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Unformatted text preview: = B2
x D2 − x D1 (3)
(4) (5) (6) Combine Eqs. (5) and (6) to eliminate B1. After rearrangement, the recycle ratio is:
x B1 − x F x D1 − x B2
D2
=
(7)
F
x B1 − x B2 x D2 − x D1
In the limit, for pure bottoms products and azeotropic distillate products, Eq. (7) reduces to:
xAz1
D2
= 1 − xF
(8)
F
xAz 2 − xAz1 Exercise 11.14 (continued)
Analysis: (continued)
Eq. (8) shows that the recycle ratio is sensitive to the feed composition and the azeotropic
compositions at the pressures of Columns 1 and 2. The smaller the difference between the two
azeotropic compositions, the larger the recycle ratio.
For this exercise, x F = 0.20, x B1 = 0.99, and x B2 = 0.01
Let x D1 = 0.37 , which is slightly greater than the azeotropic mole fraction of 0.357.
Let x D2 = 0.44 , which is slightly smaller than the azeotropic mole fraction of 0.452.
Substituting these 5 molefraction values into Eq. (7) gives D2/F = 4.1457. Therefore D2 =
414.57 mol/s. This a very high recycle ratio. The system is technically feasible, but may not be
economically attractive. Using Eqs. (1) to (6), the following material balance is obtained for the
system:
F
Stream:
D2
F1
B1
D1
B2
Flow rate, mol/s:
Ethanol
20 182.41 202.41 19.19 183.22
0.81
Benzene
80 232.16 312.16
0.20 311.96 79.80
Total:
100 414.57 514.57 19.39 495.18 80.61
mol% Ethanol:
20
44
39.3
99
37
1
The design of the two columns is made as follows with the Chemcad program, using the Shortcut
Column model (FUG method) to obtain initial estimates of stage and reflux requirements,
followed by the SCDS Column rigorous model to finalize the designs.
Column 1:
Using the above material balance, with a combined feed, F1, the specifications for the
ShortCut Column model are 311.96/312.96 = 0.9968 for the recovery of benzene to the distillate,
and 183.22/202.41 = 0.9052 for the recovery to the distillate of ethanol. Thus, it is expected that
little rectification is necessary. The results are:
Minimum number of equilibrium stages = 5.95
Minimum reflux ratio = very small and probably in error. Therefore, the Gilliland correlation
was not reliable.
The SCDS Column model of the Chemcad program was then used to make a rigorous
calculation. Based on several runs where the number of stages, the feed stage location, and the
reflux ratio were varied, it was found that the separation was almost insensitive to the reflux
ratio, indicating that little rectification was needed. However, attempts to configure the column
as a reboiled stripper met with failure to converge. The following input data resulted in almost
satisfying the specifications. Because the separation depended mainly on the number of stages,
the specified separation could not be satisfied exactly.
Pressures as stated above.
Number of stages = 7 (includes the total condenser and the partial reboiler)
Feed stage for recycle, D2 = 3 from the top
Entry for feed, F = 4 from top
Reflux ratio = 0.05
Bottoms mole flow rate = 19.39 mol/s Exercise 11.14 (continued)
Analysis: Column 1 (continued)
Estimated distillate rate = 495.18 mol/s
Estima...
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 Spring '11
 Levicky
 The Land

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