A highly effective method has been established to identify processing or operating units necessary for the design or synthesis of azeotropic-distillation systems by resorting to the first principles and logical sequencing of such units. The materials represented in the space of the residue curve map are partitioned into lumped materials bounded by the thermodynamic boundaries and pinches. Subsequently, the operating units are identified on the basis of these lumped materials. The efficacy of the method has been amply illustrated by generating some feasible flowsheets with a set of relatively simple heuristics for the process of producing pure ethanol from its aqueous solution via azeotropic distillation, which is a typical complex process involving thermodynamic pinches, such as azeotropes, phase transition, and/or phase separation. The method is applicable to other complex processes, e.g., crystallization, extraction, reactive distillation, and their combinations. It is highly likely that the method can be an integral part of any conventional heuristic or algorithmic flowsheeting procedure because selecting plausible or candidate operating units is essential for synthesizing a flowsheet by any procedure.