Analysis Of Binary Distillation By Ponchon Savarit Method | Mass Transfer - Chemical Engineering PDF Download

5.2.2.4. Analysis of binary distillation by Ponchon-Savarit Method 

Background Principle: 
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:
                        (5.39)
For any component the material balance around the column can be written as:
        (5.40)
Overall enthalpy balance for the column yields
                    (5.41)
where H is the enthalpy of the liquid stream, energy/mol, Q_R is the heat input to the reboiler, J/s and Q_C is the heat removed from condenser, J/s. The heat balance on rearrangement of Equation (5.41) gives
             (5.42)
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.

Figure 5.21: Representation of feed, distillate and bottom streams on the enthalpy-concentration 

Substituting the Equation (5.39) into the Equation (5.40) and (5.42) we get
                                       (5.43)
               (5.44)

From the Equations (5.43) and (5.44) one can write
                             (5.45)
The Equation (5.45) can also be written on rearrangement as:
                       (5.46)
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 (x_B, H_B-Q_R/B) and (x_F, H_F). The right hand side of the Equation (5.46) represents the slope of the straight line passing through the points (x_F, H_F) and (x_D, H_D-Q_C/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  and the amount of bottoms is proportional to the horizontal distance   then from the overall material balance it can be interpreted that the amount of feed is proportional to the horizontal distance   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.

Analysis of tray column 
Consider the theoretical stage shown in Figure 5.12 and the principle by which it operates is described in the enthalpy-composition diagram as shown in Figure 5.22.

Figure 5.22: Operation principle of stage-wise binary distillation on enthalpy-concentration diagram

The vapor entering to the tray (n), V_n+1 is a saturated vapor of composition y_n+1 wheras the liquid entering to the tray is L_n-1 of composition x_n-1. The point P in the Figure 5.22 represents the total flow to the tray. The point P lies in a straight line joining xn-1 and yn+1. The distance  proportional to the quantity L_n-1 and the distance  proportional to the quantity Vn+1 as per lever rule. So 
            (5.47)
The sum of the liquid and vapor leaving the plate must equal the total flow to the plate. So the tie line must pass through the point P which represents the addition point of the vapor V_n and liquid L_n leaving the tray. The intersection of the tie line with the enthalpy-composition curves will represent the compositions of these streams. Around the tray n, the material balances can be written as:
                                (5.48)
          (5.49)

The enthalpy balance around the tray gives
                             (5.50)
Where H_V is the enthalpy of the vapor and H_L is the enthalpy of the liquid. From the material and enthalpy balance Equations above mean that the stream that added to V_n+1 to generate L_n is same to the stream that must be added to V_n to generate L_n-1. In the Figure 5.22, Δ represents the difference point above and below the tray. This point of a common difference point can be extended to a section of a column that contains any number of theoretical trays.