*Wed, 16 Dec 2015*

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.

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) + x`_{D} /(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.

`W`

_{F}= F.exp(- Area under the curve)`W`

_{F}= 5.80 mols

Distillate mols collected is obtained as following.

`D = F - W`

_{F}`D = 44.20 mols`

Average composition of distillate collected x_{D} is calculated as following.

`x`

_{D}= (x_{F}F - x_{W}W_{F})/D`x`

_{D}= 0.779

Spreadsheet for Multi-stage Binary Batch Distillation

Linear Programming in Excel Pipe Network Analysis