A cascade like Fig. 12.12, in which no attempt is made to reprocess the partially depleted tails streams leaving each stage, will be called a simple cascade. In a simple cascade the feed stream for one stage is the heads stream from the next lower stage of the cascade. This type of cascade connection is used in the lower stages of the Norsk Hydro electrolytic heavy-water plant where the tails streams have too little deuterium to warrant processing for deuterium recovery. The theory of such a cascade is developed in Sec. 6.

When partially depleted tails have sufficient value to warrant reprocessing, a countercurrent recycle cascade like Fig. 12.13 may be used. This cascade flow scheme is by far the most

Stage heads

Froction

desired component

Stage toils

Figure 12.12 Simple cascade, no reprocessing of tails.

common. It is approached, for example, in a bubble-plate distillation column and is used in a battery of series-connected solvent extraction mixer-settlers or in the gaseous diffusion cascade of Fig. 12.2.

Such a countercurrent cascade separates feed containing zp fraction of desired component flowing at rate F into product containing yp fraction of desired component flowing at rate P and waste, or tails, containing хц/ fraction of desired component flowing at rate W. These six compositions and flow rates are called the external variables of the cascade.

Feed for each stage consists of heads from the next tower stage and tails from the next higher stage. These interstage flow rates and compositions will be called the internal variables of the cascade.

The portion of the cascade between the feed point and product end is called the enriching section; the portion between the feed point and waste end is called the stripping section. The purpose of the enriching section is to make material of product composition; the purpose of the stripping section is to increase the recovery of desired isotope from feed. The enriching section is essential in making product of the desired grade; the stripping section is used only to reduce the amount of feed required to make a given amount of product. When feed has no value, as with water feed for a deuterium plant, the stripping section may be eliminated altogether.

Stages of the cascade are numbered consecutively from 1 at the waste end of the plant to n at the product end. The highest stage of the stripping section is numbered rtg.

The streams that move away from the ends of the cascade, that is, the tails stream in the enriching section and the heads stream in the stripping section, are known as reflux.

The theory of a recycle cascade is developed in Sec. 7.