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Ioannis S. Fragkopoulos School of Chemical Engineering and Analytical Science (SCEAS)
University of Manchester, Manchester, M13 9PL, UK
Email: [email protected]
Modelling of Electrochemical Promotion in Heterogeneous
Catalytic Systems
Friday, December 19, 2014, 01:00 PM, Research Seminar, Chemical Engineering UPatras Seminar Room
Outline
1. Electrochemical Promotion of Catalysis
2. Motivation & objectives
3. Macroscopic model
4. Multi-scale framework
5. Multi-scale framework using the Gap-Tooth method
6. Conclusions & future work
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 02
Electrochemical Promotion of Catalysis
1 Stoukides, M., Vayenas, C.G. (1981): J. Catal., 70, 1, 137-146. 2 Vayenas C.G., Bebelis S., Pliangos C., Brosda S., Tsiplakides D. (2001):The Electrochemical Activation of Catalysis. Plenum Press.
" EPOC is the enhancement of catalytic activity 1
" by applying potential between the catalyst and a reference electrode
" due to an electrochemically controlled BackSpillover (migration) " of species (e.g. [Oδ- - δ+]) produced in the Triple Phase Boundaries (TPBs) " forming a double layer which affects the binding strength of the adsorbed species.
" EPOC can lead to up to 600% increase in the surface reaction rate 2
" This enhancement is non-Faradaic. " is sometimes permanent under current interruption " is also known as Non-Faradaic Electrochemical Modification of Catalytic Activity (NEMCA).
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 03
Ø Reduction of environmental pollution is an issue of great concern nowadays. Ø Air pollutants are very effectively being converted to harmless emissions
v using appropriate heterogeneous catalytic systems.3
Heterogeneous Catalysis
Electrochemical Promotion
Ø Short catalytic life time (deactivation) Ø High preparation cost (pricy metals) Ø Incapability of controlling
v the catalytic performance ‘in situ’
Ø Increased life time and activity of a catalyst Ø Lower catalyst loading and operating cost Ø Capable of controlling and modifying
v the catalytic performance ‘in situ’
vs.
Motivation & Objectives
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 04
3 Katsaounis A. (2008): Global NEST J., 10, 226-236.
Motivation & Objectives
Ø The main objective is the formulation of an accurate framework for an EPOC system • to be used in conjunction with a good range of experimental data in order to:
v obtain insights on relevant complex phenomena v compute reliable estimates of parameters such as
• effective diffusion coefficients and reaction rate constants v ultimately enable EPOC (scaled-up) system robust design and control
• leading to the incorporation of the addressed effect in commercial systems q such as exhaust gas treatment and fuel cells.
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 05
Macroscopic Model 4
4 Fragkopoulos I.S., Bonis I., Theodoropoulos C. (2013): Chem. Eng. Sci., 104, 647-661.
The Reactor Design and the 3-D & 2-D Computational domains
Ø Electrochemically Promoted CO oxidation on Pt/YSZ Ø Multi-dimensional isothermal framework
• for the simultaneous simulation of v PDEs for mass and charge conservation v Electrochemical processes at TPBs
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 06
# Reaction Description Rates 5
1 Adsorption-Desorption of O2
2 Adsorption-Desorption of CO
3 Surface reaction of CO.S with O.S
4 Surface reaction of CO.S with BSS.S
5 Desorption of BSS.S
Catalytic Reactions
+ ⋅ ⋅É1
( )-1
2 2 2g
k
kO S O S
+ ⋅É2
( )-2
g
k
kCO S CO S
⋅ + ⋅ → + ⋅3
( )2 2g
k
O S CO S CO S
⋅ + ⋅ → + ⋅4
( )2 2g
k
BSS S CO S CO S
⋅ → + ⋅5
( )2 2 2g
k
BSS S O S
θ=2
21 12
AO Sr k C
( )θ
θ=
2
-1 -1 21-O
O
r k
( )θ
θ=
2
5 5 21-BSS
BSS
r k
θ θ=4 4 CO BSSr k
θ θ=3 3 O COr k
θ=2 2ACO Sr k C
θ=-2 -2 COr k
='2 -2 3 4- - - ,COR r r r r ='
4 5- - ,BSSR r r
Rate constants: π
= =, 1,22
ii
S i
S RTk iN M
⎛ ⎞= =⎜ ⎟
⎝ ⎠,
-exp , -1,-2,3ii o i
Ek k iRT
+ = -2 -14 5 10k k s
Species’ rates: θ θ θ θ=1- - -S O CO BSS='1 -1 3- - ,OR r r r
5 Kaul D.J., Sant R., Wolf E.E. (1987): Chem. Eng. Sci. 42, 6, 1399-1411.
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 07
" Electrochemical Reaction
" Current Density of Cathode (Butler-Volmer) 6
- 2
( )2 13 22 YSZgO e O −⎡ ⎤× + →⎢ ⎥⎣ ⎦
0 exp exp (1 )C C C C C Ce en F n FJ JRT RT
α η α η⎡ ⎤⎛ ⎞ ⎛ ⎞
= − − −⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦
6 Tseronis K., Bonis I., Kookos I.K., Theodoropoulos C. (2012): Int. J. Hydr. Energy, 37, 1, 530-547.
Cathodic TPBs (Boundaries, P6 & P8)
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 08
" Electrochemical Reactions
" Current Density of Anode
" Butler-Volmer
2 - ( ) ( )2 2 (1)YSZ g gO CO CO e− + +É
2 - ( )
12 2 2 (2)YSZ gO O e− +É
2 -
- - 2 (3)YSZO O eδ δ− ⎡ ⎤+ +⎣ ⎦É
1 2 3A A A AJ J J J= + +
0, exp exp (1 ) , i 1,2,3A A A A A Ae ei i
n F n FJ JRT RT
α η α η⎡ ⎤⎛ ⎞ ⎛ ⎞
= − − − =⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦
parallel electrical circuit analogy 7
7 Achenbach E. (1994): J. Power Sources, 49, 333-348.
Anodic TPBs (Boundaries, P1 & P3)
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 09
" Electronic phase: Pt, Au " Ionic phase: YSZ support
" B.C. Cathode, Cathodic TPBs: P7:
" B.C. Electrolyte, TPBca: TPBan: Else:
" B.C. Anode, Anodic TPBs: P2:
/ Q , ,j A Cj j
dJ j io el
dtρ
+∇⋅ = =
-j j jJ σ= ∇Φ
ρ: charge density σ: electric conductivity Φ: electric potential
( )- - C C Cel el Jσ⋅ ∇Φ =n C
el cellΦ =Φ
( )- - -A A Ael el Jσ⋅ ∇Φ =n 0A
elΦ =
( )- - - Cio io Jσ⋅ ∇Φ =n ( )- - A
io io Jσ⋅ ∇Φ =n 0∇Φ =io
Macroscopic Model: Charge balances
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 10
" Pt catalytic surface (B1 & B2)
" R’BSS also includes the Faradaic term:
" At Points P1 & P3 (No Flux):
" At Point P2 continuation is considered for all the species
" Mass transfer phenomena at cathode are ignored
D: diffusivity θ: coverage R’: reaction rate
( )- 0, ,j jD j CO Oθ⋅ ∇ = =n
( )3 12
A
elec O CO BSSS
JrFN
θ θ θ= − + +
( ) '- , , ,ii i i
dD R i O CO BSS
dtθ
θ+∇⋅ ∇ = =
Macroscopic Model: Mass balances
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 11
Ø Parameter estimation • using a tailored 2-D modelling framework • in conjunction with closed-circuit experimental data
v available in the literature 8
8 Yentekakis I.V., Moggridge G., Vayenas C.G., Lambert R.M. (1994): J. Catal. 146, 292-305.
0
10
20
30
40
50
60
70
0 1 2 3 4 5 6 7 8
Λ, e
nhan
cem
ent
fact
or, 1
03
Pcoinlet , kPa
T = 372 oC Po2
inlet = 5.8 kPa
Parameter Estimation
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 12
Sensitivity Analysis
Parameter (Units) Estimated Value % Change in
parameter % Resultant
change in rCO2
SO2 (-) 7.69x10-5 -10
+10
-10.96
11.21
SCO (-) 5.38x10-1 -10
+10
16.44
-13.38
EA,-1 (J mol-1) 243139 -50
+100
-5.68
0.00
EA,-2 (J mol-1) 99618 -1
+1
30.03
-24.64
EA,3 (J mol-1) 35186 -10
+10
4.76
-8.02
γA,1 (A m-2) 5.01x108 -50
+100
0.00
0.00
γA,2 (A m-2) 2.92x1011 -50
+100
0.00
0.00
γA,3 (A m-2) 3.42x104 -50
+100
0.13
-0.20
Non-Faradaic Contribution
Faradaic Contribution
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 13
" 3D Macroscopic model for charge balances " 2D Microscopic model for catalytic surface micro-processes (kMC)
The Computational Domain
9 Fragkopoulos I.S., Theodoropoulos C. (2014): Electrochim. Acta, 150, 232-244.
Multi-scale Model 9
Ø Dimensions vary • from 100-5000 nm
Ø More accurate and realistic approach v simulates the phenomena of interest
• at their appropriate length-scales.
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 14
10 Reese J.S., Raimondeau S., Vlachos D.G. (2001): J. Comp. Phys., 173, 302-321.
" kMC simulation for surface dynamics on Pt " Transition probabilities of micro-processes 10
" 1 and 2-site conditional probabilities:
" At each time step, a reaction is probabilistically chosen. " Sites are also chosen in a probabilistic way and reaction takes place. " Number of individual surface sites and time variable are updated.
( )( )
∗ ∗ ∗ ∗ ∗ ∗
∗ ∗ ∗ ∗ ∗ ∗
∧
∗ ∗ ∗
∧
∗
∧
∧
Γ = ⋅ ⋅ ⋅ ⋅
Γ = ⋅ ⋅ ⋅
Γ = ⋅ ⋅ + ⋅
Γ = ⋅ ⋅ + ⋅
21 1
2 2
3 3
4 4
tot O
tot CO
CO O CO O CO O
CO BSS CO BSS CO BSS
k P X P P
k P X P
k P P P P
k P P P P
AA
T
P ∗
∗
Ω=Ω
( )4
1
4
B A jj
A BB
jP
∗ ∗
∗∗
∗
=
⋅ Ω
=⋅Ω
∑
( )
∗ ∗ ∗
∗
∗ ∗ ∗
∗ ∗ ∗
∧
− −
∧
− −
∧
∧
∗∗ ∗
Γ = ⋅ ⋅
Γ = ⋅
Γ = ⋅ ⋅
Γ = ⋅ ⋅ + ⋅ =
1 1
2 2
5 5
, , , ,
O O O
CO
BSS BSS BSS
X diff X diff X X X
k P P
k P
k P P
k P P P P X CO BSS
Microscopic Model
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 15
Multi-scale Framework Algorithm
kMC
Required time
reached YES NO
Initial Conditions T, Pi, Φcell
Faradaic Rates BSS Flux
FEM Updated
Gas Species Partial
Pressures Micro-catalytic
Rates Coverages
Updated Gas Species
Partial Pressures
& Time
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 16
Multi-scale vs. Macroscopic 9
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 17 9 Fragkopoulos I.S., Theodoropoulos C. (2014): Electrochim. Acta, 150, 232-244.
Multi-scale: Temperature Effect 9
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 18
9 Fragkopoulos I.S., Theodoropoulos C. (2014): Electrochim. Acta, 150, 232-244.
Ø Catalytic surface is split into a number of ‘representative’ lattices v whose area is only a fraction of the actual catalytic area 11
11 Gear C.W., Li J. and I.G. Kevrekidis (2003): Phys. Lett. A., 316, 190-195.
Multi-scale interpolation: The Gap-Tooth
Ø The computationally expensive (or even intractable) large micro-scopic simulations v can be performed with efficiency.
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 19
Ø Considering only the diffusion micro-process for only one species
Ø Validation of 1-D Gap-Tooth framework considering no gaps v against the Single Lattice simulation using
• Random distribution of ingoing species • Boundary distribution of ingoing species • Thin ‘zone’ distribution of ingoing species around the edges
Gap-Tooth Validation via a Diffusion system
Ø The single lattice dynamics can be sufficiently captured • using the (1-10) zone distribution of ingoing species
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 20
Ø 1100 by 100 sites of Single Lattice (Pt) v represented by 5 teeth of 100 by 100 sites (dx=100 sites, Dx=250 sites)
The Gap-Tooth
The Single Lattice
O1,k,r O2,k,r O3,k,r O4,k,r
O2,k,l O3,k,l O4,k,l O5,k,l I1,k,r I2,k,r I3,k,r I4,k,r
I2,k,l I3,k,l I4,k,l I5,k,l
dx
Dx
Tooth 1
Tooth 2
Tooth 3
Tooth 4
Tooth 5
Gap-Tooth in Open Circuit system
Ø Considering all the open circuit (CO oxidation) micro-processes v and the diffusion micro-process for CO
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 21
Open Circuit: CO Coverage and CO2 Rate Profiles
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 22
2-D Gap-Tooth Multi-scale System
Ø 1800 by 400 sites of entire catalytic lattice (Pt) represented by: v 5 teeth of 200 by 100 sites in x-direction (dx=200 sites, gapx=200 sites, Dx=400 sites) v 2 teeth of 200 by 100 sites in y-direction (dy=100 sites, gapy=200 sites, Dy=300 sites)
The Gap-Tooth
The Single Lattice
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 23
Multi-scale CO2 Rate Profiles 12,13
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 24
12 Fragkopoulos I.S., C. Theodoropoulos (2014): Comp. Aid. Ch., 33, 931-936. 13 Fragkopoulos I.S., C. Theodoropoulos (2015): Comp. Chem. Eng., to be submitted.
ü Formulation of a multi-dimensional macroscopic model • Parameter estimation under closed -circuit conditions • Non-Faradaic effect much greater than the Faradaic one
ü Extension of the multi-scale framework to use the Gap-Tooth method • Very accurate representation for a fraction of the computational cost
Ø Parameter estimation • using a good range of experimental data
v for both open and closed-circuit conditions
Conclusions & Further Work
ü Development of a 3D Multi-scale framework • Exhibits similar dynamic trends with the macroscopic model • Quantitative differences are observed
v for the set of utilised operating conditions
Ø Parallelisation of Gap-Tooth • using message passing interface (MPI)
Modelling of Electrochemical Promotion in Heterogeneous Catalytic Systems | 19/12/2014 | Research Seminar | 25
Acknowledgements
" The financial contribution of the Engineering and Physical Sciences
Research Council (EPSRC) UK: " Grant EP/G022933/1
" Doctoral Prize Fellowship 2013/2014
Thank You!