Critical flow pressure

As normally designed, vapor flow through a typical high-lift safety reliefs valve is characterized by limiting sonic velocity and critical flow pressure conditions at the orifice (nozzle throat), and for a given orifice size and gas composition, mass flow is directly proportional to the absolute upstream pressure. 

Back pressure reduces the pressure drop across the orifice of any type of PR valve. This results in reduced discharge rates in the case of vapors, if the back pressure exceeds the critical flow pressure. For liquids, any back pressure reduces the pressure drop and results in a lower discharge rate. 

If the superimposed back pressure is less than the calculated critical flow pressure, the capacity of a conventional PR valve in vapor service is unaffected and back pressure is not a factor. However, builtup back pressure on a conventional pressure relief valve will affect its flow capacity and operating characteristics, and should not exceed 100% of its set pressure. If total back pressure (superimposed plus built-up) is greater than the calculated critical flow pressure, the capacity of a conventional PR valve in vapor service is affected, and total back pressure is incorporated into the sizing procedure. Any back pressure reduces the capacity of a conventional PR valve in liquid service, and... 

In the above equation, is the critical velocity (m/s), K is the ratio of specific heats (Cp/C ) at inlet conditions, P is the pressure in the restriction at critical flow conditions (KPa, absolute - Note that this term is known as the critical flow pressure ), and p, is the density of the fluid at the critical flow temperature and pressure (kg/m ). 

If the pressure Pj downstream of the restriction is less than the critical flow pressure, then the maximum obtainable flow which occurs at critical velocity is a function of P, and P but is unaffected by Pj. If Pj is greater than P , however, then the flow is termed "subcritical," and the rate is a function of P, and Pj. There are thus two equations for sizing PR valves in vapor service, depending on whether the flow is critical or subcritical. 

The first step in sizing a PR valve for vapor flow is to determine the critical flow pressure P from the following equation ... 

Gas Specific Heat Ratio K = Cp/C, Critical Flow Pressure Ratio, P,/P,... 

For the exceptional cases of subcritical flow (e.g., where a PR valve is designed for a low set pressure and the total superimposed plus built-up back pressure exceeds the critical flow pressure), the following equation may be used applied ... 

We shall first consider the case of non-flashing liquids. In this situation, there is no critical flow pressure limiting the flow of liquid through a PR valve orifice, as opposed to the case of vapor flow. The discharge rate is a function of the pressure drop across the valve and can be estimated by the following expression ... 

By trial and error procedure, determine the amount of liquid which flashes by an isoenthalpic (constant enthalpy) expansion to the critical flow pressure (or actual pressure if greater than critical) for the flashed vapor. 

Calculate individually the orifice area required to pass the flashed vapor component, using Equation (5a), (3b), (4), (5), or (6), as appropriate, according to service, type of valve and whether the back pressure is greater or less than the critical flow pressure. 

Calculate individually the orifice area required to pass the unflashed hquid component, using Equation (8). The pressure drop term Pj should be made equal to the set pressure minus the total back pressure developed by the vapor portion at critical flow pressure, except when the critical flow pressure is less than the calculated total back pressure (superimposed plus built-up), considering the combined liquid and vapor flow. In the latter case, P should be made equal to set pressure minus the calculated total back pressure. 

Note The curves above represent a compromise of the values recommended by a number of relief valve manufacturers and may be used when the make of the valve or the actual critical f ow pressure point for the vapor or gas is unknown. When the make is known, the manufacturer should be consulted tor the correction factor. These curves are for set pressures of 50 pounds per square inch gauge and above. They are limited to back-pressure below critical flow pressure for a given set pressure. For subcntical flow back-pressures below 50 pounds per square inch gauge, the rnanufacturer must be consulted tor values of Kk. 

When/if the downstream pressure exceeds the critical flow pressure, then sub-critical pressure will occur and the equations for sub-critical flow should be used. 

For rupture disk sizing the downstream pressure is assumed to reach the critical flow pressure although the dowm stream pressure initially may be much low er. Under these conditions the flow through the orifice that the disk produces on rupture is considered to be at critical flow. The assumptions of critical pressure do not apply... 

To select the proper sizing equation, determine whether the flowing conditions are sonic or subsonic from the equations. When the absolute pressure downstream or exit of the throat is less than or equal to the critical flow pressure, P., then the flow is critical and the designated equations apply [33a]. WTien the downstream pressure exceeds the critical flow pressure, P,., then sub-... 

The second category covers subsonic flow, which occurs when the downstream pressure of the valve nozzle exceeds the critical flowing pressure. Under these conditions, the flow will decrease with an increasing backpressure, even though the upstream pressure will remain constant. The backpressure... 

Unlike European norms, API 520 has always published typical backpressure correction factors in its code. These curves serve only as a guide and represent a sort of average for a number of manufacturers. API states that they can be used when the make of the valve is unknown (which is rather unlikely) or for gases and vapours when the critical flow pressure point is unknown. 

As a side note, it needs to be noticed that the backpressure correction factors given by API 520 are for pressures above 3.45 Barg (50 psig) only and that they are limited to backpressures below critical flow pressure for a given pressure. For everything below 3.45 Barg, the manufacturer should in any case be contacted. 

When the fluid flowing through the valve is a compressible gas or a vapor, then the design must consider whether critical flow is achieved in the nozzle of the valve. The critical flow rate is the maximum flow rate that can be achieved and corresponds to a sonic velocity at the nozzle. If critical flow occurs, then the pressure at the nozzle exit cannot fall below the critical flow pressure Pcf, even if a lower pressure exists downstream. The critical flow pressure can be estimated from the upstream pressure for an ideal gas using the equation... 

Any consistent set of units may be used for pressure as long as the absolute pressure is used, not the gauge pressure. The ratio PcfIPi is called the critical pressure ratio. Typical values of this ratio are given in Table 13.6. If the downstream pressure is less than the critical flow pressure, then critical flow will occur in the nozzle. It can be seen from the table that this will be the case whenever the upstream pressure is more than two times the downstream pressure. Since most relief systems are operated close to atmospheric pressure, critical flow is the usual case. 

Table 13.6. Critical Flow Pressure Ratios (Adapted from API RP 520)...

Some values of critical flow pressure ratio have been determined experimentally and do not necessarily agree with predictions from equation 13.104. 

The expression used to determine the relief area for vapor discharge when the back pressure is less than the critical flow pressure is ... 

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