This is Part 11 of a series.
The previous entry in this series tried to improve the flash predictions for mixtures containing methane and helium by modifying the critical constants of helium used in the GERG-2008 EOS [1]. However, no obvious improvement was achieved. It has been nearly a year since that entry was made and I believe I now know why it failed.
In the paper by Rowland et al. [2], three parameters in the cubic equation of state for helium were adjusted to achieve good predictions:
The main issue I overlooked previously is that, although it is possible to modify the critical constants in the equation of state for helium without modifying the predicted properties of the pure fluid, this does not counteract the fact that the equation of state has already captured the quantum behaviour of helium. The way to address this issue is to apply the corresponding-states method to substitute another equation of state, one for a fluid similar to helium but which behaves classically. The clear choice is argon as the only other noble gas in the GERG-2008 EOS [1].
I entered the parameters for the equation of state for argon from Kunz and Wagner [1] and benchmarked that they were implemented correctly versus TREND 4.0 [3]. The way to apply this equation of state to helium is to overwrite directly the critical temperature and density i.e.
methane = AdvancedThermo.get_fluid_component("methane")
helium_pseudo = AdvancedThermo.get_fluid_component("argon")
# impose critical parameters from Messerly et al. [4]
helium_pseudo.Tc = 13.0
helium_pseudo.ρc = 28400.0
mixture = AdvancedThermo.create_mixture([methane,helium_pseudo])
We can run this mixture against the pTxy dataset like so for comparison
with GERG-EOS 2008 (from Part 10).
file = "test\\pTxy_methane_helium.csv"
N = 128
AdvancedThermo.flash_statistics(file, N, mixture)
All 128 points are found to be in two-phase equilibrium. Below is shown a comparison
with GERG-2008 and the two models with critical parameters from Messerly et al. [4], one
with γv = γT = 1, the other with
γv and γT based on arithmetic means
(refer to Part 8).
Results for GERG-2008 EOS [1]a
-----------------------------
Statistic lnK(methane) lnK(helium)
AAD 0.36743472024844487 2.487039581867481
Bias -0.33229410009211424 -2.4684691120311237
RMS 0.5575148892589821 2.9733531350213824
Max -1.851716348867873 -6.865761787762258
a 3 points predicted as single phase
Results for Messerly A (Tc = 13, ρc = 28400, γv = γT = 1)
---------------------------------------------------------
Statistic lnK(methane) lnK(helium)
AAD 0.26489927657770695 4.7461282880805875
Bias 0.2623402338662945 -4.7461282880805875
RMS 0.35026614207251144 4.954421788500007
Max 0.968708207573741 -9.236025396725864
Results for Messerly B (Tc = 13, ρc = 28400, γv = 1.086694, γT = 2.044932)
--------------------------------------------------------------------------
Statistic lnK(methane) lnK(helium)
AAD 0.1088891203290949 2.0533041628104294
Bias -0.06686421440790496 -1.6112875562832072
RMS 0.1536885807051663 2.489708677488299
Max -0.5232589167612254 -5.515580526268846
The results for Messerly B are the best I've seen so far in this series; even superior to GERG-2008 EOS!
This is without fitting the critical constants, which is likely to improve things further still.
The code so far can be obtained by downloading the zip file.
[1] Kunz and Wagner, J. Chem. Eng. Data, 2012, 57, 3032 (link to publisher)
[2] Rowland et al., J. Chem. Eng. Data, 2017, 62, 2799 (link to publisher)
[3] Span et al., TREND. Thermodynamic Reference and Engineering Data 4.0. Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum, 2019
[4] Messerly et al., J. Chem. Eng. Data, 2020, 65, 1028 (link to publisher)
| Go to Home | How to cite this page | Permalink to this page |