1. The water-gas-shift reaction: A reaction network analysis of the microkinetic model
Caitlin Callaghan, Ilie Fishtik and Ravindra Datta
Fuel Cell Center and Department of Chemical Engineering,
Worcester Polytechnic Institute
Worcester, MA 01609
9/9/03

2. Research Objectives
Develop a predictive microkinetic model for LTS and HTS water gas shift catalysts
Identify the rate determining steps
Develop reduced kinetic model
Simulate the reaction for copper catalysts
Eventual goal is a priori design of catalysts for the water-gas-shift-reaction in fuel reformers for fuel cells

3. Developing the Model Identify (q) surface intermediates:
H2OS, COS, CO2S, H2S, HS, OHS, OS, HCOOS
UBI-QEP method used to generate ERs and calculate the energetic characteristics (H, Ea) of each ER based on three types of reactions:
1. AB(g) + S  ABS
2. AB(g) +S  AS + BS
3. AS + BCS  ABS + CS
Pre-exponential factors from transition state theory
101 Pa-1s-1 – adsorption/desorption reactions
1013 s-1 – surface reactions

4. Adsorption and Desorption
Elementary Reactions
s1 : H2O + S  H2OS
s2 : CO + S  COS
s3 : CO2S  CO2 + S
s4 : HS + HS  H2S + S
s5 : H2S  H2 + S
s6 : H2OS +S  OHS + HS
s7 : COS + OS  CO2S + S
s8 : COS + OHS  HCOOS + S
s9 : OHS + S  OS + HS
s10 : COS + OHS  CO2S + HS
s11 : HCOOS + S  CO2S + HS
s12 : HCOOS + OS  CO2S + OHS
s13 : H2OS + OS  2 OHS
s14 : H2OS + HS  OHS + H2S
s15 : OHS + HS  OH + H2S
s16 : HCOOS + OHS  CO2S + H2OS
s17 : HCOOS + HS  CO2S + H2S
Adsorption and Desorption
Reactions

5. Reaction Rate & Affinity
Thermodynamic transition state theory (TTST)
The net rate is:
Degree of reversibility and the direction of the reaction flux
For A > 0, the reaction proceeds in the forward (positive net flux)
For A < 0, the reaction proceeds in the reverse direction (negative net flux)

6. Exchange Rate
As the affinity approaches zero, the forward and reverse rates approach a common value, the exchange rate, r,0.
Linear free energy relation:
Application of the linear free energy relation to the rate of an ER yields:
where

7. Reaction Route Network
START
STOP
The analogy between a mountain trek and a reaction network

8. Reaction Routes
A reaction route (RR) is defined as a linear combination of p ERs s ( = 1,2,…,p)
If an ER is involved in more than one RR, its rate is equal to the sum of its stoichiometric number for the RR times the flux of the each RR.

9. Network Analysis – Kirchhoff’s Laws
Kirchhoff’s Current Law (KCL)
At the nodes, under QSS conditions, the algebraic sum of the rates (currents) of the elementary reactions are equal to zero
Kirchhoff’s Voltage Law (KVL)
The algebraic sum of the affinities along each ER is equal to zero
Ohm’s Law

10. WGSR Reaction Routes (s13 and s16 neglected)
Full Reaction Routes
Empty Reaction Routes

11. 15-step Water Gas Shift Reaction Reaction Route Network
Aoverall
The complete electric circuit analog to the WGSR

12. Resistance Comparisons
Experimental Conditions
Space time = 1.80 s
FEED: COinlet = 0.10
H2Oinlet = 0.10
CO2 inlet = 0.00
H2 inlet = 0.00

13. Reaction Route Graph

14. Reaction Route Resistance

15. Quasi Equilibrium Approximation
Aoverall

16. Linearly Independent RRs for WGSR on Cu(111)

17. Rate Expressions
The net flux of a reaction is the sum of the fluxes of the RRs in which it is involved:
Dominant RRs: RR2, RR3, and RR6
r = JII + JIII + JVI = r8 + r10 + r15

18. Simplified Rate Expression
r = r8 + r10 + r15
where
Assume that OHS is the QSS species.

19. Simulation of Microkinetic Model for Copper, 17-step
Experimental Conditions
Space time = 1.80 s
FEED: COinlet = 0.10
H2Oinlet = 0.10
CO2 inlet = 0.00
H2 inlet = 0.00

20. Conclusions UBI-QEP and TST provide reliable microkinetic models.
Reaction network analysis is a useful tool for reduction, simplification and rationalization of the microkinetic model.
Analogy between a reaction and electrical network is useful.
The analogy between reaction routes and electrical circuits provides a deeper understanding of kinetics and mechanisms.
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.