Types of Separations Cascades

The countercurrent (recycle) cascade (Fig. 8.3) is much more useful because by reprocessing the waste stream a larger fraction of the desired isotope is recovered. In a recycle cascade the i th stage is fed by a mixture of the product, Y( i) from the (i — l) th, and the waste, X(i+ X) from the (i + l) th, stage. A distillation column 

In Equation 8.3 yp is the product analysis at the last stage and P is the product withdrawal rate, andXi+i is the waste withdrawal at stage (i + 1). The ratio (Xi+i/P) is 

At total reflux the concentration differences on successive stages are at their maximum but as production begins and reflux deceases these concentration ratios decrease. They reach unity (no enrichment) at minimum reflux. Materials balance considerations lead to Equation 8.5. 

When a lies close to 1 the minimum reflux ratio is large, but since Xj varies with stage number so does [n(i+1)/P]MiN- At the feed point in a 235U plant enriching to 90% 235U, (nf/P)MiN is 29,100, but at the product end of the cascade it approaches zero. 

A practical isotope separation plant can operate at neither minimum reflux (where the separation is zero, but the rate of production is high), nor at minimum number of stages (where the rate of production is zero, but the separation is high). A compromise is required. Since optimum reflux varies with stage number it is customary to employ tapered cascades for isotope separation. This results in marked savings in material hold-up, and in plant size and investment. 

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