[peterzwart]

Hi All,

I face an engineering problem on which I cannot find an answer. Hence I was wondering whether someone on this forum could help me out.

Please find below our situation. Lets image we have a cylindrical vessel with an open bottom. This vessel is submerged in seawater. This situation is represented by the left image. In this case air is trapped within the vessel. The volume of the air is close to identical to the inner volume of the vessel.

Than we submerge the vessel all the way to 3000 meters of seawater. The hydro static pressure increases to about 300 bar and acts on the gas. As a consequence the gas is compressed and will shrink to a volume of about 1/300 of its original volume. This entrapped air resides at the top of the internal vessel volume.

Now I have two questions:
1. At what rate will the air dissolve in the seawater? (e.g. how long will it take before half the air is dissolved in the seawater?)
2. Will the entire air be dissolved into the seawater or will a part of it remain?

It doesn't have to be seawater, also guidance on normal water would already be great.

Our parameters:
- Internal volume of the vessel: 1.3 m3
- Temperature at 3000 meter, 4 degrees Celcius.
- Air temperature when submerged: 20 degrees celcius.



Any guidance would be greatly appreciated.

Thank you.
With kind regards,
Peter

[Borek]

2. Will the entire air be dissolved into the seawater or will a part of it remain?

All air will be easily dissolved.

Rate problem is much more difficult - calculating such thing from the first principles is notoriously difficult, it is typically much easier to find the answer experimentally. Could be people working with gases/diving/high pressures do have some table and approximate methods to estimate such things.

Can you add a valve at the top of the vessel to get rid of the problem?

[Enthalpy]

I won't risk any prediction. This situation is not a matter of equilibrium, because all the Ocean is available to dissolve a little bit of air. So yes, it's a question of rate, which depends essentially on diffusion speed in water or of mixing speed in water by turbulence. Experiment, sure.

If the goal is to keep air at depth, reduce the contact area with water (vessel shaped as a cone with apex up), and more importantly, slow down the movements of water, for instance with some felt.

It's quite possible that some components of atmospheric air dissolve more slowly. That is, CO₂ disappears quickly, then Ar, but N₂ disappears last. So before all gas is dissolved, the concentration of N₂ increases.
https://www.engineeringtoolbox.com/gases-solubility-water-d_1148.html

[peterzwart]

Dear All,

Thank you very much for your insights. I agree on your arguments and think we need experimentation. Also thank you for your suggestions to minimize the dissolution rate.

With kind regards,
Peter

[Corribus]

If you have information about diffusion constants and partition coefficients (solubility coefficients) at relevant temperatures and pressures, plus geometry of the system, it would in principle be possible to calculate parameters of interest from solutions to the diffusion equation. This could be done under limits of "efficient mixing", in which the concentration of air components are set at constant (minimum) equilibrium value, or "no mixing", in which air components have to diffuse away from the boundary layer. Intermediate degrees of mixing, where rate of mixing is competitive with diffusion rate, is your real problem variable here. But, if upper and lower limits are acceptable to you, reasonable timescale estimates could probably be made.

As noted by Enthalpy, air is a complex mixture, though, so that would have to be factored in. As a first approximation, you could consider air to be composed of a single species.

This would be a fun diffusion problem to play around with