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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

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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.

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**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.

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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.

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**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.

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**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.

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**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

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**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

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**Constructing the RR Graph**

2 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

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**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

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**Constructing the RR Graph**

4 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

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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

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**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

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Network Reduction

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**Reduced Rate Expression**

Aoverall Assume that OHS is the QSS species. where water gas shift reaction

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**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

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Energy Diagram

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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)

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**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

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MSR/WGSR Apparatus

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Objective Tasks Theoretical Work

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Objective Tasks Experimental Work

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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

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