145787608 psv sizing calculations
DESCRIPTION
PSV Sizing CalculationsTRANSCRIPT
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 =