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69.2
0.801
0.350
69.6
0.796
0.300
70.2
0.789
0.250
71.2
0.777
0.200
73.1
0.754
0.150
76.8
0.705
0.100
84.9
0.578
0.050
95.1
0.361
0.020
107.1
0.000
0.000 The McCabeThiele plot for these data are shown on the next page. The equilibrium stages for
total reflux are stepped off between the equilibrium curve and the 45oline, which represents the
operating line, from the acetone xD = 0.95 down to the acetone xB = 0.02.
From the plot, there are 5 minimum stages, which is 35% higher than the 3.7 minimum stages
computed from the Fenske equation. The Fenske equation is not reliable for highly nonideal
binary systems. Exercise 9.6 (continued)
Analysis: McCabeThiele method (continued) Exercise 9.7
Subject:
Minimum equilibrium stages and distribution of nonkey components using the
Fenske equation for distillation of a paraffin hydrocarbon mixture.
Given: Column pressure of 700 kPa. Feed composition and split for two key components in
Fig. 9.23. Kvalues from Figs. 2.8 and 2.9.
Find: Minimum number of equilibrium stages.
Distribution of nonkey components at total reflux.
Analysis: To apply the Fenske equation, the geometric mean relative volatility between the
distillate and bottoms is needed. From the following crude estimate of the split of all nonkey
components, compute the bubblepoint temperatures of the distillate and bottoms and use the Kvalues at those temperatures to get the relative volatilities. Use the bubblepoint equation, Eq.
(412). The following results are obtained for a distillate bubble point of 68oF (20oC) and a
bottoms bubble point of 257oF (125oC):
Component
Propane
Isobutane
nButane
Isopentane
nPentane
nHexane
nHeptane
nOctane
Total Feed,
kmol/h
2500
400
600
100
200
40
50
40
3930 Distillate,
kmol/h
2500
399
594
15
5
0
0
0
3513 Kvalue,
distillate
1.250
0.490
0.340
0.138
0.108
0.038
0.013
0.005 K xD
0.8895
0.0557
0.0575
0.0006
0.0002 1.0035 Bottoms,
kmol/h
0
1
6
85
195
40
50
40
417 Kvalue,
bottoms
5.70
3.25
2.65
1.45
1.23
0.65
0.33
0.19 K xB
0.0078
0.0382
0.2955
0.5751
0.0623
0.0222
0.0177
1.0188 For the two key components, nC4 and iC5, the relative volatilities at the top and bottom are,
respectively (0.34/0.138) = 2.46 and (2.65/1.45) = 1.83. The geometric mean αnC4,iC5 =
[(2.46)(1.83)]1/2 = 2.12. From the Fenske equation, (912), log
N min = d nC4 biC5 d iC5 bnC4 log α nC4 ,iC5 log
= 594 85
6
15
log 2.12 = 8.4 To compute the distribution of nonkey components at total reflux, use for the lighter than light
key components, LLK, Eq. (915), and use Eq. (916) for the heavier than heavy key, HHK, with
iC5 as the reference component, r, and the above value of Nmin. Analysis: (continued) Exercise 9.7 (continued)
fi Thus, for the LLK, i, bi = 1+ fi
For the HHK, i, di =
1+ d iC5
biC5
d iC 5
biC5
d iC5
biC5 =
α N min
i,iC5 α iN min
,iC 5
α iN min
,iC5 fi
15 8.4
1+
α i,iC5
85 (1) 15 8.4
α i ,iC5
85
=
15 8.5
1+
α i ,iC5
85
fi (2) Using the above Kvalues to compute geometric mean values of αi, iC5 , followed by use of Eqs.
(1) and (2) with the material balance, fi = di + bi , the following re...
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 Spring '11
 Levicky
 The Land

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