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Unformatted text preview: integral
ln(W0/W)
0.2561
0.2506
0.2449
0.2392
0.2333
0.2273
0.2212
0.2149
0.2085
0.2020
0.1953
0.1885
0.1816
0.1745
0.1672
0.1599
0.1523
0.1446
0.1368
0.1288
0.1207
0.1124
0.1039
0.0953
0.0866
0.0776
0.0685
0.0592
0.0498 4.483
4.575
4.674
4.780
4.894
5.017
5.150
5.293
5.449
5.618
5.803
6.006
6.228
6.474
6.746
7.050
7.390
7.773
8.209
8.709
9.286
9.960
10.759
11.719
12.894
14.364
16.257
18.783
22.322 0.00453
0.00462
0.00473
0.00484
0.00496
0.00508
0.00522
0.00537
0.00553
0.00571
0.00590
0.00612
0.00635
0.00661
0.00690
0.00722
0.00758
0.00799
0.00846
0.00900
0.00962
0.01036
0.01124
0.01231
0.01363
0.01531
0.01752
0.02055 0.00453
0.00915
0.01388
0.01872
0.02367
0.02876
0.03398
0.03935
0.04488
0.05059
0.05650
0.06262
0.06897
0.07558
0.08247
0.08969
0.09728
0.10527
0.11373
0.12272
0.13235
0.14271
0.15395
0.16625
0.17988
0.19519
0.21271
0.23326 W/W0
1.000
0.995
0.991
0.986
0.981
0.977
0.972
0.967
0.961
0.956
0.951
0.945
0.939
0.933
0.927
0.921
0.914
0.907
0.900
0.893
0.885
0.876
0.867
0.857
0.847
0.835
0.823
0.808
0.792 A plot of the ethanol mole fraction in the instantaneous distillate as a function of mol% distilled
is given on the following page. Exercise 13.12 (continued)
Analysis: Rayleigh distillation (continued) Exercise 13.12 (continued)
Analysis: (continued)
Distillation with 2 stages plus a reboiler:
To obtain the maximum cumulative distillate purity for 20 mol% distilled, operate close to total
reflux, L/V = 1. The relationship between yD and xW in Eq. (1), with x = xW and y = yD, is
obtained from a McCabeThiele diagram by drawing a series of operating lines of slope = L/V =
1 (45o line). For each operating line, starting from the intersection with the 45o line, which is yD,
3 stages are stepped off to determine the corresponding xW. A typical construction that starts
from yD = 0.65 is shown on the next page, where the xW = 0.02. Other sets of values are given in
the following table, which also includes values of the integrand, f = 1/(yD  xW), from which the
integral is evaluated by the trapezoidal rule with variable increments of ∆xW. For example, the
increment of the integral from x1 to x2 is (x1  x2)(f1/2 + f2/2).
The increments are summed over the region from xW = 0.033 to the value corresponding to 20
mol% distilled.
xW yD from
McCabeThiele f = 1/(yD  xW) 0.033
0.030
0.020
0.010
0.005
0.001 0.663
0.66
0.65
0.61
0.55
0.40 1.587
1.587
1.587
1.667
1.834
2.506 Increment of
Integral Cumulative
ln(W0/W) 0.0048
0.0159
0.0163
0.0088
0.0087 0.0048
0.0207
0.0370
0.0458
0.0545 From the above table, at xW = 0.001, a very low value, ln(W0/W) = 0.0545. Thus, W/W0 =
0.947 or only 5.3% distilled. Thus, essentially all of the ethanol will be distilled when 20 mol%
of the charge has been distilled.
The composition of the cumulative distillate is given by Eq. (136), which becomes:
yD avg = W0 x0 − Wx x0 − W / W0 x 0.033 − 0.8(0.0)
=
=
= 0165
.
W0 − W
1 − W / W0
1 − 0.8 It should be noted from the above table that if only 5.3 mol% of the charge were distilled,...
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 Spring '11
 Levicky
 The Land

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