A steady-state diffusion model comprising of diffusion and reaction in a catalyst pellet was used to study and understand the effect of the approximation of the catalyst effectiveness factor in the modeling of trickle bed reactors. The hydrogenation of alpha-methylstyrene was chosen as the case study reaction from literature for liquid-limited reaction conditions. The effectiveness factor values in this study were sensitive to reactor scale equations during the prediction of reactor performance. The approximation of accounting for the overall catalyst effectiveness factor in the reactor scale model equations from different models and solving the reactor scale model equations by different modeling approaches was assessed. It was observed that evaluating the overall effectiveness factor from pellet scale model equations and integrating the parameter in the reactor scale axial dispersion model at every local axial collocation point to simulate the reactor performance showed better agreement to the experimental data. This approach evaluates the effectiveness factor locally with the variation of the reactant concentration at different axial points across the reactor rather than using one value for the entire reactor. The approach of using a single effectiveness factor for the whole bed and using the effectiveness factor approximated as a fitted polynomial to the reactant concentrations did not properly predict the reactor performance.