The separative capacity Д of a stage receiving feed of atom fraction z at rate Z and producing heads of atom fraction у at rate M and tails of atom fraction x at rate N is

Д = M(2y — 1) In + N(2x — 1) In jZ— — Z(2z — 1) In (12.253)

Substitution of Eq. (12.10) for M, (12.11) for N, (12.18) for у in terms of z, and (12.20) for x in terms of z into Eq. (12.253) and simplification leads to

Л = ^TZ-f W — 1) In 7 ~ (7 — 1) In (3 + z [((З + 1X7 — 1) In/3 — (7 + 1 № — 1) In 7] )

(12.254)

In this general expression, the ratio of total flow to a stage to separative capacity of the stage, Z/Д, is a function of stage feed composition z. Hence, for this general case, the total flow to all stages cannot be obtained simply as DfZ/A), as was done in Sec. 11. That is, the concept of separative capacity does not provide a simple, accurate way of evaluating the total flow in general for a p-up, q-down cascade. There are, however, a number of practically important special cases for which the term in braces of Eq. (12.254) is substantially or completely independent of z, in which the separative capacity may still be used.