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hi all,
i want to know how to calculate the number of stages required in a distillation column for azeotropic distillation.
the feed is 60% acetic acid,35% water and 5% formal dehyde.
thanks in advance
tushar
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Number Of Stages In Azeotropic Distillation
Started by Guest_tushar kumar_*, Jun 27 2003 10:17 PM
7 replies to this topic
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#2
Guest_Dave_*
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Posted 28 June 2003 - 02:02 PM
There are two ways I would approach this kind of problem. For both of them, you will need to know the volatility of the components involved.
The long way of doing it is to perform stagewise calculations. You should know the top and bottom compostions (or at least some sort of specification).
First, start with the stripping section. For each component, use the equilibrium equation to calculate the vapour fraction of each component from the known/specified liquid fractions coming out the column (remember the equilibrium relationship relates streams leaving a stage). Then, using the equation of the lower operating line, you can calculate the liquid composition coming down from the stage above using the vapour composition leaving the reboiler (remember operating lines relate streams entering and passing in a stage).
This should give you the composition in the bottom tray. Repeat this for the new liquid composition for each stage until your liquid composition equals the feed composition. This is why you need the volatilities of the components. you can look these up, or use an equilibrium chart if you have one, or possibly use the equilibrium constants given for some materials in De Priester charts.
Now the enriching section. You basically repeat the procedure used for the stripping section, but using the equation for the upper operating line, and starting from the feed liquid composition. You stop when the liquid composition equals the top liquid composition. The number of x values you calculate gives you the number of stages.
The shortcut method is to make the problem PSEUDO BINARY. You establish what the LIGHT KEY and HEAVY KEY components are (the least volatile component in the top product and the most volatile component in the bottom product respectively). Ratio the volatilities to obtain your relative volatility.
Now, substitute your specified compostions into the FENSKE-UNDERWOOD equations to establish (N+1)min [N is the number of stages, minimum being at total reflux]. You then need to establish the minimum reflux ratio. I can think of two ways of doing this, one being a quick estimate that only applies for a boiling liquid feed (i.e. q=1), and a more rigorous approach using paired equations. I suggest using the second.
Now, find your actual reflux ratio. You do this by applying a cofficient to the minimum reflux ratio, I'd go for somewhere between 1.2 and 1.6 (see the article on this website called 'Experience Based Rules of Chemical Engineering' which suggests 1.2 to 1.5). A larger reflux ratio will give a smaller column with higher running costs, a smaller reflux ratio gives a larger column with lower running costs.
Now, with these results, I would use the GILLILAND CORRELATION to establish the number of stages.
Sorry this is a bit long-winded, but it is a lengthy problem.
In addition to all this, you will need to know the state of the feed (i.e. the slope of the q line), and the 'internal traffic' i.e., the amount of stuff flowing around different parts of the column. Note that somewhere along the way you'll be required to assume constant molar overflow (your operating line equations), so you'll need to check this assumption will apply to your case.
A note on the 'azeotrope' bit - you'll need to know where the azeotrope is, because you won't be able to distil out the components beyond it (you'll never get a mixture of alcohol and water beyond ~96%, for example).
Hope that this is some help to you - I haven't been able to put up the equations, because I can't word process them here, and anyway I can't remember all of them without my notes in front of me. If you're having trouble finding them, and you can afford to wait a few days, let me know and I can perhaps email them to you or something.
Regards,
Dave.
The long way of doing it is to perform stagewise calculations. You should know the top and bottom compostions (or at least some sort of specification).
First, start with the stripping section. For each component, use the equilibrium equation to calculate the vapour fraction of each component from the known/specified liquid fractions coming out the column (remember the equilibrium relationship relates streams leaving a stage). Then, using the equation of the lower operating line, you can calculate the liquid composition coming down from the stage above using the vapour composition leaving the reboiler (remember operating lines relate streams entering and passing in a stage).
This should give you the composition in the bottom tray. Repeat this for the new liquid composition for each stage until your liquid composition equals the feed composition. This is why you need the volatilities of the components. you can look these up, or use an equilibrium chart if you have one, or possibly use the equilibrium constants given for some materials in De Priester charts.
Now the enriching section. You basically repeat the procedure used for the stripping section, but using the equation for the upper operating line, and starting from the feed liquid composition. You stop when the liquid composition equals the top liquid composition. The number of x values you calculate gives you the number of stages.
The shortcut method is to make the problem PSEUDO BINARY. You establish what the LIGHT KEY and HEAVY KEY components are (the least volatile component in the top product and the most volatile component in the bottom product respectively). Ratio the volatilities to obtain your relative volatility.
Now, substitute your specified compostions into the FENSKE-UNDERWOOD equations to establish (N+1)min [N is the number of stages, minimum being at total reflux]. You then need to establish the minimum reflux ratio. I can think of two ways of doing this, one being a quick estimate that only applies for a boiling liquid feed (i.e. q=1), and a more rigorous approach using paired equations. I suggest using the second.
Now, find your actual reflux ratio. You do this by applying a cofficient to the minimum reflux ratio, I'd go for somewhere between 1.2 and 1.6 (see the article on this website called 'Experience Based Rules of Chemical Engineering' which suggests 1.2 to 1.5). A larger reflux ratio will give a smaller column with higher running costs, a smaller reflux ratio gives a larger column with lower running costs.
Now, with these results, I would use the GILLILAND CORRELATION to establish the number of stages.
Sorry this is a bit long-winded, but it is a lengthy problem.
In addition to all this, you will need to know the state of the feed (i.e. the slope of the q line), and the 'internal traffic' i.e., the amount of stuff flowing around different parts of the column. Note that somewhere along the way you'll be required to assume constant molar overflow (your operating line equations), so you'll need to check this assumption will apply to your case.
A note on the 'azeotrope' bit - you'll need to know where the azeotrope is, because you won't be able to distil out the components beyond it (you'll never get a mixture of alcohol and water beyond ~96%, for example).
Hope that this is some help to you - I haven't been able to put up the equations, because I can't word process them here, and anyway I can't remember all of them without my notes in front of me. If you're having trouble finding them, and you can afford to wait a few days, let me know and I can perhaps email them to you or something.
Regards,
Dave.
#3
siretb
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Posted 30 June 2003 - 02:00 AM
Do not use Dave's shortway for mixtures like water-acetic. This is far too dangerous.
As a rule, the shortcut methods like Gilliland's fail when approaching an azeotrope.
If you do not want to go all the way through the "long way", select two keys (light and heavy) and plot the vapor composition vs liquid composition. If you have an azeotrope, the line will cross the diagonal.
Then use the old Mac Cabe & Thiele method, (zoom in near azeotrope)
As a rule, the shortcut methods like Gilliland's fail when approaching an azeotrope.
If you do not want to go all the way through the "long way", select two keys (light and heavy) and plot the vapor composition vs liquid composition. If you have an azeotrope, the line will cross the diagonal.
Then use the old Mac Cabe & Thiele method, (zoom in near azeotrope)
#4
Guest_Dave_*
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Posted 30 June 2003 - 11:04 AM
Ah, thanks for pointing that out. I only really included the shortcut method for completeness, I'd go about it the long way myself (it doesn't take that long to do).
I don't really like McCabe Thiele myself, I don't seem to get the same number of stages twice if I step off on a hand-drawn graph! And then you have to decide how you're going to calculate the stage efficiencies.
Cheers for the comment though - it is so easy to forget details like that from time to time!
Dave
I don't really like McCabe Thiele myself, I don't seem to get the same number of stages twice if I step off on a hand-drawn graph! And then you have to decide how you're going to calculate the stage efficiencies.
Cheers for the comment though - it is so easy to forget details like that from time to time!
Dave
#5
Guest_Guest_tusharkumar_*
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Posted 01 July 2003 - 04:05 AM
hi,
actually my problem was a bit different than what u all have thot.the problem is that we want to obtain a product of 95 % ACETIC ACID using the method of azeotropic distilation...the entrainer we have to use is butyl acetate..
thanks,
i hope that this clears some of the doubts
tushar
i
actually my problem was a bit different than what u all have thot.the problem is that we want to obtain a product of 95 % ACETIC ACID using the method of azeotropic distilation...the entrainer we have to use is butyl acetate..
thanks,
i hope that this clears some of the doubts
tushar
i
#6
Guest_Dave_*
Guest_Dave_*
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Posted 02 July 2003 - 11:51 AM
Hi,
You've actually lost me now. I wouldn't consider "azeotropic distillation" to be a "method".
Distillation is a separation technique, and it happens with some mixtures that you have one (or more) azeotrope(s), i.e. the equilibrium line crosses the operating line. You can't separate past azeotropes.
I don't know what you mean by "the entrainer we have to use is butyl acetate" either. Entrainment is something you don't want too much of in a distillation column. We had a pilot-scale packed column at my Uni, and if the air flow was too high water would spray out the top of the column and someone would get a shower - this was entrainment because the column had flooded.
This problem you have - I assume its an academic one - what is it for? Tutrial, coursework, exam practice, design project etc. What I'm getting at is how much information you've been given to solve this problem with? Unless its a design project, I would have thought you've been given a bit more than you've posted so far.
Perhaps you could post the whole problem as it was given to you here, and then either I or someone else could could have a better look at it and make some suggestions.
It has confused me that you've introduced Butyle acetate as another component to the three from before. Are you sure this is a distillation application, and not some sort of solvent extraction problem? (I've only just graduated myself, and thus haven't met this particular set-up before, so I do need some more information if I'm to be any help to you).
Dave
You've actually lost me now. I wouldn't consider "azeotropic distillation" to be a "method".
Distillation is a separation technique, and it happens with some mixtures that you have one (or more) azeotrope(s), i.e. the equilibrium line crosses the operating line. You can't separate past azeotropes.
I don't know what you mean by "the entrainer we have to use is butyl acetate" either. Entrainment is something you don't want too much of in a distillation column. We had a pilot-scale packed column at my Uni, and if the air flow was too high water would spray out the top of the column and someone would get a shower - this was entrainment because the column had flooded.
This problem you have - I assume its an academic one - what is it for? Tutrial, coursework, exam practice, design project etc. What I'm getting at is how much information you've been given to solve this problem with? Unless its a design project, I would have thought you've been given a bit more than you've posted so far.
Perhaps you could post the whole problem as it was given to you here, and then either I or someone else could could have a better look at it and make some suggestions.
It has confused me that you've introduced Butyle acetate as another component to the three from before. Are you sure this is a distillation application, and not some sort of solvent extraction problem? (I've only just graduated myself, and thus haven't met this particular set-up before, so I do need some more information if I'm to be any help to you).
Dave
#7
siretb
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Posted 03 July 2003 - 01:37 AM
Dave: He means azeotropics distillation, which IS a method. The idea is to add a third component, that will form an azeotrope with one of the other two to make the separation easier.
Also entrainement refers not to physical entrainement, but to the fact one component "entrains" another.
Very often this will lead to 2 liquid phases.
In this case, that would be a choice. For the question on how to count the necessary stages, I am sorry but in such cases I only use the heavy artillery.
I'd get a model (NRTL/HOC or sometimes UNIQUAC or even UNIFAC), plug it into a process simulator and let the program do the calculations.
The model parameters can be foundd in Gmelin's books. I cannot immediatly give you the model parameters, sorry.
Be careful to include in the model the vapor phase association to acetic.
Also entrainement refers not to physical entrainement, but to the fact one component "entrains" another.
Very often this will lead to 2 liquid phases.
In this case, that would be a choice. For the question on how to count the necessary stages, I am sorry but in such cases I only use the heavy artillery.
I'd get a model (NRTL/HOC or sometimes UNIQUAC or even UNIFAC), plug it into a process simulator and let the program do the calculations.
The model parameters can be foundd in Gmelin's books. I cannot immediatly give you the model parameters, sorry.
Be careful to include in the model the vapor phase association to acetic.
#8
Guest_Dave_*
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Posted 10 July 2003 - 02:33 PM
OK, I'll see if I my thermodynamics is good enough to have a stab at this....
You will need to know the azeotrope composition(s) - I assume you've been given them, I wouldn't want to have to sift through loads of books to find it.
You can use the 'long' multicomponent methods I posted earlier - but the equilibrium relationship you use is the one based on 'K' values, the ones I mentioned you can look up for hydrocarbons in De Priester Charts.
Let the component you are considering be called 'i'. K(i) is given by:
K(i) = {GAMMA(i)*FOL(i)}/{PI*PHI(i)}.....................1
(apologies for the way it's written, I can't paste equations onto the message board). GAMMA is the liquid phase activity coefficient, FOL is the standard state fugacity coefficient for the liquid, PI is the sytem pressure, PHI is the fugacity coefficient.
PHI is calculated using:
ln(PHI) = INTEGRAL{{Z-1}/P}dP.............................2
Where P is pressure, Z is compressibility, and you integrate between 0 and P. I would look-up how Z varies with pressure using (for example) Perry, then plot this function with these values against pressure and integrate numerically (i.e. trapezium rule or Simpson's rule).
FOL is given by:
FOL = P'*PHI'*(exp((PI-P')/RT)*Vm).........................3
Vm is the liquid molar volume (look this up), P' is the pure component vapour pressure, calculated using the Antione eqn:
lnP' = A - B/(T+C).......................................................4
Where A, B, C are constants you look-up, T is temperature in Kelvin.
PHI' is the fugacity coefficient of the pure component at saturation, calculated using equation 2.
The tricky bit here is GAMMA. You can calculate it using the Wilson equation:
ln{GAMMA(k)} = 1 - ln{SUM(x(j)*A(k,j))) - SUM{(x(i)*A(i,k))/SUM(x(j)*A(i,j))}...
................................................................................
..5
where A is the Wilson Constant for a Binary Pair. k, i, and j are suffixes representing components. This equation may be used to find GAMMA values for multi-component mixtures, based on constants for binary situations.
Another possibility for estimating GAMMA is from azeotropic data (remember I said you'd need it?). The equation is:
GAMMA(i) = PI/P'(i)....................................................6
where P', PI, and GAMMA have the same meaning as before for component i (with P' calculated at the azeotropic temperature). I don't think that you can apply this equation to establish GAMMA for multicomponent situations (but I'm not sure, someone correct me if I'm wrong), but by using this equation to find GAMMA for BINARY azeotropic data, you can substitute into eqn 5 to find the Wilson Constants (if you can't look them up anywhere) and then estimate GAMMA for a multicomponent situation).
Having applied eqns 2 through 6, return to eqn 1 and calculate K. The equilibrium relationship for a component i is now:
y(i) = K(i)*x(i).............................................................7
Use this in the stagewise calculation procedure I described before to estimate the number of stages. Start at the reboiler, and remember(!) that you won't distill out a component past the point of the azeotrope (note that there may be more than one azeotrope).
A word of warning: as Siretb rightly pointed out, adding an entrainer can lead to two liquid phases being formed, and the Wilson equation isn't suitable for representing systems that represent two phases over the concentration range of interest. In this case, I don't know what you can do, save resort to UNIQUAC or UNIFAC as Siretb suggests. There are other equations of state around, if you want to look for a more suitable one than Wilson's.
Siretb; thanks for pointing that out. For some reason it totally left my mind that it is a method for moving the position of an azeotrope.
Sorry everyone about the length of the post; I just hope it's all right (like I say, my thermodynamics is a bit rusty, it wasn't fantastic to begin with). If anyone spots any mistakes, please point them out so I don't make them again!
Regards,
Dave.
You will need to know the azeotrope composition(s) - I assume you've been given them, I wouldn't want to have to sift through loads of books to find it.
You can use the 'long' multicomponent methods I posted earlier - but the equilibrium relationship you use is the one based on 'K' values, the ones I mentioned you can look up for hydrocarbons in De Priester Charts.
Let the component you are considering be called 'i'. K(i) is given by:
K(i) = {GAMMA(i)*FOL(i)}/{PI*PHI(i)}.....................1
(apologies for the way it's written, I can't paste equations onto the message board). GAMMA is the liquid phase activity coefficient, FOL is the standard state fugacity coefficient for the liquid, PI is the sytem pressure, PHI is the fugacity coefficient.
PHI is calculated using:
ln(PHI) = INTEGRAL{{Z-1}/P}dP.............................2
Where P is pressure, Z is compressibility, and you integrate between 0 and P. I would look-up how Z varies with pressure using (for example) Perry, then plot this function with these values against pressure and integrate numerically (i.e. trapezium rule or Simpson's rule).
FOL is given by:
FOL = P'*PHI'*(exp((PI-P')/RT)*Vm).........................3
Vm is the liquid molar volume (look this up), P' is the pure component vapour pressure, calculated using the Antione eqn:
lnP' = A - B/(T+C).......................................................4
Where A, B, C are constants you look-up, T is temperature in Kelvin.
PHI' is the fugacity coefficient of the pure component at saturation, calculated using equation 2.
The tricky bit here is GAMMA. You can calculate it using the Wilson equation:
ln{GAMMA(k)} = 1 - ln{SUM(x(j)*A(k,j))) - SUM{(x(i)*A(i,k))/SUM(x(j)*A(i,j))}...
................................................................................
..5
where A is the Wilson Constant for a Binary Pair. k, i, and j are suffixes representing components. This equation may be used to find GAMMA values for multi-component mixtures, based on constants for binary situations.
Another possibility for estimating GAMMA is from azeotropic data (remember I said you'd need it?). The equation is:
GAMMA(i) = PI/P'(i)....................................................6
where P', PI, and GAMMA have the same meaning as before for component i (with P' calculated at the azeotropic temperature). I don't think that you can apply this equation to establish GAMMA for multicomponent situations (but I'm not sure, someone correct me if I'm wrong), but by using this equation to find GAMMA for BINARY azeotropic data, you can substitute into eqn 5 to find the Wilson Constants (if you can't look them up anywhere) and then estimate GAMMA for a multicomponent situation).
Having applied eqns 2 through 6, return to eqn 1 and calculate K. The equilibrium relationship for a component i is now:
y(i) = K(i)*x(i).............................................................7
Use this in the stagewise calculation procedure I described before to estimate the number of stages. Start at the reboiler, and remember(!) that you won't distill out a component past the point of the azeotrope (note that there may be more than one azeotrope).
A word of warning: as Siretb rightly pointed out, adding an entrainer can lead to two liquid phases being formed, and the Wilson equation isn't suitable for representing systems that represent two phases over the concentration range of interest. In this case, I don't know what you can do, save resort to UNIQUAC or UNIFAC as Siretb suggests. There are other equations of state around, if you want to look for a more suitable one than Wilson's.
Siretb; thanks for pointing that out. For some reason it totally left my mind that it is a method for moving the position of an azeotrope.
Sorry everyone about the length of the post; I just hope it's all right (like I say, my thermodynamics is a bit rusty, it wasn't fantastic to begin with). If anyone spots any mistakes, please point them out so I don't make them again!
Regards,
Dave.
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