Mass Transfer
Mass transfer covers diffusion, interphase transfer with overall coefficients, and the separation equipment built on them: absorption, distillation, extraction, drying and adsorption. Exam items are usually staged-column or flux calculations where the driving force must be chosen consistently.
Core rules
- Diffusion. Fick's law J_A = −D_AB dc_A/dz. For equimolar counter-diffusion the flux is simply proportional to the concentration difference; for A diffusing through stagnant B, divide by the log-mean mole fraction of B: N_A = (D_AB P/RTz)·ln[(1−x_A2)/(1−x_A1)].
- Coefficients. Sh = k_c d/D; typical correlations are Sh = 0.023Re^0.83Sc^0.33 for turbulent tubes and Sh = 2 for a stagnant sphere.
- HTU/NTU. Packed height Z = HTU × NTU; NTU is the integral of dx/(x − x*) and the HTU carries the packing and flow information.
- Distillation. Material balance plus the q-line for feed condition (q > 1 subcooled liquid, q = 0 saturated vapour). Fenske gives minimum stages: N_min = ln[(x_D/(1−x_D))((1−x_B)/x_B)]/ln α_avg.
- Absorption. Kremser or the operating line with L/G; minimum solvent sets the pinch at the bottom.
Worked example
A column separates a binary feed with relative volatility 2.5 at total reflux into x_D = 0.95 and x_B = 0.05. Fenske: (0.95/0.05) = 19 and (0.95/0.05) = 19 for the bottoms term, so N_min = ln(19 × 19)/ln 2.5 = 5.889/0.9163 = 6.43. Round up to 7 stages including the reboiler, i.e. about 6 theoretical stages plus the reboiler.
Traps
- Using an arithmetic mean driving force in a concentrated absorption column where the log mean is required.
- Flipping Henry's law constant between y = Hx and x = Hy conventions.
- Treating the q-line as vertical for a two-phase feed (that is the saturated-vapour case, q = 0).
- Mixing overall and film coefficients without the 1/K = 1/k + m/k' resistance addition.
- Ignoring that HTU has units of length while NTU is dimensionless.