145787608 psv sizing calculations

4. Relief Valve Sizing

Topics to be CoveredGeneral Sizing Sizing Procedure API ‘KA’ vs. ASME ‘KA’

Gas / Vapor Sizing – Sonic Flow Equations, Variables, Units of Measure Gas Properties Back Pressure Rupture Disc

Gas / Vapor Sub-Sonic Flow Equations, Variables, Units of Measure Pressure & Vacuum

Topics to be CoveredSteam Sizing Equations, Variables, Units of Measure Sec. VIII vs. Sec I Sonic vs. Subsonic

Liquid Sizing Equations, Variables, Units of Measure Back Pressure

Fire Sizing API 521 – Unwetted Vessels API 521 – Wetted Vessels API 2000

Must Consider TheOne Worst Case Scenario

Blocked Discharge

External Fire

Thermal Expansion

Runaway Reaction

Tube Rupture In Heat Exchanger

Basic Sizing Procedure

Establish Set Pressure of PSV

Determine Required Relief Capacity

Select PSV Size That Will Flow At Least That Capacity At The Relieving Pressure

In 1962, the ASME Section VIII CodeWas Revised, Requiring That “K”

Be Used In Sizing Calculations(10% Safety Factor) Instead of “KD”

K = KD x 0.90

API & ASME ‘KA’ Values

The NB “Red Book” is a Bi-Annual publication of the Pressure Relief Device

Certifications by the National Board of Boiler and Pressure Vessel Inspectors.

The NB allows advertised deviations from the Red Book “K” and “A” values,

however…

Advertised KA ASME KA(per NB Red Book)

Since 1962, most PRV manufacturers

have Overstated their “K” values,

and Understated their “A” values.

API vs ASME Orifice AreasAGC JOS-E Series

API DESIGNATION API EFFECTIVE AREA (SQ IN)

ASME / NB CERT. AREA (SQ IN)

D 0.110 0.124E 0.196 0.221F 0.307 0.347G 0.503 0.567H 0.785 0.887

API vs ASME Orifice AreasAGC JOS-E Series

API DESIGNATION API EFFECTIVE AREA (SQ IN)

ASME / NB CERT. AREA (SQ IN)

J 1.287 1.453K 1.838 2.076L 2.853 3.221M 3.600 4.065N 4.340 4.900

API DESIGNATION API EFFECTIVE AREA (SQ IN)

ASME / NB CERT. AREA (SQ IN)

P 6.380 7.205Q 11.05 12.47R 16.00 18.06T 26.00 29.35

API vs ASME Orifice AreasAGC JOS-E Series

Example of Different Manufacturers KA Values“J” Orifice (API = 1.287 in2)

NATIONAL BOARD CATALOG

K KA K KA

0.859 0.953 1.287 [8.303]

0.855 0.95

0.877 0.975

A, in2 [cm2]A, in2 [cm2]

1.287 [8.303]

1.287 [8.303]

1.226 [7.910]

1.223 [7.888]

1.255 [8.095]

1.228 [7.925]

1.279 [8.252]

1.312 [8.464]

1.430 [9.226]

1.496 [9.652]

1.496 [9.652]

FARRISPOPRV

CONSOLID.DSOPRV

AGCPOPRV

API & ASME ‘KA’ ValuesAPI – Preliminary SizingASME – Models Actual Valve Performance

API – Uses API 526 Standard Orifice AreasASME – Uses NB-18 Actual Certified Orifice Areas

API – Coefficients of Discharge Gas / Vapor = 0.975 Liquid = 0.650

ASME – Coefficients of Discharge Use De-rated Value (K) for sizing Varies from Manufacturer to Manufacturer and Model Type to

Model TypeAdvertised KA ASME KA

Gas / Vapor Sizing

ENGLISH UNITS

OR

METRIC UNITS

OR

SONIC Flow - Generally When Set Pressure 15 psig [1.03 barg]

cbKKCKPMTZVA

102.17

cbKKCKPMTZVA

132.6

MKKCKPTZWA

cb1

MKKCKP

TZWAcb1

316.1

VOLUMETRIC FLOW

MASS FLOW

Formula SymbolsSYMBOL

AP1VWZCKDKKbKcTM

DESCRIPIPTIONCalculated Orifice AreaInlet Flowing Pressure [P1 = Pset + Pover – Ploss + Patm]

Volumetric Flow RateMass Flow RateCompressibility Factor (if unknown, assume Z = 1.0)

Gas Constant (if unknown, assume C = 315)

Actual Coefficient of DischargeASME Coefficient of Discharge [K=0.90 x Kd]

Back Pressure Correction FactorRupture Disc Combination Correction FactorRelieving TemperatureMolecular Weight

UnitsSYMBOL

AP1VWZCKDKKbKcTM

ENGLISHin2

psiaSCFMlb/hr

------------------

°R = °F + 460---

METRICcm2

baraNm3/hrkg/hr

------------------

K = °C + 273---

Compressibility Factor, Natural Gas, 0.60 SG

PRESSURE, psig [barg]

1.2

1.1

1.0

0.5

0.9

0.8

0.7

0.6

0 500[34]

1000[69]

1500[103]

2000[138]

2500[172]

3000[207]

3500[241]

4000[276]

4500[310]

5000[345]

MW = 17.40(0.6 sp gr)

T = ºF [ºC]500º [260] 400º [204] 300º [149]200º [93] 100º [38] 0º [-18]

Gas Constant

RATIO OF SPECIFIC HEATS, k

C

400

380

360

340

320

1.0 1.2 1.4 1.6 1.8 2.0

11

12520

kk

kkC

Typical Properties of Gases

ACETYLENE 26 343 1.26AIR 29 356 1.40AMMONIA 17 348 1.31ARGON 40 378 1.67BENZENE 78 329 1.12BUTADIENE 54 329 1.12CARBON DIOXIDE 44 345 1.28CARBON MONOXIDE 28 356 1.40ETHANE 30 336 1.19ETHYLENE 28 341 1.24FREON 22 86 335 1.18HELIUM 4 377 1.66HEXANE 86 322 1.06

GasMolecularWeight

“C”Factor

“k”, Ratio OfSpecific Heats

Typical Properties of Gases (cont’d)

HYDROGEN 2 357 1.41HYDROGEN SULFIDE 34 349 1.32METHANE 16 348 1.31METHYL MERCAPTON 48 337 1.20N-BUTANE 58 326 1.09NATURAL GAS (SG=0.60) 18.9 344 1.27NITROGEN 28 356 1.40OXYGEN 32 356 1.40PENTANE 72 323 1.07PROPANE 44 330 1.13PROPYLENE 42 332 1.15STEAM 18 348 1.31SULPHUR DIOXIDE 64 346 1.29VCM 62 335 1.18

Gas Molecular Weight

“C”Factor

“k”, Ratio OfSpecific Heats

Back PressureCorrection Factor1.001.00

0.900.90

0.800.80

0.700.70

0.600.60

0.000.00

00 1010 2020 3030 4040 5050% Built-Up Back Pressure (gauge)% Built-Up Back Pressure (gauge)

At 110% ofSet PressureAt 110% of

Set Pressure

~

Unbalanced Conventional Direct Spring PRVUnbalanced Conventional Direct Spring PRV

Back PressureCorrection Factor

Balanced Bellows Direct Spring PRVBalanced Bellows Direct Spring PRV1.001.00

0.900.90

0.800.80

0.700.70

0.600.60

0.500.5000 1010 2020 3030 4040 5050

% Back Pressure (gauge)% Back Pressure (gauge)

At 110% ofSet PressureAt 110% of

Set Pressure

Effect of Back Pressure on Liftof Pressure Relief Valve Types

100

90

80

70

60

500 10 20 30 40 50 90 100

% R

ated

Lift

ConventionalSpring Operated

PRV

Pilot Operated PRV(Standard)

Balanced BellowsSpring Operated PRV

% Back Pressure (gauge)% Back Pressure (gauge)

A Perfect Nozzle (KD = 1.0)100

% Back Pressure

% R

ated

Cap

acity 80

60

40

20

0

0 20 40 60 80 100

k=1.3

53%

P1 P2

Back Pressure Correction FactorAGC Piston POPRV (Gases)

Kb

= Absolute Pressure Ratio

0.0

k = 1.0k = 1.2k = 1.4

k = 1.6k = 1.8

k = 2.0

0.0 0. 2 0.4 0.6 1.00.8

1.0

0.8

0.6

0. 4

0.2

P2

P1

PSV With Rupture DiscAt Inlet

Do PSV Calculation, thenApply “Combination Factor” for thatModel PSV & Model/Material of RD*As Established by the NB Testing.

*Listed in back of NB “Red Book”

ORDe-rate PSV Capacity by 10%.

PRV With Rupture DiscAt Outlet

No PSV De-Rating Necessary

Gas / Vapor Sizing

ENGLISH UNITS

OR

METRIC UNITS

OR

SUBSONIC Flow - Generally When Set Pressure < 15 psig [1.03 barg]

112510 PFKMTZVA

D

14645 PFK

MTZVAD

MPFKTZWA

D 1735

MPFKTZWA

D 1558

VOLUMETRIC FLOW

MASS FLOW

Formula SymbolsSYMBOL

AP1VWZ

KDMTF

DESCRIPIPTIONCalculated Orifice AreaInlet Flowing Pressure [P1 = Pset + Pover – Ploss + Patm]

Volumetric Flow RateMass Flow RateCompressibility Factor (if unknown, assume Z = 1.0)

Actual Coefficient of DischargeMolecular WeightRelieving TemperatureSubsonic Flow Factor

UnitsSYMBOL

AP1VWZ

KDMTF

ENGLISHin2

psiaSCFMlb/hr

---------

°R = °F + 460---

METRICcm2

baraNm3/hrkg/hr

---------

K = °C + 273---

Subsonic Flow Factor

k

kk

PP

PP

kkF

1

1

2

2

1

2

1

For Pressure:P1 = Inlet Flowing Pressure [P1 = Pset + Pover – Ploss + Patm]

P2 = Pressure at Valve Outlet [P2 = Pback + Patm]

For Vacuum:P1 = Atmospheric Pressure [P1 = Patm]

P2 = Pressure at Valve Outlet [P2 = Pvacuum set + Punder + Patm]

k = ratio of specific heatsWHERE:

“F”Factor

0.55

0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

1.00 0.90 0.80 0.70 0.60 0.50 0.40

k = 1.90k = 1.40

k = 1.00

F

= Absolute Pressure RatioP2

P1

AGC Series90 & 9000

Steam Sizing

ENGLISH UNITS

METRIC UNITS

SONIC Flow - Generally When Set Pressure 15 psig [1.03 barg]

15.51 PKKKKWA

bPS

15.52 PKKKKWA

bPS

Formula SymbolsSYMBOL

AP1WKKSKPKb

DESCRIPIPTIONCalculated Orifice AreaInlet Flowing Pressure [P1 = Pset + Pover – Ploss + Patm]

Mass Flow RateASME Coefficient of DischargeSuperheat Correction FactorHigh Pressure Correction Factor (over 1600 psig)

Back Pressure Correction Factor

UnitsSYMBOL

AP1WKKSKPKb

ENGLISHin2

psialb/hr

------------

METRICcm2

barakg/hr

------------

KS – Superheat Correction FactorSet

Pres.psig1520406080

100120140160180200220240260280300350400450500

Sat.Steam

oF250259287308324338350361371380388395403409416422436448460470

Total Steam Temperature, oF2801.001.00

3001.001.001.00

3201.001.001.001.00

3400.990.991.001.001.001.00

3600.990.990.990.991.001.00

3800.980.980.990.990.991.001.001.001.00

4000.980.980.980.980.990.990.991.001.001.001.001.00

4200.970.970.970.970.980.980.980.990.990.990.991.001.001.001.00

4400.960.960.960.960.970.970.970.980.980.980.990.990.990.991.001.001.00

4600.950.950.950.950.960.960.960.960.970.970.970.980.980.980.990.991.001.00

4800.940.940.940.940.940.950.950.950.950.960.960.960.970.970.970.980.990.991.001.00

5200.930.930.930.930.930.940.940.940.940.940.940.950.950.960.960.960.970.970.980.99

[ENGLISH]

5000.930.930.930.930.930.940.940.940.940.950.950.950.950.960.960.960.970.980.990.99

KS – Superheat Correction FactorSET

PRES.barg1.031.382.764.145.526.908.279.6511.012.413.815.216.617.919.320.724.127.631.034.5

SAT.STEAM

oC121126142153162170177183188193198202206210213217225231238243

TOTAL STEAM TEMPERATURE, oC1381.001.00

1491.001.001.00

1601.001.001.001.00

1710.990.991.001.001.001.00

1820.990.990.990.991.001.00

1930.980.980.990.990.991.001.001.001.00

2050.980.980.980.980.990.990.991.001.001.001.001.00

2160.970.970.970.970.980.980.980.990.990.990.991.001.001.001.00

2270.960.960.960.960.970.970.970.980.980.980.990.990.990.991.001.001.00

2380.950.950.950.950.960.960.960.960.970.970.970.980.980.980.990.991.001.00

2490.940.940.940.940.940.950.950.950.950.960.960.960.970.970.970.980.990.991.001.00

2600.930.930.930.930.930.940.940.940.940.950.950.950.950.960.960.960.970.980.990.99

2710.930.930.930.930.930.940.940.940.940.940.940.950.950.960.960.960.970.970.980.99

[METRIC]

KP - High Pressure Correction Factor

Pressure, psig [barg]

1.25

1.15

1.05

0.951500

[103.4]1900

[131.0]2300

[158.6]2700

[186.2]3100

[213.8]3500

[241.3]

KP

0.1906P - 10000.2292P - 1061

KP =

Steam Sizing Notes

Sec. VIII – Use 10% over pressureSec. I – Use 3% over pressure

Sonic Flow – Use Steam EquationsSub-Sonic Flow – Use Gas/Vapor Equations

Liquid Sizing

ENGLISH UNITS

METRIC UNITS

BAVW

L

PPKKKGVA

38

BAVW

L

PPKKKGVA

094.5

Formula SymbolsSYMBOL

APAPBVLGK

KWKV

DESCRIPIPTIONCalculated Orifice AreaInlet Flowing Pressure [P1 = Pset + Pover – Ploss]

Outlet Flowing Pressure [P2 = Pback]

Required CapacitySpecific GravityASME Coefficient of Discharge [K=0.90 x Kd]

Back Pressure Correction FactorViscosity Correction Factor

NOTE: Temperature is not required to calculate orifice area.

UnitsSYMBOL

APAPBVLGK

KWKV

ENGLISHin2

psigpsiggpm------------

METRICcm2

bargbargm3/hr

------------

Liquid Thermal Expansion Relief

GCBHVL 500

VL=B =H =G =C =

Liquid Flow Rate, gpmCubicle Expansion Coefficient per °FTotal Heat Transfer Rate, BTU/hrSpecific GravitySpecific Heat, BTU/lb°F

Per API 521, Section 3.14

Fire SizingThe Procedure Used In Fire Sizing Depends On The CodesAnd Engineering Practices Applied At Each Installation.Some Procedures That May Be Used For Fire Sizing:

The Procedure Used In Fire Sizing Depends On The CodesAnd Engineering Practices Applied At Each Installation.Some Procedures That May Be Used For Fire Sizing:

Recommended Practices For The DesignAnd Installation Of Pressure RelievingSystems In Refineries. (SET 15 psig [1.03 barg])

Venting Atmospheric And Low PressureStorage Tanks (SET < 15 psig [1.03 barg])

Design Of Lp Gas Installations

Storage And Handling Liquefied PetroleumGasses (National Fire Protection Association)

Stationary Storage Tanks

Recommended Practices For The DesignAnd Installation Of Pressure RelievingSystems In Refineries. (SET 15 psig [1.03 barg])

Venting Atmospheric And Low PressureStorage Tanks (SET < 15 psig [1.03 barg])

Design Of Lp Gas Installations

Storage And Handling Liquefied PetroleumGasses (National Fire Protection Association)

Stationary Storage Tanks

API RP 521

API 2000

API 2510

NFPA 58

CGA S-1.3

API RP 521

API 2000

API 2510

NFPA 58

CGA S-1.3

API 521 (Fire) – Unwetted Vessels

1

'PAFA S

A =F’ =

AS =P1 =

Calculated PSV Orifice Area, in2

Relates to Bare Vessel MetalTemperature at Relief (if unknown, F’=0.042)

Exposed Surface Area of Vessel, ft2

Relieving pressure, psia [P1 = Pset + Pover – Ploss + Patm]

Per API 521, Section 3.15

API 521 (Fire) – Unwetted VesselsF’ Operating Factor

ºF G

asºF

Gas

700

600

500

400

300

200

100

00.005 0.015 0.025 0.035 0.045 0.055

k = 1.001

k = 1.4

Operating Factor, F

Conservative

6506.0

1

25.111406.0'

CKTTTF wall

Minimum

Twall, °RT1, °R

API 521 (Fire) – Wetted Vessels

82.0000,21 wetAFQ

Q =F =

Awet =

Total Heat Input to Wetted Surface, BTU/hrEnvironmental Factor Total Wetted Surface Area, ft2

Per API 521, Section 3.15

82.0500,34 wetAFQ

Prompt Fire-Fighting Efforts & Adequate Drainage

Exists

Prompt Fire-Fighting Efforts & Adequate Drainage

Does Not Exists

Step 1

VerticalVessel

HorizontalVessel

Sphere

Max.Dia.

25 ft.

Ground

API 521 (Fire) – Wetted VesselsTotal Vessel Wetted Surface Area, ft2, Up to 25 ft. Above

Ground Level or, (in the Case of a Sphere) to theElevation of Largest Diameter - Whichever Is Greater.

API 521 (Fire) – Wetted VesselsVESSEL FBare (Un-Insulated) 1.0

InsulatedConductance Value: 4 btu/hr/ft2/°F 0.3

2 0.151 0.075

Earth Covered, Above Grade 0.03

Bare With Water Spray 1.0

Underground 0.0

VESSEL FBare (Un-Insulated) 1.0

InsulatedConductance Value: 4 btu/hr/ft2/°F 0.3

2 0.151 0.075

Earth Covered, Above Grade 0.03

Bare With Water Spray 1.0

Underground 0.0

API 521 (Fire) – Wetted Vessels

vapHQW

W =Q =

Hvap =

Required Valve Capacity, lb/hrTotal Heat Input to Wetted Surface, BTU/hrLatent Heat of Vaporization, BTU/lbEXAMPLES: AMMONIA 589

BENZENE 169BUTANE 166CO2 150ETHANE 210ETHYLENE 208 METHANE 219PROPANE 183WATER 970

EXAMPLES: AMMONIA 589BENZENE 169BUTANE 166CO2 150ETHANE 210ETHYLENE 208 METHANE 219PROPANE 183WATER 970

Step 2

API 521 (Fire) – Wetted Vessels

MKKCKPTZWA

cb1

MKKCKP

TZWAcb1

316.1

ENGLISH METRIC

Use Vapor Equations to Calculate Required Orifice Area.Use the Boiling Temperature of the Liquid (Flash to Vapor) for “T”.

Use Relieving Temperature for orifice sizing.Use Operating Temperature for soft good selection.

If unknown, we suggest using 200°F [93°C]

Step 3

API 2000 (Fire)

82.01107FAV

V =F =A =

Venting Requirement, ft3/hr, air (60°F)Environmental Factor (if unknown, F=1.0) Exposed Surface Area of Vessel, ft2

Set Pressure < 15 psig [1.03 barg]

API 2000 (Fire) - Surface Area 2800 ft2

A, ft2

2030405060708090100120140160180200250300

SCFMAIR

352527702878105312281403158017802100245028003167351729834417

A, ft2

35040050060070080090010001200140016001800200024002800

over 2800

SCFMAIR

4800520059006533713377008217873392839783

10,23310,65011,03311,73312,367

use formula

Using the calculated, required,relief valve capacity and setpressure, use air capacity tables(10% overpressure) in catalogsto select orifice area and valve size. For set pressures 15 psig and below, be sure to use the actual KD

Reference: API 2000, Sections 1.5.2 and 2.3

ASME “K”0.90

KD =