7 replies to this topic

[adw07]

Hi all,

I making a model applying the Peng-Robinson equation of state but all of the sources (I've checked quite a few) are a bit ambiguous as to which mole fractions to use in the cubic equation:

Z^3 + (1-B ) Z^2 + (A-3B^2 - 2B) Z + (B^2 + B^3 - AB) = 0

Where A = Sum( Sum ( xi xj Aij ))) and B = Sum ( xi Bi). (Here using liquid mole fractions, x)

Individually A and B are different if you use x, y or z. Can anyone tell me which mole fractions should be used? Thanks for any help.

[MrShorty]

Unless there's more to the question than I'm seeing:

Use x if you are calculating the properties of a liquid phase.
Use y if you are calculating the properties of a vapor phase.
Use z if you are calculating the properties of a feed (assuming said feed is single phase).

[adw07]

Thanks for your reply.

The cubic equation needs to be solved to find the compressibilities of both the vapour and liquid phases, Zv and Zl. In the two phase region three real roots are produced, the smallest is Zl and the largest Zv.

My question is, since the cubic equation yields both the vapour and liquid compressibilities, which mole fraction is used to define the parameters A and B used in the cubic equation?

From the initial calculations I've done so far, each mole fraction set (z,y and x) give different results,with x giving the most reasonable solutions.

I am unsure why the liquid mole fractions should define the compressibility for both phases, or am I missing something?
Thanks

[breizh]

Hi ,
Additional input :

http://www.ceb.cam.a...hermo/pure.html

hope this helps

Breizh

[MrShorty]

The answer is still the same. This means that in a VLE routine, where you have two phases, you will have two sets of parameters. One set based on x, from which you will calculate Zliq. Another set based on y, from which you will calculate Zvap.

[amitkatyal.asim]

The answer is still the same. This means that in a VLE routine, where you have two phases, you will have two sets of parameters. One set based on x, from which you will calculate Zliq. Another set based on y, from which you will calculate Zvap.

A readymade product of the type you wish to make is available at www.eq-comp.com. You can check it out.

[adw07]

OK guys thanks for the help, I'll use the mole fractions for each phase to define the other properties for that phase.

[adw07]

Hi, further to my initial query the flash solver for my uni project is now up and running. However, although it is generally giving good results for certain conditions it is:

a) converging to a trivial solution (Initial Phase Stability Analysis (Michelson 1982b) shows mixture is 2 - phase, however the the iteration process converges to a vapour fraciton of 1 )

b ) Not converging at all - Maximum iterations in inner loop reached (which minimises fugacity difference)

c) Giving values outside acceptable physical constraints i.e. vapour fraction less than zero

Can anyone please point me in the direction of any information sources about dealing with these problems / or offer any suggestions on how to alleviate them? Since this is only a small part in the background of my model it needs to be robust to handle the majority of input conditions.
Any help much appreciated, thanks