## McCabe Thiele Diagram

This article shows how to draw McCabe Thiele diagram for doing binary distillation analysis in a spreadsheet.

Example

Determine total number of stages and feed stage for separation
of a binary mixture with relative volatility (α) 2.5, Feed
composition (z_{F}) 0.36, Distillate Composition
(x_{D}) 0.915, Bottom composition (x_{B}) 0.05
and feed quality (q) 1.5. Reflux ratio to be 1.5 times the
minimum reflux ratio (R_{m}).

Minimum Reflux Ratio (R_{m})

Calculate the intersection of q-Line and equilibrium curve.

`y = qx /(q-1) - z`

_{F}/(q-1)`y = αx / (1+ x (α - 1))`

Solving above equations gives a quadratic expression, which is solved for positive roots.

`x² (q(α-1)) + x (q - z`

_{F}(α -1) - α(q-1)) - z_{F}= 0`x`

_{1}= 0.470`y`

_{1}= 0.689

Draw a line from ( x_{D}, y_{D}) passing through
( x_{1}, y_{1}) with an intercept x_{D}
/ (R_{m} + 1) on Y axis.

`x`

_{D}/ (R_{m}+ 1) = 0.450`R`

_{m}= 1.032

Reflux ratio is calculated as 1.5 times the minimum reflux ratio.

`R = 1.5 x R`

_{m}`R = 1.55`

Operating Lines

Intersection of q-Line and rectification section operating line is calculated.

`y = qx /(q-1) - z`

_{F}/(q-1)`y = Rx /(R+1) + x`

_{D}/(R+1)`x2 = 0.451`

`y2 = 0.633`

Draw rectification section operating line from (x_{D},
y_{D}) to (x_{2}, y_{2}) and stripping
section operating line from (x_{2}, y_{2}) to
(x_{B}, y_{B}).

Draw Stages

Start drawing steps from (x_{D}, y_{D}). Draw a
horizontal line by calculating x value from equilibrium curve
based on y_{D}. Check whether this x value is greater
than x_{2}. As long as it is greater than x_{2}
rectification section operating line is used for calculation of
y value. For next step this new value of y is used and rest of
the steps are repeated. If x becomes less than x_{2}
stripping section operating line is used for calculation of y
value. It is continued till it is greater than x_{B}.

Feed stage is determined by checking at each stage when x value
becomes less than x_{2}, similarly total number of
stages are determined by checking at each stage when x value
become less than x_{B}. At last stage value of x is
calculated and difference with x_{B} is added to give
total number of stages.

`Feed Stage = 5`

`Total Stages = 11.26`

Resources

- Spreadsheet for Binary Distillation analysis based on McCabe Thiele method