Pressure vessel cascading with a regulator?

Hi all,

I am trying to determine what approach to use to solve the following scenario:

I have a pressure vessel with pressure P1 and volume V1. I have another vessel of pressure P2 and volume V2. Vessel #1 is supposed to be a high-pressure storage vessel and vessel #2 is supposed to be rated for lower pressures.

Now just say I wanted to fill up vessel #2 to its maximum capacity using some of the high-pressure gas inside vessel #1, and was looking to determine how much gas inside vessel #1 I used up. This concept would be pretty simple, as all I would have to do is find the equilibrium pressure using P3 = (P1×V1+P2×V2)/(V1+V2).

The catch, however, is that vessel #2 is not allowed to exceed a specific pressure because is is rated for a lower pressure as I mentioned before. Therefore, a step-down pressure regulator would have to be added between the high pressure and low pressure vessels with a maximum set pressure of x psig (the maximum expected operating pressure of vessel #2).

My question is this: how would this added pressure regulating device affect the formula and the approach used to determine how much of the higher pressure gas is used up? The two vessels won't exactly find an "equilibrium" per se since vessel #2 would only be able to hold x psig. How can I find out how much of the high pressure gas is used up during this operation?

Thanks in advance for any insight.

Mike