This application combines the power of residue curve maps (RCMs) and combinatorial analysis for the synthesis of separation systems for ternary mixtures. RCMs provide knowledge of feasible distillation separations. The skilled engineer can interpret the RCM to define distillation towers and related unit operations for separating azeotropic mixtures. Combinatorial analysis is combined with the unit operation definitions to handle the synthesis task. The MSG algorithm determines when a feasible flowsheet superstructure (maximal structure) has been established. The SSG algorithm then extracts all of the feasible flowsheets from the maximal structure.