Chemical, Process & Catalysis Engineering
O’Connell Overall Distillation Tray Efficiency Formula & Actual Tray Count N_act
Convert theoretical equilibrium stages into actual sieve/valve trays using H. E. O’Connell’s (1946, AIChE) Overall Column Efficiency correlation E_0 (%) = 50.3 * (alpha * mu_L)^(-0.226) and Actual Tray Count -INT(-N_th / (E_0 / 100)).
Bridge the gap between McCabe-Thiele / Gilliland ideal stages and real industrial trays!
Shortcut Fenske-Underwood-Gilliland and graphical McCabe-Thiele designs output Ideal Equilibrium Stages N_th — assuming vapor and liquid leave every tray in 100% thermodynamic equilibrium! In real industrial fractionators, high liquid viscosity mu_L (in cP = mPa·s, evaluated at average column temperature) slows liquid-phase molecular diffusion, while high relative volatility alpha shifts mass-transfer resistance into the liquid film!
Correlating plant test data across commercial hydrocarbon and chemical fractionators, H. E. O’Connell (1946, Trans. AIChE) established the classic preliminary design equation E_0 (%) = 50.3 * (alpha * mu_L)^(-0.226) (valid for 0.1 <= alpha * mu_L <= 10 cP; excluding the reboiler, which counts as ~1 equilibrium stage on its own), converting ideal column stages N_th into integer actual trays via N_actual = -INT(-N_th / (E_0 / 100))!
| System Property (alpha = 2.50, Feed Liquid Viscosity mu_L = 0.32 cP, N_th = 18 Stages) | Formula | Evaluated Result |
|---|---|---|
| O’Connell Volatility-Viscosity Product alpha * mu_L | =B2 * B3 | 0.800 cP |
| Overall Column Plate Efficiency E_0 (%) | 50.3 * (alpha * mu_L)^(-0.226) | 52.90% |
| Exact Fractional Actual Trays N_th / (E_0 / 100) | =B4 / (E_0 / 100) | 34.02 trays |
| Rounded-Up Installed Sieve Trays N_actual | -INT(-N_th / (E_0 / 100)) | 35 actual trays |
O’Connell Overall Distillation Column Efficiency E_0 (%)
Evaluates 50.3 * (alpha * mu_L)^(-0.226) for key-component relative volatility alpha > 1.0 in B2 and molar-average feed viscosity mu_L > 0 (cP) in B3.
=IF(OR(B2 <= 1, B3 <= 0), "Requires Relative Volatility alpha > 1.0 and Viscosity mu_L > 0 cP", ROUND(50.3 * ((B2 * B3) ^ (-0.226)), 2))Rounded-Up Actual Installed Column Tray Count N_actual
Divides theoretical column stages B4 (excluding reboiler) by fractional efficiency E_0 / 100 and rounds strictly upward using universal -INT(-x).
=IF(OR(B2 <= 1, B3 <= 0, B4 <= 0), "Invalid Volatility, Viscosity, or Theoretical Stage Count", -INT(-(B4 / ((50.3 * ((B2 * B3) ^ (-0.226))) / 100))))Try the example
Use the original values or change them to test your understanding.