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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
Example: the water gas shift reaction
99
Constructing the RR GraphConstructing the RR Graph
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
Example: the water gas shift reaction
1010
Constructing the RR GraphConstructing the RR Graph
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
Example: the water gas shift reaction
1111
Constructing the RR GraphConstructing the RR Graph
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
Example: the water gas shift reaction
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
Example: the water gas shift reaction
R1 R2 R6
R17 R8
R3 R5
R15
R11R4
R12R9
R14 R10
R7
AOR
1313
Analysis, reduction and Analysis, reduction and simplificationsimplification
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
Example: the water gas shift reaction
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
Analysis, reduction and Analysis, reduction and simplificationsimplification
Example: the water gas shift reaction
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
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)
Complete MechanismMechanism without s
17
Effect of R17 on Conversion
R1 R2 R6
R17 R8
R3 R5
R15
R11R4
R12R9
R10
R7
AOR
1515
Analysis, reduction and Analysis, reduction and simplificationsimplification
Example: the water gas shift reaction
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
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)
Complete MechanismMechanism without s
9 and s
12
Effect of R9 and R12 on Conversion
R1 R2 R6
R8
R3 R5
R15
R11R4
R12R9
R10
R7
AOR
1616
Analysis, reduction and Analysis, reduction and simplificationsimplification
Example: the water gas shift reaction
Experimental Conditions: Space time = 1.80 sFEED: COinlet = 0.10; H2Oinlet = 0.10
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
Example: the water gas shift reaction
Experimental Conditions: Space time = 1.80 sFEED: COinlet = 0.10; H2Oinlet = 0.10
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
Example: the water gas shift reaction
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.