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If a pressure relief valve is open, is it somehow possible to quantify the rate at which the pressure in the reactor will decrease?

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    $\begingroup$ Pressure drop across the valve? flow rate? $\endgroup$
    – Solar Mike
    Dec 1, 2021 at 19:00
  • $\begingroup$ with pure liquid the pressure drop will be almost instantaneous. With gas it's a PV=nRT equation. Determine the mass flow rate from the PRV, change the mass of gas in the vessel. If this is a chemical reactor you need to account for production rates as well. $\endgroup$
    – Tiger Guy
    Dec 1, 2021 at 19:37
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    $\begingroup$ the valve will specify flow characteristic in some form. then a rough estimate can be made depending on size and compressibility. Re: Tiger Guy's comment, a fast decompression of gas, if not too high pressure, can be approximated as adiabatic... (which tells us how much a given amount of flow in decompression goes into reducing P vs into reducing T) $\endgroup$
    – Pete W
    Dec 1, 2021 at 21:23
  • $\begingroup$ Yes, several; that is what certain engineers do ( I forgot the name , maybe risk). They look at factors like rupture discs vs valves, pipe length and diameter to flare tower , liquid knockout, boiling liquid in the reactor, connections to other reactors. So it is not a one sentence answer. $\endgroup$ Jan 10, 2022 at 19:15

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If you have opportunity, just measure it. Resulting chart curve's equation can be estimated by a regression equation. Differentiate it for a given time and find the instantaneous rate.

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