PSV SIZING FOR GAS OR VAPOR RELIEF
(Single Phase)
Critical Flow Behavior: If a compressible gas is expanded across a nozzle, an orifice, or the end of a pipe, its velocity and specific volume increase with decreasing downstream pressure. For a given set of upstream conditions the mass rate of flow through the nozzle will increase until a limiting velocity is reached in the nozzle. It can be shown that the limiting velocity is the velocity of sound in the flowing fluid at that location. The flow rate that corresponds to the limiting velocity is known as the critical flow rate.
Critical flow pressure: The absolute pressure ratio of the pressure at the nozzle exit at sonic velocity (Pcf) to the inlet pressure (P1) is called the critical pressure ratio. Pcf is known as the critical flow pressure.
If the inlet pressure (PSV relieving pressure) is P1
Outlet pressure at sonic velocity is Pcf
Than
Critical Flow Pressure rato =Pcf/P1
Normally critical flow pressure Pcf is 0.40 to 0.60 of inlet pressure P1, it’s a thumb rule.
Example: If inlet relieving pressure is 10 bar than critical flow will occur when the downstream pressure will reach 6 bar to 4 bar.
Note: Under critical flow conditions, the actual pressure at the nozzle exit of the pressure relief device cannot fall below the critical flow pressure even if a much lower pressure exists downstream(let say atm pressure). At critical flow, the expansion from nozzle pressure to downstream pressure takes place irreversibly with the energy dissipated in turbulence into the surrounding fluid.
Explanation: if the relieving pressure of PSV is 10 bar and critical flow pressure is 4 bar, than minimum pressure at outlet of PSV will be 4 bar. This means that if the back pressure is more than the pressure required at the downstream of the PSV for critical flow condition, at that moment of time you cannot utilize the full relief capacity of PSV (which occurs at critical flow condition). So you need to oversize (oversize means ratio of actual orifice area to the required area at critical flow condition) the PSV orifice area for compensating the backpressure.
The critical flow pressure ratio in absolute units may be estimated using the ideal gas relationship:
where
Pcf = critical flow nozzle pressure, in psia,
P1 = upstream relieving pressure, in psia,
k = ratio of specific heats for any ideal gas.
The sizing equations for pressure relief devices in vapor or gas service fall into two general categories depending on whether the flow is critical or subcritical.
1. If the pressure downstream of the nozzle is less than, or equal to, thecritical flow pressure, Pcf, then critical flow will occur, and API 520-I 3.6.2 procedures should be applied.
2. If the downstream pressure exceeds the critical flow pressure, Pcf, then subcritical flow will occur, and the API 520-I procedures in 3.6.3 or 3.6.4 should be applied.
3.6.2 Sizing for Critical Flow: Pressure relief devices in gas or vapor service that operate at critical flow conditions may be sized using following Equations, Each of the equations may be used to calculate the effective discharge area, A, required to achieve a required flow rate through a pressure relief device. A pressure relief valve that has an effective discharge area equal to or greater than the calculated value of A is then chosen for the application from API Std 526.
where
A = required effective discharge area of the device,[in.2] .
W = required flow through the device, [lb/hr].
C = coefficient determined from an expression of the ratio of the specific heats (k = CP/Cv) of the gas or vapor at inlet relieving conditions. This can be obtained from Figure 32 or Table 8. Where k cannot be determined, it is suggested that a value of C equal to 315 be used.
Kd = effective coefficient of discharge. For preliminary sizing, use the following values:
= 0.975 when a pressure relief valve is installed with or without a rupture disk in combination,
= 0.62 when a pressure relief valve is not installed and sizing is for a rupture disk.
P1 = upstream relieving pressure, psia. This is the set pressure plus the allowable overpressure plus atmospheric pressure(14.7).
Kb = capacity correction factor due to back pressure.
This can be obtained from the manufacturer’s literature or estimated for preliminary sizing from Figure30. The back pressure correction factor applies to balanced bellows valves only.
For conventional and pilot operated valves, use a value for Kb equal to 1.0
Kc = combination correction factor for installations with a rupture disk upstream of the pressure relief valve
= 1.0 when a rupture disk is not installed,
= 0.9 when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value.
T = relieving temperature of the inlet gas or vapor, R (°F + 460).
Z = compressibility factor for the deviation of the actual gas from a perfect gas, a ratio evaluated at inlet
relieving conditions.
M = molecular weight of the gas or vapor at inlet relieving conditions.
V = required flow through the device, scfm at 14.7 psia and 60°F.
G = specific gravity of gas at standard conditions referred to air at standard conditions [normal conditions]. In other words, G = 1.00 for air at 14.7 psia and 60°F.
3.6.3 Sizing for Subcritical Flow, Gas or Vapor (Single Phase):
(Conventional and Pilot-Operated Pressure Relief Valves)
US Customary Units:
where
A = required effective discharge area of the device,[in.2].
W = required flow through the device,[lb/hr].
k = ratio of the specific heats.
r = ratio of back pressure to upstream relieving pressure, P2/P1.
Kd = effective coefficient of discharge. For preliminary sizing, use the following values:
= 0.975 when a pressure relief valve is installed with or without a rupture disk in combination,
= 0.62 when a pressure relief valve is not installed and sizing is for a rupture disk.
Kc = combination correction factor for installations with a rupture disk upstream of the pressure relief valve.
= 1.0 when a rupture disk is not installed,
= 0.9 when a rupture disk is installed in combination with a pressure relief valve and the combination does not have a published value.
Z = compressibility factor for the deviation of the actual gas from a perfect gas, evaluated at relieving inlet conditions.
T = relieving temperature of the inlet gas or vapor, R (°F + 460).
M = molecular weight of the gas or vapor.
P1 = upstream relieving pressure, psia. This is the set pressure plus the allowable overpressure plus atmospheric pressure (14.7).
P2 = back pressure, psia.
V = required flow through the device, scfm at 14.7 psia and 60°F.
G = specific gravity of gas at standard conditions referred to air at standard conditions (normal conditions). In other words, G = 1.00 for air at 14.7 psia and 60°F.
3.6.3.3 Balanced Pressure Relief Valves
Balanced pressure relief valves should be sized using Equations 3.2 through 3.4 in paragraph 3.6.2(critical flow equations).
The back pressure correction factor in this application accounts for flow velocities that are subcritical as well as the tendency for the disc to drop below full lift (the use of subcritical flow equations are appropriate only where full lift is maintained). The back pressure correction factor, Kb, for this application should be obtained from the manufacturer.
