1. Experimentation and Application of Reaction Route Graph Theory for Mechanistic and Kinetic Analysis of Fuel Reforming Reactions
Caitlin A. Callaghan, Ilie Fishtik, and Ravindra Datta
Fuel Cell Center
Chemical Engineering Department
Worcester Polytechnic Institute
Worcester, MA
Alan Burke, Maria Medeiros, and Louis Carreiro
Naval Undersea Warfare Center
Division Newport
Newport, RI

2. Introduction
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 Kirchhoff’s Laws
Example: the analysis of the WGS reaction mechanism*
* Callaghan, C. A., I. Fishtik, et al. (2003). "An improved microkinetic model for the water gas shift reaction on copper." Surf. Sci. 541: 21.

3. Reaction Route Graph Theory
Ref. Fishtik, I., C. A. Callaghan, et al. (2004). J. Phys. Chem. B 108:
Fishtik, I., C. A. Callaghan, et al. (2004). J. Phys. Chem. B 108:
Fishtik, I., C. A. Callaghan, et al. (2005). J. Phys. Chem. B 109:
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
Recently, we have developed a powerful new tool combining both graph theory and electrical network theory for mechanistic and kinetic interpretation.
Our RR graphs differ from the more familiar “Reaction Graphs” in that our branches represent the elementary reaction steps and the nodes represent the connectivity of those steps and comprise several species while the Reaction Graph represents each species as a node and their participation in reactions by the branches. Furthermore, our RRGT may be expanded to the case of more complex reaction mechanisms while the Reaction Graph is typically applied to mono-molecular reaction mechanisms.
This tool provides a methodology for analysis, reduction and simplification of reaction mechanisms. The enumeration of reaction routes is systematic; the dominant reaction routes are easily identified via the network analysis. The RDS, QSSA and MARI assumptions are no longer arbitrary, but based on rigorous De Donder affinity analyses and result in the derivation of explicit and accurate rate expressions based on those reaction routes which are shown to dominate the kinetics of the mechanism.

4. RR Graphs
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
A RR graph may be viewed as hikes through a mountain range. In this analogy, the valleys represent the energy levels of the reactants and products and a hike from one valley to an adjacent valley is representative of an elementary reaction step. Finally, we view the trek over a mountain pass as the energy barrier an elementary reaction step must overcome to proceed from reactants to products.

5. RR Graph Topology Full Routes (FRs): Empty Routes (ERs):
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
The RR graph is described in terms of four major characteristics: the Overall Reaction Routes, RRs in which the desired OR is produced; the Empty Reaction Routes, RRs in which a zero OR is produced (a cycle); the Intermediate Nodes, nodes in which only the elementary reaction steps are participants; and, finally, the Terminal Nodes, nodes in which, not only do the elementary reaction steps participate, but also the OR.

6. Electrical Analogy Kirchhoff’s Current Law Kirchhoff’s Voltage 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 a b c d e f g i h
The reduction of a mechanism is the result of the application of electrical network theory to the RR graph. In this analogy, we find that Kirchhoff’s Current Law corresponds to conservation of mass. That is, at any given node, the rates (which we associate with current) must sum to zero. Further, Kirchhoff’s Voltage Law is analogous to thermodynamic consistency (where the affinity, here in terms of dimensionless affinity, corresponds to voltage). In other words, in a cycle, the affinities must sum to zero. Finally, we view each elementary reaction step as a resistor and associate with it a resistance determined by Ohm’s Law as it corresponds to the De Donder relation.

7. The WGSR Mechanism On Cu(111) ADSORPTION DESORPTION
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.
water gas shift reaction

8. Constructing the RR Graph
Select the shortest MINIMAL FR 1 s1 s2
s14
s10 s3 s5 s5 s3
s10
s14 s2 s1
water gas shift reaction

9. Constructing the RR Graph2
Add the shortest MINIMAL ER to include all elementary reaction steps
s12 + s15 – s17 = 0
s4 + s11 – s17 = 0
s7 + s8 – s12 = 0
s7 + s9 – s10 = 0
s4 + s6 – s14 = 0
s4 + s9 – s15 = 0
s11
s17 s8
s12 s1 s2
s14
s10 s3 s5 s6 s7 s4 s9
Only s13 and s16 are left to be included
s15
s15 s7 s9 s4 s6 s5 s3
s10
s14 s2 s1 s8
s12
s17
s11
water gas shift reaction

10. Constructing the RR Graph
Add remaining steps to fused RR graph 3
s12 + s13 – s16 = 0
s13 – s14 + s15 = 0 
s11 
s17 s8
s12 s1 s2
s14
s10 s3 s5 s6 s7 s4 s9
s15
s16
s13
s13
s16
s15 s7 s9 s4 s6 s5 s3
s10
s14 s2 s1 s8
s12
s17
s11
water gas shift reaction

11. Constructing the RR Graph4
Balance the terminal nodes with the OR OR s1 s2
s14
s10 s3 s5
s13
s15
s11 s8 s6 s7
s16
s17 s9
s12
s12 s4 s4
s17 s9
s16 s7 s6 s8
s11
s15
s13 s5 s3
s10
s14 s2 s1 OR
water gas shift reaction

12. Microkinetics
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
water gas shift reaction

13. Resistance Comparisons
Experimental Conditions
Space time = 1.80 s
Feed: COinlet = 0.10
H2Oinlet = 0.10
CO2 inlet = 0.00
H2 inlet = 0.00
water gas shift reaction

14. Network Reduction

15. Reduced Rate Expression
Aoverall
Assume that OHS is the QSS species.
where
water gas shift reaction

16. Model vs. Experiment for WGS Reaction
Experimental Conditions
Space time = 1.80 s
FEED: COinlet = 0.10
H2Oinlet = 0.10
CO2 inlet = 0.00
H2 inlet = 0.00
water gas shift reaction

17. Energy Diagram

18. ULI Objectives
Elucidate the mechanism and kinetics of logistics fuel processing using a building block approach (i.e. CH4, C2H6 …, JP-8)
In first 1-2 years, utilize theoretical and experimental research to methodically investigate reforming of methane on various catalysts
CH4 + H2O  CO + 3H2 (MSR)
CH4 + ½ O2  CO + 2 H2 (CPOX)
CO + H2O  CO2 + H2 (WGS)

19. Experimental Approach
Catalysts of interest: Ni, Cu, Ru, Pt, CeO2, and commercially available catalysts for steam and autothermal reformation
Both integral and differential experiments used to study kinetics (Tmax ≈ 800 oC)
WPI: (External reforming)
Test in-house fabricated catalysts
Methane steam and autothermal reformation reactions
NUWC: (Internal & External reforming)
Apparatus available at NUWC for internal reforming with SOFC button cell tests
Commercial catalyst testing – external steam and autothermal reforming of methane

20. MSR/WGSR Apparatus

21. Objective Tasks
Theoretical Work

22. Objective Tasks
Experimental Work

23. Benefits to the Navy
Extend fundamental understanding of reaction mechanisms involved in logistics fuel reforming reactions
Gather data on air-independent autothermal fuel reformation with commercially available catalysts
Develop new catalytic solutions for undersea fuel processing
Develop relationship between ONR and WPI