The Ostwald coefficients (volume of gas per volume of oil) for the solubility of hydrogen and other gases at 1 atmosphere partial pressure and at 273K, in hydrocarbons:

Hydrogen 0.039
Nitrogen  0.075
Oxygen    0.15
Methane  0.31
CO₂         1.0

There are empirical formulas for corrections o/a of temperature changes and oil densities differing from 980 kg/m³. See also ASTM D2779-92(2002).

Assuming gases are ideal, doubling the pressure wouldn't change the Ostwald coefficient, since the solubility doubles but the volumes halves (PV=RT). The number of dissolved gas molecules would, of course, double.

Electrical utilities have a lot of interest in this area.

When large transformer cooling oil degrades (from high voltage electrical effects) hydrogen is produced from the oil degradation. The detection of this hydrogen signals transformer problems.

Suggest you contact transformer maintainance people at your local electrical power utility - you might find out more than you ever want to know.

Post also to forum238 Electrical Power group.

25632:  I'm calculating, based on your numbers, a (considerably) higher solubility for N2 in hydrocarbons than in water.  Is this correct, or did I screw up somewhere?

Moltenmetal

If you convert the solubility of nitrogen in water, as given by the CRC Handbook of Chemistry and Physics, mol fraction → L/L, you'll find the difference is not so large. At 15 Celsius I got a solubility of 0.017 L/L vs. 0.075, as above, for oils.

As a general explanation on the particular behaviour of water in regard to solubility of non-polar gases, see

25362:  it's the ~5x greater solubility of nitrogen and 10x greater solubility of oxygen in oils than in water (based on your Ostwald coefficients) that surprised me.  And the 1:1 vol/vol solubility of CO2 in oils that really shocked me!

I happen to have the data submitted by a reputable european engineering company for the solubility of air in an oil with a sp. gr. = 0.8942 at 60^oC → 0.069 L/L.
Perry VI gives for air/water a Henry law constant H = 10.1×10⁴, for the same conditions → 0.0123 L/L. The ratio : 5.6.

At zero Celsius, for nitrogen in water, Perry gives H = 5.29×10⁴, resulting in a mol fraction x = 1.89×10^-5 → 0.0235 L/L, lowering the ratio to ~3.2.

BTW, the Ostwald coefficients for the solubility of gases in oils were taken from table 2.9 in Engineering Tribology by Stachowiak and Batchelor, Tribology series, 24, Elsevier.

I forgot to mention that CO2 reacts with water. A fact that could explain its enhanced solubility.

From another source for the air solubility in aircraft hydrocarbon fuels, which appear to follow Henry's law at 20 Celsius:

density     viscosity         surf. tension    solubility
  kg/L        mm²/s              mN/m         % vol

 0.725         0.64                 18.5           22.9
 0.781         1.69                 23.5           17.5
 0.872        17.7                  26.5            9.7

As the pressure drops on climbing, air is released taking fuel vapor with it.