Details

The McCabe–Thiele graphical solution method for binary distillation is used to determine the number of equilibrium stages needed to achieve a specified separation in a distillation column. This method assumes:

1. The distillation column is adiabatic.

2. Constant molar overflow (CMO), which means that for every mole of vapor condensed, one mole of liquid is vaporized. This results in constant liquid and vapor flow rates between stages (the exception being the flow rates of the stages above and below the feed stream, which are not equal). This assumption requires that:

2a. Specific heat changes are small compared to latent heat changes between stages and .

2b. Heat of vaporization is the same for both components and thus independent of concentration.

3. Heat of mixing is negligible.

The equilibrium curve was calculated using the modified Raoult's law:

,

,

where and are the liquid and vapor mole fractions ( for methanol, for water), , , is total pressure and is the saturation pressure, which is calculated using the Antoine equation:

,

where is temperature, and , and are Antoine constants.

The activity coefficients are calculated using the two-parameter Margules model:

,

,

where and are the Margules parameters for a methanol/water mixture.

The operating lines for the rectifying and stripping sections are used to determine the number of stages. First the feed and rectifying operating lines are calculated:

,

,

where is the vapor quality of the feed, is the mole fraction of methanol in the feed, is the liquid mole fraction of methanol in the distillate and is the reflux ratio.

The operating line for the stripping section is found by drawing a line through the bottoms composition on the – line and the intersection of the feed line (also called the line) and rectifying line . The feed line intersects the rectifying line at :

,

,

the slope of the stripping line is calculated from and and the intercept is found:

.

View the screencast videos at [1] and [2] for a step-by-step explanation of the McCabe–Thiele method.

References

[1] McCabe–Thiele Graphical Method Example Part 1 [Video]. (Mar 6, 2014) www.youtube.com/watch?v=Cv4KjY2BJTA.

[2] McCabe-Thiele Graphical Method Example Part 2 [Video]. (Mar 6, 2014) www.youtube.com/watch?v=eIJk5uXmBRc.