In this article, rigorous mathematical analysis is used to prove that
the necessary condition for multiple steady-state solutions to exist i
n two-stage separation process problems involving ternary mixtures is
the tendency of the mixture to exhibit a second liquid phase. The unre
alistic solution multiplicity that exists in these problems when phase
splitting is not included in the model equations used to solve them,
vanishes when phase splitting is included. The standard specification
of reflux ratio and bottoms flow rate has been investigated.