Engineering & Science
Underwood Minimum Reflux Ratio (Rmin) & Eduljee-Gilliland Distillation Correlation
Calculate binary saturated-liquid Underwood minimum reflux ratio R_min = (1 / (alpha - 1)) * ((xD / xF) - alpha * ((1 - xD) / (1 - xF))) and the Eduljee-Gilliland theoretical stage parameter Y = 0.75 * (1 - X^0.5668).
Complete the Fenske-Underwood-Gilliland (FUG) shortcut distillation design!
In chemical refinery and solvent-recovery design, Fenske's equation gives minimum trays N_min at total reflux—but real columns operate at a finite economic reflux ratio R = L / D (~1.2 to 1.5 times R_min)! For a binary mixture with relative volatility alpha > 1 fed as a saturated boiling liquid (thermal quality q = 1), Arthur J. V. Underwood's pinch-point equation gives the exact minimum reflux ratio: R_min = (1 / (alpha - 1)) * ((xD / xF) - alpha * ((1 - xD) / (1 - xF))), where xF and xD are feed and distillate mole fractions!
Once you choose operating reflux multiplier m_R = R / R_min (e.g., 1.30), H. E. Eduljee's (1975) algebraic fit to Edwin Gilliland's famous graphical correlation maps reflux abscissa X = (R - R_min) / (R + 1) directly to stage ordinate Y = (N - N_min) / (N + 1) = 0.75 * (1 - (X ^ 0.5668)), so actual theoretical stages follow as N = (N_min + Y) / (1 - Y)! Separating a benzene-toluene feed (alpha = 2.50, xF = 0.45) to xD = 0.95 requires R_min = 1.2559; harder separation at alpha = 2.00 jumps R_min to 1.9293 (+54% more reboiler steam)!
| Binary Column Case (xF = 0.45, xD = 0.95, q = 1) | Relative Volatility alpha | Underwood R_min | Eduljee-Gilliland Y (at R = 1.3*Rmin) |
|---|---|---|---|
| Benzene-Toluene (Easier Split) | alpha = 2.50 | 1.2559 | Y = 0.5008 |
| Closer-Boiling Isomers | alpha = 2.00 | 1.9293 (+53.6% reflux!) | Y = 0.4799 |
| Unphysical Volatility alpha <= 1 | Azeotrope / Equal Volatility | Guarded Input Error | "Invalid Distillation Inputs" |
Binary Saturated-Liquid (q = 1) Underwood Minimum Reflux Ratio R_min
Validates alpha > 1 and 0 < xF < xD < 1, then evaluates (1 / (alpha - 1)) * ((xD / xF) - alpha * ((1 - xD) / (1 - xF))).
=IF(OR(B2 <= 1, B3 <= 0, B4 <= B3, B4 >= 1), "Invalid Distillation Inputs", ROUND((1 / (B2 - 1)) * ((B4 / B3) - (B2 * ((1 - B4) / (1 - B3)))), 4))Eduljee-Gilliland Stage Ordinate Y = (N - N_min) / (N + 1) at Operating Multiplier B5
Computes X = ((m_R - 1) * R_min) / (m_R * R_min + 1) and returns 0.75 * (1 - X^0.5668).
=IF(OR(B2 <= 1, B3 <= 0, B4 <= B3, B4 >= 1, B5 <= 1), "Invalid Distillation Inputs", ROUND(0.75 * (1 - (((((B5 - 1) * ((1 / (B2 - 1)) * ((B4 / B3) - (B2 * ((1 - B4) / (1 - B3)))))) / ((B5 * ((1 / (B2 - 1)) * ((B4 / B3) - (B2 * ((1 - B4) / (1 - B3)))))) + 1))) ^ 0.5668)), 4))Try the example
Use the original values or change them to test your understanding.