1

Sizing OfPressure Relief Valves

2

Must Consider The Must Consider The One Worst Case ScenarioOne Worst Case Scenario

Blocked DischargeBlocked Discharge

External FireExternal Fire

Thermal ExpansionThermal Expansion

Runaway ReactionRunaway Reaction

Tube Rupture In Heat ExchangerTube Rupture In Heat Exchanger

3

Basic Sizing ProcedureBasic Sizing Procedure

Establish Set Pressure Of PRVEstablish Set Pressure Of PRV

Determine Required Relief CapacityDetermine Required Relief Capacity

Select PRV Size That Will Flow At LeastSelect PRV Size That Will Flow At Least That CapacityThat Capacity

4

Orifice AreaOrifice Area

AAN N = AREA OF D= AREA OF DN N

(NOZZLE DIAMETER),(NOZZLE DIAMETER),OROR

AACC = CIRCUM. OF D = CIRCUM. OF DNN X X LIFT, [“CURTAIN LIFT, [“CURTAIN

AREA”] AREA”] WHICHEVER WHICHEVER IS IS SMALLERSMALLERLIFTLIFT

DDNN

5

Gas/Vapor SizingGas/Vapor Sizing

A =A =35,250 V TZM35,250 V TZMCKCKddPP1 1 KKbbKKcc

A =A =V TZMV TZM6.32 CK6.32 CKddPP1 1 KKb b KKcc

W TZW TZ

CKCKddPP1 1 KKbbKKcc M MA =A =

OROR

ENGLISH UNITSENGLISH UNITS METRIC UNITSMETRIC UNITS

OROR

13,160 W TZ13,160 W TZ

CKCKddPP1 1 KKbbKKcc M MA =A =

Sonic Flow - Generally When Set Pressure Sonic Flow - Generally When Set Pressure >> 15 psig [1.03 barg] 15 psig [1.03 barg]==

Per API 520, Section 3.6.2.1Per API 520, Section 3.6.2.1

6

Formula SymbolsFormula SymbolsAA Calculated Orifice AreaCalculated Orifice AreaPP11 Inlet Flowing Pressure Inlet Flowing Pressure [P[P11= P= Pset set + P+ Pover over + P+ Patmatm]]VV Volumetric Flow RateVolumetric Flow RateWW Mass Flow RateMass Flow RateZZ Compressibility Factor Compressibility Factor (if unknown, assume Z=1)(if unknown, assume Z=1)CC Gas Constant Gas Constant (if unknown, assume C=315)(if unknown, assume C=315)KKdd Coefficient Of DischargeCoefficient Of DischargeKKcc Combination Correction for installation with Combination Correction for installation with rupture discrupture disc [Kc = 0.90 with rupture disc , Kc = 1 w/o [Kc = 0.90 with rupture disc , Kc = 1 w/o rupture disc]rupture disc]KKbb Back Pressure FactorBack Pressure FactorTT Relieving TemperatureRelieving TemperatureMM Molecular WeightMolecular Weight

7

UnitsUnits

AA inin22 mmmm22

PP11 psiapsia kPaakPaaVV SCFMSCFM NmNm33/min/minWW lb/hrlb/hr kg/hrkg/hrZZ …… ……CC …… ……KKDD …… ……KK …… ……TT °R = °F + 460°R = °F + 460 °K = °C + 273°K = °C + 273MM …… ……

ENGLISHENGLISH METRICMETRIC

8

Compressibility Factor, Natural Gas, Compressibility Factor, Natural Gas, 0.60 S.G.0.60 S.G.

(Example)(Example)

PRESSURE, psig [barg]PRESSURE, psig [barg]

1.21.2

1.11.1

1.01.0

0.50.5

0.90.9

0.80.8

0.70.7

0.60.6

00 500500[34][34]

10001000[69][69]

15001500[103][103]

20002000[138][138]

25002500[172][172]

30003000[207][207]

35003500[241][241]

40004000[276][276]

45004500[310][310]

50005000[345][345]

ZZ

MW = 17.40MW = 17.40(0.6 sp gr)(0.6 sp gr)

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

9

( )( )C = 520C = 520kk

k + 1k + 1k - 1k - 122

k + 1k + 1

RATIO OF SPECIFIC HEATS, k = RATIO OF SPECIFIC HEATS, k = CCPP

CCVV

CC

400400

380380

360360

340340

320320

1.01.0 1.21.2 1.41.4 1.61.6 1.81.8 2.02.0

10

Typical Properties of GasesTypical Properties of Gases

ACETYLENEACETYLENE 2626 343 343 1.261.26AIRAIR 2929 356 356 1.401.40AMMONIAAMMONIA 1717 348 348 1.311.31…………………….... …… … … ………………………….... …… … … ……N-BUTANEN-BUTANE 5858 326326 1.09 1.09NATURAL GAS (0.60)NATURAL GAS (0.60) 18.918.9 344344 1.27 1.27NITROGENNITROGEN 2828 356356 1.401.40OXYGENOXYGEN 3232 356356 1.40 1.40PENTANEPENTANE 7272 323323 1.07 1.07PROPANEPROPANE 4444 330330 1.131.13PROPYLENEPROPYLENE 4242 332332 1.15 1.15STEAMSTEAM 1818 348348 1.311.31

GasGas MolecularMolecular

WeightWeight “ “C”C”

FactorFactor “ “k”, Ratio Ofk”, Ratio Of Specific HeatsSpecific Heats

If Gas/Vapor Is Unknown, Use: C = 315If Gas/Vapor Is Unknown, Use: C = 315

11

100100

9090

8080

7070

6060

505000 1010 2020 3030 4040 5050 9090 100100

KK bb

% R

ated

%

Rat

ed

Lift

Lift

ConventionalSpring OperatedPRV

Pilot Operated PRV

Balanced Bellows Spring Operated PRV

Effect Of Back Pressure On LiftThe manufacturer should be consulted for applicable correction factor

12

API 520 Effective Nozzle API 520 Effective Nozzle Coefficient of DischargeCoefficient of Discharge

Use 0.975 for Gas Service (KUse 0.975 for Gas Service (Kdd =0.975) =0.975)

Use API 526 Standard for Orifice SizeUse API 526 Standard for Orifice Size

API Considers This API Considers This PRELIMINARYPRELIMINARY Sizing Sizing

13

In 1962 The ASME Section VIII Code Was Revised, Requiring

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

“Kd”

K = Kd x 0.90

14Page

FOR SONIC GAS FLOWFOR SONIC GAS FLOW

The NB Allows Published Deviations From “K” And “A” The NB Allows Published Deviations From “K” And “A” Values In The “Red Book”. However - -Values In The “Red Book”. However - -

Advertised KA Advertised KA ASME KA (Per NB “Red Book”) ASME KA (Per NB “Red Book”)

[The NB “Red Book” is “Pressure Relief Device Certifications” Published [The NB “Red Book” is “Pressure Relief Device Certifications” Published Bi-Annually By The National Board of Boiler and Pressure Vessel Inspectors.]Bi-Annually By The National Board of Boiler and Pressure Vessel Inspectors.]

==

W = CKAPW = CKAP MMTZTZ

15Page

Since 1962, Most PRV Manufacturers

Have Overstated Their “K” Values

And Understated Their “A” Values.

16Page

API vs ASME Orifice AreasAPI vs ASME Orifice AreasAGC JOS-E SeriesAGC JOS-E Series

DD

API [inAPI [in22 ] ]

0.110

0.196

0.307

0.503

ASME / NB ASME / NB cert. [incert. [in22 ] ]

API API DesignationDesignation

0.124

0.221

0.347

0.567

API API DesignationDesignation

API [inAPI [in22 ] ] ASME / NB ASME / NB cert. [incert. [in22 ] ]

EE

FF

GG

HH

JJ

KK

LL

MM

0.785 0.887

1.287

1.838

2.853

3.600

1.453

2.076

3.221

4.065

NN 4.340 4.900

17Page

Example: Gas ServiceExample: Gas Service““J” ORIFICE (API = 1.287 inJ” ORIFICE (API = 1.287 in22))

[8.303 cm[8.303 cm22]]NATIONAL BOARDNATIONAL BOARD CATALOGCATALOG

KK KAKA KK KAKA

0.859 0.953 1.287 [8.303]

0.855 0.95

0.877 0.975

A, inA, in22 [cm [cm22]]A, inA, in22 [cm [cm22]]

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

AG/CPOPRV

(MARK II)

18Page

Sizing InformationSizing Information

When selecting orifice areas and nozzle coefficients, When selecting orifice areas and nozzle coefficients, either select the ASME area and nozzle coefficient, or either select the ASME area and nozzle coefficient, or the equivalent API area and nozzle coefficient.the equivalent API area and nozzle coefficient.

Mixing ASME and API values is incorrect and may Mixing ASME and API values is incorrect and may result in a dangerous sizing error.result in a dangerous sizing error.

19

PRV With Rupture Disc At Its Inlet

Do PRV Calculation,Then

Apply The “Combination Factor” For That Model

PRV And That Model And Material Of RD* As

Established By National Board Testing.

De-rate PRV Capacity By 10%.Or

* (As Listed In Back Of The National Board “Red Book”)

20

Subsonic Flow for Gas/VaporP1 < 15 psig (1.03 barg) - Non ASME Coded

Valve

A =A = V ZTMV ZTM4645 FK4645 FKddKKc c PP1 1 (P(P11- - PP22))

A =A = W ZTW ZT

735 FK735 FKDDKKc c MP MP11(P(P11-P-P22) )

OROR

A =A = 47.95 V ZTM47.95 V ZTM FKFKDDKKcc P P11(P(P11-P-P22))

A =A =17.9 W ZT17.9 W ZT

FKFKDD K Kcc MP MP11(P(P11-P-P22))

OROR

ENGLISH UNITS METRIC UNITS

21

F = Subsonic flow factor

F =F =( )( ) [[(( )) - - (( )) ]]kkk-1k-1

PP22

PP11

22

kk

k+1k+1

kk

PP22

PP11

Where :Where :K = Ratio of Specific HeatsK = Ratio of Specific HeatsPP11 = Inlet Flowing Pressure [P = Inlet Flowing Pressure [P11 = P = Pset set + P+ Poverover – P – Ploss loss + + PPatm atm ]]PP22 = Pressure at Valve outlet [P = Pressure at Valve outlet [P22 = P = Pbackback + P + Patmatm ] ]

Subsonic Flow for Gas/Vapor

22

“F” FactorAG/C

Series 90 And 9000

0.550.55

0.500.50

0.450.45

0.400.40

0.350.35

0.300.30

0.250.25

0.200.20

0.150.15

0.100.101.001.00 0.900.90 0.800.80 0.700.70 0.600.60 0.500.50 0.400.40

k = 1.90k = 1.90k = 1.40k = 1.40

k = 1.00k = 1.00

= Absolute Pressure Ratio = Absolute Pressure Ratio PP22

PP11

FF

23

ENGLISH UNITS METRIC UNITS [ ]

Sonic Flow - Steam

Orifice Area, inOrifice Area, in22 [mm [mm22]] Flow Rate lbs/hr [kg/hr]Flow Rate lbs/hr [kg/hr] Coefficient Discharge Coefficient Discharge Superheat Correction FactorSuperheat Correction Factor High Pressure Correction FactorHigh Pressure Correction Factor (over 1600 psig [110 barg])(over 1600 psig [110 barg]) Back Pressure FactorBack Pressure Factor Rupture Disc Combination Correction Rupture Disc Combination Correction Set + Overpressure + Atmospheric P, psia [kPaa]Set + Overpressure + Atmospheric P, psia [kPaa]

AAWWKKdd

KKSHSH

KKNN

KKbb

KKcc

PP11

== == == == ==

==

== ==

A =A = WW51.5 P51.5 P11KKdd K KSHSH K KNN K Kbb K Kcc

A =A = 190.4 W190.4 WPP11KKdd K KSHSH K KNN K Kbb K Kcc

Per API 520 Section 3.7.1

24

KKSHSH Superheat Correction Factor Superheat Correction FactorSetSet

Pres.Pres.psigpsig15152020404060608080100100120120140140160160180180200200220220240240260260280280300300350350400400450450500500

Sat.Sat.SteamSteam

ooFF250250259259287287308308324324338338350350361361371371380380388388395395403403409409416416422422436436448448460460470470

Total Steam Temperature, Total Steam Temperature, ooFF2802801.001.001.001.00

3003001.001.001.001.001.001.00

3203201.001.001.001.001.001.001.001.00

3403400.990.990.990.991.001.001.001.001.001.001.001.00

3603600.990.990.990.990.990.990.990.991.001.001.001.00

3803800.980.980.980.980.990.990.990.990.990.991.001.001.001.001.001.001.001.00

4004000.980.980.980.980.980.980.980.980.990.990.990.990.990.991.001.001.001.001.001.001.001.001.001.00

4204200.970.970.970.970.970.970.970.970.980.980.980.980.980.980.990.990.990.990.990.990.990.991.001.001.001.001.001.001.001.00

4404400.960.960.960.960.960.960.960.960.970.970.970.970.970.970.980.980.980.980.980.980.990.990.990.990.990.990.990.991.001.001.001.001.001.00

4604600.950.950.950.950.950.950.950.950.960.960.960.960.960.960.960.960.970.970.970.970.970.970.980.980.980.980.980.980.990.990.990.991.001.001.001.00

4804800.940.940.940.940.940.940.940.940.940.940.950.950.950.950.950.950.950.950.960.960.960.960.960.960.970.970.970.970.970.970.980.980.990.990.990.991.001.001.001.00

5205200.930.930.930.930.930.930.930.930.930.930.940.940.940.940.940.940.940.940.940.940.940.940.950.950.950.950.960.960.960.960.960.960.970.970.970.970.980.980.990.99

(ENGLISH)(ENGLISH)5005000.90.933

0.90.933

0.90.933

0.90.933

0.90.933

0.90.944

0.90.944

0.90.944

0.90.944

0.90.955

0.90.955

0.90.955

0.90.955

0.90.966

0.90.966

0.90.966

0.90.977

0.90.988

0.90.999

0.90.999

25

SETSETPRES.PRES.bargbarg1.031.031.381.382.762.764.144.145.525.526.906.908.278.279.659.6511.011.012.412.413.813.815.215.216.616.617.917.919.319.320.720.724.124.127.627.631.031.034.534.5

SAT.SAT.STEAMSTEAM

ooCC121121126126142142153153162162170170177177183183188188193193198198202202206206210210213213217217225225231231238238243243

TOTAL STEAM TEMPERATURE, TOTAL STEAM TEMPERATURE, ooCC1381381.001.001.001.00

1491491.001.001.001.001.001.00

1601601.001.001.001.001.001.001.001.00

1711710.990.990.990.991.001.001.001.001.001.001.001.00

1821820.990.990.990.990.990.990.990.991.001.001.001.00

1931930.980.980.980.980.990.990.990.990.990.991.001.001.001.001.001.001.001.00

2052050.980.980.980.980.980.980.980.980.990.990.990.990.990.991.001.001.001.001.001.001.001.001.001.00

2162160.970.970.970.970.970.970.970.970.980.980.980.980.980.980.990.990.990.990.990.990.990.991.001.001.001.001.001.001.001.00

2272270.960.960.960.960.960.960.960.960.970.970.970.970.970.970.980.980.980.980.980.980.990.990.990.990.990.990.990.991.001.001.001.001.001.00

2382380.950.950.950.950.950.950.950.950.960.960.960.960.960.960.960.960.970.970.970.970.970.970.980.980.980.980.980.980.990.990.990.991.001.001.001.00

2492490.940.940.940.940.940.940.940.940.940.940.950.950.950.950.950.950.950.950.960.960.960.960.960.960.970.970.970.970.970.970.980.980.990.990.990.991.001.001.001.00

2602600.930.930.930.930.930.930.930.930.930.930.940.940.940.940.940.940.940.940.950.950.950.950.950.950.950.950.960.960.960.960.960.960.970.970.980.980.990.990.990.99

2712710.930.930.930.930.930.930.930.930.930.930.940.940.940.940.940.940.940.940.940.940.940.940.950.950.950.950.960.960.960.960.960.960.970.970.970.970.980.980.990.99

[METRIC][METRIC]

KKSHSH Superheat Correction Factor Superheat Correction Factor

26

Liquid FlowPer API 520 Sec 3.8.1

Q GQ G 38 K38 Kdd K KWW K KCCKKVV P P1 1 - P- P22

A =A =

= Orifice Area, in= Orifice Area, in22 [mm [mm22]]= Req’d Capacity, USGPM [liters/min]= Req’d Capacity, USGPM [liters/min]= Backpressure Correction Factor= Backpressure Correction Factor= Rupture Disc Combination Factor= Rupture Disc Combination Factor= Viscosity Correction Factor (Assume 1.0)= Viscosity Correction Factor (Assume 1.0)= Set + Overpressure - Inlet Pressure Loss, psig [kPag]= Set + Overpressure - Inlet Pressure Loss, psig [kPag]= Back Pressure, psig [kPag]= Back Pressure, psig [kPag]

A A Q Q KKWW

KKcc

KKVV

PP11

PP22

ENGLISH UNITS

11.78 Q G11.78 Q GKKdd K KWW K KCCKKVV P P1 1 - P- P22

A =A =

METRIC UNITS

27

Determining“Kv” Viscosity Correction Factor

R = Reynold’s Number

A = Next Larger Orifice Area Than Calculated, Assuming Kv = 1.0, in2 [mm2]G = Specific GravityQ = Required Capacity, USGPM [liters/min] µ = Absolute Viscosity (Centipoises) U = Viscosity (Saybolt Seconds Universal)

12,700 QU A

R =

2800 G Qµ A

R =

ENGLISH UNITS

METRIC UNITS31,313 G Q

µ AR =

WHERE:

28

““KKvv” Viscosity Correction Factor” Viscosity Correction Factor

Reynolds's NumberReynolds's Number

0.90.9

1.01.0

0.80.8

0.70.7

0.60.6

0.50.5

0.40.4

0.30.3100100 1,0001,000 10,00010,000 100,000100,000

KKVV

29

If Kv = 1.0, Calculation is complete

If Kv < 1.0, Repeat calculation until Kv does not change

30

API 520 Effective Nozzle API 520 Effective Nozzle Coefficient of DischargeCoefficient of Discharge

Use 0.65 for Liquid ServiceUse 0.65 for Liquid Service

Use API 526 Standard for Orifice SizeUse API 526 Standard for Orifice Size

API Considers This API Considers This PRELIMINARYPRELIMINARY Sizing Sizing

31

Liquid Thermal Expansion Relief

GPM = Flow Rate (gal./min.) B = Cubicle Expansion Coefficient Per °F H = Total Heat Transfer Rate (btu/hr) G = Specific Gravity C = Specific Heat (btu/lb/°F)

Per API 521, Section 3.14

GPM = BH500 G C

32

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:

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])

API RP 521, PART 1

API 2000

=>

33

Reference API 521, Section 3.15

API 521(Fire) – Unwetted Vessels(SET 15 psig [1.03 barg])=>

P1

A =F AS

GASGAS

= Environment /Operating Factor 0.042 (Conservative; Relates To Bare Vessel Metal Temperature At Relief)= Total Exposed Surface Area Of Vessel,ft2

= Set Pressure + Allowable Overpressure (21%) + 14.7, psia

= Calculated PRV Orifice Area, in2

F

As

P1

A

34

º F G

asF

Gas

700700

600600

500500

400400

300300

200200

100100

000.0050.005 0.0150.015 0.0250.025 0.0350.035 0.0450.045 0.0550.055

k = 1.001k = 1.001

k = 1.4k = 1.4

Operating Factor, FOperating Factor, F

ConservativeConservative

API RP521, Part 1 F Operating Factor

35

API RP521 (Fire) – Wetted Vessels

Q = Total Heat Input To Wetted Surface Of Vessel, btu/hr

F = 1.0 (Assumes No Vessel Insulation)

A = Total Vessel Wetted Surface, ft2

(Up To 25 Ft. Above Ground Level Or, In The Case Of A Sphere, To The Elevation Of Largest Diameter - Whichever Is Greatest)

LIQUIDLIQUID

Reference API 521, Section 3.15

Q = 21,000 F(Awet)0.82

36

Total Vessel Wetted Surface, ft2, Up To 25 ft. Above Ground Level Or, In The Case Of A Sphere, To The Elevation

Of Largest Diameter, Whichever Is Greater.

VerticalVerticalVesselVessel

HorizontalHorizontalVesselVessel

SphereSphere

Max.Max.Dia.Dia.

25 ft.25 ft.

GroundGround

37

API 521 (Fire) – Wetted Vessels

W = Required Valve Capacity, lb/hrQ = Total Heat Input to Wetted Surface, BTU/hrHvap = Latent Heat of Vaporization, BTU/lb

Examples : Ammonia 589Butane 166CO2 150

Methane 219Water 970

W = QHvap

38

Api 521 (Fire) – Wetted VesselsApi 521 (Fire) – Wetted Vessels

W TZW TZ

CKCKddPP11KKb b KKcc M MA =A =

ENGLISH UNITSENGLISH UNITS METRIC UNITSMETRIC UNITS

13,160 W TZ13,160 W TZ

CKCKddPP1 1 KKbbKKcc M MA =A =

Use Vapor Equations to Calculate Required Orifice AreaUse Vapor Equations to Calculate Required Orifice Area Use the Boiling Temperature of the Liquid (Flash to Vapor) for “T”Use the Boiling Temperature of the Liquid (Flash to Vapor) for “T”If known , we suggest using 200If known , we suggest using 200ooF [93F [93ooC]C]

39

API 2000(Fire) - Surface Area < 2800 ft2

A, ftA, ft22

20203030404050506060707080809090

100100120120140140160160180180200200250250300300

SCFMSCFMAIRAIR

352352527527702702878878

105310531228122814031403158015801780178021002100245024502800280031673167351735172983298344174417

A, ftA, ft22

350350400400500500600600700700800800900900

1000100012001200140014001600160018001800200020002400240028002800

over 2800over 2800

SCFMSCFMAIRAIR

48004800520052005900590065336533713371337700770082178217873387339283928397839783

10,23310,23310,65010,65011,03311,03311,73311,73312,36712,367

use formulause formula

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

Reference: API 2000, SectionsReference: API 2000, Sections1.5.2 and 2.31.5.2 and 2.3

ASME “K”ASME “K”0.900.90

KKD D ==

40

Set Pressure – Blowdown – Operating GapMultiple Valves Single Valve

5%

10%

90%

85%

Max Accumulation

Max Set

Max Operating

10% Operating Gap

Max Accumulation

ASME Sec. VIII UG-125(c1), UG-134(a)

16%

MAWP

80%

(Blowdown)

All OtherCert. Testing

7%10%

75%

25%

Non-CompressibleFluid

Set Pressure Tolerance:< 70 psi, + 2 psi>70 psi, + 3%

95%

5% Mfg.

Prov.Cert.

Compressible Fluid

General

41

Set Pressure – Blowdown – Operating Gap

Multiple Valves Single Valve

10%

90%

85%

Max Accumulation

Max Set

Max Operating

10% Operating Gap

Max Accumulation

ASME Sec. VIII UG-125 (c2), UG-134 (b)

21%

MAWP

80%

(Blowdown)

Comp.Fluid

10%

75%

25%

Non-Comp.Fluid

Set Pressure Tolerance:< 70 psi, + 2 psi>70 psi, + 3%

External Fire