CHE-38

Underwood minimum reflux

Rmin = [xD/xF − α(1−xD)/(1−xF)]/(α−1) for a binary saturated-liquid feed.

Reading speed

DistillationUnderwood 1948

Governing equation

R_{\min}=\dfrac{x_D/x_F-\alpha(1-x_D)/(1-x_F)}{\alpha-1}

where

x_D: Distillate mole frac. (—)
x_F: Feed mole frac. (—)
\alpha: Relative volatility (—)
R_{\min}: Minimum reflux (—)

Lecture brief

Historical brief

From CSTR/PFR mole balances and Arrhenius rates to McCabe–Thiele stages and NTU exchangers, chemical engineering is conservation plus equilibrium. The lab is that design arithmetic. This sheet (CHE-38 — Underwood minimum reflux) is the form associated with Underwood 1948. Working symbols: $x_D$ , $x_F$ , $\alpha$ $\rightarrow$ $R_{\min}$ . Underwood solved the pinch of a McCabe–Thiele construction. For a binary this closed form is the saturated-liquid limit.

Purpose

Purpose: compute

R_{\min}

from

x_D

x_F

\alpha

in Chemical engineering via

R_{\min}=\dfrac{x_D/x_F-\alpha(1-x_D)/(1-x_F)}{\alpha-1}

Rmin = [xD/xF − α(1−xD)/(1−xF)]/(α−1) for a binary saturated-liquid feed. Use it when a real chemical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

x_D = 0.950\,\mathrm{—}

x_F = 0.400\,\mathrm{—}

\alpha = 2.200\,\mathrm{—}

, the governing relation

R_{\min}=\dfrac{x_D/x_F-\alpha(1-x_D)/(1-x_F)}{\alpha-1}

yields

R_{\min} = 1.826\,\mathrm{—}

. An x–y diagram, a pinch, an Rmin tick. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Distillate mole frac. x_D0.95 —Feed mole frac. x_F0.4 —Relative volatility \alpha2.2 —

Outputs

Minimum reflux R_{\min}1.826 —

Reading speed

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Narration of this film

An x–y diagram, a pinch, an Rmin tick.

Underwood solved the pinch of a McCabe–Thiele construction. For a binary this closed form is the saturated-liquid limit.

Reading speed

Watch on YouTube