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Separation Process Principles- 2n - Seader &amp; Henley - Solutions Manual

# 82 1182 mols estimated temperatures stage 1 35oc stage

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Unformatted text preview: continued) Analysis: (continued) Substitute Eq. (3) into (4) to eliminate D1. After rearrangement, x D1 − x B2 D2 = B2 (6) 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 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: 1 − xAz1 D2 = xF (8) F 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: F Stream: D2 F1 B1 D1 B2 Flow rate, mol/s: Ethanol 30 42.91 72.91 0.00007 72.91 30.00 Water 70 5.85 75.85 69.94 5.91 0.06 Total: 100 48.76 148.76 69.94 78.82 30.06 mol% Ethanol: 30 88 49.0 0.0001 92.5 99.8 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. Column 1: 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 ethanol in liquid Overhead Overhead to Feed 1 Feed 1 Feed 1 to Feed 2 Feed 2 Feed 2 to Bottoms Bottoms Relative Geometric volatility average relative ethanol to volatility water 1.020 1.05 1.086 1.97 3.587 6.56 12.0 0.925 0.88 0.30 0.000001 Minimum stages by Fenske equation 10.7 2.2 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 relative volati...
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