This study aims to determine the operating conditions to implement the Dimethylphthalate removal using an activated carbon prepared from Arundo donax, carbonized at 358 degrees C during 13 min. To achieve this objective, the study is conducted in batch and dynamic mode. Several kinetic models are applied, namely pseudo-first order, pseudo-second order, intragranular, and Bangham models. The pseudo-second-order model fits the data perfectly, the estimated regression coefficients >0.999. The intragranular diffusion takes place in two stages. The two-parameter (Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich) and three-parameter models (Redlich-Peterson, Sips, and Toth) are applied to model the equilibrium isotherms. The nonlinear regression methodology based on the error functions (hybrid fractional error function, Marquardt's percent standard deviation, average relative error, Sum of the absolute errors) is applied. The HYBRID fits properly the data showing that the Temkin model gives the best fitting (R-adj(2) = 0.992), and the Dubinin-Radushkevich model the worst (R-adj(2) = 0.793). The thermodynamic study shows that the adsorption occurs according to a physical process. The DMP desorption is more effective with a 5% NaOH solution. In dynamic mode, the runs are conducted in fixed bed column. The effect of the bed height, the DMP initial concentration, and the flow rate on the breakthrough curves is investigated, then these breakthrough curves are modeled using the Thomas and Bed Depth Service Time models. The regeneration of the exhausted Arundo donax activated carbon is performed in a column, after 5 cycles, the breakthrough time decreases from 65.3 to 26.8 h, however, the exhaustion time varies less rapidly.