The use of ordinary differential equations as a shortcut technique for the description of distillation columns has been well established over the last 3 decades. Residue curve maps (RCMs) have been employed as a graphical representation tool in the analysis and interpretation of the behavior of distillation systems. However, RCMs enable one to gain insight into infinite-reflux column behavior only. This paper will be the first part of a series that looks at column profile maps (CPMs) obtained by using the difference point equation. CPMs represent the finite-reflux case, and the map depends on the values of the difference point and the net flow rate. This paper focuses on analyzing the behavior of distillation systems for ideal thermo and shows how using CPMs one can devise more creative designs. The focus of the second part lies in analyzing systems with nonideal behavior and develops tools for the synthesis of distillation.

The first paper of this series [Tapp, M.; Holland, S. T.; Hildebrandt, D.; Glasser, D. Ind. Eng. Chem. Res. 2004, 43 (2), 364] analyzed the behavior of ternary homogeneous distillation systems by using column profile maps, which are generated by using the difference point equation. Ideal thermodynamics was assumed, and it has been shown how using column profile maps one can devise more creative designs. This paper explores the mathematics and the topology of the maps for systems with ideal and nonideal thermodynamics by looking at the occurrence of singular points in ternary homogeneous systems depending on the values of the design parameters of the difference point and the reflux ratio. Eigenvalue and eigenvector maps have been introduced, and their usefulness for manipulating phase diagrams and therefore the column profiles has been shown. The focus of the third part lies in the application of the tools presented in this paper for distillation process synthesis and design.

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