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Column tray efficiency
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Calibration data:

ml of water(VB) ml of methanol (VA) Mole fraction of methanol (X) RI
100 0 0   1.33
90 10 0.059   1.3315
80 20 0.1233   1 .3325
70 30 0.194   1.3345
60 40 0.273   1.3336
50 50 0.36   1.337
40 60 0.458   1.3345
30 70 0.568   1.337
20 80 0.69   1.3345
10 90 0.837   1.3305
0 100 1   1.3235

 

Fit RI vs mole fraction curve and find out to polynomials ,one for the water rich section(bottom composition) and the other for the methanol rich section(distillate composition).

 

Formulae :

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»R«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mi mathvariant=¨bold¨»L«/mi»«mi mathvariant=¨bold¨»D«/mi»«/mfrac»«/math»

Intercept = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msub»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»D«/mi»«/msub»«mrow»«mi mathvariant=¨bold¨»R«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math»

Overall effeciency of the packed distillation column = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»(«/mo»«msub»«mi mathvariant=¨bold¨»N«/mi»«mi mathvariant=¨bold¨»T«/mi»«/msub»«mo»§nbsp;«/mo»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«mi mathvariant=¨bold¨»N«/mi»«/mfrac»«mo»§#215;«/mo»«mn»100«/mn»«/math»

Observation and calculations :

RI of feed =1.337

RI of distillate =1.3345

From the  calibration curve corresponding mole fraction of methanol are  :

Xf =0.5

XD =0.8

L/D =1(say)

Intercept =0.4

Average value of relative volatilty for methanol - water system is 3.32

 

Using the x-y data for methanol - water system available in perry we construct the McCabe- thiele diagram with the above given data and strike of the number of equilibrium stages

 

Total no. of ideal stages(including reboiler)=7

No. of ideal stages reqd. NT-1 = 6

No. of actual stages = 7

Therefore overall efficiency of the packed distillation column = 85.7%

 

 

 

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