Cascade minimum reflux ratio

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. 

The minimum reflux ratio to establish a positive concentration gradient in the cascade follows from Equation 17... 

A. Acrivos and N. R. Amundson On the Steady State Fractionation of Multicomponent and Complex Mixtures in an Ideal Cascade Part 2—The Calculational of the Minimum Reflux Ratio, Chem. Eng. Sci., 4(2) 68 (1955). 

These equations all show that the minimum reflux ratio increases as the composition departs more from product or tails composition. In isotope separation cascades in which a is close to unity, the minimum reflux ratio is enormous. For example, at the feed point of a plant... 

Yet, as the product end of this cascade is approached, the minimum reflux ratio approaches zero. 

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. 

Here y-p is the isotopic composition at the top stage, P is the product withdrawal rate, and, as before, X,+i is the tails withdrawal rate at the (i + l)th stage. The ratio Xi+JP) is the reflux, which for a simple countercurrent cascade is independent of stage number (i.e., such a cascade is squared off). Note that /, and X4+1 approach each other as Xi+JP approaches infinity, which happens at total reflux. In that case, the number of stages required to carry out a given overall separation is a minimum and is given by the Fenske equation (Fenske 1932) ... 

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