Conventional solid oxide fuel cells (SOFCs) could suffer from carbon deposition when fueled with hydrocarbons. For comparison, a new type of SOFC with porous electrolyte can resist carbon deposition because it allows oxygen molecules to transport from the cathode to the anode. As the transport of O-2 to the anode lowers the fuel cell performance and causes the risk of explosion, the rate of O-2 transport must be well controlled to ensure efficient and safe operation. Following our previous model, this paper focuses on electrolyte porosity optimization under various inlet methane mole fractions, inlet oxygen mole fractions and inlet gas flow rates. Furthermore, a new design with a partial porous electrolyte is proposed and numerically evaluated. The new design significantly improves the electrochemical performance compared with all-porous one. A conversion rate >90% from methane to syngas is achieved at the 0.33 inlet CH4 mole fraction with the new design. The results enhance the understanding of all porous solid oxide fuel cells and the mechanism underlying, inspiring novel designs of solid oxide fuel cells.