How to calc "sweep-through inerting" time

[UKRichardP]

I need to calculate the time necessary to inert a 450 litre vessel using "sweep-through inerting" with nitrogen.

The nitrogen is supplied via a 1" dairy pipe (21.5mm inside diameter) which is regulated down to 50 mBar just 1 metre before entering the vessel. So when inerting we have a 50mBar flow entering the vessel and a 1" pipe venting to atmosphere.

The aim is to reduce the oxygen level to 6.5% and I need to calculate how long this will take.

I've found a calculation for sweep-through inerting that calculates the volume of nitrogen necessary to achieve this oxygen level :-

Q = (450 ltrs / 0.25) ln (0.21/0.065) /1000 = 2.11 m3 or 2110 litres. Where 0.25 is an efficiency factor for single pipe exhaust.

So I have the quantity and the pressure of nitrogen and the pipe size. I just need a calulation or guideline to determine the time. We will of course confirm the O2 levels in the vessel during commissioning but I'd like to be able to make a reasonable estimate for an initial software setpoint.

Thanks in advance !

 

[epoisses]

Richard, I guess it all depends on the pressure regulator size and the upstream pressure. But... rather than spending hours to figure this out, why wouldn't you simply assume 5 minutes and improve that number with a measurement? (as long as you don't want to do the calcs just for fun...)

 

[UKRichardP]

Well you're right - funnily enough I was going to go for 7 minutes and then just see what happens but we are a little way off being in a position to do that test.

It would be desirable to be able to calculate and estimate in order for us to determine how we structure the recipe with other functions such as mixing etc.

Thanks !
Richard

 

[25362]

The recognized formula (in consistent units) for the friction drop, used to estimate the velocity V is:

[Δ]P_f = 50 mBar ~ [4f (L/D)+1][ρ]V²/2​

An iterative procedure would show whether, by finding the Reynolds' number, the assumed value for f was actually in the ballpark.

Knowing the pipe cross-section and the total volume of nitrogen passing through, one can then estimate the duration of the sweep-through purging step.

 

[jalvarez]

??
The time to inert your vessel will strongly depend on its shape. Supposing a vertical cilinder, N2 entering in the top, flowing down and exiting by the bottom, you will have a "plug type" flow and you simply can calculate the time with your flow rate and your 450 lts. If the diameter is high compared with the height, you will need more time for your N2 to reach the sides... but I don't see any quick manner to estimate this.
Just to take into account: I remember a tank that was inerted injecting hot N2, from top to bottom. We reach our 1% O2 target only spending something like 30% more N2 than the volume of the tank. It was not quick, anyway...
Have a safe day
J.Alvarez