The present study shows a methodology for analyzing and designing a cylindrical packed-bed reactor considering stationary and dynamic models. The design comprises the reactor's stationary and dynamic governing differential equations for mass and heat transfer under multi-dimensional approaches. The results included simulation of concentration, temperature, and reaction rate profiles via the 1-D and 2-D differential equations solution with FlexPDE software. The analysis was complemented with a scaled 3-D dynamic model implemented in COMSOL Multiphysics. Both FlexPDE and COMSOL Multiphysics relied on the finite element technique to solve the governing differential equations. The simulated concentration and temperature profiles from both FlexPDE and COMSOL models were compared to experimental data gathered from literature (specifically from a Fischer-Tropsch process to produce low-molecular-weight hydrocarbons in a configuration of cylindrical packed-bed reactors). Simulated concentration and temperature profiles from the 2-dimensional dynamic model and the COMSOL model were in good agreement with the trend observed in experimental data. Finally, the predicted reaction rate profiles from the COMSOL model and the 2-dimensional dynamic model followed the temperature trend, thus reflecting the temperature dependence of the reaction.