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Fractional distillation brings rising vapor into contact with descending liquid in a fractionating column. Packing supplies contact area; it does not act as a sieve for individual molecules. Repeated exchange can enrich the rising vapor in the more volatile component. Some condensed liquid returns downward as reflux, rather than all being withdrawn as distillate.^[ref]

An equilibrium stage is an idealization of this contact. A real fractionating column has finite contact time and imperfect wetting and mixing; its length is not automatically a count of equilibrium stages. Product withdrawal and reflux affect the separation together. Thus the repeated ideal-stage enrichment example illustrates the composition advantage of repeated equilibration, but supplies neither a column design nor a specified reflux requirement.^[ref]

Reflux is condensed liquid returned toward the heated part of a distillation apparatus. In a fractionating column, descending reflux contacts rising vapor. Returning more condensate also changes the amount available for collection, so enrichment and product recovery must be considered together.^[ref]

Stipulate a constant relative volatility $\alpha =2$. The vapor-liquid equilibrium model then becomesAn initial liquid mole fraction $x_0=3/10$ gives an equilibrium vapor mole fraction $y_0=6/13\approx 0.461538$. Now imagine completely condensing a small sample of that vapor and using this condensate as a fresh liquid for another equilibration. Repeating this formal operation givesThese are original model calculations of ideal-stage enrichment. They are not measured compositions, a reflux design, or successive compositions of one pot undergoing simple distillation. That pot loses the more volatile component and becomes depleted; each step here instead starts from the previous enriched condensate. The displayed sequence specifies compositions, not the recoverable amount at each step.

The algebra makes the enrichment especially transparent. With composition odds $r_n=x_n/(1-x_n)$, every formal step doubles the odds, soFor every finite $n$, $x_n<1$, although $x_n\to 1$ as $n\to \infty$. This explains why repeated ideal equilibration can improve composition without making finite-step perfect separation a consequence of the model.