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Advanced Physico-chemical Methods of Treatment for Industrial Wastewaters  107























              Figure 2.9 Ion exchange: depicting mass transfer and the rate controlling step.


              these processes, it can be safely assumed that diffusion is the rate-controlling
              step. A number of diffusion models, both pseudo-homogeneous and hetero-
              geneous, have been developed for various processes. The main disadvantage
              in mathematical modeling of sorption processes is that many times, gener-
              alized models are not available and a system specific mathematical treatment
              has to be developed.
                 Ion exchange treatment, similarly to adsorption, is commonly practiced in
              plants using a fixed-bed column chromatographic operation (Figure 2.10).
              The flow of liquid can be upflow or downflow, and well-established principles
              of column design for fixed-bed operation are applicable. It should be pointed
              out that in the ion exchange column, the resin bed is normally only filled up to
              50% to have free space for the expansion of the resin bed due to swelling. Free
              space is also required in the backwashing step, which results in fluidization of
              the bed due to upflow backwash. The kinetics and pressure drop consider-
              ations dictate the selection of suitable resin bead size.
                 In the column chromatographic operation, the resin bed is progressively
              consumed in terms of available capacity through the exchange of pollutant
              species. The unreacted zone moves in the direction of flow, as shown in
              Figure 2.10. When the reaction front reaches the end of column, the pol-
              lutant starts appearing in the exit solution, and the concentration profile in
              the effluent takes the shape of a breakthrough curve. The lower limit of the
              permissible concentration of the pollutant is usually set as the breakthrough
              point, and the column is switched for the regeneration cycle, once the
              breakthrough point is reached. Thus, the nature of the breakthrough curve
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