Vapor Fraction of Hydrocarbon Mixture

[mnmz]

Introduction: This is a detailed question about a very specific part of PVT analysis. It involves a binary mixture whose vapor fraction does not seem physically possible to me, even though all of my analytical tools tell me that it is correct. So then:

I am approximating the Rachford-Rice forumla via Newton's method and Bisection.
I am estimating the brackets based on a fluid phase equilibria article.
I have found the aforementioned article to be most helpful when the mixture i am approximating the vapor fraction for lies within the 2-phase region (since the article helps me to avoid the asymptotes).
I also have another equation which i am trying to validate my results for a binary mixture:

simplified vapor fraction = -((z2/k1-1) + (z1/k2-1));

where z is the mole fraction, k is the equilibrium ratio, and 1,2 specify which component the parameter belongs to.

I approximated the Rachford-Rice formula, and solved the simplified vapor fraction formula for the following binary mixture:

.8 mole fraction methane and .2 mole fraction ethane at 100 F and 750 psia.

The vapor fraction which i get from both of my tools are very close to -15.xxx, which implies that this mixture at the stated temperature and pressure is a super-cooled liquid.
This does not seem physically possible. If this result is indeed "correct" please let me know why.

 

[zdas04]

I can't speak to your arithmetic, but I put your mixture in RefProp.exe at your conditions NIST says it is a superheated gas. Enthalpy is 364.16 BTU/lbm, c(p) is 0.60371 BTU/(lbm R). Entropy is 0.99760 BTU/(lbm R). Looks like a gas.

I've never heard of a "super-cooled liquid", do you mean "sub-cooled liquid"? Regardless, it is a superheated gas.

David

 

[mnmz]

Yes, i did mean a sub-cooled liquid.
I think the problem is clear now, and i will spell it out for anyone else who stumbles upon this post.
The vapor fraction domain which is being examined is split into 3 parts which are cut by two asymptotes (which are functions of the maximum and minimum equilibrium ratios).
A solution which will satisfy the Rachford-Rice calculation exists in all three parts of the domain. Two of these are always trivial.
The key to knowing where to look for the desired solution is by examining the equilibrium ratios. If none of these values are less than 1, as in this example, then your fluid is a super heated gas. If all of these values are less than one, the mixture is a sub cooled liquid.
I think i just need to expand the limit of my bisection when i am looking in the single phase regions of the domain.
Thank you sir.

 

[PaoloPemi]

Newton is the usual way to solve Rachford-Rice keeping K (equilibrium values) constant, the result is the classical successive substitution method, not sure if you are referring to this procedure explained in every good book discussing phase equilibria, there have been published many tricks and suggestions for evaluating quickly if the mixture is stable or not, every good software includes specific tests, Refprop is not the best for VLE but it is certainly a reference when calculating densities, enthalpies etc., I work with gas compressors and have purchased both Refprop and Prode Properties, good compromise in my opinion (altough I am sure there are much more expensive but featured software)

 

[dcasto]

STREAM CRITICAL TEMPERATURE (CUBIC EOS) F -50.1326
STREAM CRITICAL PRESSURE (CUBIC EOS) PSIA 959.0680

DEW POINT TEMPERATURE AT STREAM PRESSURE F -42.3603
BUBBLE POINT TEMPERATURE AT STREAM PRESSURE F -82.5295

You won't see a drop of liquid until -42F and you are below the criticle pressure.