Mass Transfer and Separation Processes
What the exam tests
Stage-wise and rate-based separations: distillation (McCabe–Thiele, Fenske, Gilliland), absorption and stripping (Kremser), extraction, drying, adsorption and membranes, plus mass-transfer coefficients and HTU/NTU.
Core rules
- An equilibrium stage leaves its streams in equilibrium; the operating line comes from a mass balance; the feed line (q-line) reflects the thermal condition of the feed.
- Minimum reflux corresponds to a pinch; minimum stages from Fenske: N_min = ln[(x_D/(1−x_D))((1−x_B)/x_B)]/ln α_avg, counting the reboiler as a stage.
- Gilliland correlates actual stages at finite reflux; design reflux is commonly 1.2–1.5 R_min.
- Kremser for absorption, with absorption factor A = L/(mV): N = ln[(1 − 1/A)((y_in − mx_in)/(y_out − mx_in)) + 1/A]/ln A.
- Rate-based design: packed height Z = HTU × NTU, with HTU = G/(K_G a P).
- Drying splits into constant-rate and falling-rate periods; only free moisture is removable at reasonable rates.
Worked example
Fenske with α = 2.5, x_D = 0.98, x_B = 0.02. The ratio term is (0.98/0.02)(0.98/0.02) = 49 × 49 = 2401. N_min = ln(2401)/ln(2.5) = 7.78/0.916 = 8.5, so 9 theoretical stages including the reboiler - about 8 trays plus the reboiler, or 9 trays if a partial condenser is counted.
Traps
- Treating relative volatility as constant across a wide boiling range.
- Designing below R_min; no number of trays reaches specification there.
- Confusing Murphree tray efficiency with overall column efficiency.
- Ignoring the q-line when locating the feed stage.
- Using a K-value source inconsistent with the operating pressure and temperature.