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.