Melissa Tweedie
May 1, 2014

http://www.ztekcorporation.com/
CHP Propane Fueled SOFC
Power Plant for large automotive applications http://fuelcellsworks.com/

http://www.ceramatec.com
Reference 2

Electrochemistry
Fuel
Air
Anode Electrode ERL
Electrolyte
Cathode ERL
Cathode Electrode BL
Anode Interconnect
Anode FF
Anode Electrode BL
Cathode FF
Cathode Interconnect




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
Fuel Cell
MSR Reaction
WGS Reaction
Electrochemical Reactions
Concentration Polarization
Activation Polarization
Ohmic Polarization
Types of SOFC Heat Sources
Type Relative % Contribution
Consumption 27
Generation
Generation
Generation
Generation
Generation
6
47
< 1
16
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
Cathode ERL
Cathode BL, FF
Interconnects
Q = 0
Q = 0
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/H
2
Reaction
◦ If carbon activity is greater than 1 then carbon will form in the cell


Electrochemistry
◦ Anode Oxidation of CO and H
2
Fuels
◦ Cathode Reduction of O
2
◦ 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


H
2 kinetics

CO Kinetics


O
2
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 length
Cell height
Interconnect Height
Fuel channel height
Anode Backing Layer Height
Anode ERL Layer Height
Anode and Cathode Interconnect
Anode Electrode and Anode ERL Layer
Cell Dimensions (mm)
100 Air channel height
3.31
0.5
0.6
0.6
0.03
Cathode Backing Layer Height
Cathode ERL Layer Height
Electrolyte Height
Cell Materials
Stainless Steel
1.0
0.05
0.01
0.02
Ni-YSZ (Nickel - Yttria Stabilized Zirconia)
Electrolyte
Cathode Electrode and Cathode ERL Layer
YSZ (Yttria Stabilized Zirconia)
LSM-YSZ (Strontium doped Lanthanum
Manganite – Yttria Stabilized Zirconia)

Permeability (m 2 )
Porosity
Pore Diameter (µm)
Physical Properties and Parameters
Anode
2.42 x 10 -14
0.489
0.971
Electronic/Ionic/Pore Tortuosity
Electronic/Ionic Volume Fraction
7.53, 8.48, 1.80
0.257, 0.254
Electronic/Ionic Reactive Surface Area per Unit Volume (m 2 /m 3 )
3.97x10
Solid Thermal Conductivity (W/m-K) 11
6 , 7.93x10 6
Solid Specific Heat Capacity (J/kg-K) 450
Solid Density (kg/m 3 ) 3310
Electrolyte
Thermal Conductivity (W/m-K)
Specific Heat Capacity (J/kg-K)
Solid Density (kg/m 3 )
2.7
470
5160
Cathode
2.54 x 10 -14
0.515
1
7.53, 3.4, 1.80
0.232, 0.253
3.97x10 6 , 7.93x10 6
6
430
3030
Interconnect
20
550
3030


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
H
2
H
2
O
CO
0.30
0.07
0.30
0.17
0.20
0.27
0.30
0.07
0.30
0.07
0.50
0.40
0.40
0.40
0.40
CO
2
CH
4
0.10
0.01
0.10
0.01
0.10
0.01
0.10
0.01
0.20
0.01
N
2
0.02
Inlet Temperature (K) 1023
Cathode Inlet Velocity (m/s) 6.5
Anode Inlet Velocity (m/s) 0.5
Outlet Pressure (atm) 1.0
0.02
0.02
Operating Conditions
0.12
0.02
Anode Fuel Feed x i
Varies
Cathode Air Feed x i
.21 O
2
.79 N
Operating Voltage (V) 0.6 to 1.0
2


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
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
H
2

Case 1 Anode:
No reactions,
κ=2.42x10
-5
CO
2




Highest WGS rate observed with greatest amount of
H
2
O in fuel (3)
Increased CO
2 in fuel results in negative reaction rate in FF (5)
Increased CO in fuel increases WGS rate
(1)




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All carbon activities in this study below 1, case 1 with highest observed activities
Increasing H
2 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-H
2 reaction (0.766)
Higher carbon activity at electrode inlets

Case
Comparison of Maximum Temperatures for each Case at E cell
=0.7
1 2 3 4 5
Max
Temperature (K)
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/m 2

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

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Model agrees reasonably well with experimental data, data at slightly different conditions.
Case 1 best performance with max power density
720W/m 2 , Case 4 2 nd 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
1917, 2011.
, vol 15, pp.1893-
M. Tweedie Thesis. CFD Modeling and Analysis of a Planar Anode
Supported Intermediate Temperature
Solid Oxide Fuel Cell. May, 2014.