"Real" Thirds.

[Doppler]

There are more variables than mentioned... but you have identified that gas compressibility (van der waals equation) can have a significant effect.

Almost without exception, experience tells us that a diver in a low or no-flow cave will use a greater volume of gas on the way in than on the way out. Factors that contribute include:

Drop in temperature since water is often cooler than ambient air.
Rate of breathing. Most divers are more stressed at the beginning of a dive than at the end
Auxiliary consumption (wing/drysuit etc.) is greater when dive begins... a generalization but certainly the case in majority of instances

Two factors that many divers fail to account for are: Gas compressibility, non-calibrated gauges.

Therefore, my seat-of-the-pants, pull a number outta your arse guess would be gauge drop pressure upon exit would be about 10 percent less than expected.

 

[oszillodrom]

If you plot the difference in the rate of pressure drop (i.e. how much faster or slower your pressure gauge drops at constant air consumption rate compared to an ideal gas, expressed as a percentage), you can see that over ~165 bar your pressure drops faster than you would expect, after which it drops slower than expected, with a minimum of ~10% slower at ~100 bar. This makes sense as the gas behaviour changes from being exclusion volume dominated to being dominated by attractive forces, after which it approximates ideal behaviour at low pressures.



Again, these are fun(?) thought experiments with propably limited applicabilty to real life.

 

[j2s]

Too many 'variables'....SAC, temp, current, tank temps, capacity-vs-psi, depth, %mix etc. to calculate exact psi.....It's an 'approximation'.......