Helium support: could these experimental data be useful?

[LunarPerovskite]

Hi Mark and everyone,
Would it be possible to add helium support to the gas solubility calculations in pyResToolbox? Here are some experimental studies that might be useful:

• Gardiner and Smith (1972): helium solubility in water at pressures up to 600 atm, including information on the effect of NaCl.
• Gerth (1983): experimental results on how dissolved salts affect helium solubility.
• Schwenk et al. (2022): helium concentrations in water equilibrated with air at approximately 25–80°C.
• Jenkins et al. (2019), WHOI data: an author-provided spreadsheet containing helium measurements in fresh water and seawater at atmospheric pressure.
• Warr et al. (2015): experimental measurements of helium distribution between water and a CO₂-rich phase at elevated pressures.
  Could these studies provide a useful starting point, or would additional experimental data be needed, particularly for brines and gas mixtures?
  Thank you for your time and for maintaining pyResToolbox.

[mwburgoyne]

Hi Juan, thanks for the pointers. Helium is in 3.8.3, out now (pip install -U pyrestoolbox).

What's in it

• Solubility (Søreide-Whitson flash): a helium-water kij fitted to Gardiner & Smith (1972) and Gerth (1983) from your list, plus Abrosimov & Lebedeva (2013), Pray et al. (1952) and Potter & Clynne (1978). That covers 20-163 °C and 1-1000 bar. Mean error in dissolved mole fraction is 2-7% by source below 150 °C. I haven't validated it above 200 °C.
• Brine: salting-out uses S&W's Eq 8, which matches the measured helium Sechenov coefficients in NaCl (Gardiner & Smith, Gerth) to 0.007 mean absolute error. The two papers disagree with each other at 25 °C (about 0.078 vs 0.092 on a molality basis). One thing to be aware of: Gardiner & Smith's fitted polynomials (their Table II) don't reproduce their own measured points in Tables I and VII, so I fitted to the measured points. At 100 °C I relied on Potter & Clynne instead.
• Brine density: dissolved helium lowers it. The volume of dissolved helium is anchored on the densimetric 24.6 cm³/mol of Zhou & Battino (2001). There's no viscosity correction because I couldn't find any data.
• Gas properties: helium is also in the BNS Z-factor, viscosity and thermal model (he= on the gas functions). Note that helium's Tc in that model is a deliberately non-standard 6.35 °R, chosen to get viscosity right; the docs explain why.

from pyrestoolbox import brine, gas
mix = brine.SoreideWhitson(pres=3000, temp=150, ppm=50000, sg=0.65, y_He=0.05)
mix.x['He'], mix.bDen
gas.gas_z(p=2000, sg=0.6, degf=120, he=0.05)

On the rest of your list

• Schwenk et al. (2022) and the WHOI/Jenkins data are atmospheric-pressure, air-equilibrated measurements. At that end the fit is already tied down by Abrosimov & Lebedeva and Potter & Clynne, so I didn't use them.
• Warr et al. (2015) is helium partitioning between water and a CO₂-rich phase. That's a three-component system, so I didn't use it to fit the helium-water parameter. It would make a good test of the mixture behaviour later.

Where more data would help

1. Water content of helium-rich gas. There's none that I could find, so for now helium borrows H₂'s non-aqueous kij (0.468), and water content in helium-rich gas is unvalidated.
2. Helium solubility in brine above 100 °C.
3. Solubility of helium in mixtures (He with CH₄ or CO₂). Helium's interaction parameters with the other gases are currently zero.
4. Dissolved-helium effect on brine viscosity.

If you have any of these, I'd be keen to see them. Full details are in the brine docs (Helium section) and the gas docs (Helium in BNS). The same helium extension is also in the Søreide-Whitson refresh repository, where it's labelled as post-publication and not part of the paper.

[LunarPerovskite]

Thank you Mark, this is very useful! and was very quick!

It’s great to see helium incorporated. I’ll also start testing it in some geological scenarios and will share anything useful I find.

I don’t have those helium data at hand, but I’ll look through the literature and datasets I’ve been working with to see if I can find something suitable.