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Pressure Safety Valve Basic Design guide - Liquid flow

Pressure Relief Valve sizing

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1. Introduction and warning
2. Critical flow or subcritical flow ?

5. Other calculation codes

6. Selection of standard pressure relief valve orifice

7. Excel calculation tool

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1. Introduction and warning

This design guide aims the reader at understanding the basic concepts behind the design and sizing of pressure relief valves for liquid flow but not at designing a valve for operational purposes. It is based on published sources but should not be considered for the detail design and selection / ordering of a pressure safety valve. Indeed, pressure safety valves are of utmost importance for the safety of the process, as they are most often the last resort to avoid an explosion, their design must therefore be done only by reputable companies. Only after having clearly defined the application, the position of the valve...etc... with the valve supplier, can he advise properly the plant operator and finalize the design of the valve.

The calculation below are derived from API520 and adapted from various sources. Those calculations are valid for liquid only. Other types of services will require a different calculation code. API for example has other standards for gas service or low pressure / vacuum valves. ASME or ISO have their own guidelines.

2. Safety valve sizing - liquid service

For liquid, the following formula can be used (WARNING - This formula is not valid for gases, for gases under pressure, please refer to this page) :

With :

P₁ = upstream relieving pressure in kPa g (set pressure + allowable overpressure)

P₂ = backpressure in kPa g

A = required effective discharge area of the safety valve in mm²
Q = required flow through the valve in l/min

G = specific gravity of the liquid at the flowing temperature, referred to water in standard conditions

K_d = coefficient of discharge, it can be read from manufacturer data for a given pressure safety valve, however the following values can be used for a 1st approximation :

        K_d = 0.65 for a pressure relief valve, with or without a rupture disc upstream

        K_d = 0.62 for a rupture disc

K_w = capacity correction factor due to back pressure

        K_w = 1 for atm back pressure
        K_w is not used for conventional and pilot operated valves (don't require correction)

        K_w to be estimated from tables and charts for balance bellow valves (see figure 1)

Kc = correction factor if a rupture disc is installed prior to the valve

        Kc = 1 when no rupture disc is installed prior to the valve

        Kc = 0.9 if a rupture disc is used in combination with the valve

Kv = correction factor due to viscosity

T = temperature of the gas or vapor upstream the valve at the moment it is released in K
Re = Reynolds number

μ = fluid viscosity in cP

The coefficient K_w to account for back pressure on balanced bellow safety valves can be determined thanks to the following abacus :

Figure 1 : Capacity Correction Factor, Kw, Due to Back Pressure on Balanced-Bellows

The coefficient K_v can be calculated thanks to the following formula :

3. Other calculation codes

Note that ISO 4126 also offers correlations for safety valves sizing

4. Selection of Standard Relief Valves Orifice

The sizes of discharge areas is actually standardized and manufacturers will propose sizes accordingly. The Engineer, after having calculated the required size with the calculation sequence above, needs to select a standard size offering a discharge area higher than the calculated value.

Standard letter / designation	Orifice area in in2	Orifice area in cm2
D	0.110	0.71
E	0.196	1.26
F	0.307	1.98
G	0.503	3.24
H	0.785	5.06
J	1.28	8.30
K	1.84	11.85
L	2.85	18.40
M	3.600	23.23
N	4.340	28
P	6.38	41.16
Q	11.050	71.29
R	16	103.22
T	26	167.74

5. Excel calculation tool

Note : the tool is supporting liquid flow in pressure, for gas service please refer to this page

Link to Excel calculation tool

Source

Various sources based on API 520