The dynamics of a packed bed, used for handling enormous quantities of effluent wastewater from industrial discharge, is a very important issue from a design point of view. Semi empirical Thomas and BDST Models are applied to analyze the dynamic behavior of packed beds filled in with GAC and PAC. Variations in breakthroughs with respect to exhaustion time, various bed depths, flow rates and influent solute concentrations are studied. The linearized BDST model gives very high values of R2=0.9959 (for 20% breakthrough) and R2=0.9578 (for 85% breakthrough), indicating the validity of the model for the present column system for both 20 and 85% of breakthroughs. For breakthroughs, below the 50% saturation, the BDST model is used to estimate the design of columns with various scale-ups of the process for other flow rates and initial adsorbate concentrations without any additional experiments. BDST coefficients of lower breakthroughs, below 50%, can also be used for evaluating other parameters such as critical bed depth, adsorption capacity and rate constant. The values of BDST constants, N0 and K, are not affected by changing flow rates for a particular adsorbent combination and changing influent concentrations. The validity of the Thomas model is ensured by the high R2 values, ranging from 0.855 to 0.925, while estimating the Thomas kTh and q0.