Multiple steady states in ideal two-product distillation

Simple distillation columns with ideal vapor-liquid equilibrium may display multiple steady-state solutions. Two fundamentally different sources for the multiplicity are presented. Both bring about the unexpected result that increasing reflux makes separation worse in the top part of the column. It corresponds to an unstable operating point. The first type of multiplicity is found for columns with mass or volume inputs (e.g., mass reflux and molar boilup). Even for constant molar flows, the transformation from the actual input units to molar units may become singular (corresponding to a pitchfork bifurcation point), resulting in multiple steady-state solutions. The results are highly relevant in practice, as industrial columns usually have inputs on a mass or volume basis. The second type for specifications on a molar basis (e.g., molar reflux and molar boilup) depends on the presence of an energy balance in the model. The multiplicity is caused by interactions between flows and compositions in the column.