Leakage Rate Calculation through a Closed Shut Down Valve

[BigRon1]

Hello,

I am trying to get to grips with calculating the leakage rate through a closed Emergency Shut Down Valve for the purposes of Performance Standard testing. For simplicity I have distilled the problem thus:

I have an inelastic, sealed, gas filled vessel with a volume V, held at initial pressure P1. I inject (or leak) gas into the vessel over a period of time (t seconds) and the pressure inside the vessel increases to P2.

Q1) How can I calculate/estimate the injection flow rate (m3/sec) assuming a constant vessel temperature, given I know the pressure increase and volume of the vessel?
Q2) If the temperature change from the pressure increase is taken into consideration, what effect would that have on the calculation?

I've put the problem in an illustration for further simplicity:

Thank you in advance.

Best regards,

B.R.

 

[LittleInch]

You can get the volume change you need from P1V1/T1 = P2V2/T2

As the pressure is higher, the volume is lower. This change of the state 1 volume is caused by extra gas filling the fixed volume of the cylinder.

So if say the cylinder is 100 cc and the volume change required to get your pressure difference is 40cc, then you have injected 40cc of gas AT Pressure P2.

Hence you can get your average actual volume flow. This would need to be converted to get standard volume flow.

The difficulty here is that the pressure keeps changing as you go from P1 to P2 so either the inlet pressure needs to change to keep the actual volume flow constant or the actual volume flow is higher to start with than at the end point.

If temp changes then just add it into the formula, just remember to use degrees K.

For what I think you're using this for, so long as P1 and P2 are < 10% of the pressure on the other side of the valve, you can probably assume the standard gas flow rate is the same at the start point and the end point. More than that and you're into a transient analysis

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[BigRon1]

Apologies for the long delay in response. Many thanks for your help.

Best regards,

BR

 

[LittleInch]

Thanks. That is possibly the longest period between answe and response I've ever seen, but better late than never which is much worse. Hope it helped.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.