a reaction network analysis of the wgsr microkinetic model
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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 InstituteWorcester, 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
Identify (q) surface intermediates: H2OS, COS, CO2S, H2S, HS, OHS, OS, HCOOS
UBI-QEP methodUBI-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 ABS2. AB(g) +S AS + BS3. AS + BCS ABS + CS
Pre-exponential factors from transition state theory 101 Pa-1s-1 – adsorption/desorption
reactions 1013 s-1 – surface reactions
UBI-QEP Ref. Shustorovich, E.; Sellers, H. Surf. Sci. Reports 1998, 31, 1.
jE
jA Elementary Reaction Steps
:jE
:jA
s1: 0 106 CO + S COS 12.0 1014
s2: 0 106 H2O + S H2OS 13.6 1014
s3: 5.3 4 1012 CO2S CO2 + S 0 106
s4: 15.3 1013 HS + HS H2S + S 12.8 1013
s5: 5.5 6 1012 H2S H2 + S 0 106
s6: 25.4 1013 H2OS + S OHS + HS 1.6 1013
s7: 10.7 1013 COS + OS CO2S + S 28.0 1013
s8: 0 1013 COS + OHS HCOOS + S 20.4 1013
s9: 15.5 1013 OHS + S OS + HS 20.7 1013
s10: 0 1013 COS + OHS CO2S + HS 22.5 1013
s11: 1.4 1013 HCOOS + S CO2S + HS 3.5 1013
s12: 4.0 1013 HCOOS + OS CO2S + OHS 0.9 1013
s13: 29.0 1013 H2OS + OS 2OHS 0 1013
s14: 26.3 1013 H2OS + HS OHS + H2S 0 1013
s15: 1.3 1013 OHS + HS OS + H2S 4.0 1013
s16: 0.9 1013 HCOOS + OHS CO2S + H2OS 26.8 1013
s17: 14.6 1013 HCOOS + HS CO2S + H2S 14.2 1013
Adsorptionand
DesorptionSteps
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-1s-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:
r
k ai
i
i1
r
expo
BGk T
kh RT
:r
:k ai
i
ir 1
n
expo
BGk T
kh RT
::
1 1 expr
r r rr
A
:
1 1 1
ln ln ln lnqn n
i i o o k k i ii k i
AK P
RT
A
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.
,0
0( )
rr
AA
ln1
rr
Rv r r
:
G:
,0
1R
r
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.
1
p
RR s
1
p
TA A
Tr σ J
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
AT r = 0
rR
A
Water Gas Shift Reaction Full Reaction Routes
RR1 = s1 + s2 + s3 + s4 + s5 + s6 + s7 + s9 RR2 = s1 + s2 + s3 + s4 + s5 + s6 + s10 RR3 = s1 + s2 + s3 + s4 + s5 + s6 + s8 + s11 RR4 = s1 + s2 + s3 + s4 + s5 + s6 + s8 + s9 + s12 RR5 = s1 + s2 + s3 + s4 + s5 + s6 + s7 + s11 - s12 RR6 = s1 + s2 + s3 + s5 + s6 + s7 + s15 RR7 = s1 + s2 + s3 + s5 + s6 + s8 + s12 + s15 RR8 = s1 + s2 + s3 + s5 + s7 + s9 + s14 RR9 = s1 + s2 + s3 + s5 + s10 + s14 RR10 = s1 + s2 + s3 + s5 + s8 + s11 + s14 RR11 = s1 + s2 + s3 - s4 + s5 + s7 + s14 + s15 RR12 = s1 + s2 + s3 + s5 + s7 + s11 - s12 + s14 RR13 = s1 + s2 + s3 + s5 + s8 + s9 + s12 + s14 RR14 = s1 + s2 + s3 - s4 + s5 + s8 + s12 + s14 + s15
RR15 = s1 + s2 + s3 - s4 + s5 + s7 - s12 + s14 + s17 RR16 = s1 + s2 + s3 - s4 + s5 + s8 + s14 + s17 RR17 = s1 + s2 + s3 + s5 + s6 + s8 + s17 RR18 = s1 + s2 + s3 + s5 + s6 + s10 - s11 + s12 + s15 RR19 = s1 + s2 + s3 + s5 + s6 + s10 - s11 + s17 RR20 = s1 + s2 + s3 + s5 + s6 + s7 - s12 + s17 RR21 = s1 + s2 + s3 + s5 + s6 + s7 + s9 - s11 + s17 RR22 = s1 + s2 + s3 + s5 + s6 + s8 - s9 + s11 + s15 RR23 = s1 + s2 + s3 + s5 + s6 - s9 + s10 - s12 + s17 RR24 = s1 + s2 + s3 + s5 + s6 - s9 + s10 + s15 RR25 = s1 + s2 + s3 + s5 + s7 + s11 + s14 + s15 - s17 RR26 = s1 + s2 + s3 + s5 + s8 + s9 + s14 - s15 + s17
(neglect s13 & s16)
Water Gas Shift Reaction Empty Reaction Routes
ER1 = -s12 - s15 + s17 ER2 = -s4 - s11 + s12 + s15 ER3 = -s4 - s11 + s17 ER4 = -s4 - s6 + s14 ER5 = -s4 + s7 - s10 - s12 + s17 ER6 = s4 - s7 + s10 - s15 ER7 = -s4 + s7 - s8 - s11 + s15 ER8 = -s4 - s7 + s8 - s9 + s17 ER9 = -s4 + s8 - s10 + s12 + s15 ER10 = -s4 + s8 - s10 + s17 ER11 = -s4 - s9 - s12 + s17
ER12 = -s4 - s9 + s15 ER13 = -s6 + s11 - s12 + s14 - s15 ER14 = -s6 + s11 + s14 - s17 ER15 = -s6 - s7 + s10 + s12 + s14 - s17 ER16 = -s6 - s7 + s10 + s14 - s15 ER17 = -s6 - s7 + s8 + s11 + s14 - s15 ER18 = -s6 + s7 - s8 + s9 + s14 - s17 ER19 = -s6 - s8 + s10 - s12 + s14 - s15 ER20 = -s6 - s8 + s10 + s14 - s17 ER21 = -s6 + s9 + s12 + s14 - s17 ER22 = -s6 + s9 + s14 - s15
(neglect s13 & s16)
Aoverall
R1 R2
R14 R10
R5R3R8
R11
R6 R17
R12R7
R9n2
n4
n3 n5
n6
n7
R15
R4
n1 n8
The complete electric circuit analog to the WGSR
15-step Water Gas Shift Reaction
Reaction Route Network
n0 n9
Network Reduction (1)
Aoverall
R1 R2
R14 R10
R5R3R8
R11
R6 R17
R12R7
R9n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9
Aoverall
R1 R2
R14 R10
R5R3R8
R11
R6 R17
R12R7
R9n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9
Aoverall
R1 R2
R14 R10
R5R3R8
R11
R6 R17
R12R7
R9n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n91.E-02
1.E+01
1.E+04
1.E+07
1.E+10
0 0.005 0.01 0.015 0.02 0.025
1/T (1/oC)
Res
ista
nce
-1
1ra
te(s
)
R 14
R 4 + R 6
Experimental ConditionsSpace time = 1.80 s
FEED: CO inlet = 0.10H2Oinlet = 0.10
CO2 inlet = 0.00
H2 inlet = 0.00
1.E-02
1.E+01
1.E+04
1.E+07
1.E+10
0 0.005 0.01 0.015 0.02 0.025
1/T (1/oC)
Res
ista
nce
-1
1ra
te(s
)
R 14
R 4 + R 6
Aoverall
R1 R2
R10
R5R3R8
R11
R6 R17
R12R7
R9n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9
1.E-05
1.E-01
1.E+03
1.E+07
1.E+11
1.E+15
1.E+19
0 0.005 0.01 0.015 0.02 0.025
1/T (1/oC)
Res
ista
nce
-1
1ra
te(s
)
R 11
R 9 + R 12
Network Reduction (2)
Experimental ConditionsSpace time = 1.80 s
FEED: CO inlet = 0.10
H2Oinlet = 0.10
CO2 inlet = 0.00
H2 inlet = 0.00
Aoverall
R1 R2
R10
R5R3R8
R11
R6 R17
R12R7
R9n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9
Aoverall
R1 R2
R10
R5R3R8
R11
R6 R17
R12R7
R9n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9
Aoverall
R1 R2
R10
R5R3R8
R11
R6 R17
R12R7
R9n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9
Aoverall
R1 R2
R10
R5R3R8
R11
R6 R17
R12R7
n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9
1.E-05
1.E-01
1.E+03
1.E+07
1.E+11
1.E+15
1.E+19
0 0.005 0.01 0.015 0.02 0.025
1/T (1/oC)
Res
ista
nce
-1
1ra
te(s
)
R 11
R 9 + R 12
Network Reduction (3)
Experimental ConditionsSpace time = 1.80 s
FEED: CO inlet = 0.10H2Oinlet = 0.10
CO2 inlet = 0.00
H2 inlet = 0.00
1.E-04
1.E-01
1.E+02
1.E+05
1.E+08
0 0.005 0.01 0.015 0.02 0.025
1/T (1/oC)
Res
ista
nce
-1
1ra
te(s
) R 17
R 4 + R 11
Aoverall
R1 R2
R10
R5R3R8
R11
R6 R17
R7
n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9Aoverall
R1 R2
R10
R5R3R8
R11
R6 R17
R7
n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9
Aoverall
R1 R2
R10
R5R3R8
R11
R6 R17
R7
n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9
Aoverall
R1 R2
R10
R5R3R8
R11
R6
R7
n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9
1.E-04
1.E-01
1.E+02
1.E+05
1.E+08
0 0.005 0.01 0.015 0.02 0.025
1/T (1/oC)
Res
ista
nce
-1
1ra
te(s
) R 17
R 4 + R 11
Water Gas Shift ReactionEnergy Diagram
node 1
Pot
enti
al E
ner
gy (
kca
l/mol
)
0
10
20
30
40
50
-10
-20
-30
-40
-50
Reaction Coordinate
node 2
node 3
node 4node 7
node 5
node 8node 9
node 10
node 6s5
s3
s15
s4
s7
s6s1
s2
s8
s11
s10
from the RR network
Quasi Equilibrium & RDS
1.E-06
1.E-03
1.E+00
1.E+03
1.E+06
0 0.005 0.01 0.015 0.02 0.025
1/T (1/oC)
Res
ista
nce
-1
1ra
te(s
)
R 6
R 2R 3,R 5
R 1
1.E-04
1.E+00
1.E+04
1.E+08
0 0.005 0.01 0.015 0.02 0.025
1/T (1/oC)
Res
ista
nce
R 4
-11
rate
(s) (R 8+R 11)R 10
R 8+R 10+R 11
Aoverall
R10
R8R11R6
R7
n2
n4
n3 n5
n6
n7
R15
1.E-06
1.E-03
1.E+00
1.E+03
1.E+06
0 0.005 0.01 0.015 0.02 0.025
1/T (1/oC)
Res
ista
nce
-1
1ra
te(s
)
R 6
R 2R 3,R 5
R 1
Aoverall
R1 R2
R10
R5R3R8
R11
R6
R7
n2
n4
n3 n5
n6
n7
R15
R4
n1 n8n0 n9
1.E-04
1.E+00
1.E+04
1.E+08
0 0.005 0.01 0.015 0.02 0.025
1/T (1/oC)
Res
ista
nce
R 4
-11
rate
(s) (R 8+R 11)R 10
R 8+R 10+R 11
Linearly Independent RRs for WGSR on Cu(111)
RRI RRII RRIII RRIV RRV RRVI RRVII
s1: CO + S COS 1 1 1 0 0 1 1 s2: H2O + S H2OS 1 1 1 0 0 1 1 s3: CO2S CO2 + S 1 1 1 0 0 1 1 s4: HS + HS H2S + S 1 1 1 0 -1 0 0 s5: H2S H2 + S 1 1 1 0 0 1 1 s6: H2OS + S OHS + HS 1 1 1 0 -1 1 1 s7: COS + OS CO2S + S 1 0 0 -1 0 1 0 s8: COS + OHS HCOOS + S 0 0 1 1 0 0 1 s9: OHS + S OS + HS 1 0 0 0 0 0 0 s10: COS + OHS CO2S + HS 0 1 0 0 0 0 0 s11: HCOOS + S CO2S + HS 0 0 1 0 0 0 0
s12: HCOOS + OS CO2S + OHS 0 0 0 1 0 0 0
s14: H2OS + HS OHS + H2S 0 0 0 0 1 0 0 s15: OHS + HS OS + H2S 0 0 0 0 0 1 0 s17: HCOOS + HS CO2S + H2S 0 0 0 0 0 0 1 Net: RRI: H2O + CO CO2 + H2 JI
RRII: H2O + CO CO2 + H2 JII RRIII: H2O + CO CO2 + H2 JIII RRIV: 0 = 0 JIV RRV: 0 = 0 JV RRVI: H2O + CO CO2 + H2 JVI
RRVII: H2O + CO CO2 + H2 JVII
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
r1 = JII + JIII + JVI r6 = JII + JIII + JVI r11 = JIII r2 = JII + JIII + JVI r7 = JVI r12 = 0 r3 = JII + JIII + JVI r8 = JIII r14 = 0 r4 = JII + JIII r9 = 0 r15 = JVI r5 = JII + JIII + JVI r10 = JII r17 = 0
rOR = JII + JIII + JVI = r8 + r10 + r15
Reduced Rate Expression
rOR = r8 + r10 + r15
2 22 2
22
1/ 22 1/ 26 1 H O 0 8 10 2 15 H 4 5 CO H
OR 1/ 2H O CO6 6 15 H
8 10 2 CO1/ 24 5
1COk K P θ k k K P k P K K P P
rKP Pk K k P
k k K PK K
where
2
2
0 1/ 2H
1 H O 2 1/ 24 5
1
1 CO
PK P K P
K K
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
0
0.2
0.4
0.6
0.8
1
0 100 200 300 400 500 600
Temperature (oC)
Co
nv
ers
ion
of
CO
Experiment
Equilibrium
Simplified Model
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.