In some isotope separation plants, notably those using distillation or exchange processes, it is more economic to use a constant interstage flow rate over a considerable composition interval rather than a flow rate that decreases steadily from the feed point to the product ends, as is characteristic of an ideal cascade. Cohen [C3] has called such cascades “squared-off’ cascades and has derived equations for their separation performance. This section summarizes the derivation for a close-separation, squared-off cascade.

In the enriching section of a cascade with constant tails flow rate N, the change in composition x with stage number і is given by differential equation (12.128). The number of
enriching stages nn needed to span the composition range between Xi and x2 is then obtained by integration of

di_ _ _____________ 1_____________

dx (a — 1)*(1 — x) — (P/N)(yp — x)

If a constant value of N is used for the entire enriching section spanning the composition range from zF to yp,

________ Ыур ~ zF)__________

yp + zp — 2yP zF-c(yp — Zp)

In the stripping section similar equations hold, with substitution of — W for P and xw for yp in Eqs. (12.224) through (12.227). Equation (12.228) for a square stripping section, with constant value of N on all stages, becomes

__________ b(zF ~ xw)__________

zF + xw — 2zF xw — c(xw — zF)