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Unformatted text preview: feed tank, call it xC, is restricted
to the range of 0.10 to 0.25. At time zero, it is 0.10 and then increases, but can not exceed 0.25.
The instantaneous mole fraction of H in the bottoms, call it xB, is restricted to the range of 0.0 to
0.10. It starts at a low value and increases, but probably falls far short of 0.1 because of the
relatively large relative volatility, as indicated in the following. Vaporliquid equilibrium data
are given in Figs. 4.3 and 4.4, from which the following data are extracted for the range of
interest:
T, o C
y of H
x of H 125
0.00
0.0 120
0.193
0.05 115
0.34
0.1 110
0.46
0.15 106
0.55
0.2 102
0.63
0.25 98
0.69
0.3 95
0.74
0.35 92
0.785
0.4 90
0.82
0.45 87
0.85
0.5 These data are plotted in the McCabeThiele diagram on the next page, where it is seen that in
the range of interest, the slope of the equilibrium curve is almost constant at approximately 3.9.
A typical operating line is shown, with 3 stages stepped off. Because the slope of the operating
line is also constant at a value of 2 and there are only 3 stages, an algebraic method is reasonable
to obtain the relationship between xB and xC for use in the following form of Eq. (133): ln W0
100
= ln
= 0.916 =
Wt
40 xCt
x0 = 0.10 dxC
xC − x B (1) For 3 stages, the algebraic equation derived by combining the equilibrium equations, y = 3.9x,
with the operating lines, y = (L/V)x  xB = 2x  xB is:
xC = 22xB. The value of xCt that
satisfies Eq. (1) is derived by integrating Eq. (1) numerically with the trapezoidal rule as follows: Exercise 13.18 (continued) Analysis: (continued)
xC
xB
I = 1/(xC  xB)
Iavg∆xC
∆ xC
0.100 0.00455
10.48
0.110
0.005
9.52
0.010
0.100
0.132
0.006
7.94
0.022
0.192
0.154
0.007
6.80
0.022
0.162
0.176
0.008
5.95
0.022
0.140
0.198
0.009
5.29
0.022
0.124
0.220
0.010
4.76
0.022
0.111
0.242
0.011
4.33
0.022
0.100
0.250
0.0114
4.18
0.008
0.034
If the righthand column is added from xC = 0.100 to 0.242, the sum is 0.929, which is too large.
From xC = 0.100 to 0.220, the sum is 0.829, which is too small. For 0.916, xC = 0.249 and the
corresponding instantaneous bottoms H mole fraction = 0.0113. The cumulative bottoms mole
fraction for H is approximately 0.008. Exercise 13.19
Subject: Complex batch binary distillation with a middle feed vessel, a rectification section,
and a stripping section.
Given: Equipment arrangement of Fig. 13.9.
Find: A calculation procedure of the McCabeThiele type.
Analysis: For a binary mixture, if the middle feed vessel is located in the optimal location, the
composition of the charge will remain constant during the distillation. Thus, if the reflux ratio
and distillate rate are kept constant, the batch distillation will behave like a continuous
distillation, with constant compositions of the distillate and bottoms. Therefore, the standard
McCabeThiele method presented in Chapter 7 applies. With a middle feed vessel, a binary
mixture can be separated into nearly pure products.
The general case of multicomponent batch distillation in a column with a middle feed
vessel is considered in detail by A. G. Davidyan...
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This document was uploaded on 02/24/2014 for the course CBE 2124 at NYU Poly.
 Spring '11
 Levicky
 The Land

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