# Pressure Safety Valve Basic Design guide - Liquid flow

## Pressure Relief Valve sizing

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

## 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.

Note that this page is not discussing the choice and calculation of the design scenario, which is the process events leading to the maximum flow released through the valve. The required flow must be defined thanks to a risk analysis and process calculations.

## 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) :

Equation 1 : pressure safety valve required discharge area
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
Kd = 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 :
Kd = 0.65 for a pressure relief valve, with or without a rupture disc upstream
Kd = 0.62 for a rupture disc
Kw = capacity correction factor due to back pressure
Kw = 1 for atm back pressure
Kw is not used for conventional and pilot operated valves (don't require correction)
Kw 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 Kw 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 Kv can be calculated thanks to the following formula :

Equation 2 : coefficient Kv calculation

The Reynolds number can be calculated thanks to the following equation :

Equation 3 : Reynolds number calculation

## 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