Countercurrent cascades, ideal cascade

Of the variety of cascades identified we will consider first countercurrent cascades of various types. 

This result is valid, in general, from the definitions of o, and 0(2 (see relation (2.2.5)). 

Consider now stage n in an ideal cascade. From relation (9.1.2), we obtain, for a binary system. 

We can follow a similar procedure for the number of stages Min the stripping section. For stage 1  

Assume now that ajj, and x are independent of n. Considering stage n + 1), we find for its feed in an ideal cascade 

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Figure 3.24 Countercurrent cascade of ideal stages, transfer from phase L to V.

A countercurrent cascade for leaching is shown in Figure 14-3A. We will consider the (idealized) case where entrainment of liquid with the solid underflow can be ignored. The assumptions are ... 

Calculate the values of the total light fraction flow rate (upflow) from stage 1 to stage N in the enriching section of an ideal cascade, as described in Example 9.1.2 for uranium isotope separation using countercurrent gas centrifuges. The overhead top product flow rate is 2 gmol/time = 1.18 Xiit = 0.9, xif = 0.0072. Employ the result provided in Problem 9.1.1. 

Refer to Fig. 3, where there is shown a cascade of three ideal stages operated in countercurrent. A solute balance may be written for any stage, such as stage 2, for example ... 

Because of its importance, only the continuous countercurrent method is discussed here. Also, since the stage method is normally used, the differential-contact method is not considered. In common with other stage cascade operations, leaching may be considered, first, from the standpoint of ideal stages and, second, from that of stage efficiencies. 

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