Advanced Thermodynamics

Thermodynamic properties of natural gas mixtures containing helium - Part 9b

15 May 2022

This is Part 9b of a series.

In Part 9a, I reported that the Julia package Clapeyron.jl did not have a flash procedure implemented. Recently, I was contacted by one of the package authors to inform me that a flash algorithm has been added; the focus of this post will be to check its performance against my flash benchmarks for mixtures containing methane and helium.

The first step is to obtain the latest version of the package (at the time of writing this is 0.3.6):

  ] add https://github.com/ypaul21/Clapeyron.jl#master

  using Clapeyron
  model = GERG2008(["helium","nitrogen"])
  (x,n,G) = tp_flash(model,2e6,90,[0.5,0.5])

  ([0.9616497782871675 0.038350221712832484; 0.09980808558719821 0.9001919144128017], 
   [0.44653730380779205 0.01780773519709112; 0.05346269619220795 0.4821922648029089], 
   -2.010398635641377)

I tried using the following code to run the flash against the benchmarks:

using Clapeyron
using CSV

model = Clapeyron.GERG2008(["methane","helium"])
file = "test\\flash_benchmark_GERG2008_methane+helium.csv"
for row in CSV.File(file)
    z = [row.z1, 1-row.z1]
    (x,ϕ,G) = Clapeyron.tp_flash(model,row.p*1e3,row.T,z)
    if (abs(x[1,1]-row.x1)>2.e-6 && abs(x[2,1]-row.x1)>2.e-6) || 
       (abs(x[2,1]-row.y1)>2.e-6 && abs(x[1,1]-row.y1)>2.e-6)
        @info row
    end
end

  DETPFlash(;
      numphases = 2;
      max_steps = 1e4*(numphases-1),
      population_size =20,
      time_limit = Inf,
      verbose = false, 
      logspace = false
  )

for row in CSV.File(file)
    z = [row.z1, 1-row.z1]
    (x,ϕ,G) = Clapeyron.tp_flash(model,row.p*1e3,row.T,z,DETPFlash(time_limit=4))
    if (abs(x[1,1]-row.x1)>2.e-6 && abs(x[2,1]-row.x1)>2.e-6) || 
       (abs(x[2,1]-row.y1)>2.e-6 && abs(x[1,1]-row.y1)>2.e-6)
        @info row
    end
end

I observe no common feature to all of the failure cases: several of them appear to be returning a phase composition that is essentially pure methane or pure helium; some of the failure cases are reaching the allotted time limit (even when increased to 10 seconds) but so are some of the successful cases.

As noted above, some cases are timing out after 10 seconds. However, even those that terminate on their own are taking more than 1 second, with some exceeding 6 seconds. For comparison, my flash algorithm can return in under 4 milliseconds. The speed of the calculations is an issue, especially if the results are incorrect about 25 % of the time.

Discussion

Overall, the flash algorithm in Clapeyron.jl is unreliable and slow when applied to mixtures of methane and helium modelled with the GERG-2008 EOS. As I have detailed in this series, helium presents unique challenges for the flash so it is possible that the algorithm performs better on other systems. I have not spent any time trying to debug the failures I observed. However, if some additional information had been returned from the flash it could have facilitated that effort, e.g.:

• return the phase fraction for each phase
• return fugacity coefficients for each component in each phase
• return the density of each phase

References

[1] Kunz and Wagner, J. Chem. Eng. Data, 2012, 57, 3032 (link to publisher)

[2] Span et al., TREND. Thermodynamic Reference and Engineering Data 4.0. Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum, 2019