Unformatted text preview: together with the yx table are solved for x and W/W0. Eq. (2) must be integrated
numerically. One way to do this is to fit the equilibrium data to a polynomial equation. Using
the data from x = 0.2782 to 0.9622, the fit to a cubic equation is:
y = 0.913992 + 0.25125x  0.315062x2 + 0.133892x3 (3) Substitute Eq. (3) into Eq. (2) and integrate using a spreadsheet with the trapezoidal rule for a ∆x
increment of 0.01 starting from x = 0.85 with decreasing values of x. As an example, using this
method for the first four increments, the integral is equal to ∆x[ 0.5fx=0.40 + fx=0.39 + fx=0.38 +
fx=0.37 + 0.5fx=0.36 ], where f = 1/(yx). At each step , W/W0 is computed and then the mole fraction
of water in the cumulative distillate from Eq. (1), repeating until a value for the latter of 0.98 is
achieved.
The complete spreadsheet is given below. From it, the following result is obtained:
x = 0.22 and W/W0 = 0.1711. x
0.85
0.84
0.83
0.82
0.81
0.80
0.79
0.78
0.77
0.76
0.75
0.74
0.73
0.72
0.71
0.70
0.69
0.68
0.67
0.66
0.65
0.64
0.63
0.62
0.61 y
0.98215
0.98209
0.98204
0.98199
0.98195
0.98191
0.98186
0.98182
0.98178
0.98174
0.98169
0.98165
0.98159
0.98154
0.98148
0.98141
0.98134
0.98126
0.98117
0.98107
0.98096
0.98084
0.98071
0.98057
0.98041 f =1/(yx) Value of
Integral
7.567
7.038
6.577
6.173
5.816
5.497
5.212
4.955
4.722
4.510
4.316
4.138
3.975
3.824
3.684
3.554
3.432
3.319
3.214
3.115
3.022
2.934
2.851
2.773
2.700 0.0730
0.1411
0.2049
0.2648
0.3214
0.3749
0.4257
0.4741
0.5203
0.5644
0.6067
0.6472
0.6862
0.7238
0.7600
0.7949
0.8286
0.8613
0.8930
0.9236
0.9534
0.9823
1.0105
1.0378 W/W0 y in cum
distillate
0.9296
0.8684
0.8148
0.7674
0.7252
0.6874
0.6533
0.6224
0.5944
0.5687
0.5452
0.5235
0.5035
0.4849
0.4677
0.4516
0.4366
0.4226
0.4094
0.3971
0.3854
0.3744
0.3640
0.3542 0.9820
0.9820
0.9820
0.9819
0.9819
0.9819
0.9819
0.9819
0.9819
0.9819
0.9818
0.9818
0.9818
0.9818
0.9818
0.9818
0.9818
0.9817
0.9817
0.9817
0.9817
0.9817
0.9817
0.9816 0.60
0.59
0.58
0.57
0.56
0.55
0.54
0.53
0.52
0.51
0.50
0.49
0.48
0.47
0.46
0.45
0.44
0.43
0.42
0.41
0.40
0.39
0.38
0.37
0.36
0.35
0.34
0.33
0.32
0.31
0.30
0.29
0.28
0.27
0.26
0.25
0.24
0.23
0.22
0.21
0.20 0.98024
0.98006
0.97985
0.97964
0.97940
0.97915
0.97888
0.97859
0.97828
0.97794
0.97759
0.97721
0.97681
0.97638
0.97593
0.97546
0.97495
0.97442
0.97386
0.97327
0.97265
0.97200
0.97132
0.97060
0.96986
0.96908
0.96826
0.96741
0.96652
0.96559
0.96463
0.96362
0.96258
0.96150
0.96037
0.95921
0.95800
0.95674
0.95544
0.95410
0.95271 2.630
2.564
2.501
2.441
2.384
2.330
2.279
2.229
2.182
2.137
2.094
2.053
2.013
1.975
1.938
1.903
1.869
1.837
1.806
1.775
1.746
1.718
1.691
1.665
1.640
1.615
1.592
1.569
1.547
1.525
1.505
1.485
1.465
1.446
1.428
1.410
1.393
1.376
1.360
1.344
1.329 1.0645
1.0904
1.1158
1.1405
1.1646
1.1882
1.2112
1.2338
1.2558
1.2774
1.2986
1.3193
1.3396
1.3596
1.3791
1.3983
1.4172
1.4357
1.4539
1.4718
1.4895
1.5068
1.5238
1.5406
1.5571
1.5734
1.5894
1.6052
1.6208
1.6362
1.6513
1.6663
1.6810
1.6956
1.7099
1.7241
1.7382
1.7520
1.7657
1.7792
1.7926 0.3...
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 Spring '11
 Levicky
 The Land

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