Benzene–Toluene Column Floods After a Feed Increase
A sieve-tray column separates benzene from toluene at 1 atm (relative volatility 2.4). At design it processes 100 kmol/h of saturated liquid feed containing 45 mol% benzene, producing 98 mol% benzene overhead and 2 mol% in the bottoms with 22 theoretical trays, a reflux ratio of 2.0, and 2.8 MW reboiler duty. Design tray pressure drop is 0.6 kPa per tray, and the vendor rates the trays at 82% of flood at design rates. After a debottleneck, feed rises to 118 kmol/h at the same composition. Overhead benzene has fallen to 96.5% and is still declining; bottoms benzene is 2.8%. Reboiler duty is at 96% of maximum, tray pressure drop is now 1.1 kPa per tray, and the condenser cooling-water valve is fully open with condensate leaving at 52°C. Reflux remains at 2.0 times distillate, and the reflux drum level is steady. Operations proposes raising reflux to 2.6 to recover purity.
1. Calculate the minimum reflux ratio with Underwood's method and decide whether raising reflux to 2.6 is a sound response.
Read the worked answer
Underwood for a saturated-liquid feed (q = 1):
- Solve 2.4(0.45)/(2.4 − θ) + 0.55/(1 − θ) = 0, giving θ = 1.47.
- Then Rmin + 1 = 2.4(0.98)/(2.4 − 1.47) + 1(0.02)/(1 − 1.47) = 2.535 − 0.043 = 2.49.
- So Rmin = 1.49 and the design R = 2.0 is about 1.34 Rmin.
At the new condition the vapor rate is approximately D(R + 1). With xD = 0.965 and xB = 0.028, D = 118(0.45 − 0.028)/(0.965 − 0.028) = 53.1 kmol/h, so vapor traffic is 53.1 × 3.0 = 159 kmol/h. Design vapor traffic was about 44.8 × 3.0 = 134 kmol/h, so the column is already at roughly 159/134 = 1.19 times design vapor load, or about 97% of flood. Raising reflux to 2.6 would lift vapor traffic to 53.1 × 3.6 = 191 kmol/h, about 42% above design, and would almost certainly flood the trays. The proposal is unsound. The operating problem is capacity, not insufficient reflux.
2. Interpret the pressure-drop and purity trends. Distinguish among flooding, weeping, and condenser limitation, and name the first three field measurements you would take.
Read the worked answer
The pressure drop has risen from 0.6 to 1.1 kPa/tray while vapor load rose about 19% and purity fell. That pattern points to excessive vapor loading, downcomer backup, or flooding - not weeping. Weeping usually lowers tray pressure drop and efficiency because liquid drains through the holes; here the pressure drop is nearly double. Condenser limitation is also present: cooling water is fully open, condensate is subcooled to 52°C, and reflux drum level is steady. If the condenser cannot condense all overhead vapor, column pressure rises, vapor density increases, and flooding worsens. The cold reflux also adds internal condensation and liquid load.
First measurements: (1) top and bottom column pressure plus the full tray ΔP profile, to locate the flooded section; (2) reflux temperature and condenser cooling-water inlet/outlet temperatures, to quantify subcooling and condenser duty; (3) reboiler steam flow and feed temperature, to confirm the actual vapor load. A gamma scan or tracer test would follow if the pressure profile is ambiguous. Do not raise reflux before establishing the hydraulic limit.
3. Estimate the maximum feed rate that keeps the trays at 82% of flood, and propose two debottleneck options.
Read the worked answer
At constant reflux ratio and feed composition, vapor traffic scales approximately with feed rate. The trays are at 82% of flood at 100 kmol/h; at 118 kmol/h they are at about 82 × 1.18 = 97% of flood. To stay at 82% of flood, the maximum feed is therefore close to the original 100 kmol/h. Even that assumes the condenser can handle the load; the condenser is already at maximum water flow and subcooling the condensate.
Two defensible options:
- Reduce feed to about 100 kmol/h, or divert the excess to storage or a second column, until hardware is changed.
- Replace the trays with higher-capacity/higher-efficiency trays and add condenser and reboiler capacity so the column can handle 118 kmol/h at a reflux ratio near 2.0. The revamp must include downcomer and condenser checks, not just tray capacity.
A third option - feed preheat or subcooling - should not be accepted without a heat-balance check, because the reboiler is already at 96% of maximum. Increasing reflux is the worst choice because it adds vapor load to an already flooded column.