Rodrigues166' has presented empirical and semi-empirical approaches which may be used to design ion exchange columns when the solute in the feedstream is c0 and the flow-rate is u0. The breakthrough point is usually set at the point where the effluent concentration increases to 5 % of c0. The design equations relate the total equilibrium ion exchange capacity (0 to the volume of resin required (Vr) to the time of breakthrough (tB).
In the empirical approach, the overall mass balance is given by the equation:
Eq. (17) ^ = (1- z)Q!s Q0 (the mass capacity factor)
and Fis the bed volume with void space e.
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 V^ of the feedstream containing Ca^. It is added at a flow rate (FL) for an exhaustion time t^. The concentration of Ca4^ as it passes through the column element is reduced from xexl to xex2- Therefore, the resin, which has an equilibrium ion exchange capacity C, increases its concentration of Ca" fromj^ to^i-In this model, fresh resin elements are continuously available at a flow rate (Fs)=v/t0, which is another way of saying the mass transfer zone passes down through the column.
The lower part of Fig. 21 shows the operating lines for this process. The ion exchange equilibrium line describes the selectivity in terms of a Freundlich, Langmuir or other appropriate model.
The equations for the points in the lower part are given by:
(Ca~ in the exhausted streamstream)
and the slope of the operating line:
HMD VAlft IN
HMD VAlft IN
Ca in solution
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