A warning against treating one equilibrium diagram as a universal map for all operating conditions.
The final technical sections qualify fixed-boundary diagrams and extend the theory to multicomponent real mixtures.
For real azeotropic mixtures, separation lines and product domains can change with reflux and operating conditions; an apparent crossing of a total-reflux boundary may reflect that the applicable distillation space has shifted. The governing vector equations remain compact, but solution and visualization complexity grow rapidly with component count.
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5.2.2.2–5.3, Partial reflux and multicomponent azeotropic mixtures
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