Batch distillation is widely used in chemical processing industries when high value added, low volume chemicals must be separated. This article shows how to model and solve a multi-stage binary batch distillation problem in excel.

Example

The 50 mol feed comprising 70% mols of A and 30% mols of B is to be distilled in the multi-stage batch distillation with 5 equilibrium stages on top of the reboiler (still pot). Reflux is returned to the column as a saturated liquid with the constant reflux ratio of 1.5. Relative volatility of A is 1.8. It is desired to reduce the mols of A in still to 10%. Determine average distillate composition, final amount of liquid in still pot and total amount of distillate collected.

A material balance is done across the column and following relationship commonly known as Rayleigh Equation is derived.

Where F (Initial mols fed in still), W_F (Mols left in still at any time), x_F (Initial mol fraction in feed), x_W (Mol fraction in still at any time) and x_D (Distillate composition at any particular time).

Equilibrium curve is obtained from relative volatility.

 y = αx / (1+ x (α - 1))

Operating line is obtained as following.

 y = Rx /(R+1) + xD /(R+1)

Relationship between x_D and x_W is obtained by performing stage-by-stage calculations. A value of x_D is selected and stages are stepped off (for a given number of equilibrium stages) to find the value of x_W. It is done for all possible values of x_D ranging from 0 to 1. A plot of 1/(x_D - x_W) vs x_W is made.

Area under curve is calculated from x_W to x_F by calculating area of trapezoid formed in small intervals.

 Area (Cell P59) = (N60-N59)*(O60+O59)/2)

Area of all trapezoids in the range from x_W to x_F are added to get area under curve.

 Area = 2.153

Amount left in still, W_F is calculated as following.

 WF = F.exp(- Area under the curve)
 WF = 5.80 mols

Distillate mols collected is obtained as following.

 D = F - WF
 D = 44.20 mols

Average composition of distillate collected x_D is calculated as following.

 xD = (xF F - xW WF)/D
 xD = 0.779 

Resources

1. Spreadsheet for Binary Batch Distillation