We present a systematic procedure for entrainer selection and synthesis of heterogeneous azeotropic distillation flowsheets. First, we partition the flowsheet into tasks (mixing, decantation, and distillation) and identify the main distillation task. Then, we investigate the location of this task in the residue curve maps (RCMs) reported by Kiva et al. (Kiva, V. N.; Hilmen, E. K.; Skogestad, S. Chem. Eng. Sci. 2003, 58 (10), 1903-1953). Third, we analyze feasibility constraints on the main distillation task and the effect of pressure on these constraints. Furthermore, we demonstrate the case that performing this task requires a combination of the concepts of heterogeneous and extractive distillations in a hybrid scheme. The developed procedure is illustrated for 11 representative ternary mixtures. For these mixtures, the sensitivity of reflux and stage requirements of the column carrying out the main distillation task to continuous degrees of freedom (e.g., composition) and discrete degrees of freedom (e.g., use of multiple feeds) is discussed, besides other mixture-specific problems.