How To Calculate Time To Fill Gas In Closed Vessel 1

[robin72]

Hi all
I want to derive equation to determine time to fill gas in closed vessel.
- Gas will feed to vessel with constant pressure at P1.
- Gas will feed to vessel until pressure vessel reach to feed pressure Pi-->P
- Time to fill gas in vessel until pressure vessel = feed pressur is required.

I can derive equation by using "law of conservation of mass" as below;

rho*v1*Apipe = [Vt*Mw/(ZRT)]*d(P-Pi)/dt

but I cannot find the function of v1 with differential pressure between P1 and P.

Anyone please kindly help me to clarify how to determine the function of feed gas velocity with pressure drop of (P1-P)

Thank you for your kindly help.

 

[zdas04]

Dang this sounds like a school problem. I'm going to roll the dice and assume that it isn't.

You have two distinct filling periods: (1) while P1 > P(c) (see faq378-1201 for a good discussion of choked flow and critical pressure); (2) when the two pressures are too close together to give you choked flow.

The first time period is really easy to calculate fill rate and resulting pressure, velocity is sonic and mass flow rate is a function of P1.

After the tank pressure reaches P(c), your first-principles approach fails miserably and you have to resort to empirical equations. Take a look at Crane Technical Paper 410 for the necessary equations.

On the other hand, if your vessel final pressure is less than P(c) then the whole process is very straight forward. Just determine the mass of gas that represents your final pressure and divide that by the mass flow rate since it is constant for sonic velocity with a constant upstream pressure.

David