce

(ra

te-1

)

R11

R9 + R12

R9 + R12 vs. R11

273 373 473 573 673 773 8730

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Co

nv

ers

ion

of

CO

Temperature (K)


9 and s

12

Effect of R9 and R12 on Conversion

R1 R2 R6

R8

R3 R5

R15

R11R4

R12R9

R10

R7

AOR

1616




CO2 inlet = 0.00; H2 inlet = 0.00

R1 R2 R6

R8

R3 R5

R15

R11R4 R10

R7

AOR

273 373 473 573 673 773 873-15

-10

-5

0

5

10

15

20

25

Re

sis

tan

ce

(1

/ra

te(s

-1))

Temperature (K)

R1R

2R

3R

5R

6

Rate determining steps?s6: H2OS + S OHS + HSs7: COS + OS CO2S + Ss8: COS + OHS HCOOS + Ss10: COS + OHS CO2S + HSs11: HCOOS + S CO2S + HSs15 : OHS + HS OS + H2S

Modified Redox

Associative

Formate

1717

The reduced rate The reduced rate expressionexpression

2 22 2

22

1/ 22 1/ 26 1 H O 0 8 10 2 15 H 4 5 CO H

OR 1/ 2H O CO6 6 15 H

8 10 2 CO1/ 24 5

1COk K P θ k k K P k P K K P P

rKP Pk K k P

k k K PK K

where

2

2

0 1/ 2H

1 H O 2 1/ 24 5

1

1 CO

PK P K P

K K

OHS is the QSS

species



CO2 inlet = 0.00; H2 inlet = 0.00

R6

R10

R15

R8R11

R7

AOR

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

Co

nv

ers

ion

of

CO

Temperature (K)

EquilibriumSimplified MechanismExperiment

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

Co

nv

ers

ion

of

CO

Temperature (K)

RRoverall

RRassociative

RRformate

RRmodredox

Equilibrium

1818

Energy diagramEnergy diagram


n1

Pot

e nti

a l E

ner

g y (

kca

l/ mo l

)

0

10

20

30

40

50

-10

-20

-30

-40

-50

Reaction Coordinate

s5s3

s15

s4

s7

s6s1

s2

s8

s11

s10

n2

n3

n4 n7

n5 n6

n8

n9

n10

1919

General conclusionsGeneral conclusions Reaction network analysis is a useful tool for reduction, Reaction network analysis is a useful tool for reduction,

simplification and rationalization of the microkinetic model.simplification and rationalization of the microkinetic model.– Allows for a more systematic approach for the analysis of Allows for a more systematic approach for the analysis of

microkinetic mechanisms.microkinetic mechanisms.

Analogy between a reaction network and electrical network Analogy between a reaction network and electrical network exists: exists: – rate = current rate = current – affinity = voltageaffinity = voltage– resistance = affinity/rate.resistance = affinity/rate.

Reaction stoichiometry translates into the network connectivity Reaction stoichiometry translates into the network connectivity (i.e. IN, TN)(i.e. IN, TN)

Application of RR graph theory to the analysis of the WGS Application of RR graph theory to the analysis of the WGS reaction mechanism validated the reduced model and confirmed reaction mechanism validated the reduced model and confirmed earlier resultsearlier results** based solely on a conventional microkinetic based solely on a conventional microkinetic analysis.analysis.

* Callaghan, C. A., I. Fishtik, et al. (2003). Surf. Sci. 541: 21.

visualization, reduction and simplification of a water gas shift mechanism through the application...

Documents

kirchhoff s laws example

reaction graphs

reaction routes fr

overall reaction

reaction network analysis

reaction routes er

products elementary

wgs reaction mechanism