Application of reaction route graphs to microkinetic analysis and design of water-gas-shift catalysts Fuel Cell Center Chemical Engineering Department Worcester Polytechnic Institute Worcester, MA Caitlin A. Callaghan, Ilie Fishtik and Ravindra Datta

Introduction  First principles calculations are becoming indispensable  Molecular rearrangements on surfaces can be “seen”  Reaction energetic calculations are becoming more reliable  Microkinetic models are becoming increasingly available  What more can be done?

LHHW Approach  Rate expressions derived based on RDS, QE, QSSA, MARI  Fitted to data  Basic mechanism and assumptions are generally arbitrary Microkinetic Approach  Involves elementary reaction kinetics  No simplifying assumptions made  Arbitrary mechanism  Substantial computational effort is required  Opaque Kinetics

Reaction Route Graph Theory  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

RR Graphs A RR graph may be viewed as hikes through a mountain range: –Valleys are the energy levels of reactants and products –Elementary reaction is hike from one valley to adjacent valley –Trek over a mountain pass represents overcoming the energy barrier

RR Graph Topology  Overall Reaction Routes (ORRs): –a RR in which the desired OR is produced  Empty Reaction Routes (ERRs): –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

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

The WGSR Mechanism 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)

Constructing the RR Graph 1.Select the shortest MINIMAL ORR s1s1 s2s2 s 14 s 10 s3s3 s5s5 s5s5 s3s3 s 14 s2s2 s1s1 OR = s 1 + s 2 + s 3 + s 5 + s 10 + s 14

Constructing the RR Graph 2.Add the shortest MINIMAL ERR 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

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 13 – s 14 + s 15 = 0 s 12 + s 13 – s 16 = 0 s 13 s 16

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 s9s9 s9s9 s7s7 s8s8 s7s7 s 11 s8s8 s 13 s 16 OR s4s4 s4s4

Microkinetics  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 A overall R1R1 R2R2 R 14 R 10 R5R5 R3R3 R8R8 R 11 R6R6 R 17 R 12 R7R7 R9R9 n2n2 n4n4 n3n3 n5n5 n6n6 n7n7 R 15 R4R4 n1n1 n8n8 + –

Network Reduction 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 A overall R1R1 R2R2 R 14 R 10 R5R5 R3R3 R8R8 R 11 R6R6 R 17 R 12 R7R7 R9R9 n2n2 n4n4 n3n3 n5n5 n6n6 n7n7 R 15 R4R4 n1n1 n8n8 + – R 4 + R 6 vs. R 14

Network Reduction 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

Network Reduction 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 Effect of R 14 on Conversion

Network Reduction A overall R1R1 R2R2 R 10 R5R5 R3R3 R8R8 R 11 R6R6 R 17 R 12 R7R7 R9R9 n2n2 n4n4 n3n3 n5n5 n6n6 n7n7 R 15 R4R4 n1n1 n8n8 + – R 4 + R 11 vs. R 17 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

Network Reduction R 4 + R 11 vs. R 17 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

Network Reduction 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 Effect of R 17 on Conversion

Network Reduction A overall R1R1 R2R2 R 10 R5R5 R3R3 R8R8 R 11 R6R6 R 12 R7R7 R9R9 n2n2 n4n4 n3n3 n5n5 n6n6 n7n7 R 15 R4R4 n1n1 n8n8 + – R 9 + R 12 vs. R 11 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

Network Reduction R 9 + R 12 vs. R 11 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

Network Reduction 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 Effect of R 9 and R 12 on Conversion

Network Reduction A overall R1R1 R2R2 R 10 R5R5 R3R3 R8R8 R 11 R6R6 R7R7 n2n2 n4n4 n3n3 n5n5 n6n6 n7n7 R 15 R4R4 n1n1 n8n8 + – 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

Reduced Rate Expression where Assume that OHS is the QSS species. A overall R 10 R8R8 R 11 R6R6 R7R7 n2n2 n3n3 n5n5 n6n6 n7n7 R 15

Microkinetic Model Simulation for Cu 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

Conclusions  Predicted kinetics can provide for reliable microkinetic models.  Reaction network analysis is a useful tool for reduction, simplification and rationalization of the microkinetic model.  Analogy between a reaction network and electrical network exists.  The analogy between reaction routes and electrical circuits provides a useful interpretation of kinetics and mechanism  Application of the proposed formalism to the analysis of the WGS reaction mechanism validated the reduced model developed earlier based solely on a numerical RR analysis.