# Analysis of binary distillation by Ponchon-Savarit Method

The method is concerned with the graphical analysis of calculating the theoretical stages by enthalpy balance required for desired separation by distillation process (Hines and Maddox, 1984). In this method, the enthalpy balances are incorporated as an integral part of the calculation however it is not considered in the analysis separation by distillation process by McCabe-Thele method. This procedure combines the material balance calculations with enthalpy balance calculations. This method also provides the information on the condenser and reboiler duties. The overall material balance for the distillation column is as shown in Figure 5.11:

where H is the enthalpy of the liquid stream, energy/mol, QR is the heat input to the reboiler, J/s and QC is the heat removed from condenser, J/s. The heat balance on rearrangement of Equation (5.41) gives

The Equation (5.41) is rearranged as Equation (5.42) for the convenience to plot it on the enthalpy-concentration diagram. The points represented by the feed, distillate and bottom streams can be plotted on the enthalpy-concentration diagram as shown in Figure 5.21.

Comparing the Equation (5.46) with the points plotted on Figure (5.21), it is found that the left hand side of the Equation (5.46) represents the slope of the straight line between the points (xB, HB-QR/B) and (xF, HF). The right hand side of the Equation (5.46) represents the slope of the straight line passing through the points (xF, HF) and (xD, HD-QC/D). From this it can be said that all three points are on a same straight line. The amount of distillate as per Equation (5.45) is proportional to the horizontal distance  F B x x and the amount of bottoms is proportional to the horizontal distance D F x x , then from the overall material balance it can be interpreted that the amount of feed is proportional to the horizontal distance  D B x x . This leads to the inverse lever rule. Based on this principle, the analysis of distillation column is called Enthalpy-composition analysis or Ponchon-Savarit analysis of distillation column.