Can you add example for gas-polymer system using SL eos?

[YogeshkumarCD]

Sanchez Lacombe eos for like Polystyrene and CO2 system.

[longemen3000]

hi!, yes, we could add one. some particularities on the current SL implementation:

• we use ε (epsilon), v0 (vol, molar) and m (segment) instead of the T⋆, P⋆,ρ⋆ formulation. you can transform between those by doing:

P⋆ = R̄*T⋆/v0 -> v0 = R̄*T⋆/P⋆
T⋆ = ε/R̄ -> ε = R̄*T⋆
ρ⋆ = Mw/m*v0  m -> Mw/v0*ρ⋆ or Mw = m*v0*ρ⋆

• we use the neau implementation, that is based in a consistent formulation at the pure component limit. (but this paper seems to disagree with that https://www.doi.org/10.1103/PhysRevApplied.8.044009 ?. we can define different mixing rules, but to be honest, there is a lot of discrepancies on how to implement SL in a way that is both physically consistent and gives accurate predictions.

• for polymer-gas systems in SL context, normally the gas phase of the polymer is assumed zero. we can do that with some of our solvers (bubble_pressure, bubble_temperature, dew_pressure, dew_temperature and MichelsenTPFlash.

with that in mind, now we can go to a concrete example:

First, we need some parameters. for PS we can obtain some data from here (DOI: 10.1039/c8sm00794b) (note that they dont use the Neau formulation, so i would expect inaccurate results):

so, for CO2 (SI units): (P⋆,T⋆,ρ⋆) = (419.9e6,341.8,1.397e3)
and for PS (SI units): (P⋆,T⋆,ρ⋆) = (421.8e6,687.8,1.118e3)

so, we need in this particular implementation, the molecular weights. for CO2, Mw = 44.009 (g/mol). for PS, it depends, but we can suppose 20000 (g/mol) ? (we can also suppose the segment diameter and obtain the molecular weight from there)

using this utility function:

function sl_transform(P,T,rho, Mw)
  R = Clapeyron.R̄ #gas constant
  v0 = R*T/P
  epsilon = R*T
  m = (0.001*Mw)/(rho*v0) #Mw in g/mol
  return epsilon,v0,m
end

we obtain that (epsilon,vol,segment) for those two is:

CO2 (epsilon,vol,segment): (2841.8833228847775, 6.768000292652483e-6, 4.654625296462685)
PS: (5718.687388765798, 1.355781742239402e-5, 1319.4666294134743)

with the data, we can build our model. let's ignore the unlike values (kij, lij) for now.

we put this data in a CSV (we can just pass a string and Clapeyron will recognize it as a CSV if it starts with the correct text):

species_data = """Clapeyron Database File
SL example parameters [csvtype = like]
species,epsilon,vol,segment,Mw
CO2,2841.8833228847775, 6.768000292652483e-6, 4.654625296462685,44.009
PS20000,5718.687388765798, 1.355781742239402e-5, 1319.4666294134743,20000
"""
model = Clapeyron.SL(["CO2","PS20000"],userlocations = [species_data])

that should result in:

julia> model = Clapeyron.SL(["CO2","PS20000"],userlocations = [species_data])
SanchezLacombe{SLk0k1lMixingRule, BasicIdeal} with 2 components:
 "CO2"
 "PS20000"
Contains parameters: Mw, segment, epsilon, vol