Pressure Relief Valve Sizing Calculations – Critical Gas Flow Service

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Sample Problem Statement

Design a pressure relief valve for the following service.

Protected equipment : Separator vessel
Relief service : Fuel Gas
Reason for relief : Blocked gas discharge
Relieving Rate : 10,000 kg/hr
Gas Density : 4.1 kg/m3
Ratio of specific heats for the gas (CP/CV) : 1.35
Compressibility factor of gas = 0.95
Relieving temperature = 200C
Set pressure : 5 barg
Accumulation : 10%
Back pressure at relief valve discharge : 0.5 barg
Type of relief valve : Conventional

Solution

This sample problem for relief valve sizing calculation can be solved in following steps, which are based on pressure relief valve sizing procedures described in API RP 520 Part I. The first step is to determine whether the gas flow type is critical or sub-critical.

Step1

The first step is to determine if the flow conditions are critical. For this purpose the critical flow pressure (Pcf) downstream to the relief valve has to be calculated using the following equation from API RP 520 Part I,

P1 : Relieving pressure upstream to relief valve in bara
P1 = 6.51 bara (including 10% accumulation)

k : Ratio of specific heats of the gas .. (CP/CV)
k = 1.35

Pcf : Critical flow pressure for the given flow conditions in bara
Pcf = 3.5 bara

If the pressure downstream or back pressure of the relief valve is lower than the critical flow pressure, then the flow is said to be of critical type. In this case, the actual pressure downstream to the relief valve cannot fall below the critical flow pressure even if much lower pressure exists further downstream to the valve. Mass flow relieved cannot increase any further, for the given set of flow conditions upstream to the valve.

In the present case, back pressure (1.5 bara) < Pcf (3.5 bara). Hence the flow is of critical type.

Step2

Next step is to use the relief valve sizing procedure given in the API 520 part I for critical flow type gas relief valve. The following equation is used,

… (1)

A : orifice are requirement in mm2

W : flowrate in kg/hr
W = 10,000 kg/hr

T : Temperature in Kelvin
T = 273.16 + 20 = 293.26 K

Z : compressibility factor of gas
Z = 0.95

C : coefficient for fire case as a function of k (CP/CV) as per following equation,

Here, C = 351.6

P1 : Relieving pressure upstream to relief valve in bara
P1 = 6.51 bara (including 10% accumulation)

Kd : Coefficient of discharge
Kd = 0.975 for gas service

Kb : capacity correction factor due to back pressure
Kb = 1 (for conventional relief valves with near atmospheric backpressure)

KC : combination correction factor for use of rupture discs
KC = 1 (for absence of rupture disc upstream to the valve)

Plugging this data into equation (1), the minimum required orifice area for the relief valve is calculated to be,
A = 22.0 cm2

Step3

The next higher available orifice area should be selected for the pressure relief valve to be actually installed. Referring to the table of standard orifice sizes given in EnggCyclopedia’s relief valve sizing calculator,

Next high available orifice area is selected to be A = 23.20 cm2 and the corresponding designating letter is ‘M’. Available valve size is ‘4M6′, which correspond to different nozzle sizes for suction and discharge nozzles of the pressure relief valve. For a ‘4M6′ valve suction nozzle is of 4″ size and discharge nozzle of 6″ size.

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