chem

Distillation (McCabe-Thiele) & Absorption

VLE, relative volatility, the stepping method for theoretical stages, reflux-ratio economics, and gas-absorption design with HTU/NTU.

RelianceIOCLGAILDr. Reddy's

Key formulas

y = αx / (1 + (α−1)x)
Constant-relative-volatility equilibrium: The straight-ish VLE line McCabe-Thiele uses; α = 2.5 gives an easy separation, α = 1.1 a brutal one.
Z = HTU × NTU (e.g. Z = HOG·NOG)
Packed column height: NOG = ∫ dy/(y*−y) from the operating/equilibrium lines; HOG from mass-transfer coefficients (kG, kL).

▸Relative volatility α = y(1−x)/[x(1−y)] decides separability: α close to 1 means many stages/high reflux; α ≥ 1 always (more volatile component richer in vapour).
▸McCabe-Thiele: plot equilibrium (y = αx/(1+(α−1)x)) and operating lines between xD, xF, xW; each step = 1 theoretical stage; feed q-line locates the intersection of rectifying/stripping lines.
▸q-line: saturated liquid q=1 (vertical), saturated vapour q=0 (horizontal), subcooled q>1, superheated q<0 — the slope q/(q−1).
▸Minimum reflux corresponds to an infinite pinch stage; total reflux gives minimum stages (Fenske). R between Rmin and total reflux; economic R ≈ 1.2–1.5 × Rmin.
▸Fenske (min stages), Underwood (Rmin), Gilliland (stages vs reflux correlation) — the shortcut trio before McCabe-Thiele.
▸Absorption: gas solubility and Henry's law p = H·x drive design; packing columns use HTU×NTU = Z; L/G ratio sets the operating line slope (below the equilibrium curve for stripping, above for absorption).
▸Tray efficiency (Murphree) 50–80%: theoretical stages ÷ efficiency = actual trays. Packed vs trayed: packed preferred for corrosive/foaming systems and low pressure drop.

Aspect	Distillation	Absorption	Stripping
Separates by	Volatility difference (heat)	Solubility difference (solvent)	Desorption (steam/gas)
Operating line vs equilibrium	Between the two, stepping stages	Above the equilibrium line	Below the equilibrium line
Energy	Reboiler + condenser duty	Solvent regeneration (downstream)	Steam or inert gas duty
Typical use	Crude/petroleum/ethanol splits	CO2/H2S/SO2 removal, gas washing	Solvent recovery, degasification

1. Relative volatility α = 1.0 means…

2. Each step (triangle) in a McCabe-Thiele diagram represents…

3. At total reflux, the number of stages is…

4. For absorption of a gas into a solvent, the operating line lies…

5. In a saturated-liquid feed, the q-line is…