Distillation

Distillation separates liquids by volatility and is the most common separation in industry. Learn stages, reflux and boil-up, McCabe–Thiele analysis, minimum stages (Fenske), minimum reflux (Underwood), Gilliland correlation, condenser and reboiler duties, and energy-saving configurations.

Refineries, petrochemical plants and distilleries rely on distillation columns: vapour rising through trays or packing contacts liquid flowing down, and each contact enriches the vapour in the more volatile component.

Designers choose the number of stages and reflux ratio — a trade-off between column height (capital) and energy (operating cost).

An analogy

A distillation column is a stack of repeated boil-and-condense steps: each tray re-boils the liquid from above and condenses vapour from below, purifying a little more at every step.

How a column works

Feed enters mid-column. The reboiler at the bottom vaporises liquid; the condenser at the top condenses vapour; part returns as reflux. The rectifying section above the feed purifies the light product; the stripping section below purifies the heavy product.

McCabe–Thiele

On an x–y diagram, step between the equilibrium curve and operating lines (rectifying: y = R/(R+1) x + x_D/(R+1); stripping line through (x_B, x_B) and the q-line intersection). Each step is one theoretical stage.

Reflux–stages trade-off

Total reflux gives minimum stages (Fenske); minimum reflux needs infinite stages (Underwood). Optimum reflux is typically 1.1–1.5 R_min. Gilliland's correlation links actual stages to reflux.

Real columns and energy

Tray efficiency (≈ 60–80 %) converts theoretical to actual trays. Rigorous stage-by-stage simulation (MESH equations) handles multicomponent, non-ideal systems. Energy savers: heat integration, heat pumps (vapour recompression), dividing-wall columns, pressure-swing and extractive distillation for azeotropes.

Formulas

• Equilibrium curve (constant α): y = α x / (1 + (α − 1) x)
• Fenske: N_min = ln[(x_D/(1−x_D)) · ((1−x_B)/x_B)] / ln α
• Underwood (sat. liquid feed, binary): R_min = [x_D/z_F − α(1−x_D)/(1−z_F)] / (α − 1)
• Gilliland (Eduljee): Y = 0.75(1 − X^0.5668), X = (R − R_min)/(R + 1), Y = (N − N_min)/(N + 1)
• Condenser duty: Q_c = D (R + 1) λ

Worked example: Minimum stages and reflux

Given: Benzene–toluene, α = 2.43; z_F = 0.4 (saturated liquid), x_D = 0.95, x_B = 0.05

Find: N_min and R_min.

• N_min = ln(19 × 19)/ln 2.43 = 5.89/0.888 = 6.6 stages
• R_min = [0.95/0.4 − 2.43 × 0.05/0.6]/1.43 = 1.52

Answer: N_min ≈ 6.6, R_min ≈ 1.52

Worked example: Actual stages and condenser duty

Given: R = 1.3 R_min = 1.975; D = 38.9 kmol/h, λ ≈ 30.8 MJ/kmol

Find: N (Gilliland) and condenser duty.

• X = (1.975 − 1.52)/2.975 = 0.153 → Y = 0.75(1 − 0.153^0.5668) = 0.491
• N = (Y + N_min)/(1 − Y) = (0.491 + 6.63)/0.509 = 14.0
• V = 38.9 × 2.975 = 115.7 kmol/h → Q_c = 990 kW

Answer: ≈ 14 theoretical stages; ≈ 1 MW condenser

Common mistakes

• Wrong: Designing at minimum reflux. — Right: R_min needs infinite stages — use ≈ 1.2–1.5 R_min.
• Wrong: Assuming theoretical stages = trays. — Right: Divide by tray efficiency (≈ 0.6–0.8).

Applications

• Refining: Crude distillation, fractionators and stabilisers.
• Petrochemicals & solvents: Olefin splitters, aromatics, solvent recovery.
• Beverages & air separation: Spirits production; cryogenic O₂/N₂ columns.

Key takeaways

• Stages + reflux trade capital vs energy.
• Fenske N_min; Underwood R_min; Gilliland N.
• McCabe–Thiele visualises stages.
• Q_c = D(R + 1)λ.

Going further

• Dividing-wall columns: Separate three products in one shell, saving ≈ 30 % energy.
• Rate-based models: Model mass transfer directly instead of equilibrium stages.
• Column control: Dual-composition control with temperature inferentials.