A Reaction Network Analysis of the WGSR Microkinetic Model Caitlin Callaghan, Ilie Fishtik and Ravindra Datta Fuel Cell Center and Department of Chemical Engineering, Worcester Polytechnic Institute Worcester, MA /17/2003

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

Developing the Model Identify (q) surface intermediates: H 2 OS, COS, CO 2 S, H 2 S, HS, OHS, OS, HCOOS UBI-QEP method UBI-QEP method used to generate ERs and calculate the energetic characteristics (  H, E a ) 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 10 1 Pa -1 s -1 – adsorption/desorption reactions s -1 – surface reactions UBI-QEP Ref. Shustorovich, E.; Sellers, H. Surf. Sci. Reports 1998, 31, 1.

Adsorption and Desorption Steps Ref. Callaghan, C. A.; Fishtik, I.; Datta, R.; Carpenter, M.; Chmielewski, M.; Lugo, A. Surf. Sci. 2003, 541, 21 Surface Energetics for Cu(111) Catalyst: Activation energies: kcal/mol Pre-exponential factors: Pa -1 s -1 (ads/des) s -1 (surface)

Reaction Rate & Affinity  Thermodynamic transition state theory (TTST)  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)  Conventional DeDonder Relation:

Exchange Rate & Resistance  As the affinity approaches zero, the forward and reverse rates approach a common value, the exchange rate, r ,0.  Reaction Resistance:  At equilibrium, the resistance is equal to the inverse of the exchange rate.

Reaction Route Network Mountain Trek  Reaction Network

Reaction Routes  A reaction route (RR) is defined as a linear combination of p elementary reaction steps s  (  = 1,2,…,p)  If an elementary reaction step 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.

Network Analysis (1)  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 empty route (ER) is equal to zero M f r = 0  f A = 0

Network Analysis (2)  Tellegen’s Theorem The power dissipated by the OR euqals the power dissipated by the elementary reactions in a RR.  Ohm’s Law: the NEW DeDonder Relation The algebraic sum of the affinities along each ER is equal to zero A T r = 0

Water Gas Shift Reaction Full Reaction Routes (neglect s 13 & s 16 )

Water Gas Shift Reaction Empty Reaction Routes (neglect s 13 & s 16 )

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 The complete electric circuit analog to the WGSR 15-step Water Gas Shift Reaction Reaction Route Network n0n0 n9n9

Network Reduction (1) 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 n0n0 n9n9 Experimental Conditions Space time = 1.80 s FEED: CO inlet = 0.10 H 2 Oinlet = 0.10 CO 2 inlet = 0.00 H 2 inlet = 0.00 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 n0n0 n9n9

Network Reduction (2) Experimental Conditions Space time = 1.80 s FEED: CO inlet = 0.10 H 2 Oinlet = 0.10 CO 2 inlet = 0.00 H 2 inlet = 0.00 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 n0n0 n9n9

Network Reduction (3) Experimental Conditions Space time = 1.80 s FEED: CO inlet = 0.10 H 2 Oinlet = 0.10 CO 2 inlet = 0.00 H 2 inlet = 0.00 A overall R1R1 R2R2 R 10 R5R5 R3R3 R8R8 R 11 R6R6 R 17 R7R7 n2n2 n4n4 n3n3 n5n5 n6n6 n7n7 R 15 R4R4 n1n1 n8n8 n0n0 n9n9

Water Gas Shift Reaction Energy Diagram from the RR network

Quasi Equilibrium & RDS A overall R 10 R8R8 R 11 R6R6 R7R7 n2n2 n4n4 n3n3 n5n5 n6n6 n7n7 R 15

Linearly Independent RRs for WGSR on Cu(111)

Rate Expressions  The net flux of a reaction is the sum of the fluxes of the RRs in which it is involved:  Reduced Network: RR 2, RR 3, and RR 6 r OR = J II + J III + J VI = r 8 + r 10 + r 15

Reduced Rate Expression r OR = r 8 + r 10 + r 15 where Assume that OHS is the QSS species.

Simulation of Microkinetic Model for Copper, 17-step 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.