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

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Unformatted text preview: kPa at the reboiler. The distillate product is the near azeotrope at 101.3 kPa and the bottoms product is 99 mol% benzene. Using the Chemcad program with the UNIFAC method, the azeotrope compositions in mol% ethanol are 35.7 at 26 kPa, and 45.2 at 101.3 kPa. A major factor in the design of a pressure-swing distillation system is the recycle-to-feed ratio, D2/F in Fig. 11.23(b), which is related to compositions as follows: Let x be the mole fraction of ethanol in any stream. Referring to Fig. 11.23(b), an overall system material balance for total flows gives: F = B1 + B2 (1) (2) An overall system balance on ethanol gives: x F F = x B1 B1 + x B2 B2 A total material balance around Column 2 gives: D1 = D2 + B 2 An ethanol balance around Column 2 gives: x D1 D1 = x D2 D2 + x B2 B2 Substitute Eq. (1) into (2) to eliminate B1. After rearrangement, x B1 − x B2 F = B2 x B1 − x F Substitute Eq. (3) into (4) to eliminate D1. After rearrangement, x D1 − x B2 D2 = 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 11.13 (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 = 0.55, 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 mole-fraction values into Eq. (7) gives D2/F = 2.309. Therefore D2 = 230.90 mol/s. Using Eqs. (1) to (6), the following material balance is obtained for the system: Stream: Flow rate, mol/s: Ethanol Benzene Total: mol% Ethanol: F D2 F1 B1 D1 B2 55 45 100 55 101.60 129.30 230.90 44 156.60 174.30 330.90 47.33 54.55 0.55 55.10 99 102.05 173.75 275.80 37 0.45 44.45 44.90 1 The design of the two columns was made 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 or TOWER 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 173.75/174.3 = 0.997 for the recovery of benzene to the distillate, and 102.05/156.6 = 0.652 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 = 6.23 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 initially on the following inpu...
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