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 , 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?   “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: 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:  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 c d e fg ih

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 Adsorption of CO Adsorption of H 2 O Desorption of CO 2 Desorption of H 2 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 -1 s -1 for adsorption/desorption reactions and s -1 for surface reactions. On Cu(111)

7 Topological characteristics Full Reaction Routes FR 1 : OR = s 1 + s 2 + s 3 + s 4 + s 5 + s 6 + s 10 FR 2 : OR = s 1 + s 2 + s 3 + s 4 + s 5 + s 6 + s 7 + s 9 FR 3 : OR = s 1 + s 2 + s 3 + s 4 + s 5 + s 6 + s 8 + s 11 FR 4 : OR = s 1 + s 2 + s 3 + s 5 + s 6 + s 7 + s 15 FR 5 : OR = s 1 + s 2 + s 3 + s 5 + s 6 + s 7 + s 9 - s 11 + s 17 Example: the water gas shift reaction Empty Reaction Routes ER 1 : 0 = -s 4 - s 6 + s 14 ER 2 : 0 = -s 4 - s 9 + s 15 ER 3 : 0 = -s 8 + s 10 - s 11 ER 4 : 0 = -s 4 - s 11 + s 12 + s 15 ER 5 : 0 = -s 4 + s 8 - s 10 + s 17 Intermediate Nodes IN 1 : r 2 - r 6 - r 13 - r 14 + r 16 IN 2 : r 1 - r 7 - r 8 - r 10 IN 3 : -r 3 + r 7 + r 10 + r 11 + r 12 + r 16 +r 17 IN 4 : r 4 - r 5 + r 14 + r 15 + r 17 IN 5 : r 6 - r 8 - r 9 - r 10 + r r 13 + r 14 - r 15 - r 16 Terminal Nodes TN 1 : -s 9 - s 10 - s 11 + s 13 - s 15 - s 16 - s 17 + OR TN 2 : s 8 - s 11 - s 12 - s 16 - s 17 + OR TN 3 : -s 7 - s 10 - s 11 - s 12 - s 16 - s 17 + OR TN 4 : s 6 + s 13 + s 14 - s 16 + OR TN 5 : -s 5 + OR

8 Constructing the RR Graph 1. Select the shortest MINIMAL FR s1s1 s2s2 s 14 s 10 s3s3 s5s5 s5s5 s3s3 s 14 s2s2 s1s1 1 Example: the water gas shift reaction

9 Constructing the RR Graph 2. Add the shortest MINIMAL ER to include all elementary reaction steps s1s1 s2s2 s 14 s 10 s3s3 s5s5 s5s5 s3s3 s 14 s2s2 s1s1 s 4 + s 6 – s 14 = 0 s 17 s 12 s 17 s 15 s6s6 s6s6 s4s4 s4s4 s9s9 s9s9 s7s7 s8s8 s7s7 s8s8 s 11 s 7 + s 9 – s 10 = 0s 4 + s 11 – s 17 = 0s 4 + s 9 – s 15 = 0s 12 + s 15 – s 17 = 0s 7 + s 8 – s 12 = 0 Only s 13 and s 16 are left to be included 2 Example: the water gas shift reaction

10 Constructing the RR Graph 3. Add remaining steps to fused RR graph s1s1 s2s2 s 14 s 10 s3s3 s5s5 s5s5 s3s3 s 14 s2s2 s1s1 s 17 s 12 s 17 s 15 s6s6 s6s6 s4s4 s4s4 s9s9 s9s9 s7s7 s8s8 s7s7 s8s8 s 11 s 12 + s 13 – s 16 = 0 s 13 – s 14 + s 15 = 0 s 13 s 16 3 Example: the water gas shift reaction

11 Constructing the RR Graph 4. Balance the terminal nodes with the OR s1s1 s2s2 s 14 s 10 s3s3 s5s5 s5s5 s3s3 s 14 s2s2 s1s1 s 17 s 12 s 17 s 15 s6s6 s6s6 s4s4 s4s4 s9s9 s9s9 s7s7 s8s8 s7s7 s 11 s8s8 s 13 s 16 OR 4 Example: the water gas shift reaction

12 Analysis, reduction and simplification  We may eliminate s 13 and s 16 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 Analysis, reduction and simplification Experimental Conditions: Space time = 1.80 s FEED:CO inlet = 0.10; H 2 O inlet = 0.10 CO 2 inlet = 0.00;H 2 inlet = 0.00 R 4 + R 6 vs. R 14 Example: the water gas shift reaction Effect of R 14 on Conversion

14 Analysis, reduction and simplification Example: the water gas shift reaction Experimental Conditions: Space time = 1.80 s FEED:CO inlet = 0.10; H 2 O inlet = 0.10 CO 2 inlet = 0.00;H 2 inlet = 0.00 R 4 + R 11 vs. R 17 Effect of R 17 on Conversion

15 Analysis, reduction and simplification Example: the water gas shift reaction Experimental Conditions: Space time = 1.80 s FEED:CO inlet = 0.10; H 2 O inlet = 0.10 CO 2 inlet = 0.00;H 2 inlet = 0.00 R 9 + R 12 vs. R 11 Effect of R 9 and R 12 on Conversion

16 Analysis, reduction and simplification Example: the water gas shift reaction Experimental Conditions: Space time = 1.80 s FEED:CO inlet = 0.10; H 2 O inlet = 0.10 CO 2 inlet = 0.00;H 2 inlet = 0.00 Rate determining steps? s 6: H 2 OS + S  OHS + HS s 7 : COS + OS  CO 2 S + S s 8 : COS + OHS  HCOOS + S s 10 : COS + OHS  CO 2 S + HS s 11 : HCOOS + S  CO 2 S + HS s 15 : OHS + HS  OS + H 2 S Modified Redox Associative Formate

17 The reduced rate expression where OHS is the QSS species Example: the water gas shift reaction Experimental Conditions: Space time = 1.80 s FEED:CO inlet = 0.10; H 2 O inlet = 0.10 CO 2 inlet = 0.00;H 2 inlet = 0.00

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. 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: 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) 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. 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.