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API vs. Pressure Relief Valve SupplierDischarge Coefficient/Orifice Area

# API vs. Pressure Relief Valve SupplierDischarge Coefficient/Orifice Area

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­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.

A =

(7.07) (Vl) √ G

(Kd) (Kc) (Kw) (Kv) √ (P1 – Pb)

Eq 5-8

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)

Re =

Eq 5-9

µ √ A´

(511 300) • (l/s)

Re =

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.

­­

Sizing

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

nozzle.

Eq 5-10

S

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

(B) (Q)

Vl =

1000 • (G) (S)

Eq 5-11

Typical values of the liquid expansion coefficient, B, at 15°C

are:

API ­

Gravity

Relative Density, G

Liquid Expansion

Coefficient, B, 1/°C

Water

1.000

0.00018

3 - 34.9

1.052 - 0.850

0.00072

35 - 50.9

0.850 - 0.775

0.0009

51 - 63.9

0.775 - 0.724

0.00108

64 - 78.9

0.724 - 0.672

0.00126

79 - 88.9

0.672 - 0.642

0.00144

89 - 93.9

0.642 - 0.628

0.00153

94 - 100

0.628 - 0.611

0.00162

n-Butane

0.584

0.0020

Isobutane

0.563

0.0022

Propane

0.507

0.0029

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

Expansion Method.14

­ izing for Fire for Partially ­

S

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.

Q

= (43 200) (F) (Aw)0.82

Eq 5-12

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

5-12

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

W

= Q / Hl

Eq 5-13

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)

A =

√ P1

­Inlet Piping

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.

Eq 5-14

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.

0.1406

= 

 (C1) (Kd)

  (Tw – T1)

  T10.6506

1.25

Eq 5-15

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

5-13

FIG. 5-7

API Pressure Relief Valve Designations

Standard Orifice Designation

Orifice

Area

cm2

Orifice

Area

(in.2)

D

0.710

0.110

E

1.265

0.196

F

1.981

0.307

G

3.245

0.503

H

5.065

0.785

J

8.303

1.287

K

11.858

1.838

L

18.406

2.853

M

23.226

3.60

N

28.000

4.34

P

41.161

6.38

Q

71.290

11.05

R

103.226

16.0

T

167.742

26.0

in.

1ì2

1.5 × 2

1.5 × 3

mm

25 × 50

38 × 50

38 × 75

2×3

3×4

3×6

4×6

6×8

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)

FIG. 5-9

Values of C1 for Various Gases

FIG. 5-8

Acetylene

Air

Ammonia

Argon

Benzene

Carbon disulfide

Carbon dioxide

Carbon monoxide

Chlorine

Cyclohexane

Ethane

Ethylene

Helium

Hexane

Hydrochloric acid

Hydrogen

Hydrogen sulfide

Iso-butane

Methane

Methyl alcohol

Methyl chloride

N-butane

Natural gas

Nitrogen

Oxygen

Pentane

Propane

Sulfur dioxide

Values of Coefficient C1 vs. k

k

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

C1

216.9274

238.8252

257.7858

274.5192

289.494

303.0392

315.37*

326.7473

337.2362

346.9764

356.0604

364.5641

372.5513

380.0755

387.1823

393.9112

400.2962

406.3669

412.1494

*Interpolated values since C1 becomes indeterminate as k approaches 1.00

Note: Calculated from Eq. 5-3.

5-14

Mol mass

26

29

17

40

78

76

44

28

71

84

30

28

4

86

36.5

2

34

58

16

32

50.5

58

19

28

32

72

44

64

k

1.28

1.40

1.33

1.66

1.10

1.21

1.28

1.40

1.36

1.08

1.22

1.20

1.66

1.08

1.40

1.40

1.32

1.11

1.30

1.20

1.20

1.11

1.27

1.40

1.40

1.09

1.14

1.26

C1

345

356

351

377

327

338

345

356

352

324

339

337

377

324

356

356

348

328

346

337

337

328

345

356

356

325

331

342

FIG. 5-10

Back Pressure Correction Factor, Kb, for Conventional Pressure Relief Valves (Vapors and Gases)14

Courtesy American Petroleum Institute

FIG. 5-11

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

5-15

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