Theoretical analysis of a solid oxide fuel-assisted electrolysis cell is performed.

Model of the electrolysis cell is proposed based on an electrochemical model.

Effect of the addition of methane on the electrolysis cell is presented.

The solid oxide fuel-assisted electrolysis cell requires lower power input than a conventional electrolysis cell.

The cathode-supported configuration is the most favorable design for the solid oxide fuel-assisted electrolysis cell.