Key features of hydrocarbon-fueled solid oxide fuel cell stack operation are elucidated by examining its local thermodynamic states with an aid of three-dimensional numerical simulations. A high-fidelity physical model, which resolves the coupling between thermo-chemical reactions and heat and mass transport, is developed and validated. To elucidate important reactions and transport phenomena, local thermodynamic state variables of hydrocarbon-fueled operation are compared with those estimated by assuming pure-hydrogen-supplied operation. Results show that thermochemical reactions proceed at high rates through the thick anode support layer. This induces complete methane conversion as soon as it is introduced to the anode and thermochemical reaction zones concentrated in the vicinity of the fuel inlet. In spite of the fast reaction processes, hydrocarbon-fueled operation has the same electrical current density profile as pure-hydrogen-supplied operation, resulting from changing its local thermodynamic states. Given that the presence of carbon substances and thermochemical reactions, in hydrocarbon-fueled operation, local chemical and electrical conditions are substantially different from those of pure-hydrogen-supplied operation. A lower hydrogen concentration induces a higher concentration overpotential and decreases a reversible electrochemical potential. A lower exchange current density is offset by increasing an activation overpotential at a given applied current. All these reduce the overall cell voltage, as compared to pure-hydrogen-supplied operation. Variation of transport properties such as diffusivities and viscosities influences heat and mass transport such that substantial stresses can be imposed on cell materials. In addition, thermal conditions result in lower incoming-gas heating and a larger heat transfer rate to a neighboring repeating unit. A larger temperature gradient near the fuel inlet may also impose stresses cell materials. A lower power output, attributed to the electrochemical losses in a form of activation and concentration overpotentials, and materials degradation can be accompanied in hydrocarbon-fueled stack operation.