9.3 Separation Factor

In the ideal cascade discussed up to this point, each stage receives as feed two streams of the same composition, a tails stream from the stage next higher in the cascade and a heads stream from the stage next lower in the cascade. In such a cascade the heads separation factor Д, tails separation factor 7, and overall separation factor a are related by

P = y=aU2 (12.230)

The cut в at which condition (12.230) is satisfied is given by

1)2

fi + l

The cut thus ranges in value from l/(/3 + 1) at z = 0 to /3/03 + 1) at z = 1. Because (3 for most isotope separation processes is close to unity, в in this type of ideal cascade must be close to |.

In some isotope separation processes it is impractical to operate a stage at a cut of 5 for mechanical or hydraulic reasons, and in others the separative capacity of the stage is higher at a cut substantially different from f. In the Becker separation nozzle process described in Chap. 14, the separative capacity of a stage producing a heads stream at a given rate is substantially higher at a cut of | than at a cut of |.

To permit operation at a cut different from ; while still ensuring that the composition of heads and tails streams entering each stage be equal requires a more complex cascade

connection scheme than the one shown in Fig. 12.13. Figure 12.25 is an example of such a more complex cascade in which the cut of each stage would be approximately 5. In this cascade the heads stream leaving a stage is fed to the stage two stages up (at higher enrichment) in the cascade and the tails stream leaving a stage is fed to the stage one stage down in the cascade. Olander [01] calls this a “two-up, one-down” cascade. The condition for an ideal cascade, that the streams entering a stage have the same composition, applied to this cascade, requires that

*/+i = Уі-г

in terms of fractions, or

£i+ 1 — Vi— 2

in terms of ratios. From the definition of separation factor a,

Vi-2 ~ ab-2

From the definition of tails separation factor 7,

Іі— 1 = ?7—2 = 7І7-2

Similarly, ?/ = 7?/-і = 72£i-2

and |,+ i = 7 %i — 73£i-2

From (12.233), (12.234), and (12.237),

a = 73 7 = aW3

a =0y

7 ~ 1 = (<* , 1)g = (a — 1)6 (12.252a)

p + q

Thus, in a process like the Becker nozzle process, in which it is desirable to design stages for a cut of |, the cascade might advantageously be of the two-up, one-down type shown in Fig.

12.25 with p = 2 and q = 1.