This work presents a generic modeling framework for the separation of heavy metal using a fixed bed adsorption column. Fixed bed model and intra particle diffusion were successfully used to describe the column behavior. The model assumes local equilibrium between the pore fluid phase and the solid phase, axially dispersed flow pattern in the column, and mass transfer resistances in the particle and in the film around the particle. Pore diffusion and surface diffusion occurs simultaneously and equilibrium is assumed to be established at any location in solid phase. The flow of mass transfer zone (MTZ) inside the column (i.e.) the concentration gradient was obtained by making the solute balance of the bulk flow and the solid balance (i.e.) adsorbent balance over the differential volume. The fluid phase mass balance describes the spatial and temporal variations of the adsorbate concentration in the main fluid-stream. The respective equations were solved simultaneously using the finite difference method (FDM), FDM code is transformed into the computer code and the results were obtained. The curve exhibits both parabolic and hyperbolic behavior. Since, Peclet number is (NPe=78.15) greater than one, so advection is the dominant partner in the process, from this we can say that diffusion is the rate controlling step. The corresponding result gave the time up to which a practical adsorber could be operated, and also the exhaustion time and maximum loading of the solid phase. From the graph the primary adsorption zone moves downward through the column to regions of fresher adsorbent is observed. Adsorption in activated carbon is usually controlled by two diffusion processes. One is the diffusion of free species through the pore space, and the other is the surface migration of the adsorbed molecules. The surface diffusion could not be ignored in the adsorption onto activated carbon, because its surface area is very large. So, intra particle diffusion model is important and was developed to predict adsorption behavior of an adsorbent pellet. The required partial differential equations were obtained by considering the adsorbate pellet as spherical; from this we get the concentration flow profile of the pellet. Initially the curve exhibits the parabolic behavior but as time proceeds it was hyperbolic nature. The main aim of solving this intra particle diffusion model was not only to analyze the kinetic behavior but also to calculate the uptake capacity of the GAC pellet and effectiveness of adsorption. Thus the concentration flow from (C = Co @ r=R) to (C = 0.34 Co @ r =0). The above said result was obtained for the simulation parameter stated below. Intra particle diffusion model were also applied to desorption of the GAC pellet. It also reveals the same result as obtained regarding the shape of the profile. It was found that the particles are not fully desorbed. Since, it has some desorption capacity. Desorption is conducted by decreasing the concentration by step-down input. The results obtained are (C = 0.34Co @ r = 0) & (C = 0 @ r =R). Desorption breakthrough were also drawn from the model obtained for the control volume (A.dz) of the column. Here, both advection and diffusion exhibits the same driving force. (i.e.) Peclet number is close to one. The nature of the curve is same for all bed heights. Initial and boundary conditions were added to the differential mass balance equation via computer code. Dankwerts boundary conditions were taken into account because the accuracy could be increased in the simulation. Pore diffusivity of 1.36*10 m/s was obtained. The desorption hysteresis was experimentally determined, and its effect was ascertained by comparing desorption curves obtained following the adsorption and desorption branches of the isotherm. In order to validate the developed model, it is necessary to compare this with the experimental results. For that experimental works were carried out in the laboratory scale. An adsorber with the 5 * 2.5 cm was used. Heavy metal in the aqueous phase was added to the column which was packed with the GAC. GAC was prepared from the raw saw dust. Ni, Cuand Zn were taken for analysis. Internal mass transfer resistance due to pore diffusion mechanism was considered in the model. Excellent agreement was observed, when the intra particle diffusion model was integrated to the whole column to get the fixed bed model. Simulation parameters were obtained from the laboratory scale. The model developed adsorption and desorption breakthrough curve were compared with the experimental results. The outcome shows that the deviation of the simulated curve with the experimental one was not very significant and encourages one to move towards the exactness. The objective of this study was to model the adsorption breakthrough curves and desorption profiles using a sound physical model, to point out the important parameters of the adsorption and desorption phenomena under the given experimental conditions, and to show the strong influence of the isotherm (i.e., the thermodynamic equilibrium) on both adsorption and desorption breakthrough profiles. It is our belief that the findings presented here are of capital importance for a proper design adsorption/desorption processes.