The formation of multicomponent azeotropes in waste-solvent streams often complicates separation and recovery of solvents. The implications of applying batch distillation to such a mixture can be studied in a residue curve map. Ahmad and {Barton} (1996) extend and generalize the theory for ternary residue curve maps applied to batch distillation to homogeneous systems with an arbitrary number of components. These theoretical results are used to develop an algorithm for elucidating the structure of the batch distillation composition simplex for a system with an arbitrary number of components. The batch distillation regions are identified by completing unstable boundary limit sets. The completed boundary limit sets accurately represent the topological structure of the composition simplex and make it possible to extract all product sequences achievable when applying batch distillation. The algorithm is demonstrated on the five-component system acetone, chloroform, methanol, ethanol, and benzene, which exhibits nine azeotropes. Furthermore, the set of batch distillation product sequences predicted is validated using a commercial dynamic batch distillation column model. Although the problem does not closely approach the limiting conditions of the theory, the predictions agree excellently with the simulations.