3.1 Separating Unit, Stage, and Cascade

The smallest element of an isotope separation plant that effects some separation of the process material is called a separating unit. Examples of a single separating unit are one stage of a mixer-settler, one plate of a distillation column, one gas centrifuge, one calutron, or one electrolytic cell.

A group of parallel-connected separating units, all fed with material of the same composition and producing partially separated product streams of the same composition, is known as a stage. Often a single unit serves as a stage, like a plate of bubble-plate column. However, in some separation methods whose units have low capacity, such as an electrolytic cell or centrifuge, it is necessary to use many units in parallel.

When the degree of separation effected by a single stage is less than the degree of separation desired between product and waste, it is necessary to connect stages in series. Such a series-connected group of stages is known as a cascade. Examples of a cascade are a complete distillation column or a battery of solvent extraction mixer-settlers.

The relation between unit, stage, and cascade is illustrated by Fig. 12.8. Each unit of this cascade might represent, for example, an electrolytic cell. The group of parallel-connected cells, each of which separates feed of composition zx into a partially enriched stream of composition у і and a partially depleted stream of composition, constitutes the first stage of this cascade. The cascade is the entire group of series — and parallel-connected cells.

A cascade that has the same number of units (i. e., the same capacity) in all stages of a group is known as a “squared-off cascade. A cascade in which the number of units, or the capacity, in each stage decreases as the produce and waste ends of the cascade are approached is called a tapered cascade. A single multiplate distillation column is an example of a squared-off cascade; a gaseous diffusion plant for uranium separation is an example of a tapered cascade.

The engineering analysis of separation processes frequently employs the concept of an ideal, or equilibrium stage. In such a stage, the feed streams, which may be one or two in number, are acted upon to produce two product streams that are in equilibrium. The use of such a concept can be employed in the design and analysis of both stagewise and continuous contacting equipment. Determination of the number of stages in a cascade required to achieve a given separation involves the determination of the number of such ideal stages followed by application of a stage efficiency, which expresses the fraction of ideal transfer achieved in the actual stages employed.