Cascades heads separation factor

Such a simple cascade, with an infinite number of stages each performing an infinitesimal amount of separation, is equivalent to type A differential st e separation. Equation (12.51) is equivalent to the form of the Rayleigh equation (12.35), when one recognizes that w in the simple cascade is equivalent to the heads separation factor 0 in differential stage enrichment, and a in the simple cascade is equivalent to the local separation factor a. ... 

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 /, tails separation factor 7, and overall separation factor a are related by... 

An extension of this development to the general, p-up, <7-down ideal cascade shows that the heads separation factor (I is... 

The cascade receives feed of fraction Zp at flow rate F and produces an upper product of fraction yp at flow rate P, a lower product of fraction yg at flow rate Q, and tails of fraction Xw at flow rate W. For this two-up, one-down cascade, p = 2, q = I, the heads separation factor /3 is... 

If the heads separation factor p is constant throughout such a simple cascade, the fraction of deuterium that may be recovered depends on the number of stages n and the overall enrichment oj in accordance with... 

A high, but attainable, overall separation factor of a = 7 will be used. A heads separation factor such as the one that would be used in an ideal recycle cascade of 3 = y/a = y/f = 2.646 will be assumed. Then the number of stages n is given by... 

In Fig. 13.15, the first m—2 stages constitute a simple cascade, operated without recycle, with constant heads separation factor 0. The recovery of deuterium from a simple cascade of m—2 stages operated at constant 0 is... 

An electrolytic hydrogen plant fed with natural water containing 0.0149 percent deuterium is operated as a simple cascade, without recycle, to produce water containing 0.142 percent deuterium. The stage separation factor a has the value 7.0, and the heads separation factor 0 is independent of stage number. 

If the separation factor for the system is known and the variation of the reflux ratio is specified as a function of stage number in the cascade, the number of ideal stages required to separate feed into product and tails of specified composition can be calculated. For example, starting with the known tails composition xn, the heads composition from stage 1,, is... 

This relation between the heads and tails separation factors and the stage separation factor is the key property of an ideal cascade. 

Figure 12.27 represents one stage of an ideal, close-separation, one-up, one-down cascade whose feed flows at rate 2M and contains Zj fraction U, Zg fraction U, and Zg = 1 — Zs — z fraction At the cut of used in such a cascade, heads flows at rate M and contains fraction and>>6 Stage tails flows at rateAf and containsXg fraction andxg Stage separation factors are defined as... 

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