This work presents the thermochemical analysis of a packed-bed reactor via multi-dimensional CFD modeling using FlexPDE and COMSOL Multiphysics. The temperature, concentration, and reaction rate profiles for methane production following the Fischer−Tropsch (F-T) synthesis were studied. To this end, stationary and dynamic differential equations for mass and heat transfer were solved via the finite element technique. The transport equations for 1-D and 2-D models using FlexPDE consider dispersion models, where the fluid and the catalyst can be treated as either homogeneous or heterogenous systems depending on the gradient extents. On the other hand, the 3-D model obtained in COMSOL deems the transport equations incorporated in the Porous Media module. The aim was to compare the FlexPDE and COMSOL models, and to validate them with experimental data from literature. As a result, all models were in good agreement with experimental data, especially for the 2-D and 3-D dynamic models. In terms of kinetics, the predicted reaction rate profiles from the COMSOL model and the 2-D dynamic model followed the temperature trend, thus reflecting the temperature dependence of the reaction. Based on these findings, it was demonstrated that applying different approaches for the CFD modeling of F-T processes conducts reliable results.