Unformatted text preview: continued)
Substitute Eq. (3) into (4) to eliminate D1. After rearrangement,
x D1 − x B2
D2 = B2
x D2 − x D1
Combine Eqs. (5) and (6) to eliminate B1. After rearrangement, the recycle ratio is:
x B1 − x F x D1 − x B2
x B1 − x B2 x D2 − x D1
In the limit, for pure bottoms products and azeotropic distillate products, Eq. (7) reduces to:
1 − xAz1
xAz1 − xAz 2
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 = 0.30, x B1 = 0.0001, and x B2 = 0.998
x D1 = 0.925 , which is slightly greater than the azeotropic mole fraction of 0.943.
x D2 = 0.88 , which is slightly smaller than the azeotropic mole fraction of 0.856. Substituting these 5 mole-fraction values into Eq. (7) gives D2/F = 0.4876. Therefore D2 =
48.76 mol/s. This a modest recycle ratio. Using Eqs. (1) to (6), the following material balance is
obtained for the system:
Flow rate, mol/s:
The design of the two columns was made as follows with the Chemcad program, by making
rough estimates of tray and reflux requirements, followed by use of the SCDS Column or Tower
rigorous models to finalize the designs.
Using the TPXY plot feature of Chemcad, it was found that the relative volatility, α, for
ethanol with respect to water, at 13 kPa, varies widely over the composition range, from 1.020 at
92.5 mol% ethanol to 12.0 at 0.0001 mol% ethanol, both mole fractions in the liquid phase.
Accordingly, it was believed that the FUG method would not give reliable estimates of stages
and reflux. To obtain rough estimates of the stage requirements and feed locations, the Fenske
equation (9-11) was applied to each of the three sections of the column, as summarized in the
following table, using a pressure of 13 kPa rather than taking into account pressure drop. Exercise 11.15 (continued)
Analysis: Column 1 (continued) Location or
Column section Mole fraction
Overhead to Feed 1
Feed 1 to Feed 2
Feed 2 to Bottoms
volatility average relative
5.2 The minimum stages were multiplied by about 2 to obtain the following estimates of equilibrium
stages for input to the SCDS model:
Total number of stages = 2(10.7 + 2.2 + 5.2) = 36.2. This was increased to 41 + total condenser
= 42 to be on the conservative side.
Feed 1, the recycle from Column 2, entering at 2(10.7) = 21.4, increased to Stage 23.
Feed 2, the fresh feed, entering at 2(2.2) = 4.4 stages further down, changed to Stage 35 after it
was found that the section between the two feeds was dominated by the lower end of the range of
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