Amount of gas lost through relief valve?

I'm trying to estimate the amount of gas lost when a relief/blowoff valve is opened on a pipeline. If I know the valve opening size, pipe size, gas pressure, and the duration the valve is left open. Ex. A 12 inch pipe operating at 400 psi has a 4 inch relief valve that is open for 5 minutes. How much gas has been release? Assume constant flow of gas. Thanks in advance

Answer:

Find the orifice size, then assume sonic velocity for ACFM flow rate times five minutes.

Below is one of many sites with software for sizing relief valves. Each relief valve has a specific orifice size usually indicated by a letter such as A, B, C etc. With this and the other information on the gas being relieved you can calculate the rate the valve is relieving when it is open. Note: most of the time you will be in the critical flow range so once the valve is open the flow rate will be constant until the pressure falls and the valve reseats.