(69g) Reformulating Underwood’s Minimum Reflux Equations to Remove the Restriction of Constant Component Relative Volatilities

Traditional approaches for estimating the minimum reflux ratio in distillation design, such as the Underwood equations, are limited by the assumption of constant component relative volatilities. This assumption restricts their applicability to ideal or near-ideal mixtures, often leading to inaccuracies in complex separations. We present a novel method that removes this constraint, providing a more versatile approach to minimum reflux ratio determination in distillation columns. Our method uses Excel’s Solver to simultaneously solve the operating line equations, the q-line equations, and recovery constraints for the light and heavy keys. By integrating a property package for vapor-liquid equilibrium (VLE) calculations, our approach accurately adapts to variable component relative volatilities throughout the column profile.

This method also addresses a key challenge in distillation design: distinguishing whether the minimum reflux condition is caused by a feed pinch or a pinch away from the feed. The method identifies pinches by examining the convergence of the solution at or away from the feed point. If a pinch at the feed is detected, the solution represents the minimum reflux condition. Alternatively, if the solution pinches away from the feed, the method adapts to determine the appropriate off-feed pinch point, ensuring precise reflux ratio estimation.

Our findings offer a practical, robust solution schema for designing distillation columns across a range of mixture types, providing valuable insights into both the location and nature of the minimum reflux pinch point. This approach expands the toolkit available for accurate, flexible distillation design in chemical engineering, particularly for non-ideal or highly variable mixtures.