Engineering & Fluid Mechanics
O’Connell Tray Efficiency Correlation Formula: Actual vs. Theoretical Distillation Plates
Convert equilibrium McCabe-Thiele / Fenske-Underwood-Gilliland distillation stages N_eq into actual column trays N_actual = ROUNDUP(N_eq / E_o, 0) using H. E. O’Connell’s correlation E_o (%) = 50.3 * (mu_L * alpha)^(-0.226).
Why viscous feeds and wide-boiling mixtures slash real sieve/valve tray efficiency!
Equilibrium distillation models compute theoretical stages N_eq assuming vapor and liquid leave every tray in 100% thermodynamic phase equilibrium—rarely achieved during milliseconds of froth contact! H. E. O’Connell (1946, Transactions of AIChE; algebraic fit by Eduljee/Seader & Henley) correlated commercial hydrocarbon and chemical fractionator test data against the product of feed liquid viscosity mu_L (in cP = mPa·s at average column temperature) and key-component relative volatility alpha: E_o (%) = 50.3 * (mu_L * alpha)^(-0.226) (valid over 0.1 <= mu_L * alpha <= 10)!
Higher liquid viscosity slows liquid-phase molecular diffusion while higher relative volatility steepens gas-liquid equilibrium resistance! For a light debutanizer (mu_L = 0.35 cP, alpha = 2.40 -> mu*alpha = 0.84), E_o = 52.32%, so N_eq = 18 theoretical stages require ROUNDUP(18 / 0.5232, 0) = 35 actual trays (excl. reboiler)—whereas a heavier, more viscous splitter (mu_L = 1.20 cP, alpha = 3.50) drops to E_o = 36.37%!
| Fractionator Feed Property (mu_L cP, alpha) | Product mu_L * alpha | O’Connell Overall Efficiency E_o (%) | Actual Trays for N_eq = 18 |
|---|---|---|---|
| Debutanizer: mu_L = 0.35 cP, alpha = 2.40 | 0.84 cP | 52.32% | 35 Actual Sieve/Valve Trays |
| Viscous Heavy Cut: mu_L = 1.20 cP, alpha = 3.50 | 4.20 cP | 36.37% | 50 Actual Sieve/Valve Trays |
| Invalid Pinch alpha <= 1.00 or mu_L <= 0 | Non-Separable | "Invalid O’Connell Distillation Inputs" | alpha > 1 Physical Guard |
O’Connell Overall Column Tray Efficiency E_o (%) = 50.3 * (mu_L_cP * alpha)^(-0.226)
Computes overall column efficiency percentage from feed liquid viscosity at average column temperature (B2, cP/mPa·s) and relative volatility alpha (B3 > 1).
=IF(OR(B2 <= 0, B3 <= 1, B4 <= 0), "Invalid O’Connell Distillation Inputs", ROUND(50.3 * ((B2 * B3) ^ (-0.226)), 2))Required Actual Column Trays N_actual = ROUNDUP(N_theoretical / (E_o / 100), 0)
Divides equilibrium stages N_eq (B4) by fractional efficiency 0.503*(mu_L*alpha)^(-0.226) and rounds up to an integer tray count.
=IF(OR(B2 <= 0, B3 <= 1, B4 <= 0), "Invalid O’Connell Distillation Inputs", ROUNDUP(B4 / (0.503 * ((B2 * B3) ^ (-0.226))), 0))Try the example
Use the original values or change them to test your understanding.