The Recycle Cascade

In the simple cascade of Fig. 12.12, whose performance was illustrated in Fig. 12.14, it is impossible to obtain high recovery of desired component because of losses in the tails streams leaving every stage. Desired component in these streams can be recovered by recycling these 

In a recycle cascade such as Fig. 12.13, feed, product, and tails quantities and compositions (the external variables) must satisfy the material-balance relations 

Because there are two equations and six variables, it is possible to specify four external variables independently. For example, these might be product rate and product, feed, and tails compositions. In such a case the other two variables would be given by 

Two material-balance relations among internal variables may also be written for each stage. Consider the portion of the cascade from the product end down to, but not including, stage i  

In the stripping section, where the direction of net flow is reversed, stage material-balance  

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To avoid the product losses the recycling cascades are employed (Figure 30.2). The cascades with reflux are more complicated and the capital costs and costs of operation are higher they are sensible only in the case of expensive row material. Technical and economic considerations on such systems were performed in basic books for isotope separation [11,12], as well as by Hwang and Kammermeyer [13]. 

This is the familiar Underwood [Ul]-Fenske [FI] equation for total reflux. The ratio of abundance ratios appearing in (12.72) is the overall separation (f2) of the recycle cascade ... 

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