The removal of reactive dye in a fixed bed column packed with orange bagasse was modelled using a model that considers the effects of axial dispersion, external and internal mass transfer limitations, and the equilibrium in the liquid-solid interface. The equilibrium and kinetic parameters were obtained through fit the model to the experimental data. In the parameters identification procedure the PSO optimization method was used. The mathematical model showed good performance when describing the dye adsorption process. Furthermore, orange bagasse is an attractive and cost-effective alternative as an adsorbent to remove reactive blue 5G dye from wastewaters.