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Adsorption and kinetic modelling of heavy metals uptake from wastewater effluents using indigenous cellulose based waste biomass, such as nipa palm nut (NPN), palmyra palm nut (PPN), oil palm empty fruit bunch (EFB), oil palm fibre (OPF), and oil palm shell (OPS), as potential raw materials for the preparation of activated carbons was studied. Full factorial design of experiments was used to correlate the preparation variables (activation temperature, activation time and acid impregnation ratio) to the lead and copper uptake from aqueous solution. Minitab Release 11.21 was used for statistical analysis. The optimum conditions for preparing activated carbon from NPN for Pb2+ adsorption were as follows: activation temperature of 5000C, activation time of 1hr and acid impregnation ratio of 2:1, which resulted in 99.82% uptake of Pb2+ and 30.20% of activated carbon yield. Different results were obtained for other adsorbents. The experimental results obtained agreed satisfactorily with the model predictions. Proximate analysis was carried out in order to determine the ash content, fixed carbon, volatile matter and moisture content of the raw materials and activated carbons produced under optimum conditions. Bulk density, pH, iodine number and surface area of the activated carbons were also determined. The Fourier Transform Infrared Spectra of the activated carbons indicated the presence of hydroxyl, carboxyl, lactones, phenols and amino groups which are important sorption sites. The results of adsorption studies showed that activated carbons produced from OPS and NPN are the most efficient adsorbents for the removal of Pb2+ from aqueous solutions while NPN and PPN are the most efficient for Cu2+ removal. The amount of Pb2+ and Cu2+ adsorbed was found to be dependent on adsorbent dosage, pH, initial ion concentration, particle size, contact time and temperature. Equilibrium data fitted well to the Freundlich, Langmuir and Tempkin models. The equilibrium data was best described by Freundlich model. The kinetic data obeyed the pseudo first-order, pseudo second-order, Elovich and Bhattachanya-Venkobachor models. Pseudo second-order best described the kinetics of the adsorption process. The determined negative free energy changes (∆G) and positive entropy changes (∆S) indicate the feasibility and spontaneous nature of the adsorption process. The positive values of enthalpy change (∆H) suggest that the adsorption process is endothermic. A mini packed bed adsorption column was fabricated and used for continuous adsorption study. The column experiments showed that adsorption efficiency increased with increase in the influent concentration and bed depth and decreased with increasing flow rate. Column adsorption kinetics was described with Thomas and Yoon and Nelson models and the kinetic constants. The comparison of the experimental breakthrough curves to the breakthrough profiles calculated by Yoon and Nelson method showed a satisfactory fit for all the adsorbents.