Question 1:
Well, API kinda of explain it in API 521 5.3 last paragraph:
In such cases, the assumption of an ideal gas can be too conservative, and Equation (8) (see 5.15.2.2.2) oversizes the pressure-relief valve. This equation should be used only when physical properties for the fluid are not available.
If you have all the fluid properties (sounds like you do to know it's critical flow), then use API 520 Part 1.
However, I think that equations in API 521 are meant for calculating required relief rate where API 520 was meant for calculating capacity. So even though the equation you cited in API 521 give an erroneous orifice size, it does give you a required relief rate later on with that orifice (eq 12). Again, it's an estimate and could be wrong.
Also, I have had air receivers with an external fire scenario before since air can expand before vessel is rupture. (for some gases, this is unlikely) so I can see how you consider external fire here. However, if you didn't know that, check out API 521 5.15.1.2 "Effect of fire on the unwetted surface of a vessel"
Question 2:
Like falah said, not enough info here. Since he answered the low pressure version, I'll take the high pressure version. Though here are the questions
1. Why would there be a thermal expansion for this storage tank (vessel)? What is the storing temperature.
2. Note, an external fire would be the controlling scenario here (I think). So spending time calculating hydraulic expansion is really a waste of time. I would suspect that thermal expansion rate would be much lower than vapor generation rate due to fire.
Edited by Olidin, 11 October 2013 - 03:53 PM.