This work is concerned with developing the tools which enable complex multidimensional relationships between vapour and liquid phases in thermodynamic equilibrium to be represented in a form which facilitates appreciation of the complex structure so that the nature of optimum solutions is more clearly understood. The detailed analysis will be based on ternary mixtures in order to provide a basis for physical interpretation and to give a complete description of the system. Still, the development of an interactive graphics-based approach to the design of multistage separation processes is presented and illustrated by reference to ternary distillation systems. It focuses attention on how design and operational decisions can be taken based on the identification of the fundamental patterns of interaction between the variables and how they relate to operational performance. The importance of the relative positioning of the operating line and equilibrium surface provides insight as to the local factors which determine the performance of the equipment. It provides a basis for determining practical values of minimum reflux ratios for a multicomponent system where only partial information is given on the product compositions.