CA Callaghan , I Fishtik, and R Datta Fuel Cell Center Department of Chemical Engineering

1. 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

2. 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 Kirchhoff’s Laws • Example: the analysis of the WGS reaction mechanism

3. What are Reaction Route Graphs? Ref. Fishtik, I., C. A. Callaghan, et al. (2004). J. Phys. Chem. B108: 5671-5682. Fishtik, I., C. A. Callaghan, et al. (2004). J. Phys. Chem. B108: 5683-5697. Fishtik, I., C. A. Callaghan, et al. (2005). J. Phys. Chem. B109: 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

4. The electrical analogy • Kirchhoff’s Current 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 e c d f g i h

5. 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

6. 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 (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.

7. 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

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

9. Constructing the RR Graph • Add the shortest MINIMAL ER to include all elementary reaction steps 2 s4 + s11 – s17 = 0 s12 + s15 – s17 = 0 s7 + s8 – s12 = 0 s4 + s6 – s14 = 0 s4 + s9 – s15 = 0 s7 + s9 – s10 = 0 s11 s17 s8 s12 s1 s2 s14 s10 s3 s5 s6 s7 s9 s4 Only s13 and s16are left to be included s15 s15 s7 s9 s4 s6 s5 s3 s10 s14 s2 s1 s12 s8 s17 s11 Example: the 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 s9 s4 s15 s16 s13 s13 s16 s15 s7 s9 s4 s6 s5 s3 s10 s14 s2 s1 s12 s8 s17 s11 Example: the water gas shift reaction

11. Constructing the RR Graph • Balance the terminal nodes with the OR 4 OR s1 s2 s14 s10 s3 s5 s15 s13 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 Example: the water gas shift reaction

12. Analysis, reduction and simplification • We may eliminate s13and 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

13. R4 + R6 vs. R14 Effect of R14 on Conversion 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

14. Effect of R17 on Conversion R4 + R11 vs. R17 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

15. R9 + R12 vs. R11 Effect of R9 and R12 on Conversion 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

16. 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

17. 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

18. Energy diagram Example: the water gas shift reaction

19. 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.