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In this case the values of (a/0)AV were assumed, and F' for A was taken as 0.5. This latter value indicates that the increment is to reduce the mols of A in the still left after the step of Table 14-5 by one-half. The values of F' for the other components were calculated from F'a — 0.5 and the average of the assumed value of (<*/&)av of Table 14-6 and the calculated values given in the last column of Table 14-5. The values of F were obtained by multiplying F' by the corresponding F value of the preceding table. The rest of the calculations are made in the same manner as those of Table 14-5.

The values of yr calculated by this method are plotted in Fig. 14-7 as a function of mol fraction of the original charge distilled. The total reflux results of Fig. 14-5 are also included in the dotted curves for comparison. As would be expected, the separation with the finite reflux ratio is not so sharp as for total reflux. This decrease in the degree of separation is particularly marked for the intermediate fraction and is least serious in the case of the least volatile fraction. The inverted and split-towers systems discussed for total reflux would be effective in increasing the purity of any given fraction.

This approximate method is most accurate for high values of (O/D) and relatively few total plates. It reduces to the total reflux method for (O/D) — °o. When the number of plates is large, they tend to pinch at the equilibrium curve and the arithmetic average for /3 is not satisfactory.

Finite Reflux Ratio with Column Holdup. The conditions in this case are similar to those discussed on page 380 for binary mixtures. The operating lines for each component are curved except for total reflux, and it is very difficult to evaluate the position of these lines. The total reflux relations given on page 382 for a binary mixture do not apply exactly in this case because it was assumed that the unit was operating with a variable reflux ratio, producing a constant overhead composition. In the case of a multicomponent mixture, it is generally

Fig. 14-7. Fractionation curve for multicomponent mixture at finite reflux ratio.

impossible to keep the overhead composition constant for all components as product is withdrawn. In certain cases, the distillate may be reasonably constant, and a similar analysis can be made.

The design methods for batch distillation allowing for liquid holdup in the column are very unsatisfactory, and it is a field that should be actively studied in view of the importance of the operation. Improvements in the design calculations for multicomponent mixtures with no liquid holdup in the column are also needed.

References

1. Colbubn and Stern, Trans. Am. Inst. Chem. Engrs37, 291 (1941).

2. Edge worth-Johnstone, Ind. Eng. Chem., 35,407 (1943); 36, 482,1068 (1944).

3. Rose, Welshans, and Long, Ind. Eng. Chem., 32, 673 (1940).

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