Invariant rectifying-stripping (IRS) curves are presented for energy analysis of distillation processes. The IRS curves are invariant to the column configuration (that is, feed location and total number of stages) and depend only on the separation problem and the operating pressure of the column. IRS curves are useful to set targets without performing multiple simulation studies. A novel method is proposed to extend the IRS curves, originally developed for simple distillation columns (with single feed and two end products), to complex multiple feed columns. In the proposed method, a column with n feeds is decomposed into n simple single feed columns. The IRS curves are generated for these simple columns and the order and location of the feeds are targeted. Then these IRS curves are added in distinct sections demarcated by the feed points to the column to obtain the composite IRS curves for the complex column. Various targets such as minimum energy requirements (that is, minimum condenser and reboiler loads), appropriate feed locations; proper order of feeds, and effect of premixing feeds can be targeted from the composite IRS curves. Thus, the composite IRS curves for complex columns retain all the advantages of the IRS curves established for the case of simple distillation columns. General guidelines are also proposed for appropriate feed preconditioning and side-exchanger duties leading to the design of energy-efficient complex distillation processes. (C) 2004 American Institute of Chemical Engineers.