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thorade / HelmholtzMedia

Modelica library for the calculation of fluid properties from a Helmholtz energy equation of state (EoS).
BSD 3-Clause "New" or "Revised" License
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debugging of Ancillary.density_pT_Soave #3

Open thorade opened 11 years ago

thorade commented 11 years ago

For Pentane at p=1e-6 and T=578.275 the Soave algorithm goes to the supercritical branch, where three roots exist. According to Span, two of the three roots result in negative densities, but in this case this is not true. Not a big problem, as this is used as starting value only, but it slows down the pT iteration.

Also, the RKS EoS should be able to correctly describe the liquid region, at least qualitatively.

thorade commented 11 years ago

see Span 2000, page 48-51 http://books.google.de/books?id=dd410GGw8wUC&pg=PA48

thorade commented 11 years ago

There is a section about solving cubic equations in "Thermodynamics - Fundamentals for Applications" by O'Connell and Haile (see Appendix C, page 620): http://www.cambridge.org/9780521582063 http://books.google.de/books?id=1rOA5I6kQ7gC&&pg=PA620

thorade commented 10 years ago

Also see paper by Deiters 2014: http://dx.doi.org/10.1021/ie4038664 And the WP articles on (solving) cubic functions: https://en.wikipedia.org/wiki/Cubic_function

thorade commented 3 years ago

Also read the references cited in this blog post: http://momentsingraphics.de/CubicRoots.html