Power to gas is an attractive option for storing excess energy from fluctuating renewable energy sources. In recent years, the concept has gained great interest. An essential part of the process chain of power to gas is the methanation of CO2. Within this work the catalytic methanation of pure CO2 and of biogas is modeled in a three-dimensional polytropic pseudo-homogeneous flow tube and numerically simulated at different loads. The results represent axial and radial quantitative information about the reaction behavior under the different boundary conditions.