Minimum stage cascade

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 two limiting cascades we have discussed are of little practical value. The minimum stage cascade produces zero amount of the maximum concentration material the minimum reflux cascade produces the maximum amount of material with no enrichment. Both of these cascades... 

The ideal cascade requires twice the number of stages as the minimum stage cascade similarly the reflux ratio in the ideal cacade is twice that in the minimum reflux cascade. 

Neither of these limiting cascade parameters are suitable for an actual isotope production task the minimum stage cascade... 

Chempak . 427, 429. 500, 616, 645, 885 Chemstation, 180 Chien s minimum reflux, 103, 104 Chien s minimum stages, 105 CMR (see Cascade Mini-Ring) Colburn ... 

An estimate of the minimum absorbent flow rate for a specified amount of absorption from the entering gas of some key component K for a cascade with an infinite number of equilibrium stages is obtained from Eq. (13-40) as... 

When a lies close to 1 the minimum reflux ratio is large, but since Xj varies with stage number so does [n(i+1)/P]MiN- At the feed point in a 235U plant enriching to 90% 235U, (nf/P)MiN is 29,100, but at the product end of the cascade it approaches zero. 

A practical isotope separation plant can operate at neither minimum reflux (where the separation is zero, but the rate of production is high), nor at minimum number of stages (where the rate of production is zero, but the separation is high). A compromise is required. Since optimum reflux varies with stage number it is customary to employ tapered cascades for isotope separation. This results in marked savings in material hold-up, and in plant size and investment. 

The no remixing cascade is termed the ideal cascade. The ideal cascade retains the most desirable features of each of the two minimum cascades discussed and leads to a finite concentration in a finite number of stages at a finite production rate. For a cascade with a large number of stages... 

With countercurrent processing, carried out using either a multistage cascade or an extraction column, the required solvent-to-feed ratio generally can be reduced by adding more and more stages or transfer units. As discussed in Minimum and)Maximum Solvent-to-Feed Ratios, the minimum practical solvent-to-feed ratio is approximated by... 

Another important concept is the calculation of the minimum number of equilibrium stages to perform a given separation. This is a theoretical concept since it occurs when one or both flowrates in a countercurrent cascade are infinite. It is useful to calculate since the actual number of stages will be larger (i.e., this is a limit). An analytical equation can be... 

The case of minimum number of equilibrium stages corresponds to infinite flow from and back into the cascade, such that no product is removed. In this case... 

The minimum number of equilibrium stages is a theoretical concept based upon infinite flows within a cascade and no feed or product streams. 

To carry out a specified separation in an actual extracting cascade with a finite number of stages, the flow ratio E/F must be greater than the minimum ratio E /F given in Eq. (4.34) or... 

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