1. Introduction and warning

2. Critical flow or subcritical flow ?

3. Critical flow safety valve
sizing

4. Subcritical flow safety valve
sizing

5. Other calculation codes

6. Selection of standard pressure
relief valve orifice

7. Excel calculation tool

The calculation below are derived
from API520 and adapted from various sources. Those calculations are
valid for a maximum allowable working pressure higher than 101325 Pa.
Other types of services will require a different calculation code. API
for example has other standards for low pressure 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.

It is 1st necessary to determine how will be the flow in case of opening of the pressure relief valve. If the difference in between the pressure within the tank and pressure at the outlet of the valve is too important, the flow will be critical.

The critical pressure above which the flow becomes critical is calculated thanks to :

With :

P_{c} = critical pressure in kPa abs

P_{1} = upstream relieving pressure in kPa abs

P_{2} = downstream pressure in kPa abs

k = Cp/Cv

The following comparison must then be done to know if the flow will be sub-critical or critical and use the right formulae :

Critical flowP_{2} ≤ P_{c} |
Critical flow |

P_{2} > P_{c} |
Sub-critical flow |

If the flow has been found to be critical, the following formula can be used :

With :

A = required effective discharge
area of the safety valve in mm2

W = required flow through the valve in kg/h

Kd = coefficient of discharge

W = required flow through the valve in kg/h

Kd = coefficient of discharge

Kd = 0.975 for a pressure relief valve, with or
without a rupture disc upstream

Kd = 0.62 for a rupture disc

Kb = capacity correction factor
due to back pressure

Kb = 1 for conventional and pilot operated valves

Kb to be estimated from tables and charts for
balance bellow valves

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

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

Z = compressibility factor of the gas at valve inlet conditions

M = molecular weight of the gas in kg/kmol

Z = compressibility factor of the gas at valve inlet conditions

M = molecular weight of the gas in kg/kmol

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

The compressibility factor can be
calculated from the reduced pressure of the gas or vapor being
released thanks to the following diagram

If the flow has been found to be
sub-critical, the following formula can be used :

The coefficient F2 can be
calculated from the following formula :

When designing a safety valve for
steam operation, another formula is recommended :

The correction factor K_{N}
can be calculated the following way :

K_{N} = 1 if P_{1}
≤ 10339 kPa abs

K_{N} = (0.02764*P_{1}-1000)
/ (0.03324*P_{1}-1061) if 10339 ≤ P_{1} ≤ 22057 kPa
abs

Ksh = superheat steam correction
factor

Ksh = 1 for saturated steam

At other steam state, it can be calculated thanks
to a table

Note that ISO 4126 also offers
correlations for safety valves sizing

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 in^{2} |
Orifice area in cm^{2} |

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 |

Note : the tool is for now only supporting gas flow in pressure,
new release for liquid service and vacuum service will be edited
later.

WARNING

www.powderprocess.net cannot be
held responsible for the use of the explanations, calculation and
calculation tools presented here, the use of the information is at the
user and its organization own risk and cost.

Source