Use a trial procedure by integrating between xpt of 0.18 and various lower limits, and converge the procedure by graphing the results. It is found that xD,avg = 0.80 when xpf = 0.04, at which time the value of the integral = 0.205 = ln (M,/Mf), so that Mf = 424 mol. Product = Mi -Mf = 520 - 424 = 96 mol. From Eq. (13-145),

Batch Rectification at Constant Overhead Composition

Bogart [Trans. Am. Inst. Chem. Eng., 33, 139 (1937)] developed the following equation for this situation with column holdup assumed to be negligible:

— (13-147) V V (1 - L/V)(Xd - Xp)2 where the terms are defined as before. The quantity distilled can then be found by

XD Xpf

The progress of a varying-reflux distillation is shown in Fig. 13-103. Distillate composition is held constant by increasing the reflux as pot composition becomes more dilute. Operating lines with varying slopes

(= L/V) are drawn from the distillate composition, and the appropriate number of plates is stepped off to find the corresponding bottoms composition.

As an example, consider distilling at constant composition the same mixture that was used to illustrate constant reflux. The following table is compiled:

L/V |
Xp |
XD — Xp |
1/(1 - L/V)(Xd - Xp) |

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