Electrochemical Model

Report
Melissa Tweedie
May 1, 2014
http://www.ztekcorporation.com/
CHP Propane Fueled SOFC
Power Plant for large automotive
applications
http://fuelcellsworks.com/
Reference 2
http://www.ceramatec.com
Anode Interconnect
Fuel
Electrochemistry
Anode FF
Anode Electrode BL
Air
Cathode FF
Cathode Interconnect
Anode Electrode ERL
Electrolyte
Cathode ERL
Cathode Electrode BL



To develop a 2-D model of a single cell solid
oxide fuel cell.
To include detailed multi-physics: fluid
dynamics, heat transfer, mass transfer,
chemical and electrochemical reactions.
To utilize the model in analyzing the
performance of varying fuel inlet
compositions.

The 2-D CFD model consisted of five physics
sub-models as follows:
◦
◦
◦
◦
◦
Fluid flow and Momentum Model
Mass Transfer Model
Heat Transfer Model
Chemical Model
Electrochemical Model
Continuity and Navier Stokes Equations
◦ Compressible flow, steady state

Fuel and Air Channels:

Porous Electrode Stokes-Brinkman equations:

Wilke and Herning & Zipperer Method to calculate
mixture dynamic viscosity



Maxwell-Stefan Equations
Maxwell-Stefan diffusivity values calculated using
Fuller method for flowfields
Effective diffusivity used in porous media combines
maxwell stefan binary diffusivity and knudsen
diffusivity

Flowfields
◦ Heat capacity and thermal conductivity for individual species
assumes ideal gases and is calculated from temperature
dependent polynomials.
◦ Mixture heat capacity
◦ Mixture thermal conductivity calculated using method of
Wassiljewa with Mason and Saxena modification

Electrodes
◦ Use of effective thermal conductivity and effective
heat capacity to account for porosity

Electrolyte and Interconnects
◦ Conduction only

Heat Generation Source Terms
Types of SOFC Heat Sources



Fuel Cell
Type
Relative % Contribution
MSR Reaction
Consumption
27
WGS Reaction
Generation
6
Electrochemical Reactions
Generation
47
Concentration Polarization
Generation
<1
Activation Polarization
Generation
16
Ohmic Polarization
Generation
3
Chemical Reaction
Electrochemical Reaction
Activation Polarization

Heat Generation Source Terms
Summary of Heat Source Equations used in Model
Anode Flow Field
Anode Backing
Layer
Anode ERL
Electrolyte
Q=0
Cathode ERL
Cathode BL, FF
Q=0
Interconnects
Q=0

Water Gas Shift Reaction

Species Balance Equations
◦ Implemented as source term in mass transfer
equation

Kinetics

Probability of Carbon Formation
◦ Boudouard Reaction
◦ CO/H2 Reaction
◦ If carbon activity is greater than 1 then carbon will
form in the cell

Electrochemistry
◦ Anode Oxidation of CO and H2 Fuels
◦ Cathode Reduction of O2
◦ Species Balance Equations

Ion and Charge Transfer
Summary of Charge Transfer Equations used in Model
Electrode Backing
Layers
Anode ERL
Cathode ERL
Electrolyte

Cell Potential (Voltage)
BC=0V


Varied BC
Relationship between potential and current
density determined by Butler-Volmer kinetic
equation
General Equation for activation polarization

H2 kinetics

CO Kinetics

O2 Kinetics

Current Density Relationships

Electronic and Ionic Conductivities
Summary of Effective Conductivity Equations used in Model
Electrode Backing
Layers
Anode ERL
Cathode ERL
Electrolyte
Cell Dimensions (mm)
Cell length
100
Air channel height
1.0
Cell height
3.31
Cathode Backing Layer Height
0.05
Interconnect Height
0.5
Cathode ERL Layer Height
0.01
Fuel channel height
0.6
Electrolyte Height
0.02
Anode Backing Layer Height
0.6
Anode ERL Layer Height
0.03
Cell Materials
Anode and Cathode Interconnect
Stainless Steel
Anode Electrode and Anode ERL Layer
Ni-YSZ (Nickel - Yttria Stabilized Zirconia)
Electrolyte
YSZ (Yttria Stabilized Zirconia)
Cathode Electrode and Cathode ERL Layer
LSM-YSZ (Strontium doped Lanthanum
Manganite – Yttria Stabilized Zirconia)
Physical Properties and Parameters
Anode
Cathode
Permeability (m2)
2.42 x 10 -14
2.54 x 10 -14
Porosity
0.489
0.515
Pore Diameter (µm)
0.971
1
Electronic/Ionic/Pore Tortuosity
7.53, 8.48, 1.80
7.53, 3.4, 1.80
Electronic/Ionic Volume Fraction
0.257, 0.254
0.232, 0.253
3.97x10 6 , 7.93x10 6
3.97x10 6 , 7.93x10 6
Solid Thermal Conductivity (W/m-K)
11
6
Solid Specific Heat Capacity (J/kg-K)
450
430
Solid Density (kg/m3)
3310
3030
Electrolyte
Interconnect
Thermal Conductivity (W/m-K)
2.7
20
Specific Heat Capacity (J/kg-K)
470
550
Solid Density (kg/m3)
5160
3030
Electronic/Ionic Reactive Surface Area
per Unit Volume
(m2/m3)

5 Separate Fuel Inlet Cases Examined
◦ Fuel concentrations chosen to represent typical syngas
composition ranges.
Simulated Fuel Feed Mole Fractions
Case
1
2
3
4
5
H2
0.30
0.30
0.20
0.30
0.30
H2O
0.07
0.17
0.27
0.07
0.07
CO
0.50
0.40
0.40
0.40
0.40
CO2
0.10
0.10
0.10
0.10
0.20
CH4
0.01
0.01
0.01
0.01
0.01
N2
0.02
0.12
0.02
Inlet Temperature (K)
0.02
0.02
Operating Conditions
1023
Anode Fuel Feed xi
Varies
Cathode Inlet Velocity (m/s) 6.5
Cathode Air Feed xi
.21 O2 .79 N2
Anode Inlet Velocity (m/s)
0.5
Operating Voltage (V)
0.6 to 1.0
Outlet Pressure (atm)
1.0


COMSOL Multi-physics FEM Modeling Software
Domain
◦ 34,400 elements-varied distribution horizontally


Segregated Pardiso Solver with parametric
voltage steps
Dampening Factor 0.05% applied to
electrochemical species and heat generation
source terms


Typical Inlet velocity profile
(0-0.0065m)
Inlet effects occurring in initial
0.2% of length


Typical Inlet pressure profile (0-0.0065m)
Inlet effects occurring in initial 0.2% of length


Case 1 Anode:
No reactions,
κ=2.42x10-14
Case 1 Anode:
No reactions,
κ=2.42x10-5
H2
CO2



Highest WGS rate
observed with
greatest amount of
H2O in fuel (3)
Increased CO2 in fuel
results in negative
reaction rate in FF (5)
Increased CO in fuel
increases WGS rate
(1)




All carbon activities in this study below 1, case 1
with highest observed activities
Increasing H2 or CO from case 1 or decreasing the
current density (incr voltage) will bring the carbon
activity closer to or above 1
Carbon activity in Boudouard reaction (0.925)
greater than CO-H2 reaction (0.766)
Higher carbon activity at electrode inlets
Comparison of Maximum Temperatures for each Case at Ecell=0.7
Case
Max
Temperature (K)

1
2
3
4
5
1036.1
1033.5
1034
1035
1033.3
Example Temperature Profile Case 1, 0.4V
Example Polarization Curve with OCV Case 1
OCV values for all cases ranged between ~0.95 to 1.0V
Case 1 Max Power Density: 720 W/m2
Example Case 1, 0.7V
ERL ranges from 1.58mm to 1.61mm
Most of the current generated in
initial 1.7% to 3.3% of total ERL thickness
Example Case 1, 0.7V
ERL-Electrolyte Interface Current Density
Inlet effects observed in initial 0.2% of total cell length






Model agrees reasonably well with experimental
data, data at slightly different conditions.
Case 1 best performance with max power density
720W/m2, Case 4 2nd best performance
WGS rate increases with more reactant species,
reverses with more product species in fuel
No carbon formation observed under operating
conditions with syngas below 0.95V
Proper selection of microstructural parameters
(permeability) important
Complexity of model allows for significant future
study of parameters, optimization, etc.
1.
2.
3.
http://www.fuelcellenergy.com/assets/PID000156_FCE_DFC3000_r3_hires
.pdf
S.A. Hajimolana et al., “Mathematical Modeling of Solid Oxide Fuel Cells: A
Review,” Renewable and Sustainable Energy Reviews, vol 15, pp.18931917, 2011.
M. Tweedie Thesis. CFD Modeling and Analysis of a Planar Anode
Supported Intermediate Temperature
Solid Oxide Fuel Cell. May, 2014.

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