Visualization, reduction and simplification of a water gas shift mechanism through the application of reaction route graphs

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Visualization, reduction and simplification of a
water gas shift mechanism through the application
of reaction route graphs

• CA Callaghan, I Fishtik, and R Datta
• Fuel Cell Center
• Department of Chemical Engineering
• Worcester Polytechnic Institute
• Worcester, MA 01609-2280, USA

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Introduction and Motivation

• Predicted elementary kinetics can provide
  reliable microkinetic models.
• Reaction network analysis, developed by us, is a
  useful tool for reduction, simplification and
  rationalization of the microkinetic model.
• Analogy between a reaction network and electrical
  network exists and provides a useful
  interpretation of kinetics and mechanism via
  Kirchhoffs Laws
• Example the analysis of the WGS reaction
  mechanism

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What are Reaction Route Graphs?
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.

• 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

Stop
Start

• 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

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The electrical analogy

• Kirchhoffs Current Law
• Analogous to conservation of mass
• Kirchhoffs Voltage Law
• Analogous to thermodynamic consistency
• Ohms Law
• Viewed in terms of the De Donder Relation

a
b
e
c
d
f
g
i
h
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Defining the RR graph topology

• Full Routes (FRs)
• a RR in which the desired OR is produced
• Empty Routes (ERs)
• a RR in which a zero OR is produced (a cycle)
• Intermediate Nodes (INs)
• a node including ONLY the elementary reaction
  steps
• Terminal Nodes (TNs)
• a node including the OR in addition to the
  elementary reaction steps

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EXAMPLE the WGSR mechanism
On Cu(111)
Adsorption of CO Adsorption of H2O Desorption of
CO2 Desorption of H2
a - activation energies in kcal/mol (? ? 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.
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Topological characteristics

• Full Reaction Routes
• FR1 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

Empty Reaction Routes ER1 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 Nodes IN1 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 Nodes TN1 -s9 - s10 - s11 s13 - s15
- s16 - s17 OR TN2 s8 - s11 - s12 - s16 - s17
OR TN3 -s7 - s10 - s11 - s12 - s16 - s17
OR TN4 s6 s13 s14 - s16 OR TN5 -s5 OR
Example the water gas shift reaction
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Constructing the RR Graph

1. Select the shortest MINIMAL FR

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s1
s2
s14
s10
s3
s5
s5
s3
s10
s14
s2
s1
Example the water gas shift reaction
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Constructing the RR Graph

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

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s4 s6 s14 0
s7 s9 s10 0
s4 s11 s17 0
s4 s9 s15 0
s12 s15 s17 0
s7 s8 s12 0
s11
s17
s8
s12
s1
s2
s14
s10
s3
s5
s6
s7
s9
s4
Only s13 and s16 are left to be included
s15
s15
s6
s4
s9
s7
s5
s3
s10
s14
s2
s1
s12
s8
s17
s11
Example the water gas shift reaction
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Constructing the RR Graph

1. Add remaining steps to fused RR graph

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s12 s13 s16 0 s13 s14 s15 0
?
s11
?
s17
s8
s12
s1
s2
s14
s10
s3
s5
s6
s7
s9
s4
s15
s16
s13
s13
s16
s15
s6
s4
s9
s7
s5
s3
s10
s14
s2
s1
s12
s8
s17
s11
Example the water gas shift reaction
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Constructing the RR Graph

1. Balance the terminal nodes with the OR

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OR
s1
s2
s14
s10
s3
s5
s15
s11
s13
s8
s6
s7
s17
s9
s16
s12
s12
s4
s4
s17
s9
s16
s7
s6
s11
s8
s15
s13
s5
s3
s10
s14
s2
s1
OR
Example the water gas shift reaction
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Analysis, reduction and simplification

• We may eliminate s13 and s16 from the RR graph
  they are not kinetically significant steps
• This results in TWO symmetric sub-graphs we only
  need one

Example the water gas shift reaction
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Analysis, reduction and simplification
Experimental Conditions Space time 1.80
s FEED COinlet 0.10 H2Oinlet 0.10 CO2
inlet 0.00 H2 inlet 0.00
Example the water gas shift reaction
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Analysis, reduction and simplification
Experimental Conditions Space time 1.80
s FEED COinlet 0.10 H2Oinlet 0.10 CO2
inlet 0.00 H2 inlet 0.00
Example the water gas shift reaction
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Analysis, reduction and simplification
Experimental Conditions Space time 1.80
s FEED COinlet 0.10 H2Oinlet 0.10 CO2
inlet 0.00 H2 inlet 0.00
Example the water gas shift reaction
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Analysis, reduction and simplification
Modified Redox
Formate
Associative
Rate determining steps? s6 H2OS S ? OHS
HS s7 COS OS ? CO2S S s8 COS OHS ?
HCOOS S s10 COS OHS ? CO2S HS s11
HCOOS S ? CO2S HS s15 OHS HS ? OS H2S
Experimental Conditions Space time 1.80
s FEED COinlet 0.10 H2Oinlet 0.10 CO2
inlet 0.00 H2 inlet 0.00
Example the water gas shift reaction
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The reduced rate expression
where
OHS is the QSS species
Experimental Conditions Space time 1.80
s FEED COinlet 0.10 H2Oinlet 0.10 CO2
inlet 0.00 H2 inlet 0.00
Example the water gas shift reaction
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Energy diagram
Example the water gas shift reaction
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General conclusions

• Reaction network analysis is a useful tool for
  reduction, simplification and rationalization of
  the microkinetic model.
• Allows for a more systematic approach for the
  analysis of microkinetic mechanisms.
• Analogy between a reaction network and electrical
  network exists
• rate current
• affinity voltage
• resistance affinity/rate.
• Reaction stoichiometry translates into the
  network connectivity (i.e. IN, TN)
• Application of RR graph theory to the analysis of
  the WGS reaction mechanism validated the reduced
  model and confirmed earlier results based solely
  on a conventional microkinetic analysis.

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