The boundary of the feasible separation region consists of several curves that are related to specific types of operating modes of the column. Some of these curves create a well-known product composition multitude, whereas other curves form a generalized distillation limit. The generalized distillation limit demarcates the sloppy splits (i.e., separations in which the composition of at least one product lies inside the composition space) from regions not accessible by distillation and depends on the thermodynamic state of the feed (a mixture of vapor and liquid in equilibrium or saturated vapor/liquid) and column equipment (total/partial condenser and total/partial reboiler). The mathematical equations describing the generalized distillation limit are obtained based on the relationships between the curves (which form the generalized distillation limit) and specific types of operating modes of the column as well as the material balances for the enriching and stripping columns. Furthermore, the vapor and liquid pinch-point curves, which go through the feed composition point, are not dependent on the thermodynamic state of the feed and column equipment. In addition, an algorithm for determining the generalized distillation limit is obtained. (C) 2017 American Institute of Chemical Engineers.