## Gas/Vapors Relief Valve

The flow through a pressure relief valve is dependent upon the absolute upstream pressure and is independent of the downstream pressure when the downstream pressure is less than the critical-flow pressure. However, when the downstream pressure is increased above the critical flow pressure, the flow through the relief valve is materially reduced.

The critical-flow pressure, PCF, may be estimated by:

As a rule of thumb if the downstream pressure at the relief valve is greater than one-half of the valve inlet pressure, then the relief valve nozzle will experience subcritical flow.

### Critical Flow

In the case of critical flow, the relief valve for gas or vapor may be sized by the following equation.

While

A=required effective discharge area, in2

W = Mass flow through the relief valve, lb/hr

C1 = coefficient determined from an expression of the ratio of the specific heats

k = specific heat ratio

r = ratio of back pressure to upstream pressure

Kd = effective discharge coefficient = 0.975

Kc = combination correction factor

= 1 when rapture disk is not installed

= 0.9 when a rapture disk is installed in combination with a pressure relief valve

Z = compressibility factor

T = relieving temperature, °R

MW = molecular weight of the gas/vapors

P1 = Upstream relieving pressure, psia

k is the specific heat ratio of the mixture. The C1 can be calculated using equation 4 or can be estimated using table 1:

kC1
0.4216.9274
0.5238.8252
0.6257.7858
0.7274.5192
0.8289.494
0.9303.0392
1.0315.37
1.1326.7473
1.2337.2362
1.3346.9764
1.4356.0604
1.5364.5641
1.6372.5513
1.7380.0755
1.8387.1823
1.9393.9112
2.0400.2962
2.1406.3669
2.2412.1494

K is provided by the manufacturer, however, for the initial estimation, 0.975 value can be used.

### Subcritical Flow

In the case of subcritical flow, the flow area can be calculated by equation 5

F2 can be seen from figure 1 or can be calculated from eq (6)

While
A=required effective discharge area, in2
W = Mass flow through the relief valve, lb/hr
F2 = coefficient of subcritical flow
k = specific heat ratio
r = ratio of back pressure to upstream pressure
Kd = effective discharge coefficient = 0.975
Kc = combination correction factor
= 1 when rapture disk is not installed
= 0.9 when a rapture disk is installed in combination with a pressure relief valve
Z = compressibility factor
T = relieving temperature, °R
M = molecular weight of the gas/vapors
P1 = Upstream relieving pressure, psia
P2 = back pressure

## Steam Relief Valve

Pressure relief devices in steam service that operate at critical flow conditions may be sized using Equation 7.

KN can be estimated by

while

Kb = capacity correction factor due to backpressure.

= 1.0 for conventional valve

KN = correction factor for Napier equation

KSH = superheat steam correction factor

= 1.0 for saturated steam

= Use table 2 for super heated steam

Set Pressure (psig)Temperature (F)
300400500600700800900100011001200
1510.980.930.880.840.80.770.740.720.7
2010.980.930.880.840.80.770.740.720.7
4010.990.930.880.840.810.770.740.720.7
6010.990.930.880.840.810.770.750.720.7
8010.990.930.880.840.810.770.750.720.7
10010.990.940.890.840.810.770.750.720.7
12010.990.940.890.840.810.780.750.720.7
14010.990.940.890.850.810.780.750.720.7
16010.990.940.890.850.810.780.750.720.7
18010.990.940.890.850.810.780.750.720.7
20010.990.950.890.850.810.780.750.720.7
22010.990.950.890.850.810.780.750.720.7
240-10.950.90.850.810.780.750.720.7
260-10.950.90.850.810.780.750.720.7
280-10.960.90.850.810.780.750.720.7
300-10.960.90.850.810.780.750.720.7
350-10.960.90.860.820.780.750.720.7
400-10.960.910.860.820.780.750.720.7
500-10.960.920.860.820.780.750.730.7
600-10.970.920.870.820.790.750.730.7
800--10.950.880.830.790.760.730.7
1000--10.960.890.840.780.760.730.71
1250---0.970.910.850.80.770.740.71
1500---10.930.860.810.770.740.71
1750---10.940.860.810.770.730.7
2000---10.950.860.80.760.720.69
2500---10.950.850.780.730.690.66
3000----10.820.740.690.650.62
Categories: S