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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

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
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
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.

slide4

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
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
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
Reaction Route Network

Stop

Start

Mountain Trek Reaction Network

reaction routes
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
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
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

15 step water gas shift reaction reaction route network
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

network reduction 1

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)
network reduction 2

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)
network reduction 3

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)
quasi equilibrium rds

R15

R7

n6

R6

R11

R8

n5

n2

n3

n7

R10

n4

Aoverall

Quasi Equilibrium & RDS
rate expressions
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
Reduced Rate Expression

rOR = r8 + r10 + r15

where

Assume that OHS is the QSS species.

simulation of microkinetic model for copper 17 step
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
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.