1. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Single-Chamber Fuel Cell Models D. G. Goodwin, Caltech Develop validated physics-based models of SCFC operation Use models along with test results to develop understanding of factors determining performance Use to aid in design optimization

2. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Multiple models Model 1: a simple model for qualitative parametric studies –Allows rapid exploration of the effects of various parameters on performance Model 2: Solves 2D channel flow assuming fully developed flow. Computes –Species concentration profiles –Current density profiles –Power output vs. load Model 3: Solves 2D reacting channel flow accurately (in development, Yong Hao) Seconds on a laptop PC Minutes on a linux workstation Minutes to hours Computational expense

3. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Model 1: a “zero-dimensional” fuel cell model Can be used to model single- or dual-chamber designs No consideration of gas flow Approximate equilibrium treatment of hydrocarbon oxidation Includes diffusion through electrodes, activation polarizations, ohmic losses Can compute current- voltage curves Written in a simple scripting language (Python) Uses the Cantera software package to evaluate thermodynamic and transport properties, and compute chemical equilibrium (www.cantera.org)www.cantera.org Good for semi-quantitative parametric studies

4. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Idealized Geometry Each side exposed to uniform gas with specified composition –No depletion in gas –Corresponds to limit of fast transport –Compositions can be set equal (single-chamber) or each independently specified (dual- chamber) Uniform cathode-side gas Uniform anode-side gas Porous Cathode Porous Anode

5. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Electrochemical Reactions Anode reactions –H 2 + O 2- = H 2 O –CO + ½ O 2- = CO 2 Cathode reaction –O 2 = 2O 2- Catalyst selectivity –Reactions allowed to occur at opposite electrode with relative rate 0 < F c < 1 –F c > 0 lowers OCV –At F c = 0, OCV = 0

6. Integrated MicroPower GeneratorProgram Review, October 18, 2002 partially-oxidized gas mixture Gas Composition Approximate treatment of partial oxidation Assume gas is a mixture of the input gas composition + equilibrium composition No selectivity assumed – CO, CO 2, H 2, and H 2 O all present 600 C Input: 1:3:12 C3H8/O2/He Inlet gas equilibrium gas F eq 1 - F eq

7. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Transport through electrodes Gas composition at electrode/electrolyte interface determined by diffusion through porous electrode Effective diffusion coefficients account for pore size, porosity, and tortuosity of electrode microstructure Concentrations at electrode/electrolyte interface used to calculate Nernst potential reactant product electrode Assumed uniform gas composition concentration gradients in electrode drive diffusion

8. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Electrode Kinetics

9. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Cathode Activation Polarization Represents largest loss Dependence on oxygen partial pressure assumed first-order Range considered

10. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Anode Activation Polarization Assumed not to be rate-limiting Anode exchange current density set to a large multiple of cathode exchange current density (100 – 1000)

11. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Electrolyte Ohmic Loss Value for GDC used

12. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Current Density Computation Nernst potential calculated using concentrations at electrode/electrolyte interfaces, and includes effects of back reaction Given E load, this equation is solved for the current density

13. Simulation of Test Results with Ni-SDCSDCSSC-Pt-SDC at 600 C

14. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Test results can be accounted for with physically- reasonable parameters Experimental Ni-SDCSDCSSC-Pt-SDC results at 600 C best fit by –I 0,c = 70 mA/cm 2 –80% electrode selectivity –50% conversion to equilibrium products Accurate modeling of transport limit requires more accurate treatment of transport processes – see Model 2 results

15. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Gas Composition Effects Increasing percent conversion to equilibrium products moves the transport limit to higher current densities For fuel-rich input mixtures, equilibrium composition contains significant CO and H 2, in addition to CO 2 and H 2 O Therefore, non-electrochemical oxidation of CO and H 2 not likely to be a problem as long as a fuel-rich mixture is used 60% 10%

16. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Single Chamber vs. Dual Chamber Dual chamber calculation sets cathode gas composition to air, and eliminates the back reactions at the electrodes Dual Single

17. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Catalyst selectivity effects More selective Less selective Catalysts must have reasonable selectivity for electrochemical reactions in order for SCFC to function

18. Integrated MicroPower GeneratorProgram Review, October 18, 2002 SCFC Loss Mechanisms Dominated by losses due to –Low cathode activity –Incomplete cathode and anode selectivity

19. Model 2: Microchannel SCFC Simulations

20. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Model Overview Inputs –Inlet gas composition, temperature, pressure –Load potential –Parameters characterizing kinetics, electrode transport, geometry, etc. Outputs –2D spatial distributions of C 3 H 8, CH 4, CO, H 2, CO 2, and H 2 O in channel –Current density profile J(x) Assumes isothermal, isobaric conditions Includes an unsealed, non-catalytic plate (interconnect) separating anode and cathode gas streams

21. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Model Geometry Electrolyte Cathode Anode Non-catalytic partition Premixed Fuel / air mixture Cathode-side flow channel Anode-side flow channel

22. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Mathematical Model Species equations finite- differenced and integrated in time to steady state. Porous electrodes handled by locally modifying diffusion coefficients Species equations solved simultaneously with equation for current density

23. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Model Problem Channel height = 700 m, length = 10 mm 200 m anode, 50 m cathode Electrode porosity 0.4, pore size 0.1 m 15 m GDC electrolyte T = 600 C, P = 1 atm Premixed 1:3 C 3 H 8 / air Partial oxidation rate at anode set to give nearly complete consumption of propane Other parameters same as in zero-D model

24. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Porous Electrode Transport Gas must diffuse through porous electrodes to reach electrochemically-active triple-phase boundary Process modeled with effective diffusion coefficients for each species that interpolate between Knudsen and ideal gas limits Effective diffusion coefficient close to the Knudsen limit reaction reactants products

25. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Partial Oxidation Global partial oxidation reaction C 3 H 8 + 3/2 O 2 => CO + 4H 2 –Produces electrochemically-active species –assumed to occur throughout the anode –May occur on the cathode also Rate modeled as first-order in C 3 H 8 and O 2 Magnitude set to lead to nearly complete conversion in the anode- side exhaust – ample residence time for complete conversion (50-100 ms vs. 1 ms) –Degree of conversion can be tuned experimentally by material choice, and anode fabrication methods

26. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Velocity Profile Porous anode Porous cathode This velocity profile is imposed, based on known solution for viscous fully-developed flow

27. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Species Distributions at Max Power flow Anode on left Cathode on right

28. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Current Density Distribution Movie shows steady-state J(x) for load potentials ranging from zero to 0.9 V

29. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Predicted Performance at 600 C Predicted OCV = 0.9 V, peak power density = 85 mW/cm 2 Easily meets target SCFC performance of 50 – 100 mW/cm 2.

30. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Conclusions Performance targets appear to be easily achievable Largest potential gains in performance: –improved cathode catalytic activity –improved electrode selectivity Separator plate may not be necessary As long as gas composition is fuel rich, non-electrochemical oxidation of CO and H 2 will not go to completion, and therefore nonselective catalyst for partial oxidation is acceptable.

31. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Future Work Validation against all available test data – single-chamber, dual-chamber, etc. Prediction of coking behavior Prediction of low-temperature performance Integration with Swiss Roll heat exchanger model to predict operating temperature

32. Integrated MicroPower GeneratorProgram Review, October 18, 2002 Summary Two numerical models have been developed to predict SCFC performance. –A simple model useful for interpreting test data –A channel flow model useful for predicting micropower generator performance Test results can be accounted for with physically- reasonable kinetic parameters Using these parameters in the channel-flow model leads to performance at 600 C that meets our targets Both models are suitable for use in design and optimization studies, including system studies with the Swiss Roll heat exchanger.