Mass Transfer
Scope
Diffusion, interphase transfer, and stagewise or rate-based separations: absorption, stripping, distillation, extraction, drying, and adsorption.
Concepts to own
- Fick's law; equimolar counterdiffusion versus diffusion through a stagnant film, where the log-mean partial-pressure driving force matters at high concentration.
- Mass transfer coefficients and correlations Sh = f(Re, Sc); Chilton-Colburn jD analogy with heat transfer.
- Rate-based design: Z = HTU × NTU, with NTU from a log-mean driving force or the Kremser equation.
- Distillation: relative volatility, McCabe-Thiele, minimum reflux at the pinch, minimum stages by Fenske, actual stages from efficiency.
- Fenske: Nmin = ln[(xD/(1−xD))((1−xB)/xB)] / ln α, counting the reboiler.
- Absorption: lean-oil rate, Kremser, and minimum solvent at the pinched bottom.
Traps
- Using mole fractions where mole ratios are required, especially in absorption with large composition change.
- Omitting the reboiler and condenser from the stage count.
- Assuming constant relative volatility across a wide boiling range.
- Confusing overall column efficiency with stage (Murphree) efficiency.
Worked example
With α = 2.5, xD = 0.95, xB = 0.05: Nmin = ln[(19)(19)]/ln 2.5 = 5.89/0.916 = 6.4, so about 7 stages including the reboiler.
Rule of thumb: at total reflux each stage multiplies the separation factor by α; when α is near 1.1, hundreds of stages are needed and you should reconsider the separation scheme.