Impedance Spectroscopy Study of an SOFC Unit Cell

Model Definition

Model Definition

• Material balances for all species using Maxwell-Stefan• Fluid flow in the open channels and in the porous electrodes:

– Navier-Stokes equations– Brinkmann equations

• Current balances and charge balances– Defined in the electrodes, pore electrolyte, and the electrolyte that

separates the anode and cathode– Electrode kinetics using Butler-Volmer including concentration

overpotential

Model Definition

• Parametric sweeps in the study are done by applying a constant average current density of 1400 [A/m2] at the steady polarization, except for the last case where the current is varied:– A floating potential condition is applied so that an unknown constant

potential is set at the current collector, but an additional equation is added that sets the integral of the current density at the current collector to a fixed value.

Specifying a Harmonic Perturbation

• Add a Harmonic Perturbation feature to the Electric Potential boundary condition

• Make the perturbation small (mV range) in order to obtain a linear approximation of the nonlinear system of equations– Laplace transform allows for solution in the frequency domain, which

is done automatically by COMSOL

A Note on Post Processing

• In the Nyquist plot the complex impedance Z is plotted, which is evaluated using integral operators at the current collector boundary

• Z = ( Pertubation Voltage ) / ( Pertubation Current )• For a more accurate evaluation of the integral of the current

density at the current collector boundary, the reacf() operator is used in combination with an integration operator using summation over the node points (See the Comsol Multiphysics Reference Manual for a general description of the reacf() operator)

• The ”Compute Differential” check box should be disabled in the Nyquist plot in this case when plotting only the resulting harmonic pertubations

Study Settings

• AC Impedance Stationary Study used• Default solver sequenced modified to use a Fully Coupled

solver

AC ImpedanceStationary StudySelected in theModel Wizard

Add a Fully CoupledSolver and disableSegregated

Influence of Cathodic Exchange Current Density

Increasing frequency

Anodic exchange current density = 0.1 [A/m2]Electrolyte conductivity = 5 [S/m]Reference diffusivity = 3.8·10-8 [m2/s]

The anodic and cathodic circles become moreseparated as the difference between the two exchange current densities increases:- Turquoise curve i0_a = i0_c

Influence of Anodic Exchange Current Density

Cathodic exchange current density = 0.01 [A/m2]Electrolyte conductivity = 5 [S/m]Reference diffusivity = 3.8·10-8 [m2/s]

The anodic and cathodic circles become moreseparated as the difference between the two exchange current densities increases:- Blue curve i0_a = i0_c

Influence of Electrolyte Conductivity

Anodic exchange current density = 0.1 [A/m2]Cathodic exchange current density = 0.01 [A/m2]Reference diffusivity = 3.8·10-8 [m2/s]

Influence of Diffusivity

Anodic exchange current density = 0.1 [A/m2]Cathodic exchange current density = 0.01 [A/m2]Electrolyte conductivity = 5 [S/m]

Influence of Current Density

Anodic exchange current density = 0.1 [A/m2]Cathodic exchange current density = 0.01 [A/m2]Electrolyte conductivity = 5 [S/m]

Anodic exchange current density = 0.1 [A/m2]Cathodic exchange current density = 0.01 [A/m2]Electrolyte conductivity = 5 [S/m]Reference diffusivity = 3.8·10-8 [m2/s]factor = 1 corresponds to 1400 [A/m2]

Concluding Remarks

• The model is small in order to run a parametric sweep and a frequency sweep in every parameter value in less than five minutes– Longer channels and larger number of channels can also be simulated

• Heat transfer analysis can also be added• There are a lot of conclusions that can be drawn from these

model studies, this only presents a scratch on the surface