A few more basic questions on Clapeyron.jl

[jlchan]

Hi Clapeyron.jl devs - thanks for putting this package out there, and for so carefully maintaining it! I'm hoping to incorporate it into some single-fluid numerical simulations; however, I have a few questions. Apologies if they are basic or naive - my background is mainly in applied math, and have only a very basic understanding of thermodynamics.

1. Is the description of how CoolProp uses the Helmholtz free energy essentially how Clapeyron.jl computes thermodynamic quantities? If so, is the Helmholtz energy residual for each non-ideal EOS independent of the ideal model (such that results change when changing the ideal model)?
2. Is there a way to initialize a simpler EOS (e.g., ideal or vdW) for debugging purposes? For example, is it possible to initialize an ideal gas vdW with a, b = 0?
3. Is there a way to express temperature as a function of internal energy and specific volume? I was thinking of using a rootfinding method to compute T(V, e) by solving VT_internal_energy(V, T) - e = 0, but it'd be nice if there was an easier way.

Thank you!

[longemen3000]

hello, i can answer some of your questions:

1. Yes. We use Helmholtz energy for our models. if you check each model, you will see the function a_res(model::MyModel,V,T,z) defined, that is equivalent to αr(δ,τ) in the CoolProp description (but in a total volume - temperature - moles basis). our ideal models are independent of our residual models, and you can change the ideal model freely:

julia> model1 = PR("propane")
PR{BasicIdeal, PRAlpha, NoTranslation, vdW1fRule} with 1 component:
 "propane"
Contains parameters: a, b, Tc, Pc, Mw

julia> model2 = PR("propane",idealmodel = ReidIdeal)
PR{ReidIdeal, PRAlpha, NoTranslation, vdW1fRule} with 1 component:
 "propane"
Contains parameters: a, b, Tc, Pc, Mw

julia> speed_of_sound(model1,101325,300.0,[1.0])
305.1475370882578

julia> speed_of_sound(model2,101325,300.0,[1.0])
248.98933553178472

2. hmm, vdW is not an ideal gas 😅, I would be interested in what properties do you want to calculate. If you don't need caloric information, you could use BasicIdeal. that model is a monoatomic (Cp = 5/2 R) ideal gas:

julia> model = BasicIdeal()
BasicIdeal()

julia> volume(model,1e5,300.15) - Rgas(model)*300.15/1e5 #volume(model) - RT/p
0.0

julia> isobaric_heat_capacity(model,1e5,300.15)/Rgas(model)
2.5

3. That is a harder question. The technical algorithm you are looking for is for an UV-flash. We have a general flash solver, but we don't have an initialization procedure that can provide initial guesses for that specific flash, nor an high level API to use. I would say it is probably easy to create that algorithm for single component models, but it is an order of magnitude harder to do it for multiple components. Any help in this area would be greatly appreciated.

[jlchan]

Thank you for the detailed response!

Let me clarify question 2, I was wondering if it would be possible to initialize a vdW model with a, b = 0 (which I thought reduced vdW to an ideal gas) for debugging purposes. I have hardcoded ideal gas and vdW implementations that I was hoping to validate my dear Clapeyron implementation with.

[pw0908]

You can do something like this:

model = vdW(["a1"]; userlocations=(;
           Tc = [0.],
           Pc = [1.],
           Mw = [1.]))

model.params.a[1] # 0
model.params.b[1] # 0

[jlchan]

Great, thank you!

That is a harder question. The technical algorithm you are looking for is for an UV-flash. We have a general flash solver, but we don't have an initialization procedure that can provide initial guesses for that specific flash, nor an high level API to use. I would say it is probably easy to create that algorithm for single component models, but it is an order of magnitude harder to do it for multiple components. Any help in this area would be greatly appreciated.

Thank you for the explanation. I am pretty far away from working on the multicomponent case, but we'd be happy to try to help when we get to that point. I'll try to look more into flash algorithms.

[longemen3000]

hello,

i got to implement a basic version of the UV flash method (just for single component models), If you can try it, it would be great:

julia> model = PR("water")
PR{BasicIdeal, PRAlpha, NoTranslation, vdW1fRule} with 1 component:
 "water"
Contains parameters: a, b, Tc, Pc, Mw

julia> result = Clapeyron.uv_flash(model,50.0,0.01)
Flash result at T = 406.162, p = 2.87199e5 with 2 phases:
 (x = [1.0], β = 0.13252, v = 2.34364e-5)
 (x = [1.0], β = 0.86748, v = 0.0115241)

julia> internal_energy(model,result)
50.000000000009095

julia> volume(model,result)
0.009999999999999998

[jlchan]

Thank you! I appreciate it, and will try it and compare it to my iterative solver soon.