How Do You Calculate the Bottoms Ethanol Fraction in Distillation?

[wiscoman]

Haven't taken a course in distillation in a long time and now myself and some others are working on getting a fuel ethanol still going and wanted to do the calculations before we moved forward.

We have a beer that is 12% alcohol and reaching a purity of 90% EtOH in the distillate.

The mass balances I believe would be:
total balance:

F= D + B
and
Ethanol balance:

F*xf=D*xd + B*xb

where F is the feed rate, D is distillate rate, and B is bottoms rate. xf is mole fraction ethanol in feed, xd is ethanol fraction in distillate, and xb is ethanol fraction in bottoms.

I figure the xd=0.9 and xf=0.12, what would the xb be equal to? Is it dictated by the VLE?

We have a McCabe program that does the step offs for the ideal plates, and it allows you to set the mole fractions, can these be set arbitrarily?Additionally, are mole fractions equivalent to volume fractions (assuming ideality)? I know mass fractions are not equivalent to mole fractions. If mole fractions are not equivalent to volume fractions, how do i convert from volume fraction to mole fraction?
Thanks!

 

[berkeman]

Haven't taken a course in distillation in a long time and now myself and some others are working on getting a fuel ethanol still going and wanted to do the calculations before we moved forward.

We have a beer that is 12% alcohol and reaching a purity of 90% EtOH in the distillate.

The mass balances I believe would be:
total balance:

F= D + B
and
Ethanol balance:

F*xf=D*xd + B*xb

where F is the feed rate, D is distillate rate, and B is bottoms rate. xf is mole fraction ethanol in feed, xd is ethanol fraction in distillate, and xb is ethanol fraction in bottoms.

I figure the xd=0.9 and xf=0.12, what would the xb be equal to? Is it dictated by the VLE?

We have a McCabe program that does the step offs for the ideal plates, and it allows you to set the mole fractions, can these be set arbitrarily?


Additionally, are mole fractions equivalent to volume fractions (assuming ideality)? I know mass fractions are not equivalent to mole fractions. If mole fractions are not equivalent to volume fractions, how do i convert from volume fraction to mole fraction?
Thanks!

You are making car fuel from beer? Is that economical? Seems like a waste of good beer.

Are you sure the General Engineering sub-forum is the right place for this post? Maybe I should move this distillation question to Chemistry?

 

[wiscoman]

Haha no, not a waste of beer. When I say beer, I mean alcohol waste streams, or cellulosic created ethanol, or corn ethanol, or anything that can be made into ethanol or that is waste. We think we can even make the stuff out of waste lake weeds with the correct enzymes. But yes, its for fuel in cars/farm equipment. I'd say this is a chemical engineering problem, I am a BS in ChE, but go figure, the jobs I've had with big companies don't have you use a damn thing you learn in school. This would be a unit operations problem. I have all the books, just can't remember how to decipher them!

 

[chemaddict]

I am lacking some resources now to fully answer your questions, but here is what I can tell you for certain:

-Volume fractions are different from mole fractions, especially when molecular weights and densities differ. Wolframalpha.com can help you get molecular weights and densities.
-The easiest way to find your mole fractions is to start with the raw amounts of each. So 30% alcohol by volume, means you have 30mL in a 100mL sample. Then you find the mass by multiplying by the density. Then the moles by dividing by the molecular weight. The hardest part of finding the mole fraction is determining what the other stuff consists of to find the total moles.
-Your mass/mole balances look right
-A still is typically for batch distillation, what you're talking about seems like a continuous distillation.
-Typically you know what the mole fraction coming into the column is, and you know what distillate purity you want. The bottoms fraction is found from a mass balance where you'd want to know your flow rates.
-Don't forget the mass balance out the other components in solving this out.

I typed all this on my phone, so please ask more questions, the more specific the better, and I'll try to help.

Edit:
The more I think about it, it sounds like you'd want to use a batch distillation procedure. Here's why:
1) It sounds like you won't have a long-term continuous stream of feed, but rather a one-time pot charge in a still
2) It sounds like your feed composition is not constant based on the several items you listed as possible sources of ethanol.

If this is the case, the simplified theory isn't too bad. Again, I don't have my separations book with me, but here is what I can offer:
1) I found this powerpoint presentation to review the batch distillation theory (don't forget that your homemade stages will have a lower-than-perfect stage efficiency): http://homedistiller.org/Lecture15-Batchdist.ppt
2) Batch distillation is typically run at constant reflux or constant distillate composition, but one has to change. It is almost always more practical to have a constant reflux and cut off the distillation when the distillate composition starts to drop (it happens suddenly).
3) Ethanol and water form an azeotrope. Yes, it sucks. See http://en.wikipedia.org/wiki/Azeotropic_distillation for more information on that. I believe the pressure-swing method is common in industry, but I'm not sure.

Good luck.