Stage separation factor

The equihbrium constant for this reaction is ca 1.022 at 100°C. The B concentrates in the Hquid phase (23). However, the vapor phase contains ca 40% undissociated complex, which lowers the effective single-stage separation factor to ca 1.014. 

Equations for Large Stage Separation Factors. The preceding results have been obtaiaed with the use of equation 2 and by replacing the finite difference, by the differential, chc/ dn both of which are vaUd only when the quantity (a — 1) is very small compared with unity. However,... 

Fhe Stag C Separation Factor. The stage separation factor, in all probabiUty, is appreciably different from the ideal-point separation factor because of the existence of four efficiency terms ... 

The stage separation factor can therefore be related to the ideal-point separation factor by an equation of the form... 

The first term may be considered as the contribution of the internal circulation or convective flow to the stage length, the second term as the contribution of the axial diffusion to the stage length. The stage separation factor is given by... 

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... 

We now appreciate the reasons for the high cost of enriched uranium. The single stage separation factors are low, as is the natural abundance. This leads inexorably... 

To attain a sufficiently high degree of separation, multiplication of the single stage separation factor is needed. This can only be accomplished by providing circulation of the separated substances. With this approach most of the enriched mixture is returned to the column. 

The elementary single stage separation factor a for a two component system is defined as... 

The overall separation depends on the single stage separation factor, the number of separating elements, and design and operating characteristics of the cascade. Equations 5-8 are insufficient to determine all the variables. It is instructive to consider three types of cascades the minimum stage cascade, the minimum reflux cascade, and the ideal cascade. The material balance equations from the i + 1 th stage to the product of the cascade lead to... 

The single stage separation factor determines the concentration change across each stage... 

The ratio [y/(l —y)]l[x/(l — x)] is called the stage separation factor and is denoted by a. Analogous separation factors are used to characterize all separation processes. A value of a close to unity indicates that the separation is difficult a value far from unity, easier. For gaseous diffusion of UF, a is so close to unity that the process must be repeated many times for a useful degree of separation. To do this, the low-pressure eiuiched UF must be recompressed to the feed pressure and cooled. The depleted UF, which experiences some pressure loss, must also be recompressed (not shown). 

The degree of separation achieved by a single stage is known as the stage separation factor, or simply the separation factor a. This is defined as the weight, mole, or atom ratio in the heads stream divided by the corresponding ratio in the tails. For a two-component mixture. 

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

To compare equilibrium times evaluated by approximate Eq. (12.204) and the lower bound Eq. (12.209), the example of an ideal cascade to perform the separation of Table 12.8 will be considered. It is assumed, in addition, that the stage holdup time h is 1 s and the stage separation factor is 1.0043, the nominal value for separating from UF6. For this... 

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... 

The development next to be given of equations for the number of stages, interstage flow rates, and fraction on each stage does depend on the process used. In subsequent numerical examples, the gaseous diffusion process with a U/ U stage separation factor of 1.00429 is assumed. 

It is proposed that B be concentrated by the gaseous diffusion process applied to BFs and "BF3. The plant is to be designed as an ideal cascade and is to separate feed containing 19 percent °B into product containing 90 percent and tails containing 8 percent. The stage-separation factor is 1.0074. 

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. 

Figure 14.7 Cross-flow gaseous diffusion stage. Stage separation factor a = > (l — )/ ( — y) stage efficiency E = (y — x)l(y — Xo) Np, Ni, N,M = molar flow rates Xp, Xf, x,y,v= mole fraction light component.

Stage separation factor. For a cross-flow gaseous diffusion stage with a cut 6 of the stage separation factor a is given by... 

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