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Abstract: "In this second paper on collocation methods for distillation design, we address the minimum reflux problem. Existing minimum reflux techniques do not work for nonsharp splits, as they use approximate geometric criteria to simplify modeling of minimum reflux conditions to a set of pinch point calculations for sharp splits. Collocation allows exact calculation of nonsharp minimum reflux and provides the missing link that geometric criteria replace. We examine the behavior of distillation near minimum reflux and get results consistent with prior work. We also show that sensitivity of trace species drops as less sharp splits for the key components are sought. We have found that collocation can be applied to sharp split minimum reflux problems, but we cannot exactly reproduce Underwood's values for constant relative volatility systems due to breakdown of the model near saddle pinches. We discuss the modeling of minimum reflux conditions with collocation and discuss the difficulties we have encountered. We can accurately calculate minimum reflux for nonsharp splits for nonideal systems, even when approaching a sharp split. We overestimate the minimum reflux for the sharp split case, using nonsharp calculations at very low impurities. We encourage discussion of the problems we have encountered."