Mass Transfer & Distillation (McCabe-Thiele, Absorption)
McCabe-Thiele stepping, Fenske/Underwood/Gilliland, absorption with NTU/HTU — the unit-operations questions refinery recruiters love.
Key formulas
Nmin = log[(xD/(1−xD))·((1−xB)/xB)] / log(α_avg)
Fenske equation (min stages): Total reflux minimum theoretical stages for a binary split.
Σ z_i(1 − K_i) / (1 + ψ(K_i − 1)) = 0, ψ = V/F
Rachford-Rice / flash: Flash-distillation vapour fraction from K-values and feed composition.
H = HTU·NTU; NTU = ∫ dy/(y − y*)
NTU / HTU: Packed-column design: separation difficulty times equipment performance = height.
p = H·x (dilute absorption)
Henry's law: Equilibrium for gas absorption; low H = very soluble gas = easier absorption.
Cheat sheet
- ▸Distillation separates by relative volatility α = y/x at equilibrium; α > 1 is essential — no amount of trays separates an azeotrope (α = 1) by simple distillation.
- ▸McCabe-Thiele: plot equilibrium curve and operating lines (q-line locates feed condition: q = 1 saturated liquid, q = 0 saturated vapour), then step off trays between them; the feed tray is where the two operating lines meet.
- ▸Minimum reflux ratio corresponds to an infinite number of stages (pinch point); minimum stages occur at total reflux (Fenske equation). Actual design sits between: use Underwood for Rmin, Gilliland to relate stages to reflux.
- ▸Absorption: dilute systems use Henry's law p = Hx; packed columns are sized with NTU (difficulty of separation) and HTU (equipment efficiency), H = HTU × NTU.
- ▸Height of packing increases with low liquid rate, poor wetting, or gas-film vs liquid-film control — identify the controlling resistance first (soluble gas → gas-film controlled).
- ▸Tray efficiencies (Murphree) typically 40–80%; real trays needed = ideal stages / efficiency.
Packed vs Tray columns
| Aspect | Packed column | Tray column |
|---|---|---|
| Contacting | Continuous (film on packing) | Staged (discrete trays) |
| Pressure drop | Low | Higher |
| Best for | Corrosive/foaming, small diameter, vacuum | Large diameter, high liquid rates, solids |
| Analysis | NTU-HTU (differential) | McCabe-Thiele stages |
| Maintenance | Packing replacement | Tray cleaning, weeping/flooding checks |
Visual
McCabe-Thiele stepping: y | equilibrium curve | / /o stepping between equilibrium | / o / and operating lines gives | / o / theoretical trays (each step = 1) | o / | / ← operating line (rectifying) +--------------------- x xB .... xF .... xD
Top 4 campus interview questions
MCQ mastery quiz
1. Relative volatility α equal to 1 means the mixture…
2. Minimum number of theoretical stages occurs at…
3. For a very soluble gas, the absorption is controlled by the…
4. The q-line for a saturated liquid feed is…