Unformatted text preview: .
0.60
0.40
111 − 1
. = 14.75 Use either the Gilliland graphs of Figs. 9.10 or 9.11, or the Gilliland correlation
equation, (934). The latter is more accurate, but requires iteration when solving for X. Apply
the equation.
N − N min 144.4 − 72.2
Y=
=
= 0.497
N +1
144.4 + 1 Using a spreadsheet to solve Eq. (934), which is nonlinear in X, we obtain X = 0.159
R − Rmin
X=
= 0.159
Solving, R = 17.73 and R/Rmin = 17.73/14.75 = 1.202
R +1 Exercise 9.14
Subject:
Number of equilibrium stages by the FUG method for the distillation of a binary
mixture of dichlorobenzene (DCB) isomers.
Given: Feed of 62 mol% pDCB and 38 mol% oDCB at approximately 1 atm. Distillate to
contain 98 mol% pDCB, and bottoms to contain 96 mol% oDCB. Total condenser and partial
reboiler. Average relative volatility = 1.154 with the para isomer as the LK. Feed condition is q
= 0.9 (10 mol% vaporized). Want R/Rmin = 1.15.
Assumptions: External reflux ratio = internal reflux ratio at the upper pinch.
Find: Number of equilibrium stages by the FUG method.
Analysis: Using the Fenske equation (911):
log
N min = xpDCB D xpDCB B xoDCB B xoDCB D log α pDCB,oDCB log
= (0.98) 0.96
(0.04) 0.02
log(1154)
. = 49.3 For minimum reflux, use the Class 1 Underwood equation (920), which applies for a binary
mixture, where the pinch composition is that of the liquid portion of the feed. From the feed
composition, determine the equilibrium liquid composition by a flash calculation for 10 mol%
vaporization. Do this by combining Eqs. (726) for the qline with (48) for equilibrium at a
constant relative volatility. Thus, applying these equations to the LK, pDCB,
αx
1154 x
.
q
zF
0.62
=
=
x−
= −9 x +
= 6.2 − 9 x
1 + x (α − 1) 1 + 0154 x
.
q −1
q −1
01
.
Solving this nonlinear equation for a positive root of x between 0 and 1 gives x = xpDCB = 0.617
Then,
xpDCB, D
Rmin = Lmin
=
D xpDCB, F − α p − DCB,o − DCB
α p − DCB,o − DCB − 1 xoDCB, D
xo − DCB, F = 0.98
0.02
.
− 1154
0.617
0.387
1154 − 1
. = 9.93 R = 1.15 Rmin =1.15(9.93) = 11.42 In the Gilliland equation, (934), X = (R  Rmin)/(R + 1) =
(11.429.93)/(11.42+1) = 0.120. Using Eq. (9.34), Y = 0.534 = (N  Nmin)/(N + 1).
Solving, N = 107 stages. Exercise 9.15
Subject: Shortcomings of the Gilliland correlation Given: Column with a small ratio of rectifying to stripping stages.
Find: Explanation for possible inapplicability of the Gilliland correlation.
Analysis: When a column has a small ratio of rectifying to stripping stages, stripping of a light
key in the stripping section may dominate over absorption of the heavy key in the rectifying
section, in determining stage requirements. The Gilliland correlation is based on reflux
considerations in the rectifying section. Alternatively, a correlation could have been developed
based on boilup considerations in the stripping section, using a modified Underwood equation for
minimum boilup ratio. Such a correlation, since it would be empirical, would seem to...
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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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