Mathematical models can be useful to predict the behavior of particulate systems, as it is the case of packed-bed bioreactors (PBBs) used for solid-state fermentation (SSF). The models also simplify the processes scale-up, and depending on the accuracy of the model, critical parameters can be predicted, as temperature, moisture content and maximum bed height. In the current paper, mathematical models and simulations were used to predict the optimal conditions for enzymes production by means of SSF in PBBs. Two models available in literature were applied: a recently proposed two-phase and two-dimensional (2-D) model and a modified Damkohler number (Da(m)) approach, considering maximum temperatures of the bed and maximum bed height to allow good production of enzymatic activities by the fungus Myceliophtora thermophila I-1D3b. Based on simulation results, experiments in bench and pilot-scale PBBs were performed and analyzed. By comparing experimental and simulated results of temperatures, the 2-D model showed to be more accurate than Da(m) approach. Despite of the temperature increase in pilot-scale PBB, the bioreactor scale-up with the fungus M. thermophila in substrate composed of sugarcane bagasse (SCB) and wheat bran (WB) (weight proportion 7: 3) could be considered as feasible for cellulolytic and xylanolytic enzymes provision, for instance, for second generation ethanol production chain, although issues related to airflow distribution and substrate shrinkage in pilot-scale PBB must still be further overcome.