Separation Processes and Unit Operations
Scope
This domain tests selection and sizing of separation operations: distillation, absorption and stripping, extraction, drying, crystallisation, membranes, and adsorption. You must distinguish equilibrium-limited from rate-limited separations and defend the choice on energy, selectivity, and operability.
Core rules
- Distillation: relative volatility alpha sets ease of separation. Minimum stages come from Fenske, minimum reflux from Underwood, and actual reflux lies between. McCabe-Thiele stepping is a graphical mass balance, not a rate calculation.
- Fenske for a binary system: N_min = ln[(xD/(1-xD))((1-xB)/xB)] / ln(alpha_avg). The answer is theoretical stages, and the reboiler may count as one.
- Absorption: use Kremser equations or an operating line. The minimum solvent rate corresponds to a pinch at the bottom.
- Drying: the constant-rate period is external heat and mass transfer controlled; the falling-rate period is internal diffusion controlled. Critical moisture content marks the change.
- Crystallisation is governed by supersaturation, nucleation, and growth. Yield alone does not define crystal size distribution or purity.
- Membrane and adsorption processes are rate or permeability limited; selectivity alone does not size the unit.
Worked example
A binary distillation has alpha = 2.5, xD = 0.98, and xB = 0.02. Estimate minimum theoretical stages. xD/(1-xD) = 0.98/0.02 = 49; (1-xB)/xB = 0.98/0.02 = 49. N_min = ln(49 x 49) / ln(2.5) = ln(2401) / 0.916 = 7.78 / 0.916 = 8.5. About 8.5 theoretical stages. A practical design rounds up to 9 and accounts separately for reboiler and condenser. The calculation assumes constant alpha; if alpha varies, use a geometric mean. At finite reflux the stage count rises, often to 1.5 to 2 times N_min, which is why energy cost and stage cost are traded.
Traps
- Treating N_min as the design stage count; it applies only at total reflux.
- Using mole fraction when the operating line is in mole ratio for absorption.
- Ignoring azeotropes. A simple distillation may be impossible without an entrainer, pressure swing, or membrane.
- Forgetting tray efficiency and hydraulics. Weeping, flooding, and entrainment can set the diameter before thermodynamics does.
A separation train is judged on overall recovery and energy, not on one column's purity alone.