This Demonstration shows how to determine the number of equilibrium stages needed for a two-component (methanol/water) separation in a counter-current distillation column. It also shows the optimal location to feed the binary mixture into the column. Check "view process flow diagram" to show the  - diagram on the left and the process flow diagram on the right. When that box is not checked, a larger - diagram is shown and you can move the cursor over the curves to see labels. The column feed has a methanol mole fraction of  and a quality of 0.5. The condenser is a total condenser, so it is not considered an equilibrium stage. Set the external reflux ratio  , as well as the methanol mole fractions in the distillate  and bottoms  streams, with sliders. The number of stages is determined by stepping off stages starting at ; the partial reboiler is an equilibrium stage. The number of equilibrium stages depends on the compositions of the exiting streams and the reflux ratio. The stages can be numbered with the first stage above the reboiler (bottom to top) or with the first stage at the condenser, use buttons to switch between these numbering options. Note that the determined by stepping off stages is often lower than the desired because reaching the exact value of the desired would require a partial stage, which is not possible.Download the CDF file to view the simulation using the free Wolfram CDF player. |
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:
.