[cenaluc]

Hi All

I have problems to work with Peng Robinson EoS for temperatures way above the Tcr of H2.

I am using the cardano method base to find the roots with the hydrogen properties: Tc=33K ; Pc=1.32MPa ; omega=-0.22
Target is to find the molar volume for normal pressure temperature range, like T1=20°C / P1=10MPa, so temperature and pressure are way above the critical values.

Well, I was expecting only one root because both P/T are above the critical values, but intermediate parameters analysis ( b^2 / 4 ) + ( m^3 / 27 ) is negative so I should expect 3 real roots with the one in the middle meaningless as usual. I can solve the cubic with the following solution:
Z³ - 0.933 * Z² - 0.105 * Z + 0.002 = 0
Z1= -0.117
Z2= +1.034
Z3= +0.017

All three are correct, so it looks ok, three solutions real, not complex as expected. But here comes the problems:
First solution is negative (!!!) : Theoretically it should provide the bubble point with but Vm= Z1 * R * T / p is negative if I use a negative Z, it does not make sense.
Second solution is above 1 : Theoretically all solutions should be in the range [0;1] if I understand the theory well.
Third solution is the middle one : I should not consider it.

Can you tell me why this math behaviour for H2? Am I too far from the critical point for this gas and I cannot use PR EOS or am I doing anything wrong?

I am obtaining the attached by plotting the data but I do not think that going negative with the volume is somethig good lol. Any suggestion??
Thanks