Theory of Cascades Terminology

A number of separative units operating in parallel, all taking feed of identical composition, and discharging partially enriched product and partially depleted waste streams comprise a stage. A single unit may suffice for a stage, but more often several units or many units are required. Because the separation per stage is almost 

The separation factor, r, in an isotope separation process is the ratio of the relative concentration of desired isotope in the product, p, to its relative concentration in the feed, f. Denoting the feed to the i th stage, the i th section of an overall plant, or the ith overall plant, as mol/s of isotope with an isotope fraction Zj, yielding product at a rate of Yj mol/s of analysis yi, and waste at a rate of Xj mol/s and isotope analysis Xj, we have for a two isotope feed 

The primed or unprimed symbols refer to isotope fractions. The single stage separation factor for infinitesimal product removal (yi/zj 0), (rj)0, is given the symbol a . The i s index the stage number. Most often a is close to unity and it is convenient to define the isotope enrichment factor (the single stage enrichment factor), e, between the i th and (i + l) th stage 

To reasonable approximation e, a and (rj+1)o are independent of stage number. In naturally occurring uranium the mass of the primed isotope, 235U, is 235, the unprimed, 238, and x /(1 — x() = 0.0072. For enrichment to 90% 235U 

For ideal gaseous diffusion of UF6 through a porous yet restrictive barrier (see Fig. 8.2), Graham s law yields 

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