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

4 for the top tray ql 594 gpm hda 003 1000433 hdf

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Unformatted text preview: . = 135 inches of liquid . 0.732 59.5 Superficial velocity based on bubbling area = Ua = 75.0(2.26/22.6) = 7.5 ft/s From Eq. (6-53), Ks = U a ρV ρ L − ρV 1/ 2 = 7.5 0.0408 59.5 − 0.0408 1/ 2 = 0.196 ft/s From Eq. (6-52), φe = exp(-4.257Ks0.91) = exp[-4.257(0.196)0.91] = 0.381 Exercise 7.48 (continued) Analysis: (b) (continued) From Eq. (6-54), Cl = 0.362 + 0.317 exp(−3.5hw ) = 0.362 + 0.317 exp[−3.5(2.0)] = 0.362 Weir length = Lw = 42.5 in. Volumetric liquid rate = qL = 2,578(18.1)/[60(8.33)(59.5/62.4)] = 97.9 gpm From Eq. (6-51), hl = φe hw + Cl qL Lw φe 2/3 97.9 = 0.381 2 + 0.362 ( 42.5 ) 0.381 2/3 = 1.22 in. liq From Eq. (6-55), with maximum bubble size = DH = 3/16 inch = 0.00476 m and liquid density = 59.5 lb/ft3 or 954 kg/m3, and σ = 58 dyne/cm = 0.058 kg/s2, hσ = 6σ / gρ L DBmax = 6(0.058) / (9.8)(954)(0.00476) = 0.0078 m = 0.31 in. liquid From Eq. (2), ht = hd + hl + hσ = 1.35 + 1.22 + 0.31 = 2.88 inches liquid = 0.098 psi/tray. (c) Applying the criterion of Eq. (6-68) to the top tray, hd + hσ = 3.39 + 0.13 = 3.52 in., which is greater than hl = 0.74 in. Therefore, weeping will not occur. Applying the criterion of Eq. (6-68) to the bottom tray, hd + hσ = 1.35 + 0.31 = 1.66 in., which is greater than hl = 1.22 in. Therefore, weeping will not occur. (d) From Fig. 6.28 for the top tray, with FLV = 0.0192 and % flood = 73%, fractional entrainment = ψ = 0.11, which is fairly high. From Fig. 6.28 for the bottom tray, with FLV = 0.0473 and % flood = 39%, fractional entrainment = ψ = 0.0065, which is very low. The fractional entrainment is defined as, ψ = e/(L + e). Rearranging, entrainment rate = e = ψL/(1 - ψ). At the top tray, e = 0.11(727)/(1 - 0.11) = 90 lbmol/h At the bottom tray, e = 0.0065(2,578)/(1 - 0.0065) = 16.9 lbmol/h (e) From Eqs. (6-70) and (6-72), the froth height in the downcomer = hdf =(ht + hl + hda) / 0.5 Estimate the head loss for flow under the downcomer from Eq. (6-71). Area for flow under the downcomer apron = Ada = Lwha = 42.5(2 - 0.5) = 63.8 in2 = 0.433 ft2 59.4 For the top tray, qL = 59.4 gpm. hda = 0.03 100(0.433) hdf = (4.26 + 0.74 + 0.056) / 0.5 = 10.1 in. liquid 2 = 0.056 in. liquid 98.3 For the bottom tray, qL = 98.3 gpm. hda = 0.03 100(0.433) hdf = (2.88 + 1.22 + 0.155) / 0.5 = 8.5 in. liquid 2 = 0155 in. liquid . Exercise 7.49 Subject: Tray hydraulics for methanol-water separation. Given: Data from Exercise 7.41, except that feed rate is increased by 30%. Find: (a) Percent of flooding. (b) Tray pressure drop in psi. (c) Entrainment rate. (d) Downcomer froth height. Is operation acceptable or should packing be used in one or both sections? Analysis: Use the material balance from Exercise 7.41. Make calculations at the top and bottom trays. But take into account the 30% increase in all flow rates. (a) At the top of the column, the reflux rate is 1.3(0.947)(768) = 945 lbmol/h. The overhead vapor rate = 1.3[0.947(768) + 768] = 1,944 lbmol/h. Use the entrainment flooding correlation of Fig. 6.24,...
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