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Non-ideal Solution W/ Azeotrope


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#1 jmatrix

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Posted 31 July 2009 - 09:26 AM

Hello fellow chemical engineers,

This is my first time posting, and it is great to see such a forum for discussion of problems etc.

This is my problem:

I have a mixture of isobutanol and water in the feed of a simple batch distillation (kettle which will be heated and the vapors drawn off and condensed separately, no refluxing). I have been given the composition of the feed, its at standard pressure and I am trying to find out how effective my separation will be and the respective composition of each compound in the vapour phase.

However, this mixture is non-ideal and I am unable to use Raoult's Law. It forms an azeotrope, (I believe at 67% w/w isobutanol) and I am unable to generate any VLE diagrams or P,T-x diagrams either. Usually experimental data is required in this case and the only place I can find such data is at the Dortmund Databank (which I would have to pay).

I have been viewing the forum and in another topic, I believe someone mentioned that you can use HYSYS to generate or view the VLE diagram but I am unsure on how to do so.

Once I have the VLE diagram then it is just a matter of using the Rayleigh equation to determine the vapour compositions and the effectiveness of the separation (which will be constrained due to the azeotrope). Am I on the right track?

Thank you

#2 MrShorty

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Posted 31 July 2009 - 10:32 AM

It seems to me you have a basic idea of how to do it.

I would advise against using HYSYS or similar for this problem, because it will short circuit part of what I think this problem is supposed to teach you (namely, how to determine the VLE diagram with minimal inputs).

You are correct that you usually need some experimental data to get VLE diagrams for non-ideal systems (and, to some extent, the more the better). I will point out that you appear to already have experimental data: namely an azeotrope composition. There's always a question of accuracy, but I'm going to assume you are familiar with using activity coefficients to generate VLE curves and suggest (and I hope I'm not short-circuiting your learning experience) that you study your text for a section that describes how to use an azeotropic composition to get at the activity coefficients.

#3 jmatrix

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Posted 31 July 2009 - 12:03 PM

QUOTE (MrShorty @ Jul 31 2009, 11:32 AM) <{POST_SNAPBACK}>
It seems to me you have a basic idea of how to do it.

I would advise against using HYSYS or similar for this problem, because it will short circuit part of what I think this problem is supposed to teach you (namely, how to determine the VLE diagram with minimal inputs).

You are correct that you usually need some experimental data to get VLE diagrams for non-ideal systems (and, to some extent, the more the better). I will point out that you appear to already have experimental data: namely an azeotrope composition. There's always a question of accuracy, but I'm going to assume you are familiar with using activity coefficients to generate VLE curves and suggest (and I hope I'm not short-circuiting your learning experience) that you study your text for a section that describes how to use an azeotropic composition to get at the activity coefficients.


Thanks for the suggestion. I understand that you can use the modified Raoult's law using the activity coefficients to determine the P-x diagrams and from there determine the x-y VLE diagram (P-x diagrams might not even be necessary).

My main problem when looking at the section on determining the activity coefficients is the use of the Margules equation. It requires experimental data (Psat, x, y) to generate a plot of (GE/x1x2RT) in order to get A21 and A12 and thus the activity coefficients.

I'm thinking that I haven't been given enough information to determine the activity coefficients


#4 MrShorty

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Posted 31 July 2009 - 02:25 PM

How much more information do you think you need?

As you consider this question, I'll mention some basic algebra/curve-fitting that I expect you should be familiar with.

If I have a process that I expect to fit to a straight line and go through the origin (y=mx), how many data points do I need? I only "need" one point to determine a value for m. How accurate my derived m will be depends entirely on how accurate my data point is, but I can determine a value for m. More data points will either help improve the accuracy of m, or tell me I need a different equation, but I really only need one point to derive an m.

For your problem, you've been given one point (the azeotropic composition). Let me ask this, given the azeotropic conditions, do you know how to calculate an activity coefficient at that condition?

#5 jmatrix

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Posted 31 July 2009 - 03:40 PM

QUOTE (MrShorty @ Jul 31 2009, 03:25 PM) <{POST_SNAPBACK}>
How much more information do you think you need?

As you consider this question, I'll mention some basic algebra/curve-fitting that I expect you should be familiar with.

If I have a process that I expect to fit to a straight line and go through the origin (y=mx), how many data points do I need? I only "need" one point to determine a value for m. How accurate my derived m will be depends entirely on how accurate my data point is, but I can determine a value for m. More data points will either help improve the accuracy of m, or tell me I need a different equation, but I really only need one point to derive an m.

For your problem, you've been given one point (the azeotropic composition). Let me ask this, given the azeotropic conditions, do you know how to calculate an activity coefficient at that condition?


To get to the point, I do not know how to calculate the activity coefficient at the azeotropic composition. I am looking through the thermodynamics book and to say the least I am unaware of calculating activity coefficients without additional data. I might be totally wrong and there might be a way to calculate the activity coefficients but I don't know it.

The curve fitting will not be a straight line that much I know and the equilibrium line will cross the 45 degree line at the azeotropic composition for the VLE diagram. Therefore, I pretty much have 3 points: the azeotropic composition, x and y at 0 and x and y at 1.

As you mentioned I will require more data to form the points "in between" to make it more accurate, but I am getting stuck at this point due to the non-ideal nature of the problem (can't use simplified Raoult's law and thus I require the activity coefficients).

#6 MrShorty

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Posted 31 July 2009 - 05:11 PM

I apologize up front if this feels incomplete. I'm trying to give you just enough information to get the thought process going, without giving so much that you fail to really learn how to do these kind of problems.
QUOTE
To get to the point, I do not know how to calculate the activity coefficient at the azeotropic composition.

Since you mentioned it, let's start with Raoult's law:
Pi=xi*P0i
where Pi is the partial pressure of component i, xi is the liquid mole fraction of component i, and P0i is the vapor pressure of pure i at system temperature. As you know, very few real world systems obey Raoult's law. So, in essence, we introduce a "correction factor" to describe how a real world system deviates from Raoult's law and we call it the activity coefficient (gi):
Pi=xi*P0i*gi
(To here we are assuming the vapor is an ideal gas.)

You seem familiar with the procedure for: given xi, P0i (or an equation to calculate P0i at T), and gi (or an equation to calculate gi at xi), determine Pi.

For your problem, you aren't given the activity coefficients. Instead, you have been given (or looked up) an azeotropic condition for this system (I assume you have T, P, and xi for the azeotrope). Your goal is to then determine what the rest of the VLE curve(s) look(s) like.

Have I given you enough of a "push" in the right direction to see how to solve this problem using the azeotropic data you have?

#7 jmatrix

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Posted 31 July 2009 - 09:24 PM

QUOTE (MrShorty @ Jul 31 2009, 06:11 PM) <{POST_SNAPBACK}>
I apologize up front if this feels incomplete. I'm trying to give you just enough information to get the thought process going, without giving so much that you fail to really learn how to do these kind of problems.
QUOTE
To get to the point, I do not know how to calculate the activity coefficient at the azeotropic composition.

Since you mentioned it, let's start with Raoult's law:
Pi=xi*P0i
where Pi is the partial pressure of component i, xi is the liquid mole fraction of component i, and P0i is the vapor pressure of pure i at system temperature. As you know, very few real world systems obey Raoult's law. So, in essence, we introduce a "correction factor" to describe how a real world system deviates from Raoult's law and we call it the activity coefficient (gi):
Pi=xi*P0i*gi
(To here we are assuming the vapor is an ideal gas.)

You seem familiar with the procedure for: given xi, P0i (or an equation to calculate P0i at T), and gi (or an equation to calculate gi at xi), determine Pi.

For your problem, you aren't given the activity coefficients. Instead, you have been given (or looked up) an azeotropic condition for this system (I assume you have T, P, and xi for the azeotrope). Your goal is to then determine what the rest of the VLE curve(s) look(s) like.

Have I given you enough of a "push" in the right direction to see how to solve this problem using the azeotropic data you have?


First, thank you very much for your help.

You are correct, I am familiar with using Antoine's equation to calculate P0i. Everything else I understand, the vapor is an ideal gas because of the low pressure at which the separation is taking place (don't need to worry about fugacity coefficients etc). The one thing which I am unfamiliar with (and here in lies the problem) is you mention "gi (or an equation to calculate gi at xi)".

If I have the data for the azeotrope (T,P and xi); in essence I should be able to calculate the gi for that point. I don't know which equation that would be?

And I might be wrong about this but:
Secondly, I believe the activity coefficient is dependent on temperature (not so much on pressure), therefore I should create a P-x diagram instead because I can constrain a degree of freedom (T as a constant), thus allowing for a relatively constant activity coefficient?

#8 MrShorty

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Posted 01 August 2009 - 12:54 AM

QUOTE
The one thing which I am unfamiliar with (and here in lies the problem) is you mention "gi (or an equation to calculate gi at xi)".
I'm using gi to represent the activity coefficient. If I knew how to do it, and trusted our internet browsers to render a greek character consistently, I'd have used the traditional greek letter gamma for the activity coefficient. In order to avoid any difficulties, I'm using the letter g instead. Earlier you mentioned the Margules equation, so I assumed you were familiar with activity coefficients.
QUOTE
If I have the data for the azeotrope (T,P and xi); in essence I should be able to calculate the gi for that point. I don't know which equation that would be?

What equation do you use for basic VLE? I'm used to equations that look somewhat like Raoult's law with various corrections applied (something like the second equation I posted previously: Pi=xi*P0i*gi
QUOTE
Secondly, I believe the activity coefficient is dependent on temperature (not so much on pressure), therefore I should create a P-x diagram instead because I can constrain a degree of freedom (T as a constant), thus allowing for a relatively constant activity coefficient?
You are correct: activity coefficient is dependent on temperature (and composition, which I expect should be obvious) and less so pressure (to the point that we almost always neglect the dependence on pressure). Calculating isotherms tends to be easier than isobars, as you've deduced. Once you understand how to calculate isotherms, it shouldn't be a huge leap to figure out how to calculate isobars (if you decide you need to calculate an isobar).

I'm not sure how best to help at this point. At the risk of muddying the water, let me ask you this: Assume that using the 2 suffix Margules equation with an A12=A21=1 represented this system (and I just pulled a parameter out of the air, I doubt it really does). Could you determine if this system forms an azeotrope and, if it does, what is the composition of that azeotrope? What if I changed the parameter to 1.5? In essence, this latter problem seems to me to represent the inverse of the original problem you were given. I'm hoping that, by seeing the inverse problem, it will help you see how to approach the original problem.

If that helps, let me know. If that doesn't help, let me know a little better what kind of problems you are familiar with (you seemed to indicate that you would know how to do this if you could use Raoult's law). Specifically, what kind of problems you have successfully used an activity coefficient equation (like the Margules equation) to solve.

#9 jmatrix

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Posted 01 August 2009 - 09:11 AM

QUOTE (MrShorty @ Aug 1 2009, 01:54 AM) <{POST_SNAPBACK}>
QUOTE
The one thing which I am unfamiliar with (and here in lies the problem) is you mention "gi (or an equation to calculate gi at xi)".
I'm using gi to represent the activity coefficient. If I knew how to do it, and trusted our internet browsers to render a greek character consistently, I'd have used the traditional greek letter gamma for the activity coefficient. In order to avoid any difficulties, I'm using the letter g instead. Earlier you mentioned the Margules equation, so I assumed you were familiar with activity coefficients.
QUOTE
If I have the data for the azeotrope (T,P and xi); in essence I should be able to calculate the gi for that point. I don't know which equation that would be?

What equation do you use for basic VLE? I'm used to equations that look somewhat like Raoult's law with various corrections applied (something like the second equation I posted previously: Pi=xi*P0i*gi
QUOTE
Secondly, I believe the activity coefficient is dependent on temperature (not so much on pressure), therefore I should create a P-x diagram instead because I can constrain a degree of freedom (T as a constant), thus allowing for a relatively constant activity coefficient?
You are correct: activity coefficient is dependent on temperature (and composition, which I expect should be obvious) and less so pressure (to the point that we almost always neglect the dependence on pressure). Calculating isotherms tends to be easier than isobars, as you've deduced. Once you understand how to calculate isotherms, it shouldn't be a huge leap to figure out how to calculate isobars (if you decide you need to calculate an isobar).

I'm not sure how best to help at this point. At the risk of muddying the water, let me ask you this: Assume that using the 2 suffix Margules equation with an A12=A21=1 represented this system (and I just pulled a parameter out of the air, I doubt it really does). Could you determine if this system forms an azeotrope and, if it does, what is the composition of that azeotrope? What if I changed the parameter to 1.5? In essence, this latter problem seems to me to represent the inverse of the original problem you were given. I'm hoping that, by seeing the inverse problem, it will help you see how to approach the original problem.

If that helps, let me know. If that doesn't help, let me know a little better what kind of problems you are familiar with (you seemed to indicate that you would know how to do this if you could use Raoult's law). Specifically, what kind of problems you have successfully used an activity coefficient equation (like the Margules equation) to solve.


Thanks for the help. I will try it out using different A12 and A21 parameters, find the activity coefficients; (gamma) and determine if the azeotropic composition matches what I have looked up (keep on trying with trial and error I suppose or perhaps use GoalSeek in Excel). And since you've mentioned the modified raoult's law (and I know all the other parameters) then I should be able to recalculate xi to verify it.

With regards to your last paragraph; in school we mostly dealt with ideal solutions and thus never really had to factor in activity coefficients or fugacity coefficients; it was taught but I never really had a chance of applying it to a non-ideal solution.

If it was just a simple Raoult's law, then all I would require is the Bubble point and the Dew point curves. Using the lever rule I would then be able to extract the (x and y) to generate the VLE curve. I understand this would be the same case with the modified Raoult's law, but I was getting stuck at determining the activity coefficients (which you've guided me into solving).

Thanks once again.

#10 jmatrix

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Posted 05 August 2009 - 09:37 AM

Just an update:

I found out that this system is partially miscible and as such forms a heterogeneous azeotrope. It also forms a LLE or VLLE depending on the conditions (composition, temperature and pressure). Without going into more details, I did require more data; particularly experimental data to ensure the accuracy of my calculations.

If I were to compare it with HYSYS, the appropriate model would have had to be NRTL with UNIFAC LLE. Trying to find the appropriate coefficients manually by hand calculations would have been a pain (if it were possible). Nevertheless, I used the Rayleigh equation and found out that I could get an almost pure water phase for the bottom of the column, and the vapor composition at the top would be at the azeotrope.

This is confirmed from textbooks on separation processes regarding heterogeneous azeotrope distillation.

#11 Trent F Guidry

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Posted 15 August 2009 - 10:11 AM

Another factor that affects which method you use to solve a VLE calculation is the desired accuracy of the results.

If you are trying to achieve very accurate correlations that can be somewhat involved.

The basic equations for this start with noting that at vapor liquid equilibrium, the temperature and pressure of both phases are equal. In addition to that, the fugacity of each component in the liquid phase is equal to the fugacity of the same component in the vapor phase.

To solve the equilibrium problem, correlations for the fugacites of the components in each phase are needed.

For the vapor phase, the Peng Robinson or Soave Redlich Kwong equations of state are usually pretty good. They can be used to find the vapor phase fugacities.

For the liquid phase, the Peng Robinson or Soave Redlich Kwong equations can also be used to determine the liquid phase fugacities, although, that approach isn’t used as often as the excess Gibbs free energy correlation approach.

For the excess Gibbs free energy correlation, I tend to prefer the UNIQUAC correlation, although the NRTL correlation is also pretty good as well. Additionally, you will need a vapor pressure correlation for each component. For this, I tend to prefer the Ambrose Wagner correlation, but other correlations, such as the Antoine correlation can also be used.

If you don’t have any experimental data for determining the excess Gibbs free energy correlation, one approach would be to use a functional group approximation method, such as the UNIFAC correlation. For the vapor pressure, the Ambrose Warner correlation is usually pretty decent and only requires the critical properties.




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