I do not believe your problem could be related to geometrical descriptions. I am sure you have a bug somewhere. You should have descriptions for the drop from thermodynamic levels at zero current density, the kinetic drop, the Ohms law drop, and transport effects. All of these should show voltage decreasing with increasing current density. My suspicion is that one or more of the first two is unimportant in one of your cases but not the other. Specifically, I would check the H2 diffusion equation, which should not be a factor with CH4 but will be with syngas. H2 diffusion should be much higher than CH4 or CO.
there are two principal thermodynamic aspects that can help you to understand your problem. The first one is the possible different thermodynamic potential of the fuel caused e.g. by different content and ballast gas as e.g. H2O or CO2 or N2 etc. The other aspect is the integration of the fuel processing in the system beeing used to recover the waste heat of the cell (chemical recycling of reaction entropy). I add two of my papers as links that could help you to better understand the problem. Good success. Regs WW
Article Reversible SOFC Model as a Base of Design and Testing
Conference Paper SOFC-Integrated Power Plants for Natural Gas
Definitely YES. When you change the feedstock of the SOFC from syngas (a mixture of CO and H2) instead of CH4 or H2 gas, the SOFC geometry will be impacted.
The reason is that the required flow rates of these different types of gases will be different for the same SOFC power output. This will affect the geometry of the SOFC among many other design features. Also, the heat dissipation from the SOFC will change.
If you have to keep the geometry the same, then the efficiency and power output of the SOFC will be impacted.