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API vs. Pressure Relief Valve SupplierDischarge Coefficient/Orifice Area
Sizing for Liquid Relief
Turbulent Flow — Conventional and balanced bellows relief valves in liquid service may be sized by use of Equation 58.14 Pilot-operated relief valves should be used in liquid service
only when the manufacturer has approved the specific application.
(7.07) (Vl) √ G
(Kd) (Kc) (Kw) (Kv) √ (P1 – Pb)
Laminar Flow — For liquid flow with Reynolds numbers
less than 4,000, the valve should be sized first with Kv = 1 in
order to obtain a preliminary required discharge area, A. From
manufacturer standard orifice sizes, the next larger orifice size,
A´, should be used in determining the Reynolds number, Re,
from the following relationship:14
(Vl) (112 654) (G)
µ √ A´
(511 300) • (l/s)
µ √ A´
determined for the geographic area and applied to the surface
area to approximate Q (W).
When the flow rate is calculated, the necessary area for relief may be found from the turbulent liquid flow equations.
a Pressure Relief Device
for Two Phase Flow
For two phase fluids and flashing liquids, a choking phenomenon limits the flow through the pressure relief valve nozzle, in
a manner similar to the choking of a gas in critical flow. In order
to estimate the relief capacity of a nozzle, it is necessary to estimate the choking pressure and then determine the two phase
physical properties at these conditions. The historical method
of calculating areas for liquid and vapor relief separately, and
then adding the two areas together to get the total orifice size
does not produce a conservative relief device size.
Improved sizing methods have been developed using the following assumptions:
•The fluid is in thermodynamic equilibrium through the
After the Reynolds number is determined, the factor Kv is
obtained from Fig. 5-15. Divide the preliminary area (A´) by Kv
to obtain an area corrected for viscosity. If the corrected area
exceeds the standard orifice area chosen, repeat the procedure
using the next larger standard orifice.
Sizing for Thermal Relief
The following may be used to approximate relieving rates of
liquids expanded by thermal forces where no vapor is generated
at relief valve setting and maximum temperature. These calculations assume the liquid is non-compressible.13
1000 • (G) (S)
Typical values of the liquid expansion coefficient, B, at 15°C
Relative Density, G
Coefficient, B, 1/°C
3 - 34.9
1.052 - 0.850
35 - 50.9
0.850 - 0.775
51 - 63.9
0.775 - 0.724
64 - 78.9
0.724 - 0.672
79 - 88.9
0.672 - 0.642
89 - 93.9
0.642 - 0.628
94 - 100
0.628 - 0.611
For heating by atmospheric conditions, such as solar radiation, the surface area of the item or line in question should be
calculated. Solar radiation [typically 787–1040 W/m2] should be
•The overall fluid is well mixed and can be represented by
weighted averaging the gas and liquid densities (this is
sometimes referred to as the non-slip assumption).
Use of these assumptions has been found to produce a result
which in most instances is close to the real flow rate through the
nozzle, and which almost always will result in a conservative
calculation of the required nozzle area. However, these methods
require additional equilibrium data along the isentropic expansion path through the relief valve. Refer to API Std 520, Part
1, for a description of the sizing methods for two-phase liquid
vapor relief. Two methods are described in API Std. 520, Part
1, Annex C; the Omega method and the Mass FluxIsentropic
izing for Fire for Partially
Liquid Filled Systems
The method of calculating the relief rate for fire sizing may
be obtained from ISO 23251 (API Std 521), API Standard 2510,
NFPA 58, and possibly other local codes or standards. Each of
these references approach the problem in a slightly different
manner. Note that NFPA-58 applies only to U.S. marine terminals, or U.S. terminals at the end of DOT regulated pipelines.
Most systems requiring fire relief will contain liquids and/or
liquids in equilibrium with vapor. Fire relief capacity in this
situation is equal to the amount of vaporized liquid generated
from the heat energy released from the fire and absorbed by the
liquid containing vessel. The difficult part of this procedure is
the determination of heat absorbed. Several methods are available, including ISO/API, and U.S. National Fire Protection Association. ISO 23251 (API Std 521) applies to the Petroleum
and Natural Gas Industries, and is the standard most commonly used to assess fire heat load in these services.
ISO 23251/API Std 52113 expresses relief requirements in
terms of heat input from the fire to a vessel containing liquids,
where adequate drainage and fire fighting equipment exist.
= (43 200) (F) (Aw)0.82
The environment factor, F, in Equation 5-12 is determined
from Fig. 5-16. Credit for insulation can be taken only if the insulation system can withstand the fire and the impact of water
from a fire hose. Specific criteria are provided in ISO 23251/
API Std 521. The appropriate equation to use where adequate
drainage and fire fighting equipment do not exist is also provided in this Standard.
configuration, and location of the relief device. For many gas
plant applications, the assumption of single phase vapor relief
is adequate for pressure relief valve sizing. See ISO 23251 (API
Std 521) for further guidance.
Awin equation 5-12 is the total wetted surface, in square meters. Wetted surface is the surface wetted by liquid when the vessel is filled to the maximum operating level. It includes at least
that portion of a vessel within a height of 8 m above grade. In
the case of spheres and spheroids, the term applies to that portion of the vessel up to the elevation of its maximum horizontal
diameter or a height of 8 m, whichever is greater. Grade usually
refers to ground grade but may be any level at which a sizable
area of exposed flammable liquid may be present.
Sizing for Fire For Supercritical Fluids
Sometimes, the phase condition at the relieving pressure and
temperature will be supercritical. API recommends to consider
a dynamic approach where the vessel contents are assumed to
be single phase (supercritical), and a step by step heat flux is
applied to the vessel walls [See ISO 23251 (API Std 521),] and
Ouderkirk10 for details. The same methodology can also be applied for gas filled systems.
Heavy hydrocarbons can be assumed to crack (i.e., to thermally decompose), and it is the user’s responsibility to estimate
the effective or equivalent latent heat for these applications.
Traditionally, a minimum latent heat value of 116 kJ/kg has
been used if the conditions can not be quantified.
The amount of vapor generated is calculated from the latent
heat of the material at the relieving pressure of the valve. For
fire relief only, this may be calculated at 121% of maximum
allowable working pressure. All other conditions must be calculated at 110% of maximum allowable working pressure for
single relief devices.
When a vessel is subjected to fire temperatures, the resulting
metal temperature may greatly reduce the pressure rating of the
vessel, in particular for vessels in vapor service. Design for this
situation should consider an emergency depressuring system
and/or a water spray system to keep metal temperatures cooler.
For additional discussion on temperatures and flow rates due to
depressurization and fires refer to Reference 7.
Latent heat data may be obtained by performing flash calculations. Mixed hydrocarbons will boil over a temperature range
depending on the liquid composition; therefore, consideration
must be given to the condition on the batch distillation curve
which will cause the largest relief valve orifice area requirements due to the heat input of a fire. Generally the calculation
is continued until some fraction of the fluid is boiled off. Other
dynamic simulation methods are also available. The latent heat
of pure and some mixed paraffin hydrocarbon materials may be
estimated using Fig. A.1 of ISO 23251 / API Std 521.13
RELIEF VALVE INSTALLATION
Relief valve installation requires careful consideration of
inlet piping, pressure sensing lines (where used), and startup
procedures. Poor installation may render the safety relief valve
inoperable or severely restrict the valve’s relieving capacity.
Either condition compromises the safety of the facility. Many
relief valve installations have block valves before and after the
relief valve for in-service testing or removal; however, these
block valves must be sealed or locked open, and administrative
controls must be in place, to prevent inadvertent closure.
When the latent heat is determined, required relieving capacity may be found by:13
= Q / Hl
The value W is used to size the relief valve orifice using
Equation 5-1 or Equation 5-4.
For vessels containing only vapor, ISO 23251 (API Std 521)13
has recommended the following equation for determining required relief area based on fire:
183.3 (F´) (A3)
The proper design of inlet piping to safety relief valves is
extremely important. Relief valves should not be installed at
physically convenient locations unless inlet pressure losses are
given careful consideration. The ideal location is the direct connection to protected equipment to minimize inlet losses. API
STD 520, Part II recommends a maximum non-recoverable
pressure loss to a relief valve of three percent of set pressure,
except for remote sensing pilot-operated pressure relief valves.
This pressure loss shall be the total of the inlet loss, line loss,
and the block valve loss (if used). The loss should be calculated
using the maximum rated flow through the safety relief valve.
F´ can be determined using Equation 5-15.13 If the result is
less than 0.01, then use F´ = 0.01. If insufficient information is
available to use Equation 5-15, then use F´ = 0.045.
(Tw – T1)
To take credit for insulation, ISO 23251 (API Std 521) requires the insulation material to function effectively at temperatures of 900°C, and to retain its shape, and most of its integrity in covering the vessel in a fire, and during fire fighting.
Typically, this requires proper insulation, plus an insulation
jacket constructed of a suitable material, and banding that can
withstand the fire conditions. However, other systems may be
able to meet these requirements.
Discharge Piping and Backpressure
Proper discharge and relief header piping size is critical for
the functioning of a pressure relief valve. Inadequate piping can
result in reduced relief valve capacity, cause unstable operation, and/or, relief device damage.
The pressure existing at the outlet of a pressure relief valve
is defined as backpressure. Backpressure which is present at
the outlet of a pressure relief valve, when it is required to operate, is defined as superimposed backpressure. Backpressure
which develops in the discharge system, after the pressure relief valve opens, is built-up backpressure. The magnitude of
pressure which exists at the outlet of the pressure relief valve,
Sizing for Fire for Liquid
Full or Nearly Full Equipment
For totally or near totally liquid filled systems, the controlling relief condition can be single vapor phase, liquid phase, or
two phase, depending on the fluid, liquid level, vessel size and
API Pressure Relief Valve Designations
Standard Orifice Designation
1.5 × 2
1.5 × 3
25 × 50
38 × 50
38 × 75
6 × 10
8 × 10
50 × 75
75 × 100
75 × 150
100 × 150
150 × 200
150 × 250
200 × 250
Valve Body Size (Inlet Diameter times Outlet Diameter)
Values of C1 for Various Gases
Values of Coefficient C1 vs. k
*Interpolated values since C1 becomes indeterminate as k approaches 1.00
Note: Calculated from Eq. 5-3.
Back Pressure Correction Factor, Kb, for Conventional Pressure Relief Valves (Vapors and Gases)14
Courtesy American Petroleum Institute
Back-Pressure Correction Factor, Kb, for Balanced Bellows Pressure Relief Valves (Vapors and Gases)14
Note: The above curves represent a compromise of the values recommended by a number of relief valve manufacturers and may be used when the make of valve or the actual
critical-flow pressure point for the vapor or gas is unknown.
When the make is known, the manufacturer should be consulted for the correction factor.
These curves are for set pressures of 350 kPa gauge and
above. They are limited to back pressure below critical-flow
pressure for a given set pressure. For subcritical-flow back
pressures below 350 kPa gauge, the manufacturer must be
consulted for the values of Kb.
Courtesy American Petroleum Institute