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

# 5 244 10 07500509 02400102 008100127 002500102 075

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Unformatted text preview: Because we have a binary mixture, this is a Class I separation, where all components distribute. Therefore, the Underwood equation that applies is (9-20): xC = , D 3 Lmin = D xC = , ∞ − α C = ,C 3 xC 3 3 3 ,D xC 3 ,∞ α C = ,C − 1 3 3 = 0.99 0.01 − α C = ,C 3 3 xC = , ∞ xC , ∞ 3 3 α C = ,C − 1 3 (1) 3 (a) For a bubble-point liquid feed, the liquid-phase mole fractions in the pinch zone are those of the total feed. Thus, xC= ,∞ = 0.70 and xC ,∞ = 0.30. The relative volatility is that at the pinch. A 3 3 bubble-point temperature on the feed composition at 300 psia gives 126oF, with α = 1.035/0.92 = 1.125. Substitution in Eq. (1) gives Lmin/D = 11.0 (b) For 50 mol% vaporization, a flash gives about the same temperature of 126oF, and therefore the same α, with liquid-phase mole fractions of 0.688 for propylene and 0.312 for propane. Substitution into Eq. (1) gives Lmin/D =11.2. (c) For a dew-point feed, the temperature still is 126oF, with liquid-phase mole fractions of 0.68 for propylene and 0.32 for propane. Substitution into Eq. (1) gives Lmin/D =11.4 Because the relative volatility is close to 1, the % vaporization of the feed has only a small effect on the minimum reflux ratio. Exercise 9.11 Subject: Minimum reflux rate and distribution of nonkey components for the distillation of a paraffin hydrocarbon mixture. Given: Column pressure of 700 kPa. Feed composition and split for two key components in Fig. 9.23. Feed is a bubble-point liquid. K-values from Figs. 2.8 and 2.9. Find: Minimum external reflux rate. Distribution of nonkey components at minimum reflux ratio. Analysis: Because of the wide range of volatility of the components in the feed, and the relative sharpness of the separation between the LK, n-butane, and the HK, isopentane, assume a Class 2 separation for estimating the minimum reflux ratio by the method of Underwood. Compute the minimum reflux using relative volatilities at the feed temperature. Because the feed is at the bubble point, use Eq. (4-12). For the pressure of 700 kPa (102 psia), a trial-and-error calculation for the bubble-point temperature gives the following results for 80oF, where nC8 is by extrapolation: Component Propane iso-Butane n-Butane iso-Pentane n-Pentane n-Hexane n-Heptane n-Octane Total: z, feed mole fraction 0.6361 0.1018 0.1527 0.0254 0.0509 0.0102 0.0127 0.0102 1.0000 K at 102 psia and 800F 1.37 0.56 0.39 0.16 0.12 0.038 0.013 0.004 Kz 0.8715 0.0570 0.0596 0.0041 0.0061 0.0004 0.0002 0.0000 0.9989 α referred to iso-pentane 8.56 3.50 2.44 1.00 0.75 0.24 0.081 0.025 The Underwood equations that apply are Eqs. (9-28) and (9-29). For a bubble-point feed, 1 - q = 0 and Eq. (9-28) becomes: α i ,r zi , F i α i ,r − θ = 1− q = 0 = 8.56(0.6361) 35(01018) 2.44(01527) 10(0.0254) .. . . + + + + 8.56 − θ 3.5 − θ 2.44 − θ 10 − θ . 0.75(0.0509) 0.24(0.0102) 0.081(0.0127) 0.025(0.0102) + + + 0.75 − θ 0.24 − θ 0.081 − θ 0.025 − θ (1) Eq. (1) has 8 roots for θ. However, only 3...
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