The paper presents a heterogeneous 2D model of a polytropic fixed bed methanation reactor for Co-SOEC syngas. The reactor with 80 mm inner diameter is operated without active cooling. Lab-scale experiments were used for model validation under variation of gas hourly space velocity (GHSV) (2000 h-1, 4000 h-1, 6000 h-1 and 8000 h-1) and pressure (1 bar, 2 bar, 4 bar, 6 bar, 8 bar, 10 bar). The conversion of Co-SOEC syngas containing a mixture of H2, CO and CO2 was calculated based on a two-step methanation kinetic model. Effective methanation kinetics was implemented based on a novel approximation of two different reaction efficiency approaches. The catalytic efficiency approximation combines conventional power law related and a Langmuir-Hinshelwood type reaction efficiency correlation by Roberts and Satterfield. It was found that mass transfer limitation is substantial for highly temperature sensitive polytropic methanation reactor modelling. Despite high exothermic behaviour without active cooling, a stable model set-up was managed entirely without parameter fitting to experimental data for a naturally cooled methanation reactor with highly reactive and undiluted syngas feed. The modelled results of Co-SOEC syngas methanation agree well with the experiments over a wide variety of pressure and GHSV. The interaction and limiting factors of mass diffusion, reaction heat removal, kinetics and thermodynamics can be thoroughly analysed based on the established model, which is a key step for developing highly efficient methanation reactor systems in industrial scale.