4 replies to this topic

[electrosin]

Hi,
I realized that UNIFAC method is a function of temperature but not pressure. How can I solve the equation for known pressure?

Thanks

[MrShorty]

In the process of deriving activity coefficient equations, it was deermined long ago that the most important quantities in calculating the activity coefficient were temperature T and liquid composition x. The effect of pressure P on the activity coefficient is generally neglected.

In short, to get the activity coefficient at a given P (T unknown), you have to figure out how P effects T (and x if it is also unknown). Usually we put the activity coefficient into a VLE equation (like a modified Raoult's law equation Pi=P0i*xi*gi where Pi is the partial pressure of component i, P0i is the pure component vapor pressure of component i at T, xi is the liquid composition of i, and gi is the activity coefficient of i), which determines the relationship between P, T, x, and y. It is generally impossible to express gi explicitly as a function of P, so we almost always have to solve the problem numerically when T is not given. I can't write the program for you, but the basic algorithm I would use would go something like:

1) Determine an "initial guess" for T. Use this value to calculate g.
2) calculate a total pressure P.
3) compare to the given pressure
4) adjust T to get P closer to the desired value.
5) Iterate until the calculated P converges on the given P.

A couple of notes: as with most any numerical algorithm, there may be cases where there is only one unique solution, cases where multiple solutions are possible, or cases where no solution is possible. You have to use what you know about the system in question to make sure you get a reasonable answer.

[electrosin]

Please look at this picture:


Chloroform - Methanol Equilibrium


You see on the diagram that it's an equilibrium of chloroform and methanol at 101,325 kPa.
The green dots are experimental data. The green curve is NRTL prediction.
Like UNIFAC, it's also the function of temperature.

I wonder how did they build it. Is it the same like what you said?
If yes, then what equation will you use to calculate P from T?

Edited by electrosin, 13 July 2011 - 02:08 AM.

[MrShorty]

I wonder how did they build it. Is it the same like what you said?

I can't really say exactly how that specific plot was generated. I can say that, if I were to generate the same plot, the basic algorithm I described above is the most straightforward algorithm I can see to do it. (Aside, for a publishable diagram, I would include fugacity coefficient and Poynting factor corrections for completeness. For simplicity of discussion, it is easiest to ignore these corrections, which would be small at 1 atm).

If yes, then what equation will you use to calculate P from T?

I would use the modified Raoult's law equation I gave above. You need to recognize that this is a composite function where gi and P0i are both functions of T.

While speaking of simplifications, can you see how to solve this problem if we neglected the activity coefficient, using Raoult's law? I find, with the generic VLE question you originally proposed, it is often easiest to first figure out how to solve the problem using Raoult's law. Because the activity coefficient (and other quantities) are essentially "correction factors" to Raoult's law, solving the problem using Raoult's law provides a basic "skeleton" for the algorithm to which you can add the appropriate "correction factors" as needed.

[electrosin]

I would use the modified Raoult's law equation I gave above. You need to recognize that this is a composite function where gi and P0i are both functions of T.

oh my God I'm asking solved question. I think I really need some sleep

While speaking of simplifications, can you see how to solve this problem if we neglected the activity coefficient, using Raoult's law? I find, with the generic VLE question you originally proposed, it is often easiest to first figure out how to solve the problem using Raoult's law. Because the activity coefficient (and other quantities) are essentially "correction factors" to Raoult's law, solving the problem using Raoult's law provides a basic "skeleton" for the algorithm to which you can add the appropriate "correction factors" as needed.

You right, I should know it..
But right now my mind is all messed up. Too much complicated equations on my head, makes me forgot even the most simple thing. I should know that Pi = P0i*xi*gi. But for 2 days it became Pi = xi*gi until I read your second post... lol

Thanks a lot, it's been a big help...