An Integrated Analytical and Extended Ponchon–Savarit Graphical Method for Determining Actual and Minimum Boil-Up Ratios in Binary Distillation

A rigorous framework for determining actual and minimum boil-up ratios in binary distillation combining analytical mass and energy balances with an extended Ponchon–Savarit graphical approach was implemented. First, global balances across the enriching and stripping sections yield a closed-form expression of the boil-up ratio (VB) based on enthalpy differences. Second, the VB was directly determined from an enthalpy–composition diagram by measuring the enthalpy segments between the saturated liquid, vapor, and heat-duty points. Applying this method to high-stage columns confirms that the two methods converge on identical VB values. Based on these findings, a unified graphical methodology was developed to determine the minimum boil-up ratio (VBmin). VBmin can be determined on the same diagram by locating the intersections of the extremal tie lines in both the enriching and exhausting sections, analogous to the reflux-pinch points. This procedure was systematically validated across the five canonical feed thermal states. The implemented method is a graphical approach based on the Ponchon–Savarit technique, developed for binary systems.