ISFragkopoulos - Seminar on Electrochemical Promotion

Ioannis S. Fragkopoulos
School of Chemical Engineering and Analytical Science (SCEAS)
University of Manchester, Manchester, M13 9PL, UK
Email: ioannis.fragkopoulos@manchester.ac.uk
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).

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
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.

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

# 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
+ ⋅ ⋅É
1
( )
-1
2 2 2g
k
k
O S O S
+ ⋅É
2
( )
-2
g
k
k
CO S CO S
⋅ + ⋅ → + ⋅
3
( )2 2g
k
O S CO S CO S
⋅ + ⋅ → + ⋅
4
( )2 2g
k
BSS S CO S CO S
⋅ → + ⋅
5
( )22 2g
k
BSS S O S
θ= 2
2
1 12 A
O Sr k C
( )
θ
θ
=
2
-1 -1 2
1-
O
O
r k
( )
θ
θ
=
2
5 5 2
1-
BSS
BSS
r k
θ θ=4 4 CO BSSr k
θ θ=3 3 O COr k
θ=2 2
A
CO 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
= =, 1,2
2
i
i
S i
S RT
k i
N M
⎛ ⎞
= =⎜ ⎟
⎝ ⎠
,
-
exp , -1,-2,3i
i o i
E
k k i
RT
+ = -2 -1
4 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.

" Electrochemical Reaction
" Current Density of Cathode (Butler-Volmer) 6
- 2
( )2
1
3 2
2
YSZg
O e O −⎡ ⎤
× + →⎢ ⎥⎣ ⎦
0 exp exp (1 )C C C C C Ce en F n F
J J
RT 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)

" Electrochemical Reactions
" Current Density of Anode
" Butler-Volmer
2 -
( ) ( )2 2 (1)YSZ g g
O CO CO e−
+ +É
2 -
( )
1
22 2 (2)YSZ g
O O e−
+É
2 --
- 2 (3)YSZ
O O eδ
δ−
⎡ ⎤+ +⎣ ⎦É
1 2 3
A A A A
J J J J= + +
0, exp exp (1 ) , i 1,2,3A A A A A Ae e
i i
n F n F
J J
RT 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)

" 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 C
j j
d
J j io el
dt
ρ
+∇⋅ = =
-j j jJ σ= ∇Φ
ρ: charge density
σ: electric conductivity
Φ: electric potential
( )- - C C C
el el Jσ⋅ ∇Φ =n C
el cellΦ = Φ
( )- - -A A A
el el Jσ⋅ ∇Φ =n 0A
elΦ =
( )- - - C
io io Jσ⋅ ∇Φ =n ( )- - A
io io Jσ⋅ ∇Φ =n 0∇Φ =io
Macroscopic Model: Charge balances

" 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
1
2
A
elec O CO BSS
S
J
r
FN
θ θ θ= − + +
( ) '
- , , ,i
i i i
d
D R i O CO BSS
dt
θ
θ+∇⋅ ∇ = =
Macroscopic Model: Mass balances

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,enhancement
factor,103
Pco
inlet , kPa
T = 372
o
C
Po2
inlet = 5.8 kPa
Parameter Estimation

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

" 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.

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 = ⋅ ⋅ + ⋅
2
1 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
A
A
T
P
∗
∗
Ω
=
Ω
( )
4
1
4
B A j
j
A B
B
j
P
∗ ∗
∗∗
∗
=
⋅ 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

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

Multi-scale vs. Macroscopic 9

Multi-scale: Temperature Effect 9

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.

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

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,lI1,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

Open Circuit: CO Coverage and CO2 Rate Profiles

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

Multi-scale CO2 Rate Profiles 12,13
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)

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!

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