Develop a simple process flow sheet to estimate distillate and bottom composition of a distillation column. Determine the actual number of stages, minimum reflux ratio and the mini... Develop a simple process flow sheet to estimate distillate and bottom composition of a distillation column. Determine the actual number of stages, minimum reflux ratio and the minimum number of stages for the operation. Read more

Steps to Solve

1. Calculate the Operating Conditions
   For an equimolar mixture of benzene and toluene, the feed composition is:
   $$ z_B = 0.5, \quad z_T = 0.5 $$
   Given the desired compositions:
   $$ y_D = 0.99 \quad (99% \text{ benzene in distillate}) $$
   $$ x_B = 0.01 \quad (1% \text{ benzene in bottoms}) $$

2. Graphically Determine Minimum Reflux Ratio (R_min)
   Use the McCabe-Thiele method:

• Plot the operating line for the distillation column based on the reflux ratio.
• The minimum reflux ratio can be found where the operating line intersects the equilibrium curve. Typically, for ideal binary distillation, it can be calculated using:
  $$ R_{min} = \frac{y_D}{1 - y_D} \cdot \left(\frac{x_B}{1 - x_B}\right) $$
  Calculate this:

3. Calculate Actual Reflux Ratio
   The actual reflux ratio is given as ( R = 3 ).

4. Calculate Minimum Number of Stages (N_min)
   Using the formula based on the McCabe-Thiele method:
   $$ N_{min} = \frac{(y_D - x_B)}{(y_D - z_F)} \cdot \left( \frac{1}{R_{min}} - \frac{1}{R} \right) $$
   This gives the theoretical stages required at minimum reflux.

5. Calculate Actual Number of Stages (N_actual)
   Using the following formula that relates the actual reflux ratio to the minimum stages:
   $$ N_{actual} = N_{min} + \frac {(R - R_{min})}{R_{min}} \cdot N_{min} $$
   Calculate this accordingly.

6. Conclusion
   Sum up the results of minimum reflux ratio, minimum stages, and actual stages for a concise conclusion.