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This is Example 10-1: EXAMPLE 10-1. Overall efficiency estimation A sieve plate distillation column is separating a feed that is 50.0 mol% n-hexane and 50.0 mol% n-heptane. The feed is a saturated liquid. Plate spacing is 24.0 in. Average column pressure is 1.0 atm. Distillate composition is xp = 0.999 (mole fraction n-hexane) and xp = 0.001. The feed rate is 1000.0 lbmol/h. The internal reflux ratio L/V = 0.8. The column has a total reboiler and a total condenser. Estimate the overall efficiency. Solution To use the O'Connell correlation we need to estimate a and u at feed composi- tion and the average temperature and pressure of the column. Column tempera- ture can be estimated from equilibrium (De Priester chart). The following values are generated from Figure 2-12: SO the XC6 T, C 0.0 0.0 98.4 0.341 0.545 85.0 0.398 0.609 83.7 0.50 0.70 80.0 1.0 1.0 69.0 Relative volatility is a = (y/x)[(1 - y)/(1-x)]. The average temperature can be estimated several ways: Arithmetic average T = (98.4 +69.0)/2.0 = 83.7, a = 2.36 Average at x = 0.5, T = 80.0, a = 2.33 Not much difference. Use a = 2.35 corresponding to approximately 82.5C. wboard The liquid viscosity of the feed can be estimated (Reid et al., 1977, p. 462) from In U mix =x, Inu, + x2 In uz (10-7a) The pure component viscosities can be estimated from logroll = al B (10-7b) where u is in cP and T is in Kelvin (Reid et al., 1977, App. A). --- nCo. A = 362.79, B = 207.08 nCj: A = 436.73, B = 232.53 Note that once Tavg? These equations give uco = 0.186, Mcz = 0.224, and Umix = 0.204. Then allmix = 0.480. From Eq. (10-6), E. = 0.62, while from Figure 10-14, E. = 0.59. To be conservative, the lower value would probably be used. and feed have been estimated, calculating E. is straightforward. 1. *alan with an Oldershaw column (a This is example 10-2: davg? EXAMPLE 10-2. Diameter calculation for tray column Determine the required diameter at the column top for the distillation column in Example 10-1. Solution We can use Eq. (10-16) with 75% of flooding. Since distillate is almost pure n-hexane, we can approximate properties as pure n-hexane at 69.0C. Physical properties: P = 0.659 g/ml (at 20); viscosity = 0.22 cP; MW = 86.17 (Perry and Green, 1984). Surface tension o = 13.2 dynes/cm (Reid et al., 1977, p. 610). The ideal gas law is used to estimate vapor density. 1b P(MW) (latm)(86.17 Pw= 1bmol RT = 0.19171b/ft? (1.314 atmft )(342 K) K lbmol Pu = (0.659)(62.4) = 41.12 lb/ft (will vary but not a lot). At the top of the column MW= MW and W. L MWL | =0.8 W V The flow parameter is V MW F W(Px. 905 = 0.0546 W PL PL - Px = (0.331) Ufood Ordinate from Figure 10-16 for 24-in. tray spacing, C = 0.36 while CD = 0.38 from Eq. (10-10e). Then K=C6 () 02 = 0.36( -5,2) 02 = 0.331 13.2 20 20 K = 0.35 if Eq. (10-10e) is used. The lower value is used for a conservative design. From Eq. (10-8) 41.12-0.1917 =K -)05 = 4.836 Po 0.1917 We will estimate n as 0.90. V = L + D. From external mass balances, D = 500.0. Since L = V(L/V) and L/V +0.8, DV 500 V- = 2500 lbmol/h 1-LN 0.2 Diameter Eq. (10-16) becomes % 4(2500)(1.314)(342) Dia = = 11.03 ft Te (0.90)(3600)(1)(075)(4.836). Since Fair's diameter calculation procedure is conservative, an 11.0-ft diam- eter column would probably be used. If n = 0.95, Dia = 10.74 ft; thus, the value of n is not critical. This is a large-diameter column for this feed rate. The reflux rate is quite high, and thus, V is high, which leads to a larger diameter. The effect of location on the diameter calculation can be explored Now Solve The following Question according to these ones: Ds. Repeat Example 10-2 exept calculate the diameter at the bottom of the column at a pressure of 700.0 kPa. The surface tension of pure n-heptane at 20C is 20.14 Homework 427 dynes/cm (0.0214 N/m), and the temperature coefficient is -0.0980 dynes/cm/K (www .surface-tension.de). Use the De Priester chart to estimate bottoms temperature. We are testing a new packing for separation of benzene and toluene. The column 1 whilaw