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Peng-Robinson roots problems for H2 at normal temperature |
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October 31, 2022, 09:56 |
Peng-Robinson roots problems for H2 at normal temperature
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Luc Cena
Join Date: Oct 2022
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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 |
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hydrogen, peng-robinson eoe, real fluids equation |
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