The heat-integrated distillation column, generally called HIM, applies the principle of internal heat integration between the rectifying section and the stripping section of a distillation column by increasing the temperature of the rectifying section with a compressor. In this work, a theoretical stage-to-stage Study of a HIDiC based on the Ponchon-Savarit method is performed. Several HIDiC design variables, Such as the number of theoretical stages, reboiler (or preheater) duty, minimum overall internal heat-transfer rate, and configuration, can easily be interpreted ill the Ponchon-Savarit (Hxy) diagram. Such ail approach brings new insights into and better understanding of the features of HIDiC. A preliminary (or shortcut) HIDiC design procedure using Hxy diagrams is also proposed. The obvious advantages are that the proposed method allows the direct design of a HIDiC and avoids trial-and-error design using a commercial simulator. In addition, the proposed graphical method call foresee possible pinch points before requiring use of a rigorous Simulator. Furthermore, the proposed graphical estimation of internal stages of a HIDiC is applied to a binary methanol-water system and compared to the rigorous simulation results obtained using Aspen Plus. Moreover, the McCabe-Thiele diagram of the HIDiC is also drawn using the extended Ponchon-Savarit method and presented in this study.