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) - zF /(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 - zF (α -1) - α(q-1)) - zF = 0
 x1 = 0.470
 y1 = 0.689

Draw a line from ( x_D, y_D) passing through ( x₁, y₁) with an intercept x_D / (R_m + 1) on Y axis.

 xD / (Rm + 1) = 0.450
 Rm = 1.032

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

 R = 1.5 x Rm
 R = 1.55

Operating Lines

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

 y = qx /(q-1) - zF /(q-1)
 y = Rx /(R+1) + xD /(R+1)
 x2 = 0.451
 y2 = 0.633

Draw rectification section operating line from (x_D, y_D) to (x₂, y₂) and stripping section operating line from (x₂, y₂) 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 x₂. As long as it is greater than x₂ 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 x₂ 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 x₂, 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

1. Spreadsheet for Binary Distillation analysis based on McCabe Thiele method