Engineering & Fluid Mechanics
Murphree Vapor Tray Efficiency (E_MV) Formula: Single-Stage Mass Transfer & Pseudo-Equilibrium
Evaluate single-plate distillation and gas-absorption performance using Eger V. Murphree’s 1925 vapor efficiency E_MV = (y_n - y_(n+1)) / (y_n* - y_(n+1)) and step off actual tray outlet compositions y_n = y_(n+1) + E_MV * (y_n* - y_(n+1)).
Measuring fractional approach to vapor-liquid equilibrium across a single real distillation tray!
Introduced by Eger V. Murphree (1925, Industrial & Engineering Chemistry), the Murphree vapor efficiency E_MV compares the ACTUAL enrichment of light-key mole fraction across tray n (y_n leaving tray n minus y_(n+1) entering from tray n+1 below) against the MAXIMUM thermodynamically possible enrichment (y_n* - y_(n+1)), where y_n* is the vapor composition in phase equilibrium with actual liquid x_n leaving tray n!
Unlike point efficiency E_OG (bounded <= 1.0), crossflow liquid concentration gradients across wide-diameter trays can occasionally push E_MV slightly above 1.0! On a McCabe-Thiele diagram with y_(n+1) = 0.042, y_n = 0.068, and equilibrium y_n* = 0.078, E_MV = (0.068 - 0.042) / (0.078 - 0.042) = 0.7222 (72.22% of the vertical equilibrium step)!
| Tray Vapor Mole Fractions (y_(n+1), y_n, y_n*) | Actual Jump (y_n - y_(n+1)) | Max Equilibrium Jump (y_n* - y_(n+1)) | Murphree Efficiency E_MV |
|---|---|---|---|
| y_(n+1)=0.042, y_n=0.068, y_n*=0.078 | +0.0260 | +0.0360 | 0.7222 (72.22%) |
| Improved Froth Contact y_n = 0.073 | +0.0310 | +0.0360 | 0.8611 (86.11%) |
| Pinch Point y_n* = y_(n+1) = 0.042 | 0.0000 | 0.0000 (Division by Zero!) | "Equilibrium Pinch or Invalid Mole Fractions" |
Murphree Vapor Tray Efficiency E_MV = (y_n - y_(n+1)) / (y_n* - y_(n+1))
Computes fractional Murphree vapor efficiency from inlet vapor mole fraction y_(n+1) (B2), actual outlet vapor y_n (B3), and equilibrium vapor y_n* (B4).
=IF(OR(MIN(B2:B4) < 0, MAX(B2:B4) > 1, B4 = B2), "Equilibrium Pinch or Invalid Mole Fractions", ROUND((B3 - B2) / (B4 - B2), 4))Murphree Percentage Tray Efficiency (%)
Expresses E_MV as a percentage approach to vapor-liquid equilibrium.
=IF(OR(MIN(B2:B4) < 0, MAX(B2:B4) > 1, B4 = B2), "Equilibrium Pinch or Invalid Mole Fractions", ROUND(100 * (B3 - B2) / (B4 - B2), 2))Try the example
Use the original values or change them to test your understanding.