Mathematical modeling of transport and electrochemical phenomena within SOFCs can lead to improved understanding of the involved physical, electrical, and chemical processes and represents a powerful tool for their development. In this context, the present work illustrates a three-dimensional CFD simulation of a planar SOFC unit cell fuelled by modeled biogas / steam mixtures. The simulations estimate the distribution of gas species, the current densities and the potentials, as well as the temperature gradients and confirm that equimolar CH4/CO2 biogas leads to improved performance, while minimal steam addition can prevent carbon deposition.