Calculating Fill Time for Pressure Vessels: Inlet Parameters & Mass Flow Rate

[Juanka]

I am needing to calculate the fill time of a pressure vessel. I know the following parameters regarding the vessel:

Volume, Temperature, Properties of the fluid media, inlet pipe diameter, flow rate of the inlet, pressure of the inlet.

I tried calculating the mass flow rate of the inlet then dividing the capacity of the tank (lbm) by the mass flow to find a time of fill. However, this number was extremely small (unrealistically small).

I know as the vessel fills the fill rate is going to go down until S.S. is finally reached. However do I have to implement a D.E. to calculate the time for the vessel to fill?

 

[Travis_King]

Is this a gas or a liquid.

 

[Juanka]

Air at 520R

 

[Travis_King]

So does your calc take into consideration the effects of compression? i.e. inlet pressure differential between empty tank and tank at desired pressure.
Air will expand to "fill" the tank really quickly. But it will take longer to get the tank up to the desired pressure.

 

[Juanka]

Yes, I am assuming my vessel pressure to be 0 psig while inlet pressure to be 420 psig.

 

[Travis_King]

Yet that obviously isn't true the instant any air enters the tank.

As I said, the gas will expand to fill the tank. The "fill" time is extremely short. The time it takes to fill to the desired pressure is another story, and your initial assumption does not hold.

 

[Juanka]

I am needing to calculate the time required to pressurize the vessel to the inlet pressure of 420 psig. I am working on a DE at the moment however I do not seem to be making much progress. Is it possible to solve this without a DE? (I am thinking it is not).

 

[Travis_King]

Not that I am aware of. The driving force behind the flow rate will be the pressure differential (for most compressors) thus the fill rate will decrease differentially as the pressure rises in the tank.

 

[Juanka]

I have attached a screenshot of my work described in Mathcad. I would like it if someone could verify whether the calculation is valid or not. (As cited before I believe it is not, I just want an outside opinion).

 

[Travis_King]

Though, if it is a screw compressure with positive displacement, then you can treat your mass flow as constant, unless I'm mistaken...

 

[Juanka]

The mass flow inlet can be assumed constant, the inlet to this vessel occupies <5% of the capacities of the compressors supplying the flow. However, I know it takes much longer than the 30 seconds to fill this vessel, for that reason I know there is an error and I am trying to work out a DE to find a solution I just wanted to rule out the non Diff-Eq method before proceeding.

 

[Travis_King]

Oh, I see one mistake, your flow is in SCFM and that should not be used to determine the fill time of your tank. Either you must determine the actual fill volume of your tank (a 6000 ft3 tank holds quite a bit more volume at 380 psig than it does at 1 atm), and divide by the SCFM flowrate to estimate your fill time, or you must determine the ACFM and use the geometric tank volume (6000 gt3).

 

[Juanka]

Good catch, this looks more like it.

Thanks