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i'm working on calculating thermodynamic properties from equations of state [1], and yeah, looking for criteria on how to distinguish from a low pressure, a nea

i'm working on calculating thermodynamic properties from equations of state [1], and yeah, looking for criteria on how to distinguish from a low pressure, a near critical pressure and a supercritical pressure is not trivial, specially when you don't know the critical point of a fluid (the case for all molecular EoS). one property i've relying on is that the second virial coefficient minimum density is always lower than the saturated gas density.. until a threshold near criticality. a lot of assumptions about a thermodynamic model fail at near-critical points. Understanding and exploiting those properties helps on building more accurate property solvers for any, existing or new, equations of state. [1] https://github.com/ypaul21/Clapeyron.jl https://github.com/ypaul21/Clapeyron.jl

bernulli 5y ago
Super interesting, and I watched the video on GitHub! Of course, for an EOS to be useful at the critical point you have to believe that there is such a thing as continuum or even thermodynamic equilibrium at the critical point ;-)
- longemen3000 5y ago
  We have a solver for the pure critical point, that just finds the (v,T) coordinate that satisfies dP/dV = 0 = d²P/dV². of course, not all EoS can even satisfy this condition. Cubics have the correct temperature and pressure (by definition) but fail on volume. SAFT equations and all EoS with association terms predicts critical points with temperatures higher than the experimental ones. a lot of MultiParameter EoS (like IAWPS95, the standard for pure water) have some anomalies at the vicinity of the critical point. Nevertheless, finding such critical points, however far from reality are from the Real fluid that is trying to represent, helps on finding where are your properties in the phase diagram. In practice, you never stay at the critical point, you pass near it and you can tell by some properties that you are passing near it. There is also new developments on "Phase equilibria" over the critical point,because it seems that supercritical fluids do present some sort of continuous phase transition between a liquid-like state and a gas-like state. there is this thing named the widom line that marks this separation, But not all EoS even present this line..., "are there phases in the supercritical fluid?" is a research question in that sense.
  - bernulli 5y ago
    I mean something different: no one has ever measured a critical volume, your dp/dv flatlines at the critical point, i.e. there is no driving force to make the fluid balance out the naturally occurring fluctuations, indeed relaxation times go to infinity at the critical point. An EOS only gives you the thermodynamic equilibrium value, attained when you let it sit for times much larger than the relaxation times. The Widom line(s) are somewhat arbitrarily and ambiguously defined, so I'm not a big fan (pseudo boiling all the way!), but the whole point there is that there is no phase equilibrium at supercritical conditions. However, just because we never observe supercritical liquids and gases simultaneously in equilibrium, does not mean they don't exist. They absolutely do and do lead to a phase transition between liquids and gases - just not coexisting. This also means that your other comment needs a revision: we absolutely do have something akin to boiling at supercritical conditions, even with macroscopic effects, such as the (subcritical) boiling crisis <> (supercritical) heat transfer deterioration.
    - longemen3000 5y ago
      Of course! we are urgently in need of a "critical boiling" relation. At the moment we are using critical isochores as a way to "extend" the saturation curve, but it is less than ideal (at least they can be calculated quickly). I agree with the Widom line, at the moment i haven't found any concrete relation to calculate those from a equation of state functional. if there is something concrete, i would be glad to code it.
      - bernulli 4y ago
        Also - could you explain why you don't count van der Waals' equation among the cubic EOS?
      - bernulli 4y ago
        That's what I work on, I'll send you an email (if I find your address somewhere)!
R0b0t1 5y ago
> one property i've relying on is that the second virial coefficient minimum density is always lower than the saturated gas density.. until a threshold near criticality. A (or even the) phenomenologically useful reason anyone ever cares about supercriticality in industry is to use a chemical as a solvent. This seems like a precise statement of what makes it so. You know anything else that would be related?
- longemen3000 5y ago
  A lot of new work on supercritical fluids is the ability of calculate properties for those. normally we don't access to those conditions, so it is tricky to measure, but there is always new work on correlations capable of explaining the anomalies present on near critical and supercritical fluids. On the viscosity front, there is this new framework named Entropy Scaling, that postulates that scaled viscosity ≈ f(residual entropy)^(2/3). There is also new work on calculation of interfacial tensions from pure equations of state,that are relevant because you could have a two phase liquid-liquid mix and you want to transport something from one liquid phase to another. Also, as the article says, over the critical point, there is no surface tension, because there is only one phase. (do not take this phrase literally, because that only happens in a pure compound, as soon as you have a mixture, the surface tension will depend on all elements of the mixture) Furthermore, some fluid mixtures present something called UCST (upper critical solution temperatures) and LCST (lower critical solution temperatures). imagine if you lower the temperature of and oil-water mixture and suddenly they start to mix. and if you keep lowering the temperature, they unmix again!, and of course, not every fluid presents those properties, but we need to understand those who do. and specially, calculate those points. Few if any industrial thermodynamic calculators can do this, because you require fourth order accurate derivatives (can this be solved with automatic differentiation like what they do with neural networks?, of course, but you need a differentiation-ready equation of state) On more macro properties, supercritical cycles are useful. you can start from a liquid and end with a gas without boiling, if you pressurize your liquid over the critical pressure (isothermically) then lower the temperature (isobarically) and finally releasing pressure (isothermically). one advantage of doing that is that you don't produce bubbles or any kinetic artifacts that are present during a normal phase transition.
- 5y ago

bernulli 5y ago

Super interesting, and I watched the video on GitHub! Of course, for an EOS to be useful at the critical point you have to believe that there is such a thing as continuum or even thermodynamic equilibrium at the critical point ;-)

longemen3000 5y ago
We have a solver for the pure critical point, that just finds the (v,T) coordinate that satisfies dP/dV = 0 = d²P/dV². of course, not all EoS can even satisfy this condition. Cubics have the correct temperature and pressure (by definition) but fail on volume. SAFT equations and all EoS with association terms predicts critical points with temperatures higher than the experimental ones. a lot of MultiParameter EoS (like IAWPS95, the standard for pure water) have some anomalies at the vicinity of the critical point. Nevertheless, finding such critical points, however far from reality are from the Real fluid that is trying to represent, helps on finding where are your properties in the phase diagram. In practice, you never stay at the critical point, you pass near it and you can tell by some properties that you are passing near it. There is also new developments on "Phase equilibria" over the critical point,because it seems that supercritical fluids do present some sort of continuous phase transition between a liquid-like state and a gas-like state. there is this thing named the widom line that marks this separation, But not all EoS even present this line..., "are there phases in the supercritical fluid?" is a research question in that sense.
- bernulli 5y ago
  I mean something different: no one has ever measured a critical volume, your dp/dv flatlines at the critical point, i.e. there is no driving force to make the fluid balance out the naturally occurring fluctuations, indeed relaxation times go to infinity at the critical point. An EOS only gives you the thermodynamic equilibrium value, attained when you let it sit for times much larger than the relaxation times. The Widom line(s) are somewhat arbitrarily and ambiguously defined, so I'm not a big fan (pseudo boiling all the way!), but the whole point there is that there is no phase equilibrium at supercritical conditions. However, just because we never observe supercritical liquids and gases simultaneously in equilibrium, does not mean they don't exist. They absolutely do and do lead to a phase transition between liquids and gases - just not coexisting. This also means that your other comment needs a revision: we absolutely do have something akin to boiling at supercritical conditions, even with macroscopic effects, such as the (subcritical) boiling crisis <> (supercritical) heat transfer deterioration.
  - longemen3000 5y ago
    Of course! we are urgently in need of a "critical boiling" relation. At the moment we are using critical isochores as a way to "extend" the saturation curve, but it is less than ideal (at least they can be calculated quickly). I agree with the Widom line, at the moment i haven't found any concrete relation to calculate those from a equation of state functional. if there is something concrete, i would be glad to code it.
    - bernulli 4y ago
      Also - could you explain why you don't count van der Waals' equation among the cubic EOS?
    - bernulli 4y ago
      That's what I work on, I'll send you an email (if I find your address somewhere)!

R0b0t1 5y ago

> one property i've relying on is that the second virial coefficient minimum density is always lower than the saturated gas density.. until a threshold near criticality. A (or even the) phenomenologically useful reason anyone ever cares about supercriticality in industry is to use a chemical as a solvent. This seems like a precise statement of what makes it so. You know anything else that would be related?

longemen3000 5y ago
A lot of new work on supercritical fluids is the ability of calculate properties for those. normally we don't access to those conditions, so it is tricky to measure, but there is always new work on correlations capable of explaining the anomalies present on near critical and supercritical fluids. On the viscosity front, there is this new framework named Entropy Scaling, that postulates that scaled viscosity ≈ f(residual entropy)^(2/3). There is also new work on calculation of interfacial tensions from pure equations of state,that are relevant because you could have a two phase liquid-liquid mix and you want to transport something from one liquid phase to another. Also, as the article says, over the critical point, there is no surface tension, because there is only one phase. (do not take this phrase literally, because that only happens in a pure compound, as soon as you have a mixture, the surface tension will depend on all elements of the mixture) Furthermore, some fluid mixtures present something called UCST (upper critical solution temperatures) and LCST (lower critical solution temperatures). imagine if you lower the temperature of and oil-water mixture and suddenly they start to mix. and if you keep lowering the temperature, they unmix again!, and of course, not every fluid presents those properties, but we need to understand those who do. and specially, calculate those points. Few if any industrial thermodynamic calculators can do this, because you require fourth order accurate derivatives (can this be solved with automatic differentiation like what they do with neural networks?, of course, but you need a differentiation-ready equation of state) On more macro properties, supercritical cycles are useful. you can start from a liquid and end with a gas without boiling, if you pressurize your liquid over the critical pressure (isothermically) then lower the temperature (isobarically) and finally releasing pressure (isothermically). one advantage of doing that is that you don't produce bubbles or any kinetic artifacts that are present during a normal phase transition.
5y ago