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Unformatted text preview: Because we have a binary mixture, this is a Class I separation, where all components
distribute. Therefore, the Underwood equation that applies is (920): xC = , D
3 Lmin
=
D xC = , ∞ − α C = ,C
3 xC
3 3 3 ,D xC 3 ,∞ α C = ,C − 1
3 3 = 0.99
0.01
− α C = ,C
3
3
xC = , ∞
xC , ∞
3 3 α C = ,C − 1
3 (1) 3 (a) For a bubblepoint liquid feed, the liquidphase mole fractions in the pinch zone are those of
the total feed. Thus, xC= ,∞ = 0.70 and xC ,∞ = 0.30. The relative volatility is that at the pinch. A
3 3 bubblepoint temperature on the feed composition at 300 psia gives 126oF, with α = 1.035/0.92 =
1.125. Substitution in Eq. (1) gives Lmin/D = 11.0
(b) For 50 mol% vaporization, a flash gives about the same temperature of 126oF, and therefore
the same α, with liquidphase mole fractions of 0.688 for propylene and 0.312 for propane.
Substitution into Eq. (1) gives Lmin/D =11.2.
(c) For a dewpoint feed, the temperature still is 126oF, with liquidphase mole fractions of 0.68
for propylene and 0.32 for propane. Substitution into Eq. (1) gives Lmin/D =11.4
Because the relative volatility is close to 1, the % vaporization of the feed has only a small effect
on the minimum reflux ratio. Exercise 9.11
Subject:
Minimum reflux rate and distribution of nonkey components for the distillation of
a paraffin hydrocarbon mixture.
Given: Column pressure of 700 kPa. Feed composition and split for two key components in
Fig. 9.23. Feed is a bubblepoint liquid. Kvalues from Figs. 2.8 and 2.9.
Find: Minimum external reflux rate.
Distribution of nonkey components at minimum reflux ratio.
Analysis: Because of the wide range of volatility of the components in the feed, and the relative
sharpness of the separation between the LK, nbutane, and the HK, isopentane, assume a Class 2
separation for estimating the minimum reflux ratio by the method of Underwood. Compute the
minimum reflux using relative volatilities at the feed temperature. Because the feed is at the
bubble point, use Eq. (412). For the pressure of 700 kPa (102 psia), a trialanderror calculation
for the bubblepoint temperature gives the following results for 80oF, where nC8 is by
extrapolation:
Component
Propane
isoButane
nButane
isoPentane
nPentane
nHexane
nHeptane
nOctane
Total: z, feed mole
fraction
0.6361
0.1018
0.1527
0.0254
0.0509
0.0102
0.0127
0.0102
1.0000 K at 102 psia
and 800F
1.37
0.56
0.39
0.16
0.12
0.038
0.013
0.004 Kz
0.8715
0.0570
0.0596
0.0041
0.0061
0.0004
0.0002
0.0000
0.9989 α referred
to isopentane
8.56
3.50
2.44
1.00
0.75
0.24
0.081
0.025 The Underwood equations that apply are Eqs. (928) and (929). For a bubblepoint feed,
1  q = 0 and Eq. (928) becomes:
α i ,r zi , F
i α i ,r − θ = 1− q = 0 = 8.56(0.6361) 35(01018) 2.44(01527) 10(0.0254)
..
.
.
+
+
+
+
8.56 − θ
3.5 − θ
2.44 − θ
10 − θ
.
0.75(0.0509) 0.24(0.0102) 0.081(0.0127) 0.025(0.0102)
+
+
+
0.75 − θ
0.24 − θ
0.081 − θ
0.025 − θ (1) Eq. (1) has 8 roots for θ. However, only 3...
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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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