Geometric methods are one of the most valuable tools for distillation process synthesis and design. The graphical representation of azeotropes, residue curves, distillation regions, and distillation boundaries provide designers with intuition, a wealth of knowledge about the entire composition space and quantitative results. In this paper we show how residue curve maps and geometric methods can be used in the synthesis and design of sequences of complex heterogeneous azeotropic distillation columns. A new algorithm for the design of heterogeneous azeotropic distillation column with top decanter is presented and applied in two design case studies of column sequences with recycle streams and top decanters. In both the cases, a feasible structure has been quickly found based on information obtained by examining the entire composition space.