Pressure Relief Valve Sizing Calculations – Blocked Liquid Discharge

Sample Problem Statement

Design a  pressure relief valve for the following service.

Protected equipment : Separator vessel
Relief service : Water
Reason for relief : Blocked liquid discharge
Relieving Rate : 100,000 kg/hr
Water Density : 1000 kg/m³
Water Viscosity : 0.8 cP
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.

Step1

As per API RP 520 Part I, the required orifice area for relief valve discharge is calculated using the following equation,

... (1)

A : orifice are requirement in mm²

Q : flowrate in lit/min
Q = 100000×1000/(1000×60) = 1666.67 lit/min

G : Specific gravity of the liquid = 1 (for water)

P₁ : upstream pressure in kPag
P₁ = 500 kPag

P₂ : downstream pressure in kPag
P₂ = 50 kPag

K_d : Coefficient of discharge
K_d = 0.65 for liquid service

K_W : correction factor
K_W = 1 (for conventional relief valves with near atmospheric backpressure)

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

K_ν : correction factor due to viscosity
K_ν = 1 (calculated using following equations from API 520 Part I)

and

Plugging this data into equation (1), the minimum required orifice area for the relief valve is calculated to be,
A = 14.17 cm²

Step2

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 = 18.49 cm² and the corresponding designating letter is 'L'. Available valve sizes are '3L4' and '4L6', which correspond to different nozzle sizes for suction and discharge nozzles of the pressure relief valves. For a '3L4' valve suction nozzle is of 3" size and discharge nozzle of 4" size. Similarly for a '4L6' valve suction nozzle is 4" and discharge is of 6" size.