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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 01609. 11/17/2003. Research Objectives .

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## A Reaction Network Analysis of the WGSR Microkinetic Model

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**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 01609 11/17/2003**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**Pre-exponential factors from transition state theory • 101 Pa-1s-1 – adsorption/desorption reactions • 1013 s-1 – surface reactions Identify (q) surface intermediates: H2OS, COS, CO2S, H2S, HS, OHS, OS, HCOOS UBI-QEP methodused 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 UBI-QEP Ref. Shustorovich, E.; Sellers, H. Surf. Sci. Reports1998, 31, 1.**Surface Energetics for Cu(111) Catalyst:**Adsorption and Desorption Steps Activation energies: kcal/mol Pre-exponential factors: Pa-1s-1 (ads/des) s-1 (surface) Ref. Callaghan, C. A.; Fishtik, I.; Datta, R.; Carpenter, M.; Chmielewski, M.; Lugo, A. Surf. Sci.2003, 541, 21**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**Stop Start 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 Mf 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 ATr = 0**Water Gas Shift Reaction Full Reaction Routes**(neglect s13 & s16)**Water Gas Shift Reaction Empty Reaction Routes**(neglect s13 & s16)**15-step Water Gas Shift ReactionReaction Route Network**n6 R7 R15 R12 R9 R1 R2 R6 R17 R3 R5 n1 n2 n3 n5 n7 n8 n0 R8 n9 R4 R11 R14 R10 n4 Aoverall The complete electric circuit analog to the WGSR**n6**n6 R7 R15 R7 R15 R12 R12 R9 R9 R1 R2 R6 R17 R3 R5 R1 R2 R6 R17 R3 R5 n1 n2 n3 n5 n7 n8 n0 R8 n1 n2 n3 n5 n7 n8 n9 n0 R8 n9 R4 R11 R4 R11 R14 R10 R10 n4 n4 Aoverall Aoverall Network Reduction (1)**n6**R7 R15 R12 R9 R1 R2 R6 R17 R3 R5 n1 n2 n3 n5 n7 n8 n0 R8 n9 R4 R11 R10 n4 Aoverall Network Reduction (2)**n6**R7 R15 R1 R2 R6 R17 R3 R5 n1 n2 n3 n5 n7 n8 n0 R8 n9 R4 R11 R10 n4 Aoverall Network Reduction (3)**Water Gas Shift ReactionEnergy Diagram**from the RR network**R15**R7 n6 R6 R11 R8 n5 n2 n3 n7 R10 n4 Aoverall Quasi Equilibrium & RDS**Rate Expressions**• The net flux of a reaction is the sum of the fluxes of the RRs in which it is involved: • Reduced Network: RR2, RR3, and RR6 rOR = JII + JIII + JVI = r8 + r10 + r15**Reduced Rate Expression**rOR = r8 + r10 + r15 where Assume that OHS is the QSS species.**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**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.

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