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McCabe thiele method
In this article I would like to use the mccabe thiele method. How important it is to calculate the number of plates in a distillation unit is how it gives the idea to calculate the reflux ratio.
- All the petrochemical and chemical industries use this method for optimization of new plants or start up new distillation units.
It is used basically for binary feed by using vapor-liquid equilibrium (VLE).
First of all I would like to discuss all assumption which is important for calculation of tray
Constant molal overflow (also called equimolal overflow)
- This occurs when the molar heat of vaporization of the liquid phase is essentially equal to that of the vapor phase .
- That is, the heat needed to vaporize one mole of liquid is roughly the same as the heat released when one mole of vapor is considered.
- Consequently, any condensation on the stage is balanced out by vaporization and flow rates within the column are changed solely by feed or product stream.
- No heat mixing will be there.
McCabe-Thiele method q-line
What is the q line ?
q line is drawn between the intersection of the operating lines and where the feed composition lies on the diagonal line.
In other words q means the mole fraction of liquid in feed. How much less volatile component present in the binary mixture it give the idea
q line are many type
- Cold feed – positive slope and lie to the right of the vertical in the T-X-Y diagram the value of q is q>1 for cold liquid, and slope of the line is positive and lies to the right of the vertical.
- Saturated liquid when in the fraction in feed vapor and liquid are the same ; this feed is called saturated liquid.The Value of q =1 for saturated liquid. Most of the cases this feed. Is used.it is a vertical line .
- Saturated vapor ( q=0 for this condition)
- For a mixture vapor -liquid feed it will lie between horizontal and vertical axis . And the slope of this line will be negative.(0<q>1)
- Superheated feed will produce a line below the horizontal.
- Rectifying and stripping line intersect on the feed line
- The column has an intermediate feed or product the same rule applies.
These points are very important in the calculation of the number of stages and reflux ratio.
Graph you can refer in standard book on the bases of the graph we have the step which is included by McCabe thiele (steps)
- Plot the equilibrium curve for the calculation of the stage.
- Draw the exact location of composition.(Xf, xw,Xd)Xf ,Xw ,Xd are the mole fraction feed , residue and distillate respectively.
- Calculate the slope of the q line
- Calculate y intercept in the rectifying section.
Draw stripping line using coordinate and intersection between rectifying and q line .
- From Xd locate (x,y) drowning horizontal lines to the. Equilibrium line of stage one .
- From the help of the y coordinate drowning a vertical line to the rectifying section . Locate the mass balance condition between (x,y)
- From y draw horizontal lines to the equilibrium line for stage 2 .
- Return to step 7 and cycle through step 7 and 8 draw subsequent vertical lines to the stripping section
- End after a predetermined number of stages.
Formula of the rectifying line
Y= R/(R+1) +XD/(R+1)
Formula of stripping section
Y= L/(L-w) – wXw/(L-w)
Where R is the reflux ratio. Formula mentioned above is very helpful to calculate composition each and every point.
Conclusion
This method is purely graphically and easy to understand the process and operation. The q line plays an important role in the T-x-y diagram.
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