Fill-time for gas into chamber

[Speedy]

Scenario as follows;

I want to fill a gas into a chamber (constant volume) to a desired pressure. I am using 2 valves in series. The valves are similar but one has a small hole drilled in the seat which in effect, acts as a flow restrictor.

I will close the drilled valve at a % of the target pressure, say 95%. When the target pressure is reached, I will close the second.

How do I calculate the theoretical fill time from the closing of the drilled valve to the closing of the second?

I can calculate the flowrate across the drilled valve but this is a function of the pressure differential which is decreasing also. I assume that I am dealing with both choked and non-choked scenarios as the target pressure may be a high % of the supply pressure also.

Based on mass-flow the choked part is easy, but what about the final non- choked part. It is a time based derivative function?
Am I over-complicating the problem?


This in effect is the same as calculating the emptying of a pressurised chamber to atmosphere, but in reverse. I just don’t have the equations to hand.

Speedy

 

[israelkk]

This is a non linear process and as you said the first part is a choked flow and then a non-chocked flow. There is no closed formula for this. You need to write some thermodynamic differential equations and solve them.

Valve orifice diameter?
Gas type?
Tank volume?
Inlet pressure?

 

[Speedy]

israelkk,

Thanks very much for that, at least I was right in my line of thinking.
I had planned to plot the aggregate or total mass in the chamber v's the inverse of the mass flow across the valve. The area under the curve then will be the fill time.Tedious but...............at least a solution.

Speedy