Sieve-Tray Column Flooding After a Purity Excursion
A 1.6 m diameter sieve-tray column with 24 trays at 0.45 m spacing separates methanol from water near atmospheric pressure. At the design case, boilup is 3.0 kg/s of vapor (density 1.15 kg/m3) and reflux ratio is 1.8; the column runs at about 70% of flood and meets 99.5% distillate purity. To recover from a low-purity excursion, the operator raises reflux to 2.6 and boilup to 4.2 kg/s. Within 30 minutes, top-tray differential pressure rises from 0.4 to 1.1 kPa per tray, the reboiler level becomes unstable, and distillate purity falls further to 98.2%. The top temperature also rises by 4 K. Feed rate and composition are unchanged. The column has a fixed 1.6 m shell; tray spacing, weir height (50 mm), and downcomer area cannot be changed during the run. Top pressure is steady, and the liquid density is 900 kg/m3.
1. Estimate the superficial vapor velocity and the fraction of flood at the new boilup. Use a Fair flooding coefficient K = 0.07 m/s. Decide whether the column is flooded or merely entraining.
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Column area = pi/4 x 1.6^2 = 2.01 m2. At 4.2 kg/s and 1.15 kg/m3, volumetric vapor flow = 4.2/1.15 = 3.65 m3/s, so superficial velocity u = 3.65/2.01 = 1.82 m/s. The Fair flood velocity is u_fl = K sqrt((rho_L - rho_V)/rho_V) = 0.07 sqrt((900 - 1.15)/1.15) = 0.07 x 27.95 = 1.96 m/s. The column is therefore at 1.82/1.96 = 93% of flood, well above the usual 80-85% design limit. The high tray pressure drop and rising top temperature confirm entrainment: liquid is being carried upward, so heavy material reaches the distillate. A downcomer-backup check is less conclusive because 1.1 kPa/tray is only about 0.12 m of liquid, well below the 0.45 m tray spacing, but jet flooding and entrainment are already severe. The correct diagnosis is operation too close to flood, not a reflux shortage.
2. Explain why raising reflux lowered distillate purity, and give a safe corrective sequence.
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Raising reflux while also raising boilup increased both vapor and liquid loads on a column that was already near its hydraulic limit. More vapor velocity increases entrainment, and more liquid load raises downcomer backup and tray froth height. Entrained heavy liquid contaminates the distillate, so purity falls even though the reflux ratio is higher. The apparent benefit of reflux is overwhelmed by loss of tray efficiency. Safely correct the condition by cutting reboiler steam first, then reducing reflux, until top-tray pressure drop returns to roughly 0.4-0.5 kPa/tray and the column is below about 80% of flood. Keep feed steady and watch reboiler level. Only after hydraulics are stable should reflux be optimized at constant boilup, in small steps, while monitoring pressure drop and top temperature. Do not chase purity by adding more reflux; that repeats the failure.
3. A 20% throughput increase is proposed. Estimate the minimum column diameter for 80% of flood at the new vapor rate, assuming vapor density is unchanged.
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At 20% higher throughput, vapor rate becomes 4.2 x 1.20 = 5.04 kg/s, giving 5.04/1.15 = 4.38 m3/s. For 80% of flood, allowable velocity = 0.80 x 1.96 = 1.57 m/s. Required area = 4.38/1.57 = 2.79 m2, so diameter = sqrt(4 x 2.79/pi) = 1.88 m. A 1.9 m or 2.0 m diameter shell would be needed, not the existing 1.6 m column. This assumes the same tray spacing and weir height and no foaming. Because the estimate is close to a standard size, a detailed hydraulic rating should confirm downcomer capacity; the practical answer is that a 20% increase is not debottlenecked by the existing shell.