Relief Valve Sizing – Critical Flow

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The flow of a compressible fluid through an orifice is limited by critical flow. Critical flow is also referred to as choked flow, sonic flow, or Mach 1. It can occur at a restriction in a line such as a relief valve orifice
or a choke, where piping goes from a small branch into a larger header, where pipe size increases, or at the vent tip. The maximum flow occurs at sonic velocity, which exists as long as the pressure drop through the orifice is greater than the critical pressure drop given by:

cal-13-1

For gases with specific heat ratios of approximately 1.4, the critical pressure ratio is approximately 0.5. For hydrocarbon service, this means that if the back-pressure on the relief valve is greater than 50% of the set pressure, then the capacity of the valve will be reduced. In other words, if the pressure in the relief piping at the valve outlet is greater than half the set pressure, then a larger relief valve will be required to handle the same amount of fluid.

As long as the pressure ratio exceeds the critical-pressure ratio, the throughput will vary with the inlet pressure and be independent of outlet pressure. For example, a relief valve set at 100 psi will have the same gas flow through it as long as the back-pressure is less than approximately 50 psi.

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