Sizing of Pressure Relief Valve

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.

Read More: Scenario of over-pressure in process industry

The critical-flow pressure, P_CF, 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

K_d = effective discharge coefficient = 0.975

K_c = 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:

k	C1
0.4	216.9274
0.5	238.8252
0.6	257.7858
0.7	274.5192
0.8	289.494
0.9	303.0392
1.0	315.37
1.1	326.7473
1.2	337.2362
1.3	346.9764
1.4	356.0604
1.5	364.5641
1.6	372.5513
1.7	380.0755
1.8	387.1823
1.9	393.9112
2.0	400.2962
2.1	406.3669
2.2	412.1494

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
K_d = effective discharge coefficient = 0.975
K_c = 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.

K_N can be estimated by

while

K_b = capacity correction factor due to backpressure.

     = 1.0 for conventional valve

K_N = correction factor for Napier equation

K_SH = superheat steam correction factor

         = 1.0 for saturated steam

= Use table 2 for super heated steam

Set Pressure (psig)	Temperature (F)
	300	400	500	600	700	800	900	1000	1100	1200
15	1	0.98	0.93	0.88	0.84	0.8	0.77	0.74	0.72	0.7
20	1	0.98	0.93	0.88	0.84	0.8	0.77	0.74	0.72	0.7
40	1	0.99	0.93	0.88	0.84	0.81	0.77	0.74	0.72	0.7
60	1	0.99	0.93	0.88	0.84	0.81	0.77	0.75	0.72	0.7
80	1	0.99	0.93	0.88	0.84	0.81	0.77	0.75	0.72	0.7
100	1	0.99	0.94	0.89	0.84	0.81	0.77	0.75	0.72	0.7
120	1	0.99	0.94	0.89	0.84	0.81	0.78	0.75	0.72	0.7
140	1	0.99	0.94	0.89	0.85	0.81	0.78	0.75	0.72	0.7
160	1	0.99	0.94	0.89	0.85	0.81	0.78	0.75	0.72	0.7
180	1	0.99	0.94	0.89	0.85	0.81	0.78	0.75	0.72	0.7
200	1	0.99	0.95	0.89	0.85	0.81	0.78	0.75	0.72	0.7
220	1	0.99	0.95	0.89	0.85	0.81	0.78	0.75	0.72	0.7
240	-	1	0.95	0.9	0.85	0.81	0.78	0.75	0.72	0.7
260	-	1	0.95	0.9	0.85	0.81	0.78	0.75	0.72	0.7
280	-	1	0.96	0.9	0.85	0.81	0.78	0.75	0.72	0.7
300	-	1	0.96	0.9	0.85	0.81	0.78	0.75	0.72	0.7
350	-	1	0.96	0.9	0.86	0.82	0.78	0.75	0.72	0.7
400	-	1	0.96	0.91	0.86	0.82	0.78	0.75	0.72	0.7
500	-	1	0.96	0.92	0.86	0.82	0.78	0.75	0.73	0.7
600	-	1	0.97	0.92	0.87	0.82	0.79	0.75	0.73	0.7
800	-	-	1	0.95	0.88	0.83	0.79	0.76	0.73	0.7
1000	-	-	1	0.96	0.89	0.84	0.78	0.76	0.73	0.71
1250	-	-	-	0.97	0.91	0.85	0.8	0.77	0.74	0.71
1500	-	-	-	1	0.93	0.86	0.81	0.77	0.74	0.71
1750	-	-	-	1	0.94	0.86	0.81	0.77	0.73	0.7
2000	-	-	-	1	0.95	0.86	0.8	0.76	0.72	0.69
2500	-	-	-	1	0.95	0.85	0.78	0.73	0.69	0.66
3000	-	-	-	-	1	0.82	0.74	0.69	0.65	0.62