As for filling cylinders real gas corrections do matter, we try to take the compressibility factor into account in Subsurface. As the theoretical physicist I thought (as I was taught) this is handled by the van der Waals equations. Turns out, in the pressure/temperature range relevant for diving cylinders is very far from getting the corrections to the ideal gas equations right. There are errors at least in the 30% range. This is probably since we are quite far away from the tri-critical point where it is supposed to be a good approximation.

In the end, we found a cubic approximation with coefficients read off from tables of compressibility factors to be an economic way to do these computations. You can find the source here.

When today somebody asked in a diving forum for a spreadsheet to calculate the resulting pressure when streaming between two cylinders, I thought I could use these interpolations to do the calculations for real gases with different compositions. Here is what I came up with.