Question for pressure engineer about cascading gas

[steves1080]

Say I had a high pressure vessel with a volume of about 1400 cubic feet and pressurized to 5,000 psig. Now say I had a lower pressure vessel with a volume of 1800 cubic feet (slightly higher) and pressurized to 2,000 psig. The goal is to "cascade" gas from the higher pressure vessel to the lower pressure vessel in order to get the lower pressure tank up to 2,700 psig. The gas would flow through a pressure regulator (with max output set point of 2,700 psig) fully opened up. The gas going into the lower pressure tank flows through a 1-inch diameter pipe and only about 30 feet in length. I've already done the calculations using the compressible mass flow rate equation for choked flow using ideal gas law assumptions and using the Cv of the regulator to determine the magnitude of the choke point. I neglected temperature, enthalpy, and pressure drop affects, and stuck to the basic physics behind it. But the answer I got for how long it would take to cascade that much gas was ~3 minutes. I am looking for an experienced pressure systems engineer to let me know if this sounds reasonable or if I need to do some more calculations. It would also be helpful to know what type of number to expect if this seems way off. For some reason I was expecting it to take much longer, but I don't have too much experience with high pressure gases. I've run my numbers multiple times, so I think I am correct.

 

[steves1080]

I should note that the gas is nitrogen, so it's basically just air

 

[Travis_King]

The flow of air through a 1" pipe will be relatively low in volume, and considering the size tank you have, there's quite a lot of it required to raise the pressure by 700 psi. Also consider that the pressure in the first tank will drop as it's volume is depleated by the flow to the second tank, thus reducing the flow rate. As an off the cuff guess I'd say 3 minutes sounds reasonable.

I haven't crunched any numbers, so take that for what it is.

 

[steves1080]

Thanks for the response. I did crunch some numbers, but the problem is that I have no way of gauging what seems reasonable. 3 minutes sounds possible to me, but on the other hand that it a lot of volume to fill that quickly.