ISFragkopoulos - Seminar on Electrochemical Promotion

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).


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

+ ⋅ ⋅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.


" 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)


" 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)


" 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


" 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


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


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 = ⋅ ⋅ + ⋅

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


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

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


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.


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,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


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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ISFragkopoulos - Seminar on Electrochemical Promotion