Good Evening All
I believe Ted is spot on when he says that the air will not behave as a gas once it has dissolved. In practice, when commissioning hydraulic systems, you try to bleed out all the air as you fill with oil but you just know that there's some pockets of air that you can't bleed out. So you operate the system gently and slowly at first to both push the air out (as a froth) and to allow it to dissolve into the oil and be "transported" out.
The dissolving and subsequent release of air doesn't take place instantaneously. So if you can gradually build up and hold the oil pressure high for a few minutes then gently depressurise and let that supersaturated oil rest in the tank for a few minutes more so that the dissolved air will come out in the tank.
What you do find is that, after a while, the hydraulic system starts to behave properly/consistently and you then know the air has been transported away. Even though you left in pockets of air during the filling process you don't find any pockets of air when you take the system apart at a later date. We don't notice the system behaving like a sponge when all the gaseous air has gone.
The problem you will have in calculating what you're trying to calculate is that it is very hard to know just how fast the air will dissolve and how fast it will release. And we keep saying AIR as if that was the gas - forgetting that air is a mixture of gases and the Nitrogen will behave differently from the Oxygen which is different to the Carbon Dioxide etc. etc.
I've added a file which gives a little more explanation (see section 2.1.4) but I believe what you're trying to calculate will be very very hard to do. Is there any way you could keep the air in a bladder so you could prevent the solution problem. BUT - you should be aware that there have been instances of hydraulic accumulators exploding because of the mixing of the oxygen and the flammable oil at high pressures. For this reason accumulators are now charged with dry nitrogen not compressed air. If you have to charge with compressed air (such as some huge drilling rig heave compensators) then you can't use mineral oil as your fluid.
But, I'm sure you're thinking, compressed air gets mixed with pressurised mineral oil when you first start up the system. You're right but it's a tricky process getting it out and it can be dangerous if you don't know what you're doing. If you rapidly compress a hydraulic [mineral] oil with entrained (rather than dissolved) air there is a risk of triggering a destructive and irritating process called "micro-dieseling". The rapid compression of the air bubble before it has had chance to go into solution causes a huge rise in its temperature. Think about it for a second ... we have: a mineral oil (the vapour of which is inside the bubble), oxygen (from the air), rapid compression and very high temperatures - remind you of anything?
Here's an interesting article:
Good luck.
DOL