Scaling-up Fixed Bed Operations

Rodrigues has presented empirical and semi-empirical approaches which may be used to design ion exchange columns when the solute in the feedstream is Cq and the flow-rate is Mq. The breakthrough point is usually set at the point where the effluent concentration increases to 5 % of Cq. The design equations relate the total equilibrium ion exchange capacity (0 to the volume of resin required (V ) to the time of breakthrough (t ). 

In the empirical approach, the overall mass balance is given by the equation  

It is usually necessary to modify this resin amount by a safety factor (1.2 to 1.5) to adjust for the portion of the total equilibrium capacity that can actually be used at flow rate u and to adjust for any dispersive effects that might occur during operation. 

The semi-empirical approach involves the use of the mass transfer zones. This approach has been described in detail specifically for ion exchange resins by Passino. He referred to the method as the operating line and regenerating line process design and used a graphical description to solve the mass transfer problems. 

For the removal of Ca from a feedstream, the mass transfer can be modeled using Fig. 21. The upper part shows an element of ion exchange column containing a volume v of resin to which is added a volume of the 

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