[How To] Calculate the height of vapor line of a batch reactor

Gud day readers........!!!

Have received some comments asking me to calculate the vapor line height of a batch reactor. Usually everybody will ask about the dia calculation, but this is something that caught my focus, because being frank i too donno the exact way to calculate the height of vapor line.

So here today, i'll demonstrate my idea to calculate the height. If you are a new reader and searching for Dia calculation of vapour line, then follow this,



This post is requested by Mr. Ram prasad.






How to calculate the column dia required for a reactor ?

How to calculate the dia of vapour column


But before going in depth calculation, i want you to know that this is just my way of calculation, there may be a direct calculation or something, but i donno those all, and openly speaking i don't like remembering all the equations, if required i'll try to derive those equations.

Is there any relation between the height and dia of vapour column ?
There is nothing like that, if there is something like that earlier i should have demonstrated you, As vapour column is meant for vapour / gas transferring from reactor to condenser, and the dia depends on the boil-up that is generated in the reactor,  height should be designed based on the vapour density, if the vapour density of a solvent that i need to distill out is high then automatically the vapour won't reach much height and in between it will get condensed. 

Anyhow, i think this knowledge is enough for getting started, if anything you need to grab just comment in the below section.




The relation between pressure, density, height / head is given by 

P ressure = D ensity x G ravitional constant x H eight 

simply, P = ꝭ x g x h.

Here today i'll calculate the vapour column height required for distilling methanol in a batch reactor.

Now lets calculate the vapour density

Lets make use of ideal gas law,

P x V = n x R x T.

P x V = ( w / W ) x R x T.

( P x W ) / ( R x T ) = w / V

ꝭ = ( P x W ) / (  R x T ).

W - boilup, R - universal gas constant, T - Boiling point or any other temp.

P - Vapour pressure.




Lets need to calculate the vapour pressure ( P ) and boil up ( W ),

Vapour pressure from Antonie equation,

Antonie equation: Log P = A - B / ( T + C ).

A, B, C are antonie constants.

These constants can be retrieved from google, anyway i'll provide those here,

Open this in new tab for antonie constants.

As the old calculation is creating some controversies, i've decided to add a new way to calculate the height of vapour line required.

Lets the case be, a 5 KL SSR with 60% methanol inside and we need to calculate the vapour line size.

The heat transfer area of 5 KL SSR is ~ 12.5 Sq.m,

The effective heat transfer area will be 12.5 x 0.6 = 7.5 Sq.m [with 60% occupancy],

Lets say the utility temp will be 80 C, and 

Initial reaction mass temperature will be 30 C,
Final reaction mass temperature will be 64 C,

Lets consider 3 C of temperature difference between jacket utility in and out,

So out let temperature will be 77 C.

LMTD = ((80 - 30)-(77-64)) / Ln((80-30)/(77-64)) = 27.46 C.

Overall Heat transfer coefficient will be ~200 KCal/Hr.Sq.m.C,

Learn how to calculate overall Heat transfer coefficient

Latent heat of Methanol is 264 KCal/Kg,

Density of Methanol is 0.79 Kg/L, Mol wt. of methanol is 32.05 g/mol.

Boil up rate based on effective heat transfer area is 155.97 Kg/hr,

Learn how to calculate the boil-up rate of solvent in reactor

Volumetric boilup is Mass boilup / Density = 197.43 L/hr,

Lets calculate the relevant vapour pressure using volumetric flow rate from the ideal gas law,

P x V = n x R x T,

P = n x R x T / V,

P = ( 155.97 / 32.05 ) x 8.314 x ( 64 + 273.15 ) / 197.43

P = 69.09 KPas = 69092.71 Pas.

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Lets calculate height based on the above mentioned relation, P = ꝭ x g x h.

h = P / ( ꝭ x g ),

h = 69092.71 / ( 1.1 x 1000 x 9.81 ) = 6.40 m.

1.1 is the vapour density of methanol

Above mentioned 1000 is to convert density from Kg/L to Kg/cu.m.


That's it......!!!

Now you got the height of vapour column that need to be arranged for a 5KL SS reactor for getting a boil up of 197 L methanol with 60% occupancy,

Hope you enjoyed the calculation here....!!!

Any queries most welcome, reach me through message / comments,

Comments are most appreciated.....!!!!

[**Calculation is slightly modified, thanks to Bhaskar for pointing out the error in unit conversion]


** The case study is changed a the previous is based on antonie equation and it'll slightly cause controversies, thats why i've modified with a fresh calculation.


Related Articles:

How to calculate Heat transfer area theoretically ? 

How to produce steam at 60 C ?

How to Design a chiller plant ?

          How to calculate U (Overall Heat Transfer Co-efficient) value ?


About The Author

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Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
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