Calculate time to pressurise tank?

[j1o2x3]

Hi I would like to know what equation I should use to determine time to pressurise tank from nitrogen supply.

Tank volume 2000 litres

Nitrogen supplied at 15 psig with a flow rate of 40 standard litres per min

How do I calculate the length of time taken to increase tank pressure to 15 psig?

 

[JStephen]

Looks like 2,000/40 = 50 minutes.

That assumes that you start with an absolute vacuum in the tank, that the flow rate is absolutely unchangeable regardless of backpressure from the tank, that the nitrogen doesn't change temperature as it passes through various valves, fittings, etc., and that a "standard liter" is measured at the same conditions that it's being stored at, as opposed to atmospheric pressure or something.

In real life, it would get more complicated.

 

[TD2K]

JS, I agree overall with your quick estimate but wouldn't it be 100 minutes? At 15 psig final pressure and an absolute vacuum starting pressure, that's 'about' 2 atmosphere changes.

 

[austsa]

If the tank is in vacuum, in 50 minutes you'll get 15psia (not 15psig). If the tank is in atmosphere already and you want a straight pressurise, ie end up with air + nitrogen mix, then it'll take about 50 mins to get to 15psig. If you want to purge the air out of the tank, then it'll take a lot longer to get to 15psig.

 

[JStephen]

If the volumetric flow rate is being measured at the 15 psig, then it'd fill the tank to 15 psig in 50 minutes, would it not? The flow being measured is at two atmospheres as well.

 

[j1o2x3]

Hi and thanks for the responses,

I made an error in my original post Im trying to calculate how long it will take to pressurise the tank to a pressure of 10 psig.

Tank will initially contain nitrogen at atmospheric pressure.

Nitrogen will be delivered to the tank at a pressure of 15 psig and flow rate of 40 standard litres per min.

 

[TD2K]

You have a given tank volume. You need to raise the pressure from 0 psig to 10 psig. The nitrogen in the tank will be at some temperature so you can calculate the number of moles you need to add.

You have a flow rate of 40 standard litres per min so you can calculate a molar flow rate. The time required drops out of that.

 

[cloa]

What's the initial pressure? That is not stated.

 

[chicopee]

Don't you love those OP's when additional constraints are imposed after everybody made suggestions. What a bummer!!!

 

[austsa]

j1o2x3,
I agree with TD2K.
If you can ignore temperature effects, then it'll take approx 33 minutes (=10/15*50mins).

 

[j1o2x3]

Hi,

Thanks for the help, 33 mins will be acceptable time.

Cheers again

 

[JStephen]

Well, the reason I didn't give this more thought in the first place is that it sounds like the 40 l/min is almost certainly the maximum flow available from some source or the minimum flow available but is unlikely to be the actual flow the whole while. And in real life, the challenge would be to deduce that flow rate, and having done that, you could integrate to get the required time.

I guess the analogy would be the electrical system on a car. If you have a battery rated for 600 cold-cranking amps, how long does it take to charge your cell phone?