In any practical separation plant, the preferred reflux ratio will clearly be greater than the minimum, which would lead to an infinite number of stages, and less than the infinite reflux ratio needed for the minimum number of stages. In most nonisotopic separation plants it is customary to select a reflux ratio somewhat greater than the minimum at the feed point and to use the same value throughout the entire enriching or stripping section, even though a smaller value would suffice toward the product or waste end of the plant. In distillation this is done because the reflux ratio in an adiabatic column remains nearly constant, and it is cheaper to add or remove heat only at the ends of the column than at a number of intermediate points. In many isotope separation plants, however, so much can be saved in the way of reduced equipment size and material holdup by reducing the reflux ratio at intervals between the feed point and the product ends of a cascade that this is usually done. Investigation of the properties of such a “tapered” cascade is therefore important in isotope separation, and of interest in other separation problems because it indicates how equipment size and holdup could be reduced in cases where the increased complexity of a “tapered” plant is justified.

Properties of a cascade with constant reflux ratio over a substantial composition interval are considered in Sec. 13.